Methods and systems for adaptive 3D dose control in volumetric 3D printing

Abstract

The present disclosure relates to a method for volumetric 3D printing of a three-dimensional object, the method comprising: obtaining a model of the object and a model of a container; computing an projection data based on the models of the object and the container; and providing projection data derived from the projection data to an illumination system configured to generate a series of projections for controlled polymerization of a photosensitive medium. The present disclosure further relates to systems for volumetric 3D printing of a three-dimensional object.

Description

[0001] Methods and systems for adaptive 3D dose control in volumetric 3D printing

[0002] The present disclosure relates to volumetric 3D printing, specifically methods and systems for dynamically controlling three-dimensional dose distributions within photosensitive resins to achieve precise polymerization.

[0003] Background

[0004] In recent years, tomographic volumetric 3D printing has emerged as a promising technology for creating complex 3D objects by projecting light patterns into photosensitive resins. Traditional methods for volumetric printing commonly employ a series of fixed light projections around a rotating container, allowing layers of material to polymerize as light patterns are exposed to the resin. This technique enables the fabrication of objects with relatively high fidelity compared to conventional layer-by-layer 3D printing processes, as it reduces artifacts associated with layering and enables smoother surface finishes. Current volumetric systems have been applied to diverse fields, including medical device manufacturing, where precision, accuracy, and surface quality are critical.

[0005] However, existing volumetric 3D printing systems face significant limitations, particularly in achieving uniform dose distribution and accurate curing across complex geometries. Most systems use static projectors in fixed orientations, which limit their ability to adapt to intricate structural details or varied exposure requirements within the resin volume. Consequently, these systems often struggle to maintain consistent polymerization throughout the entire volume of the printed object, especially in areas with high geometric complexity or fine surface detail. Additionally, the rotation of the resin container and the reliance on fixed projection patterns can introduce radial artifacts and inconsistencies in polymerization, which may compromise surface quality and necessitate additional post-processing. Such constraints reduce the achievable resolution and precision of printed objects, posing challenges for applications requiring intricate designs or high levels of customization, such as dental implants or prosthetics.

[0006] A further disadvantage is the limited adaptability of current systems to various container shapes and sizes, which restricts their use to simpler geometries.

[0007] Conventional volumetric 3D printing setups typically rely on standardized container geometries, such as cylindrical or cubic shapes, as these simplify alignment with fixed projector setups. This restriction limits the ability to optimize dose distribution for containers with more complex or irregular shapes. Furthermore, projection setups often lack sufficient flexibility to achieve uniform curing across areas farther from the projector, leading to uneven structural integrity and reduced accuracy in printed objects. The inability to adaptively control dose distribution and projector alignment reduces the versatility and precision of these systems, particularly for applications demanding intricate details and superior surface quality.

[0008] It is therefore an objective of the present disclosure to provide improved methods and systems for volumetric 3D printing, enabling greater adaptability to complex geometries, enhanced dose distribution, and increased fidelity of printed objects.

[0009] Summary

[0010] The present disclosure relates to a method for volumetric 3D printing of a three-dimensional object, the method comprising obtaining a model of the object and a model of a container; generating a target dose distribution based on the model of the object; computing, using one or more light-propagation algorithms, projection data based on the target dose distribution and the model of the container; and providing the projection data to an illumination system configured to generate a series of projections for controlled polymerization of a photosensitive medium. Additionally, the illumination system comprises at least one adjustable light source configured to be adjusted to different positions and / or orientations relative to the container. The projection data may include, for each projection, associated position and / or orientation data specifying the position and / or orientation of the adjustable light source for generating that projection.

[0011] The disclosed method achieves precise control over the polymerization process by generating and optimizing projection data to ensure uniform curing across complex geometries. The present disclosure introduces the use of target dose distributions derived from object models and adapts projection data based on container geometries, enhancing fidelity and resolution in printed objects. By employing light-propagation algorithms such as ray tracing, ray marching, and volumetric simulation, the method accurately models light-matter interactions within the photosensitive medium, mitigating undercuring and overcuring effects. This process accounts for variations in material properties, container shapes, and dynamic feedback, achieving consistent polymerization throughout the object. The present disclosure further includes a system for volumetric 3D printing, comprising a computational unit configured to execute the disclosed method and an illumination system capable of dynamically adjusting projection parameters. The illumination system may include adjustable light sources, such as projectors mounted on robotic arms or gimbals, enabling real-time positional and angular adjustments. Feedback from sensors monitoring the polymerization state informs iterative refinements to the projection data, optimizing the polymerization process in response to real-time conditions.

[0012] The present disclosure facilitates the production of high-fidelity objects with intricate details, making it particularly well-suited for medical applications, such as prosthetics, implants, and other devices requiring precise geometric and material properties. The combination of computational algorithms, adaptable hardware configurations, and responsive feedback systems provides a scalable, versatile, and efficient solution for advanced volumetric 3D printing.

[0013] Description of Figures

[0014] Various embodiments are described hereinafter with reference to the drawings. The drawings are examples of embodiments and are intended to illustrate some of the features of the presently disclosed method and system for volumetric 3D printing of a three-dimensional object.

[0015] FIG. 1 A shows examples of complex, three-dimensional computer models of objects obtained from three-dimensional meshes.

[0016] FIG. 1B shows examples of container geometries as triangulated surfaces.

[0017] FIG. 2A shows a flowchart for the steps in pattern generation and projection algorithms considering the optomechanical components and geometry of the container.

[0018] FIG. 2B shows a flowchart for the sub-steps related to configuration of the at least one light source in pattern generation and projection algorithms of FIG. 2A.

[0019] FIG. 2C shows a flowchart for the sub-steps related to the three-dimensional design of the model and its GPU-accelerated voxelization of FIG. 2A.

[0020] FIG. 3 shows a flowchart for the sub-steps related to the container characterization of FIG. 2A.

[0021] FIG. 4 shows examples of projections of both surface and solid voxelization applied to a 3D mesh model. FIG. 5 shows a flowchart for the creation of a ray tracing pipeline based on characterization of the container.

[0022] FIG. 6 shows a flowchart comprising the necessary steps in a ray marching pipeline to achieve an optimum three-dimensional dose distribution.

[0023] FIG. 7 shows examples of ray tracing for mathematically characterized containers, with parameters such as container dimensions (e.g., radius r or side lengths a, b, c) and material properties (e.g., refractive index n) are supplied to the compute shaders using uniform buffer objects.

[0024] FIG. 8A shows computer models of a cylindrical container and an object.

[0025] FIG. 8B shows computed light patterns and simulated dose distributions using the container and object of FIG. 8A.

[0026] FIG. 9A shows computer models of a truncated cone-shaped container and an object. FIG. 9B shows computed light patterns and simulated dose distributions using the container and object of FIG. 9A.

[0027] FIG. 10A shows a computer model of an arbitrary container with surface irregularities and an octree voxelization of a three-dimensional design.

[0028] FIG. 10B shows a computed light pattern using the container and three-dimensional design of FIG. 10A.

[0029] Detailed description

[0030] General description, definitions, and algorithms:

[0031] Projection data refers to the computational output used by an illumination system to deliver a precise three-dimensional dose distribution within a build volume of a container. The projection data may include a series of light projections, where each projection is defined as a spatial light distribution (e.g. pixel-wise light distribution) specifying the intensity, spatial pattern, and other characteristics of the light to be delivered.

[0032] Each light projection in the series may be associated with one or more projection parameters, including the position of the light source or projector relative to the container and the build volume, the orientation angle at which the light is directed, and the focal plane of the projection, which may be telecentric or non-telecentric. Additional parameters may include intensity modulation to adjust the overall or localized light intensity, exposure duration to define the time a projection is delivered, and wavelength specifications to optimize curing for particular materials.

[0033] The projection data is computed based on the target dose distribution and the model of the container, incorporating simulations of light interactions such as scattering, refraction, absorption, reflection, total internal reflection, beam divergence and optical heterogeneity within the container and the photosensitive medium. In some embodiments, the computations may further take into account surface irregularities and interface geometries not only of the container but also of the resin itself, for example in scenarios where the resin is poured into an open vat and illuminated from above so that light rays directly interact with a free surface of the resin. The curvature of such a free surface may be represented in the model using, for instance, an approximation based on the Young-Laplace equation or, in simpler implementations, by assuming a substantially planar surface.

[0034] These simulations ensure accurate and uniform light delivery across the build volume, adapting to the geometry of the object and container as well as the material properties of the photosensitive medium. Thus, the projection data may comprise a series of projection, each projection associated with a respective position, for example a 3D position, and / or a respective orientation, for example with respect to the container, wherein the associated position and / or orientation may be the same or different between projections.

[0035] The projection data may further comprise a 3D position of the projector together with one or more quantities describing motion of the container, such as a rotational velocity of the container and / or one or more projection angles or angular positions associated with the respective projections. Each projection may further be associated with the focal plane of the projection, intensity modulation to adjust localized or overall light intensity, exposure duration to define the time a projection is delivered, and wavelength specifications to optimize curing for specific material properties.

[0036] The projection data may comprise a series of projections, wherein the sequence and arrangement of the projections are determined using an optimization algorithm, such as a traveling salesman problem (TSP) algorithm or alternative optimization methods. These alternative methods may include genetic algorithms, simulated annealing, dynamic programming, or graph-based optimization techniques. The optimization may thus be for minimizing the production time and / or for optimizing the printing quality.

[0037] As used herein, a spatial light distribution refers to a distribution of optical energy over a two-dimensional region corresponding to a projection plane of an illumination system, defining how light intensity and other optical characteristics vary as a function of position across that region. The spatial light distribution may be represented in a discretized form, such as a pixel-wise distribution defined on a two-dimensional grid of pixels, for example when generated by a digital micromirror device (DMD), a spatial light modulator (SLM), or a projector.

[0038] In other embodiments, the spatial light distribution may be represented in alternative forms, including but not limited to continuous or semi-continuous distributions, analytic or parametric representations, scanned or time-multiplexed illumination patterns, holographic or wavefront-based representations, or combinations thereof. Regardless of representation, the spatial light distribution defines the spatial variation of light delivered into the photosensitive medium for a given projection and may be generated, stored, optimized, and applied in any suitable form consistent with the disclosed lightpropagation and dose-computation methods.

[0039] Mesh voxelization

[0040] Methods for conducting volumetric three-dimensional (3D) printing often starts by loading a 3D design, from a 3D mesh, intended for fabrication. A 3D mesh is a digital representation of a three-dimensional object composed of vertices, edges, and faces that define the object's shape and surface geometry. It can be used in computer graphics, modeling, and simulations to represent complex structures for visualization, rendering, or analysis. The quoted 3D designs are typically represented as polygon meshes in formats such as STL or OBJ files and may comprise millions of triangles. The 3D designs can be converted into a binary voxelized geometry. Voxelization is the process of converting a 3D object or model into a grid of volumetric pixels, called voxels, which represent the object in a discrete three-dimensional space. It can be used in 3D rendering, simulations, and printing to analyze or manipulate objects at a voxel level. In surface voxelization, each triangle of the mesh can be processed in parallel on Graphical Processing Unit (GPU) threads. In the context of the present disclosure, an algorithm efficiently performs conservative surface voxelization by mathematically determining which voxels overlap with each triangle's surface. By iterating over the voxels within each triangle's bounding box and applying precise tests, it ensures that all relevant voxels are accurately identified and marked, capturing fine details of the mesh's surface for high-quality volumetric representations. On the other hand, solid voxelization can be performed by projecting each triangle onto the YZ-plane and using a 2D point-in-triangle test to identify relevant grid cells. By computing the intersection along the X-axis and toggling voxel occupancy states, it applies a parity counting method to determine which voxels are inside the mesh. This approach captures the interior volume accurately and is suited for GPU acceleration.

[0041] The two voxelization approaches described above may be implemented using uniform voxel grids, in which all volume elements have the same size. In some embodiments, the volume may alternatively or additionally be represented using non-uniform or adaptive discretizations, such as octrees or other tree-based volumetric data structures. In such implementations, regions of the object or curing volume that contain fine geometric detail or that are particularly relevant for dose control may be represented at a finer spatial resolution, while more homogeneous regions may be represented at a coarser resolution. This can reduce memory usage and computational cost while preserving or enhancing accuracy in areas of interest. Tree-based representations may be used both for surface voxelization and for solid voxelization, and may integrate naturally with hierarchical or multi-resolution light-propagation and optimization methods employed for computing the projection data.

[0042] Ray tracing

[0043] Ray tracing is a computational method used to simulate the path of light as rays, calculating their interactions with objects to produce realistic effects such as shadows, reflections, and refractions in 3D scenes. Ray tracing can provide the design flexibility needed for the free movement of light sources and the accommodation of surface irregularities in the container comprising a photosensitive resin.

[0044] A photosensitive resin is a liquid material that undergoes polymerization and hardens when exposed to specific wavelengths of light and can be used in 3D printing, photolithography, and other light-based manufacturing processes. In the context of volumetric 3D printing, a light source is a device that emits controlled light to induce polymerization in the photosensitive resin. A projector is an example of a light source, capable of delivering precise light patterns to specific regions within the resin-holding container. A projector is an optical device that emits and focuses light to display images or patterns onto a surface or medium. In volumetric 3D printing, a projector serves as a light source that generates precise, patterned light to selectively polymerize photosensitive resin. It typically uses lenses, mirrors, and a light engine (such as LEDs, lasers, or digital light processing technology) to produce high-resolution and controlled illumination tailored to specific applications.

[0045] The ray tracing process can begin by generating and dispatching rays from an illumination system, such as digital micromirror devices (DMDs) embedded within light sources such as projectors. The illumination system may have at least one light source. The positions and orientations of these rays in world coordinates are influenced by several factors, including the DMD's resolution and pixel pitch, the position of the light source in the world coordinate, and the characteristics of the optical system of the light source. These optical elements shape the projection geometry and may be characterized by two primary configurations: telecentric and non-telecentric systems.

[0046] In the present disclosure a ray generation shader can produce rays in the world coordinates, taking into account the light source configuration. In a telecentric optical setup, all light rays remain substantially parallel to the optical axis as they pass through the lens system, regardless of their position in the field of view. Ray generation for these light sources follows an orthographic projection model, where pixel positions determine the ray origins, and all rays share the same direction. Conversely, non-telecentric optical systems, commonly found in off-the-shelf projectors, feature light rays that converge or diverge as they pass through the lens assembly. Unlike telecentric systems, non-telecentric setups may be modelled, for example, by treating the projector as a pinhole emitter and require, for ray generation, at least one additional parameter such as a vertical or horizontal field of view together with a position of a virtual light source, so as to account for the convergence or divergence of light rays relative to the optical axis. The light source’s 3D coordinate defines the rays’ origins, while the ray directions can be calculated based on the specified field of view. As the generated rays propagate, they may interact with various components along their paths, such as apertures, optical lenses, and the photoresin container. The method used to represent the container's shape can be used to define a ray tracing pipeline. A ray tracing pipeline is a structured sequence of computational stages used to trace rays through a 3D scene, calculate their interactions with objects, and generate visual or analytical outputs, such as reflections, refractions, shadows, or lighting effects.

[0047] If a 3D model of the container is available as a polygon mesh, the object, along with its material property file, containing information like absorptivity and refractive index, can be loaded and incorporated into an acceleration structure. This structure, typically a bounding volume hierarchy (BVH), can be built around the polygon mesh to accelerate the ray tracing process by efficiently organizing spatial data. The ray generation shader initiates the ray tracing process, and as rays traverse the scene, they pass through various shader stages. The intersection shader computes how rays intersect with the geometry, while the any-hit shader processes potential intersections and evaluates material properties to decide if an intersection should be considered. The closest-hit shader calculates the effects at the point of the nearest intersection, such as reflection, refraction, and absorption, based on the local material properties. Finally, the miss shader handles rays that do not intersect any objects. This shader pipeline enables the ray tracing algorithm to accurately model the physical behavior of light interacting with the container, effectively accounting for surface irregularities and complex material characteristics.

[0048] In the absence of a polygon mesh model, and if the container can be mathematically characterized, a shader, such as a compute shader can be used to implicitly define the external and internal surfaces of the container. This shader can be later used for intersection tests, and the resulting ray information may be shared with a traversal shader to simulate physical behaviors such as reflection, refraction, and absorption.

[0049] Ray marching

[0050] Unlike ray tracing, which primarily deals with surface interactions, ray marching accounts for volumetric effects such as absorption, scattering, and emission within the resin medium. In the context of volumetric 3D printing, ray marching can be divided into two steps: forward and backward. The forward step comprises simulating how rays propagate from the light source through the resin, calculating the light-resin interaction and determining the intensity at each pixel. The backward step comprises tracing rays from the DMD back into the resin volume to simulate the three-dimensional dose distribution within the photoresin. Together, these steps enable accurate modelling of light-resin interactions, allowing for precise control over polymerization at specific locations within the resin.

[0051] Ray marching begins once the rays exit the internal surface of the container and enter the resin volume. From this point, the rays are traversed incrementally through the voxel grids using a volume rendering or volume traversal approach, such as a Differential Digital Analyzer (DDA) algorithm. In such implementations, the DDA algorithm calculates adaptive differential steps needed to navigate along each axis based on ray’s direction ensuring that voxels along the traversal path are not skipped while significantly reducing the computational overhead. For a given ray (o, d), where o represents the ray’s origin and d its direction, the parametric variable tminrepresents the ray-bounding box intersection point which is utilized to determine the entry point (Pentry) into the grid:

[0052] Pentry O T tmin’

[0053]

[0054] For each axis i ∈ {x,y,z}, the step direction Si, initial voxel coordinate Vi, the parameter nextTifor the next voxel boundary intersection, and the incremental step deltaTi, are then defined as follows:

[0055] Si= sign(di)

[0056] Vi= ⌊(Pentry,i- bmin,i) / Δy⌋

[0057] ΔT (3)

[0058] nextTi= (Vi+ (Si> 0 ? 1 : 0)) · Δy + bmin,i- Pentry,i

[0059] / di(4)

[0060] Ay

[0061] deltaTi=

[0062]

[0063] where:

[0064] • Δy denotes the voxel spacing which is uniform across all dimensions. • sign(di') returns the sign of dt, indicating the direction of traversal along axis / . • [. J represents the floor operation, ensuring

[0065]

[0066] is an integer index within the grid. • nextTi calculates the parametric distance to the next voxel boundary along axis / .

[0067] • deltaTt defines the parametric step size required to cross one voxel along the direction dt.

[0068] The algorithm iterates through the volume grid by incrementally advancing the ray from one voxel to the next, selecting the axis with the minimum nextTiateach step. This ensures that the ray progresses through the grid in a manner that mimics its continuous path. In other implementations, a simpler traversal scheme with a constant step size along the ray may be used, which may provide lower accuracy than DDA-based traversal but can be sufficient in some scenarios.

[0069] Forward ray marching

[0070] The forward ray marching involves tracing the path of each ray as it moves through the voxel grid representing the resin, calculating the cumulative effect of the resin's optical properties on the ray's intensity. This approach relies on the Radiative Transfer Equation (RTE), which describes the change in radiance as the light propagates through a participating medium:

[0071] (w. V)L(%,5) = — atx)L x, a>)

[0072] r (6)

[0073] + < Js(x) I p(x, co, o)')L(x, oj')doj' + e(x, co)

[0074]

[0075] JS2

[0076] where the various symbols are defined as follows:

[0077] • L(%, <5): radiance at the position x along the ray in the direction d).

[0078] • (<5. V)L(%, <5): directional derivative of radiance along the ray.

[0079] •

[0080]

[0081] = °a + °s- extinction coefficient [m-1], accounting for total attenuation (both absorption and scattering).

[0082] • aa. absorption coefficient [m-1], describing the rate at which radiance is absorbed by the medium.

[0083] • as. scattering coefficient [m-1], representing the rate of radiance scattered in all directions. •

[0084]

[0085] p(x, phase function [sr1], defining the angular scattering distribution of radiance.

[0086] • e(x, <7>): emission term [Wsr-1m-3], representing radiance emitted by the medium itself in a given direction. Volumes in computer graphics are usually considered to be non-emitters.

[0087] In a purely absorbing media, where scattering and emission are negligible (as« 0, e « 0), RTE equation simplifies to:

[0088] (Zo. V)L(x, 6tJ) = — aa(x)L(x, 6tJ) (7)

[0089] For a light beam traveling from x = 0 to x=s along the direction w, we integrate the simplified RTE:

[0090] rs

[0091] L(s~) = L(0)exp (— I cra(x)dx) (8)

[0092]

[0093] Jo

[0094] For a homogeneously absorbing medium with constant oa, this reduces to the Beer-Lambert law:

[0095] L(s) = L(0)e-ff«s(9)

[0096] Using the Beer-Lambert law, the transmittance T at voxel j can be calculated as:

[0097] T = e-<^jlij (10)

[0098] Where,

[0099] • o- is the absorption coefficient of the resin, indicating how strongly the resin absorbs light at a given wavelength.

[0100] • is the sampled light dose within voxel J, obtained from trilinear interpolation. • lij is the distance that ray / travels within voxel j.

[0101] As the ray marches forward, the individual transmittances from each voxel is compounded to determine the total attenuation experienced by the ray along its path. This cumulative transmittance T, for ray / is calculated by multiplying the transmittances of all intersected voxels:

[0102] n n

[0103] Tt = T = n (11)

[0104]

[0105] ;=i j=i where n is the total number of voxels intersected by ray / .

[0106] At the exit point of the bounding box, which defines the spatial limits of the resin volume, the final transmittance Tt represents the fraction of the initial light intensity that has not been absorbed after traversing the resin. To obtain the attenuated intensity detected at pixel / , we consider the initial intensity (normalized to 1) and subtract the transmitted fraction:

[0107] ^

[0108]

[0109] = 1 - ^ = 1 - (12)

[0110] This equation indicates that reflects the total fraction of photons absorbed along the ray's trajectory from the light source to the exit point of the resin. While the equations above were derived for an absorbing medium, the RTE framework readily extends to handle ray marching in scattering or non-homogeneous media, where rays may traverse nonlinearly through the voxel grid.

[0111] Backward ray marching

[0112] In backward ray marching the rays are traced backward along their original paths into the curing volume, retracing the trajectory taken during forward ray marching. As each ray penetrates the resin volume, it intersects multiple voxels within the voxel grid representing the resin. At each voxel intersection, the transmitted light dose Vj is calculated using the same laws applied in the forward process, such as the Beer-Lambert law which accounts for the resin's absorptivity along the cumulative distance travelled by the ray from the inner surface of the container to the voxel location:

[0113] V

[0114]

[0115] j = (13)

[0116] Here, a is the resin's absorption coefficient for the given wavelength, and / 7is the cumulative distance that ray / has travelled within the resin up to voxel j. The exponential term

[0117]

[0118] represents the attenuation of light intensity due to absorption over the path length lj.

[0119] To ensure a smooth and accurate distribution of the light dose within the resin, the calculated transmitted dose Vj is assigned to the eight corner-sharing neighbor voxels surrounding the point of intersection as viewed from a projection perpendicular to the ray. This assignment is weighted based on the proximity of the ray's position to each voxel, utilizing trilinear interpolation. The weights are determined by the fractional distances along the x, y, and z axes between the ray's exact position and the centers of the neighboring voxels.

[0120] This backward traversal process is performed for every ray corresponding to each pixel in the projected image and across all light source positions and viewing angles, resulting in a comprehensive map of the cumulative light dose within the resin:

[0121] = + y7(14)

[0122] This cumulative dose map allows for the adjustment of the projected images to compensate for absorption losses and ensure that sufficient energy reaches all regions of the resin, including deeper areas that might otherwise receive less light due to attenuation. During backward ray marching, where rays may be traced in parallel on GPU, a potential race condition arises as multiple rays may attempt to write simultaneously to the same voxels, potentially introducing artifacts in the final dose distribution. To mitigate this issue, one may implement atomic operations, ensuring exclusive access to each voxel and preventing competition among rays.

[0123] Iterative dose

[0124]

[0125] Direct use of the generated light patterns from forward ray marching and their backprojection into the resin often leads to a non-uniform dose distribution within the photopolymerizable material. One may use a gradient-based iterative optimization approach to enhance the homogeneity of light dose distribution within the three-dimensional voxel space. This may be achieved by minimizing the discrepancies between the target and delivered dose distributions through successive adjustment of the pixel intensities. The objective function L is formulated as follows:

[0126] n

[0127] recon ||2+ ^J^reconj ~0|) (15)

[0128]

[0129] i = l

[0130] subject to the constraint that > 0 for all i, and where:

[0131] • Vdesign represents the design (or target) dose distribution, corresponding to the desired voxel values that define the object's geometry.

[0132] • Vrecon signifies the reconstructed (or delivered) dose distribution as determined by backward ray marching. • 0 represents the curing threshold, which is the minimum dose required to initiate polymerization in the resin.

[0133] • n is the total number of voxels in the voxel grid.

[0134] • ||. H2 denotes the squared Euclidean norm.

[0135] • > 0 enforces the nonnegativity constraint on the pixel intensities.

[0136] The first term in the objective function controls the reconstruction fidelity, ensuring that the delivered dose closely matches the desired dose distribution. The second term regularizes the dose reconstruction by penalizing deviations from the curing threshold in the voxel space.

[0137] The nonnegativity constraint, Ii > 0, is applied because pixel intensities cannot be negative in a physical system. To optimize the pixel intensities

[0138]

[0139] one may compute the gradient of the objective function with respect to each pixel intensity. The gradient of the fidelity term concerning the / -th pixel intensity is given by:

[0140] _ \ 'n.7. Brecon,]

[0141] ~ ~.^design, j ~ *recon,j) gj. (16)

[0142]

[0143] In an absorption dominant medium, the relationship between the reconstructed dose, Vreconj, and the pixel intensities, may be established using the Beer-Lambert law. The partial derivativedVr^concan be expressed as:

[0144] ^Vreconj.

[0145] (17)

[0146]

[0147] = 1

[0148] where:

[0149] • is a weighting factor of the / -th pixel, determined through bilinear sampling at the image plane. This factor accounts for the contribution of pixel / to voxel j.

[0150] • a represents the absorption coefficient of the resin.

[0151] • lj is the cumulative distance that ray / has travelled within the resin up to voxel j. Substituting this expression into the gradient of the objective function yields:

[0152] dL x

[0153] •a j / v design, j Brecon, j) (16)

[0154]

[0155] The pixel intensities may be iteratively adjusted according to this gradient using an update rule, such as:

[0156] A

[0157]

[0158] (k+1)=max(°' A(k)(19)

[0159] where:

[0160] • is the intensity of pixel / at iteration k.

[0161] • y is the learning rate or step size, controlling the magnitude of the update.

[0162] • is evaluated at /

[0163] dli

[0164]

[0165] 1(k).

[0166] The iterative process continues until the predefined optimization tolerance is reached.

[0167] Real-time rendering and synchronization

[0168] Ray marching is the central computational step in generating precise light patterns and is the most resource-intensive process. To optimize this step, one may utilize 3D textures to store voxelized volumetric mesh data and a 2D texture to store rendered projections, for example as a series of 2D textures or as a single 2D texture array. In implementations using non-uniform or tree-based representations of the volume, such as octrees or other hierarchical grids, the volumetric data and associated attributes may additionally or alternatively be stored in buffer resources such as Shader Storage Buffer Objects (SSBOs), optionally in combination with embedded 3D textures for leaf nodes or refined regions. For this purpose one may utilize shader programs executed on a graphics processing unit, for example shaders written in GLSL when using OpenGL or Vulkan, or shaders written in HLSL or other shading languages and compute APIs provided by different graphics frameworks. A forward ray-marching shader may take as input one or more 3D textures and / or buffer objects representing the voxelized or tree-based volume and may output a series of 2D images into a texture array. Conversely, a backward ray-marching shader may invert this process by taking a series of 2D textures and / or a 2D texture array and reconstructing a three-dimensional representation, for example a three-dimensional texture or an updated tree-based volume, representing the 3D dose build-up..

[0169] Compute shaders eliminate the need for traditional graphics pipeline stages such as vertex and fragment shaders. This approach provides direct access to the GPU’s parallel processing capabilities and memory architecture, allowing finer control over thread scheduling, memory access patterns, and synchronization processes. This can be beneficial during the dose optimization stage, where these shaders are invoked multiple times throughout the iterations. By adopting compute shaders, one may optimize the ray marching and dose optimization processes. Explicit workgroup configuration and efficient use of shared memory may lead to performance gains, such as a two- to three-fold increase in processing speed compared to equivalent implementations using fragment shaders.

[0170] If the light source comprises a screen, one may define a full-screen quad that covers the entire viewpoint of the light source’s screen to enable real-time rendering of the final dose distribution. This quad serves as the rendering canvas for the shader operations. During the rendering pipeline, the quad's vertex data may be processed by the vertex shader, establishing the geometric transformations required to map the 3D texture onto 2D screen space. The fragment shader may then receive the two-dimensional texture coordinates and sample the 2D texture output generated by the compute shader on-the-fly within the rendering loop. This integration between the compute shader and the rasterization pipeline allows for efficient real-time rendering of the light dose distribution.

[0171] If the light source is further characterized by a refresh rate, defining the number of times per second the light source image or light pattern is updated, the above algorithm can achieve rendering frame rates that exceed the refresh rate of the light source by combining the rasterization pipeline with the compute shader. This high frame rate can be beneficial for maintaining smooth and continuous projection of the light patterns during the printing process. To synchronize the rendered frames with the light source's refresh rate and prevent visual artifacts such as screen tearing, vertical synchronization (VSync) may be employed.

[0172] When multiple light sources are used, light pattern generation and dose optimization should be performed in parallel, taking into account each light source’s configuration. To render the final dose on each light source’s screen, resources, including a fullscreen quad, pixel buffer objects (PBOs), textures, and shaders, may be defined individually to match the specific properties of each screen, such as resolution and color format. Despite these individualized resources, all screens may share a common OpenGL context, allowing for streamlined rendering control and synchronization within a single graphics pipeline. Inside the rendering loop, synchronization fences may be utilized to ensure that all resources are fully loaded before images are displayed on the screens. These fences signal the GPU upon successful resource loading, preventing incomplete image display and ensuring accurate projection of the light patterns. This setup maintains high frame rates and precise synchronization across all light sources.

[0173] Three-dimensional dose control in containers with arbitrary shapes and sizes

[0174] It is a goal of the present disclosure to facilitate and enhance three-dimensional dose delivery to the photocurable resin by maximizing the dose received by in-part voxels while minimizing the dose in out-of-part regions, thereby increasing dose contrast.

[0175] The present disclosure allows for free movement of the light source(s). By projecting light patterns from any arbitrary position in three-dimensional space, the system enables optimal dose delivery regardless of the design's orientation. Additionally, the ray tracing and ray marching methods developed for generating the light patterns provide the versatility to use containers of arbitrary shapes and sizes, such as cylindrical or cubical containers. While cylindrical containers are commonly used in existing tomographic volumetric 3D printing due to their compatibility with tomographic principles and the simplicity of using single-axis rotation for dose delivery, they do not work optimally for all the 3D models, such as clear aligners or surgical guides..

[0176] Furthermore, the free movement of the light sources in the system, combined with ray tracing and ray marching methods, allows for the accommodation of containers of various sizes. This flexibility can be beneficial when printing larger structures, where container dimensions may vary significantly. The effectiveness of this approach depends on factors such as the optical properties of the resin and the etendue of the embedded light sources, which determine how much light can penetrate into the resin volume. If a single light source cannot deliver sufficient energy to polymerize the entire structure, multiple light sources may be employed simultaneously. By coordinating these light sources to deliver the required dose to different regions of the photoresin, the system enables the polymerization of large or complex structures in a single process. This scalability enhances the versatility of volumetric 3D printing, allowing for high-fidelity fabrication of objects with varying sizes and complexities while maintaining precise control over dose distribution. Further details

[0177] In a first aspect, the present disclosure relates to a method for volumetric 3D printing of a three-dimensional object, the method comprising: obtaining a model of the object and a model of a container; generating a target dose distribution based on the model of the object; computing projection data based on the target dose distribution and the model of the container; and providing the projection data to an illumination system configured to generate a series of projections for controlled polymerization of a photosensitive medium.

[0178] In one embodiment of the present disclosure, the illumination system may comprise at least one adjustable light source configured to be adjusted to different positions and / or orientations relative to the container.

[0179] In one embodiment of the present disclosure, the projection data may include, for each projection, associated position and / or orientation data specifying the position and / or orientation of the adjustable light source for generating that projection.

[0180] This method introduces a tailored approach to energy delivery, ensuring that light is directed only where needed, based on the geometry of the object and the container. The adaptive dose computation accounts for variations in material properties and container shapes, enabling uniform curing across the object. This approach minimizes defects such as overcuring and undercuring, which are common in existing 3D printing methods reliant on uniform or static energy dose delivery.

[0181] Examples of three-dimensional objects and container shapes are shown in FIG. 1A and FIG. 1 B, respectively.

[0182] The technical advantages of this present disclosure lie in its adaptability and precision. Unlike traditional layer-by-layer additive manufacturing, this volumetric approach eliminates the need for intermediate support structures, reduces production time, and enhances print fidelity. By directly polymerizing the entire volume or sections of the medium in a controlled manner, the method achieves higher resolution and smoother finishes than in existing technologies. Additionally, the integration of computational models with real-time adjustments allows for corrections during the printing process, enhancing accuracy and reducing material waste. These improvements make the method suitable for applications requiring complex geometries and high-quality finishes, such as biomedical implants, optical components, and advanced prototyping.

[0183] Furthermore, the use of an illumination system comprising at least one adjustable light source, whose position and / or orientation can be set for each projection, provides a distinct technical advantage over fixed-projector volumetric printing systems. The adjustable light source is operatively linked to the computed projection data, such that each projection may be assigned a predetermined illumination pose selected during the computation of the projection data. This allows the system to choose projection directions that are geometrically or optically favorable for achieving the target dose distribution, even though the pose need not be adjusted continuously during printing.

[0184] By enabling preselected illumination angles that better match the geometry of the object and the container, the system can avoid occluded regions, reduce unwanted light accumulation in out-of-part areas, and improve delivery of energy into regions requiring higher exposure. This leads to improved three-dimensional dose uniformity, increased dose contrast, and reduced artefacts compared to systems that rely on fixed projector orientation. As illustrated by the dose distributions obtained for different container shapes (e.g., FIGS. 8 and 9), the ability to assign projection-specific lightsource poses enables a more geometry-aware and directionally selective dose-delivery process, producing enhanced reconstruction accuracy and improved print fidelity across a wider range of container geometries than is achievable with fixed-geometry systems.

[0185] In one embodiment of the present disclosure, the projection data is computed using one or more light-propagation algorithms. These algorithms may comprise computational methods that model how light travels through a photosensitive medium and interacts with the material to effect polymerization. By simulating the light path and its intensity within the medium, the system may optimize energy delivery to ensure uniform curing across the object’s geometry.

[0186] Flowcharts for various algorithms comprised by the presently disclosed method are illustrated in FIG. 2. The algorithms may comprise wave-based models to account for diffraction effects, enhancing the accuracy of dose predictions in areas where geometrical optics alone would be insufficient. Implementations may vary depending on the specific material properties of the photosensitive medium, the shape of the container, and the intended resolution of the printed object. The use of light-propagation algorithms allows for dynamic adjustments during the printing process, enabling greater precision and reducing artifacts caused by uneven light exposure.

[0187] In one development the light-propagation algorithms may be based on solving Maxwell’s equations, for example using finite element methods, with particular boundary conditions and for particular geometries and material characteristics.

[0188] In one embodiment of the present disclosure, the light-propagation algorithms comprise ray tracing. This embodiment comprises calculating the paths of individual light rays as they interact with surfaces and materials, enabling the generation of a detailed model of light intensity and distribution within the photosensitive medium. Ray tracing is advantageous for accounting for reflections, refractions, and absorption within complex geometries, ensuring accurate modeling of light-matter interactions.

[0189] This embodiment may comprise using ray tracing to calculate how light rays propagate, reflect, and refract within the medium, providing detailed information about light interactions at microscopic scales. Variations of this implementation may comprise bidirectional ray tracing, which considers both forward and backward paths of light, and photon mapping, which simulates the scattering of light particles. These variations offer enhanced accuracy in predicting dose distribution in regions with intricate geometrical features or highly variable material properties. The use of ray tracing can improve the quality and resolution of printed objects by ensuring that every region of the photosensitive medium receives the appropriate light exposure.

[0190] In one embodiment of the present disclosure, the light-propagation algorithms comprise ray marching. Ray marching is a computational method that iteratively traces light rays through a medium until a termination condition, such as reaching a predefined distance or encountering an object boundary, is met. This method is effective for simulating light interactions within volumetric media, where the medium’s density and optical properties vary continuously, such as within the resin medium. FIG. 5 provides a flowchart illustrating how the ray tracing pipeline is constructed based on the chosen container characterization technique. In FIG. 7 some of the principles of ray tracing are illustrated as derived for mathematical representations of two container geometries in which the refractive index vary close to the container surface.

[0191] Ray marching may be combined with distance field representations of the object and container geometries, enabling efficient computation of light paths in complex structures. One variation of this method may comprise adaptive step sizes, where the marching interval is dynamically adjusted based on the local gradient of the medium’s density or optical properties. This adaptation improves computational efficiency and accuracy, particularly in areas with high complexity or abrupt changes in material properties. The use of ray marching allows for precise control over dose delivery, ensuring uniform polymerization even in complex geometries.

[0192] In one embodiment of the present disclosure, the light-propagation algorithms comprise volumetric simulation. Volumetric simulation may comprise detailed computational modeling of light interactions within a photosensitive medium, accounting for phenomena like subsurface scattering, absorption, and propagation within the resin medium. This facilitates uniform polymerization, even in complex geometries or non-uniform materials, by accurately predicting energy distribution. Its adaptability to various container shapes and optical properties enables the creation of high-resolution, artifact-free structures, making it ideal for applications such as biomedical devices, optical components, and intricate engineering prototypes.

[0193] In one embodiment of the present disclosure, the light-propagation algorithm comprises one or more of ray tracing, ray marching, volumetric simulation, photon mapping, path tracing, Monte Carlo-based sampling, radiative transfer modeling, light scattering simulations, beam tracing, wavefront propagation, finite element analysis for lightpropagation, bidirectional path tracing, point spread function modeling, discrete ordinates method, radiance caching, and / or combinations thereof. These algorithms collectively represent a spectrum of computational techniques for modeling light behavior in a photosensitive medium, each tailored to address specific challenges in achieving precise and uniform dose distributions. For instance, ray tracing and ray marching are effective for mapping linear light paths and resolving geometrical interactions, whereas volumetric simulation and photon mapping account for complex scattering and absorption effects within the medium. Photon mapping, for example, is advantageous in scenarios where light interacts with highly scattering or translucent materials, allowing for accurate modeling of subsurface scattering. Monte Carlo-based sampling introduces stochastic elements into the calculations, enabling robust simulation of random scattering events and improving realism in dose predictions. The utilization of stochastic methods, such as Monte Carlo for sampling of light paths may be relevant in cases where various forms of noise and / or uncertainties need to be accounted for. Wavefront propagation and finite element analysis extend these capabilities by addressing phase and wave characteristics of light, making them suitable for high-fidelity applications where diffraction or interference effects are significant.

[0194] Implementations of this embodiment may vary depending on the computational resources available and the specific requirements of the printed object. A system might integrate multiple algorithms to leverage their respective strengths, using ray tracing for geometrically straightforward regions while applying volumetric simulation for areas requiring detailed interaction modeling. The ability to combine and adapt algorithms allows for enhanced scalability and flexibility, ensuring consistent print quality across diverse applications. This comprehensive approach to light-propagation modeling enables precise energy delivery, reducing undercuring or overcuring and thereby improving the mechanical and aesthetic properties of the final object.

[0195] In one embodiment of the present disclosure, the step of computing comprises optimizing the projection data through an iterative process employing an optimization algorithm. This iterative approach involves systematically refining the parameters of the dose distribution to align the computed distribution with a desired target dose profile. The optimization process may account for variables such as light intensity, geometric constraints of the container and object, and material properties of the photosensitive medium. This ensures that the energy delivered during the printing process is precisely controlled, resulting in uniform polymerization and high-resolution object formation. An example of an iterative optimization algorithm is shown in FIG. 6. The iterative process continues until the predefined optimization tolerance is reached, indicating that the reconstructed dose distribution sufficiently matches the target dose distribution.

[0196] The optimization algorithm may utilize derivative-based methods such as gradientbased optimization, which evaluates how small changes in parameters affect the dose distribution and iteratively adjusts these parameters to minimize discrepancies.

[0197] Alternatively, stochastic methods like genetic algorithms or evolutionary strategies may be employed to explore a broader parameter space, making them suited for complex or irregular geometries. Heuristic techniques, which incorporate domain-specific knowledge, may also be applied to speed up convergence or improve solution quality. Each of these methods offers advantages depending on the specific requirements of the 3D printing scenario, such as computational speed, resolution, or adaptability to varying container shapes.

[0198] In a further development of the present disclosure, the optimization algorithm minimizes a discrepancy between a target distribution, representing the desired light dose profile for uniform curing, and a computed distribution iteratively generated by the optimization algorithm. The target distribution is defined as a three-dimensional representation of the desired polymerization within the photosensitive medium, ensuring that energy is delivered precisely to regions corresponding to the object’s geometry while avoiding unnecessary exposure elsewhere. This method refines the computed dose distribution over successive iterations, improving alignment with the target dose profile and enhancing the accuracy and quality of the 3D printing process.

[0199] The target distribution may account for the curing threshold of the photosensitive medium, which is the minimum energy required to initiate polymerization. By ensuring that the dose in regions corresponding to the object exceeds this threshold while keeping the dose outside the object below it, the method prevents defects such as overcuring, which can distort geometries, and undercuring, which can weaken the structure.

[0200] In one embodiment of the present disclosure, the target dose distribution comprises a three-dimensional distribution in which the dose within voxels representing the object exceeds a curing threshold, and the dose in voxels outside the object remains below the curing threshold. This embodiment ensures precise polymerization limited to the geometry of the intended object, preventing unintended curing in adjacent regions. The curing threshold is determined based on the material properties of the photosensitive medium, such as its sensitivity to light intensity and exposure duration, ensuring energy efficiency and structural integrity of the printed object.

[0201] An example of surface voxelization and solid voxelization applied to a 3D mesh model is shown in FIG. 4. An example of non-uniform octree voxelization of a 3D mesh model is also shown in FIG. 10. In theseexample, the voxelization was performed using an NVIDIA GeForce RTX 3060 graphics card with 12 GB of VRAM and was completed in less than 1 millisecond.

[0202] The use of voxel-based dose control enables fine-grained resolution, allowing for the production of intricate features and smooth surface finishes. This approach is suitable for objects with complex geometries, as it minimizes artifacts such as jagged edges or uneven polymerization. The threshold-based design may also incorporate additional parameters, such as regional variations in curing thresholds to accommodate material heterogeneity or specific functional requirements of different areas within the object.

[0203] In one embodiment of the present disclosure, the target dose distribution defines the threshold-based curing region within the photosensitive medium, such that only voxels corresponding to the object’s geometry reach or exceed the curing threshold. This ensures that the polymerization process is confined strictly to the intended object regions, avoiding any unintended exposure that could lead to defects or wasted material. By limiting curing to specific voxels, this method achieves a high degree of precision while maintaining consistency throughout the printing process.

[0204] The threshold-based curing region is determined by analyzing the optical and material properties of the photosensitive medium, such as its absorption coefficient, refractive index, and polymerization kinetics. These parameters allow the system to predict and control light interactions within the medium accurately. Variations of this embodiment may involve adaptive thresholding, where the curing threshold is dynamically adjusted based on local geometry or material characteristics. For example, regions of the object requiring higher structural strength could be exposed to slightly higher doses, while areas with delicate features could have lower thresholds to preserve their integrity. In one embodiment of the present disclosure, the method further comprises defining the target dose distribution to minimize exposure outside the object’s geometry by maintaining doses below the curing threshold in non-object voxels. This ensures that the polymerization process is precisely confined to the desired regions, avoiding unnecessary curing in the surrounding medium. By controlling the dose distribution in this way, the method prevents material waste, reduces the likelihood of defects, and enhances the overall efficiency and quality of the 3D printing process.

[0205] The target dose distribution may be implemented using computational algorithms that model light behavior within the photosensitive medium. For example, light-propagation algorithms such as ray tracing or volumetric simulation can predict and adjust the dose levels to ensure they remain below the curing threshold in non-object voxels. This selective exposure strategy is advantageous for applications involving high-resolution prints, as it minimizes the risk of overcuring that could otherwise blur fine details or distort the object’s structure.

[0206] In a further development of the present disclosure, the iterative process comprises adjusting intensity levels of the projections based on discrepancies between the target dose distribution and the computed dose distribution across successive iterations. This refinement ensures that the actual energy delivery during the 3D printing process aligns closely with the predetermined dose distribution, thereby achieving uniform polymerization and high fidelity in the printed object. The method allows for continuous improvement in dose accuracy through successive cycles, reducing errors, and optimizing the quality of the final structure.

[0207] The adjustment of projection intensity levels may be implemented using computational algorithms that analyze deviations in the delivered dose. For instance, an optimization routine can compare the computed dose distribution with the target profile and adjust projection parameters, such as light intensity, exposure time, or beam shape, to minimize discrepancies. This process can be performed in real time or precomputed for specific geometries and materials, ensuring adaptability to diverse printing conditions. In one variation, the adjustments may include scaling the intensity of specific light paths to compensate for regions of undercuring or overcuring, ensuring consistent polymerization throughout the volume. In one embodiment of the present disclosure, the optimization algorithm comprises or consists of a derivative-based method such as a gradient-based optimization, or a stochastic optimization, an evolutionary algorithm, or a heuristic method. These algorithms are employed to iteratively refine the computed dose distribution to match the target dose profile, ensuring uniform polymerization within the desired object geometry. Each optimization approach offers unique advantages, making them suitable for different use cases and system configurations.

[0208] A flowchart to illustrate how the algorithm may comprise an iterative refinement is shown in FIG. 6.

[0209] Derivative-based methods, such as gradient-based optimization, use mathematical techniques to calculate how small changes in input parameters influence the computed dose distribution. These methods are efficient in problems where the dose distribution can be expressed as a differentiable function of projection parameters. By evaluating gradients, the system can make precise adjustments to minimize discrepancies between the computed and target distributions, achieving rapid convergence and high accuracy.

[0210] Stochastic optimization methods, including genetic algorithms and evolutionary strategies, are more adaptable for exploring complex, non-linear parameter spaces. These techniques may be effective in scenarios involving highly intricate geometries or irregular container shapes, where deterministic approaches may struggle to identify optimal solutions. Heuristic methods, on the other hand, incorporate domain-specific knowledge to guide the optimization process, offering fast and reliable solutions for well-understood printing environments.

[0211] The implementation of these algorithms may involve hybrid approaches, combining the strengths of different optimization techniques. For example, a system might use a heuristic method to initialize the dose distribution parameters and then refine them using gradient-based or stochastic methods. These flexible and adaptable strategies ensure that the method can accommodate diverse printing requirements, achieving consistent and high-quality results across applications. In one embodiment of the present disclosure, the computing of the projection data is performed using a hierarchical or multi-resolution approach. This methodology divides the computational process into multiple levels of granularity, enabling efficient modeling of light interactions within the photosensitive medium while maintaining high accuracy. By structuring the computation hierarchically to accommodate multiple scales, the system can first approximate the overall dose distribution at a coarse resolution and then refine it progressively at finer resolutions in regions of interest, such as areas with intricate geometries or critical features.

[0212] The hierarchical approach allows the system to allocate computational resources strategically, focusing on regions that require greater precision while reducing complexity in less critical areas. For instance, the global dose distribution may be computed initially as a precomputation step to identify areas of potential undercuring or overcuring. Subsequent iterations can then increase the resolution in these regions, using finer grid sizes or more detailed simulations to enhance accuracy. This ensures that the computational process remains efficient, even for large or complex objects, while still achieving the desired fidelity.

[0213] In a multi-resolution implementation, the system may employ different computational techniques at each level of resolution. For example, a coarse global distribution might be computed using simplified ray tracing or light propagation models, while high-resolution regions may use volumetric simulation or photon mapping to account for complex scattering and absorption effects. By enabling precise and scalable dose distribution computations, this approach enhances the flexibility and efficiency of the volumetric 3D printing process.

[0214] In a further development of the present disclosure, the light-propagation algorithms comprise a simulation module configured to simulate scattering and refraction, such as to account for material properties of the photosensitive medium. This module is designed to model the behavior of light as it interacts with the medium's internal structure, including its refractive index, absorption coefficient, and scattering characteristics. By incorporating these factors into the simulation, the system achieves a more accurate representation of light distribution within the medium, ensuring uniform energy delivery and precise polymerization. The scattering simulation accounts for phenomena such as isotropic or anisotropic scattering, where light is dispersed uniformly or preferentially in certain directions. Refraction is modeled to predict how light rays bend as they pass through interfaces with varying refractive indices, such as between the medium and the container walls. These effects are particularly significant for achieving high fidelity in areas with complex geometries or sharp transitions in material properties. By accurately simulating these interactions, the module ensures that the dose distribution conforms closely to the intended object geometry.

[0215] An example of a container comprising multiple, discrete refractive indices is shown in FIG. 7. In the top panel of this figure, an outer layer has a refractive index, n2, which may be different from the refractive index of the container bulk, ns. As such, the incident ray and its trajectory changes upon passing each layer in which the refractive index changes. This may be described effectively by Snell’s law.

[0216] In one embodiment of the present disclosure, the method further comprises dynamically adjusting the projection data based on feedback, such as real-time feedback, from one or more sensors monitoring the polymerization state within the photosensitive medium. This embodiment may comprise a feedback loop that allows for real-time optimization of the light dose delivery during the printing process. By using real-time data, the system can adapt to variations in material properties, environmental factors, or unforeseen conditions that may affect the polymerization process.

[0217] The feedback mechanism can involve sensors designed to detect various parameters affecting of characterizing the polymerization state. Possible variations include incorporating multiple types of sensors for comprehensive monitoring or using advanced algorithms to predict and prevent deviations in the polymerization process before they occur. The adaptive feedback loop minimizes waste, reduces defects, and ensures the high fidelity of printed objects. This dynamic adjustment capability significantly enhances the precision and reliability of the printing process.

[0218] In a further development of the present disclosure, the sensors are configured to detect polymerization parameters including polymerization progress, temperature, scattering properties, or material density, and wherein feedback from the sensors is used to iteratively refine the projection data. This embodiment introduces a system capable of continuous monitoring and dynamic adjustment of light dose delivery by leveraging real-time data from sensor readings. These parameters provide a comprehensive view of the polymerization state, ensuring precise energy delivery and uniform curing throughout the object’s geometry.

[0219] Polymerization progress can be monitored by optical sensors that detect changes in light transmission or scattering caused by the conversion of liquid resin into a solid state. Temperature sensors can measure localized heat generated during the polymerization reaction, which is critical for detecting regions at risk of overheating or uneven curing. Sensors for material density and scattering properties enable a deeper analysis of how light propagates through the medium, accounting for variations in material composition or geometry. This rich dataset is processed by the system to adjust the dose distribution dynamically, ensuring optimized energy.

[0220] Possible implementations may involve combining multiple sensor types to provide complementary data. For example, optical sensors could monitor surface-level polymerization while thermal sensors track deeper reactions. Advanced processing algorithms, such as machine learning models, may be used to analyze sensor data, predict trends, and suggest preventive adjustments to the dose distribution. This feedback-driven approach enhances the precision and reliability of the 3D printing process.

[0221] In a further development of the present disclosure, the feedback is processed by a control system configured to evaluate differences between the actual polymerization state and an expected polymerization state, thereby informing adjustments to the projection data. The control system may interpret sensor readings, such as temperature, scattering properties, or polymerization progress, and compare these to pre-defined expectations from the computer model of the object to identify and correct deviations.

[0222] The control system may implement predictive algorithms to anticipate the outcomes of polymerization based on the current state of the medium. For example, if sensor data indicates a slower-than-expected reaction in a specific area, the system could adjust light intensity or exposure time to compensate and achieve the desired curing profile. Conversely, if overcuring is detected, the system might reduce energy delivery to prevent defects or material degradation. This process ensures that energy is delivered in a way that achieves uniform polymerization. Possible variations of this embodiment include integrating machine learning models that improve the system’s ability to predict and correct deviations over time, leveraging historical data from previous prints.

[0223] Additionally, the control system could be designed to work with multi-modal feedback, where data from optical, thermal, and acoustic sensors is combined to provide a comprehensive understanding of the polymerization state.

[0224] In one embodiment of the present disclosure, the control system operates as a closed-loop system, iteratively adjusting the projection data in response to variations in polymerization uniformity across the model, optimizing exposure for each projection cycle. This embodiment employs a feedback-driven process which may comprise realtime monitoring of the polymerization state to inform adjustments to ensure consistent and uniform curing. By dynamically optimizing the dose distribution during each projection cycle, the system minimizes the risk of undercuring or overcuring, enhancing the precision and quality of the printed object. The closed-loop system processes input from sensors measuring parameters such as polymerization progress, scattering properties, or material density.

[0225] Implementations may include advanced control algorithms such as proportional-integral-derivative (PID) controllers or machine learning models trained on historical data to predict and preempt potential issues. The system may also integrate multiple feedback mechanisms, such as combining optical and thermal sensors, to provide a more comprehensive assessment of the polymerization process. This adaptive capability makes the system suitable for complex geometries or variable material properties, ensuring consistent performance across diverse applications.

[0226] In one embodiment of the present disclosure, the projection data is configured to account for non-uniform or complex container geometries, enhancing dose distribution across varied container shapes. This embodiment addresses challenges associated with printing in containers that deviate from simple geometries, such as cylinders or spheres, by adapting the light dose to the specific contours and features of the container. This capability ensures precise and uniform polymerization, even when the container comprises complex topology. Examples of various container geometries and topologies are shown in FIG. 1 B, wherein some example containers represent surfaces that have genus higher than one and / or have non-trivial knot invariants. An example of a container with complex surface irregularities is shown in FIG. 10A. FIG. 10B shows the effect of these surface irregularities in a light pattern generated from an arbitrary orthogonal viewing angle of the container.

[0227] To implement this feature, the system may rely on advanced computational models that incorporate the container’s geometry into the dose distribution calculations.

[0228] Algorithms such as ray tracing, ray marching, or volumetric simulation may be employed to account for the way light interacts with the unique contours of the container, including reflections, refractions, and shadowing effects. This embodiment offers advantages for applications involving custom or non-standard container designs. By tailoring the dose distribution to the specific geometry of each container, the system can achieve consistent curing even in challenging scenarios. These capabilities expand the versatility and precision of volumetric 3D printing, making it suitable for advanced manufacturing tasks such as creating customized biomedical implants, intricate optical components, or other high-complexity structures.

[0229] In one embodiment of the present disclosure, the projection data is dynamically adjusted based on geometric characteristics of the container, including convex, concave, or irregular surface features, to achieve consistent polymerization. This embodiment ensures that the dose distribution accounts for the specific three-dimensional structure of the container, enabling uniform curing even in challenging configurations. By dynamically adapting the light dose to the geometric attributes of the container, the system can mitigate common issues such as uneven exposure or light scattering that arise in non-standard geometries.

[0230] A flowchart to illustrate how the geometric characteristics of the container are taken into account is shown in FIG. 3. In FIG. 8 and FIG. 9 it is shown how the resulting dose distribution depends on the geometric characteristics of the container for the same three-dimensional object. Using a truncated cone-shaped container (FIG. 9A) produces a more uniform, bi-nodal, and smoother dose distribution, especially in regions of fine structure, owing to the fact that this container geometry better matches the geometrical features of the object at hand than a cylindrical container geometry (FIG. 8A). This embodiment specifically addresses the issue of handling varying scattering characteristics of light upon passing through a container surface with varying curvature. For example, convex surfaces areas, which might cause light to converge and overexpose certain regions, can be compensated for by reducing the intensity or redirecting the light projections in those areas. Similarly, concave surfaces areas might cause light to diverge and underexpose certain regions, which can be compensated for by increasing the intensity or redirecting the light projections in those areas.

[0231] In one embodiment of the present disclosure, the method further comprises obtaining a model of the container by performing a 3D scan, wherein the scanned model is used to refine the projection data for optimized exposure. This embodiment integrates the precise geometry of the container into the printing process, ensuring that the dose distribution is tailored to the unique shape and features of the container. For instance, 3D scanning technology could be used to obtain an accurate digital representation of the container, which is then integrated into the light-propagation simulations. By leveraging 3D scanning technology, the system can account for irregularities, asymmetries, or unexpected variations in the container's structure, enhancing the accuracy of polymerization.

[0232] The 3D scanning process may involve technologies such as structured light scanning, laser triangulation, or photogrammetry, depending on the required resolution and the material properties of the container. The resulting digital model is processed to extract geometric details, which are then incorporated into computational simulations, such as ray tracing or volumetric modeling.

[0233] Variations of this embodiment could include combining scanned container data with real-time feedback systems to dynamically refine the dose distribution during printing. This capability is particularly useful in scenarios requiring precise alignment between the container and the printed object.

[0234] In a further development of the present disclosure, the computed dose distribution is provided to an illumination system comprising at least one adjustable light source capable of positioning at variable angles relative to the container, based on the dose distribution to optimize exposure. The at least one adjustable light source may comprise a projector. This embodiment involves using a system where the light source can be dynamically oriented to target specific regions of the photosensitive medium, ensuring precise delivery of energy to achieve uniform polymerization across the object geometry. By adjusting the position and angle of the light source, the method compensates for geometric complexities in the container or object, improving the accuracy and quality of the printing process.

[0235] This embodiment enables directing light to hard-to-reach areas, such as concave surfaces or intricate features, ensuring that all regions receive the appropriate dose. The system may also incorporate advanced algorithms to calculate the optimal angles and positions for the light source based on the computed dose distribution and the container's geometry. These calculations may take into account factors such as light scattering, refraction, and material properties of the medium. Variations could include the use of multiple adjustable light sources working in tandem to provide comprehensive coverage of the container, or integrating feedback mechanisms to continuously refine the light source's position during the printing process. By allowing for precise and adaptive energy delivery, this approach enhances the flexibility and reliability of volumetric 3D printing, making it suitable for advanced applications such as biomedical devices, custom optical components, and intricate engineering parts.

[0236] In one embodiment of the present disclosure, the adjustable light source is mounted on a motorized positioning apparatus, such as a robotic arm or gimbal, configured to dynamically adjust angles and positioning during the printing process. This embodiment enhances the flexibility and precision of light delivery by allowing the illumination system to adapt to the specific geometric and material characteristics of the container and object. By actively repositioning the light source, the system can target regions requiring higher precision or compensate for challenging areas such as shadows or concave surfaces. This embodiment offers a versatile way to deliver a dynamical dose distribution.

[0237] The motorized positioning apparatus may be capable of movement across multiple axes, providing a full range of motion to optimize the light source's orientation and position. For instance, a robotic arm with six degrees of freedom (three translational and three rotational) could be employed to precisely position the light source at any desired angle relative to the container. Control algorithms calculate the optimal path and positioning for the light source based on the computed dose distribution, ensuring uniform.

[0238] This approach offers significant advantages for applications requiring intricate details or high accuracy, such as biomedical implants, microfluidic devices, or optical components. The dynamic adjustment capability ensures consistent energy delivery, reducing the likelihood of defects and enhancing the overall fidelity of the printed object. Additionally, integrating the motorized apparatus with feedback mechanisms, such as sensors monitoring polymerization progress, allows the system to refine light positioning in real time, further improving the reliability and adaptability of the printing process.

[0239] In one embodiment of the present disclosure, the illumination system includes multiple independently controlled light sources, arranged to provide targeted illumination from multiple angles or positions as directed by the computed dose distribution. This configuration allows the system to deliver light selectively and precisely to different regions of the photosensitive medium. The independent control of each light source enables flexible and adaptive energy delivery, tailored to the specific requirements of the container and object being printed.

[0240] Each light source may be equipped with adjustable intensity, beam shape, and orientation capabilities, enabling precise targeting based on the computed dose distribution. The system calculates optimal settings for each light source, taking into account factors such as geometric features of the container, material properties of the medium, and the required resolution of the printed object. For example, one light source might focus on illuminating a concave area, while another ensures uniform exposure across flat surfaces. This multi-source approach reduces the risk of overcuring or undercuring in specific regions, enhancing the fidelity and structural integrity of the printed object. This embodiment may may comprise using a combination of fixed and motorized light sources, where fixed sources provide general illumination and motorized sources address specific areas requiring dynamic adjustments.

[0241] Advanced control algorithms can synchronize the operation of all light sources, ensuring that their combined effect achieves the desired dose distribution. In one embodiment of the present disclosure, each light source is individually controlled based on the projection data. This allows for precise and localized light delivery, where each light source can independently adjust its intensity, orientation, and beam profile to meet the specific energy requirements of different regions within the photosensitive medium. By tailoring the output of each light source to the computed dose distribution, the system ensures uniform polymerization across the object’s geometry, even for intricate structures.

[0242] The independent control of light sources may be implemented using advanced control algorithms that calculate the optimal parameters for each source. For instance, one light source may increase its intensity to compensate for underexposed areas, while another reduces its output to avoid overcuring in regions closer to the surface. The system could also coordinate the timing of light emissions to prevent interference or overlapping exposures that could lead to artifacts or inconsistencies in the printed object. This level of control enables the system to address challenging geometries and to collectively increase efficiency in volumetric 3D printing.

[0243] Potential variations of this embodiment include integrating real-time feedback mechanisms where sensor data informs adjustments to each light source in response to observed polymerization progress. For example, if an optical sensor detects uneven curing in a particular region, the associated light source can adapt its parameters dynamically. This approach enhances the reliability and precision of the 3D printing process.

[0244] In one embodiment of the present disclosure, the illumination system may comprise one or more light sources that are adjustable in position and / or orientation but that, for a given printing process, are operated at fixed positions and / or orientations relative to the container. In such implementations, the relative orientation between the container and the light emitted by the illumination system may be varied by rotating or translating the container, by arranging multiple such light sources at different locations around the container, and / or by selecting different projection patterns while keeping the physical positions of the light sources unchanged. In further embodiments, the illumination system may comprise one or more light sources that are mounted in fixed positions relative to the container and are not mechanically adjustable, while the computation of the target dose distribution and of the projection data based on the object model and the container model may be applied in the same way irrespective of whether the light sources are mechanically adjustable or fixed in position.

[0245] Additionally, the projection data may comprise projection images for a plurality of viewing directions. The viewing directions may comprise two or more distinct directions, for example at least two substantially non-parallel or substantially orthogonal viewing directions, optionally aligned with respective faces or surface regions of the container. In such embodiments, the illumination system may be configured such that light is projected into the container along these viewing directions, for example through faces of a polyhedral container or through selected regions of a curved container wall. The light emission for each viewing direction may be realised by a single adjustable light source that is repositioned between the viewing directions, by a plurality of light sources that are each operated at respective fixed positions associated with different viewing directions, or by a combination of adjustable and fixed-position emitters. In one example, a substantially cubical container may be used together with two substantially orthogonal viewing directions aligned with two faces of the cube, and the light may be delivered either by two light sources mounted at fixed positions on those faces or by an adjustable light source that is placed at predetermined positions for each of the two directions during the printing process.

[0246] In further embodiments, the three-dimensional object may comprise any object geometry that benefits from directed dose delivery from a limited set of viewing directions, such as lattice structures, shell structures, porous structures, or components with repeated internal features. In such cases, a subset of viewing directions comprising at least two substantially non-parallel or substantially orthogonal directions aligned with respective faces or principal axes of the container may be selected based on the orientation of dominant features of the object. For example, a lattice having struts aligned substantially along one or more principal directions may be printed in a container having corresponding faces or surface regions, using projection images generated for viewing directions aligned with those faces or regions, while the illumination system is operated such that the active light sources remain at fixed positions during dose delivery for the respective viewing directions. In such an arrangement, the geometry of the container and the selection of viewing directions may be used to control how projections fill the curing volume, irrespective of whether the active emitters are implemented as hardware-adjustable light sources held at given coordinates or as light sources mounted in fixed positions relative to the container. The same dose computation framework based on the target dose distribution and the container geometry may be used to derive projection data for these viewing directions so as to achieve uniform polymerization of the object throughout the curing volume.

[0247] In some implementations, embodiments employing at least one adjustable light source may be combined with embodiments employing one or more light sources that are operated at fixed positions. For example, one or more emitters mounted at fixed positions may provide general illumination from selected viewing directions, while one or more adjustable emitters are used to refine the dose distribution in regions that are difficult to access or that require higher accuracy. In all such implementations, the computation of the projection data may take into account the positions and / or orientations of the emitters, whether implemented as adjustable hardware or mounted in fixed positions, together with the geometry and optical properties of the container and the photosensitive medium. The light-propagation algorithms described herein, such as ray tracing, ray marching and volumetric simulation, may be applied in a similar manner for different container shapes and for different illumination configurations, including systems in which light sources are operated at fixed positions during exposure and systems in which light sources are adjusted between different positions and / or orientations, so that the dose computation framework is applicable across a wide range of projection systems.

[0248] In one embodiment of the present disclosure, the method is computer-implemented. This embodiment emphasizes the role of computational systems in executing the various steps of the volumetric 3D printing process, from dose distribution computation to dynamic control of the illumination system. By leveraging computer systems to handle the complexity of light-propagation algorithms, feedback processing, and iterative adjustments, the method achieves a high degree of precision and scalability.

[0249] The computer implementation may involve specialized hardware, such as GPUs or parallel computing clusters, to perform computationally intensive tasks like ray tracing, volumetric simulations, or real-time feedback analysis. The system can execute these calculations with speed and accuracy, ensuring that the projection data aligns with the geometry of the object and the container and that the time efficiency required for useful volumetric 3D printing processes are duly met. Additionally, the method may utilize software platforms that integrate simulation modules, control algorithms, and data acquisition systems. These platforms manage the flow of information between sensors, computational units, and motorized components of the illumination system.

[0250] This embodiment offers advantages in terms of automation and reproducibility. By automating complex calculations and adjustments, the computer-implemented method minimizes human error and ensures consistent performance across multiple production cycles. Variations of this implementation may include cloud-based systems that allow for remote monitoring and optimization, or machine learning models integrated into the software to improve accuracy and efficiency over time. This approach enhances the overall reliability, adaptability, and scalability of the volumetric 3D printing process.

[0251] In an aspect, the present disclosure relates to a computer-readable medium stores instructions that, when executed by one or more processing units, perform the method of any one of the preceding claims. This embodiment emphasizes the use of computer-readable storage to encapsulate the logic, algorithms, and processes required for the volumetric 3D printing method. The stored instructions can automate the entire workflow, from dose distribution computation to sensor integration and dynamic light source control, enabling a streamlined and highly efficient printing process.

[0252] The computer-readable medium may include various forms of non-volatile storage, such as solid-state drives, flash memory, optical discs, or cloud-based storage. These media contain software capable of executing light-propagation algorithms, optimization routines, and control mechanisms for the projection data. This embodiment offers substantial benefits in terms of portability and scalability. The software stored on the computer-readable medium can be deployed across multiple hardware platforms, enabling widespread adoption and integration into different 3D printing systems.

[0253] Possible variations include incorporating modular software components, allowing users to customize or upgrade specific functionalities, such as adding support for new materials or enhancing sensor feedback analysis. By encapsulating the logic in a computer-readable medium, the present disclosure ensures that the complex computational and operational aspects of volumetric 3D printing are accessible, reproducible, and adaptable to a broad range of applications, especially within industrial manufacturing. In a further aspect, the present disclosure relates to a method for producing a three-dimensional object comprises obtaining a computed projection data as disclosed herein, and illuminating, by an illumination system, a container accommodating a curing volume, in a series of patterns of light determined by the computed dose distribution; thereby producing the three-dimensional object. This embodiment concerns the method to produce or manufacture a three-dimensional object using the presently disclosed method, as for example encountered in industrial applications in which large quanta or an object needs to be produced repeatedly and efficiently. This embodiment is suitable for a wide range of fields, including biomedical devices, optical components, and industrial prototypes.

[0254] In one embodiment of the present disclosure, the illumination system comprises a light source which is oriented by a motorized arm or gimbal that adjusts position and / or orientation during the printing process. This embodiment allows for dynamic and precise control over the light source, enabling targeted energy delivery to specific regions of the photosensitive medium, in particular in a production or manufacturing context. By continuously adjusting the light source's position and orientation, the system can accommodate complex geometries, varying material properties, and intricate details of the object being printed.

[0255] The motorized arm or gimbal provides multi-axis movement, enabling the light source to achieve optimal angles and positions for each projection. For instance, the system can orient the light source to illuminate hard-to-reach areas, such as concave surfaces, or to compensate for distortions caused by the container’s geometry. Control algorithms calculate the optimal trajectory and positioning for the light source in real time, ensuring uniform polymerization across the entire object. Variations of this embodiment may include incorporating multiple motorized light sources to simultaneously address different regions of the container or object.

[0256] This capability significantly enhances the precision and flexibility of the volumetric 3D printing process. By allowing for adaptive energy delivery, the system reduces defects such as overcuring or undercuring, improves resolution, and ensures consistent results across diverse applications. This approach is beneficial for high-complexity manufacturing tasks where precise control over the printing process is critical to achieving functional and aesthetic requirements. In one embodiment of the present disclosure, the container may have a three-dimensional shape selected from a substantially cylindrical shape, a polyhedral shape, a prismatic shape, a substantially spherical shape, and combinations thereof. The container may comprise any one of these shapes depending on the intended application, available hardware and desired optical characteristics. A substantially cylindrical container may comprise, for example, a right circular cylinder or a slightly tapered cylinder that is approximated as cylindrical for computational purposes. A polyhedral or prismatic container may comprise containers having a finite number of planar faces, such as cubical, cuboidal, or prism-shaped vessels. A substantially spherical container may comprise an ideal sphere or a near-spherical form where deviations from a perfect sphere are within acceptable tolerances for the optical model. Combinations of these shapes may comprise containers having sections of different geometries.

[0257] This embodiment allows the system to be applied to a wide range of container geometries without being constrained to a single canonical shape. The use of substantially cylindrical containers may be advantageous for certain implementations because such containers can support rotational symmetries and may be compatible with some tomographic acquisition schemes, while polyhedral or prismatic shapes, such as substantially cubical containers, may be convenient for arranging multiple projection directions aligned with faces of the container and for stacking containers in an industrial environment. Substantially spherical containers may offer advantages when a more uniform path length distribution is desired, as rays entering the container can be arranged to traverse similar distances through the photosensitive medium. The method may be configured to adapt the projection data computation to the specific container shape selected.

[0258] The container shape may also influence the boundary conditions applied in the lightpropagation algorithms, such as ray tracing or ray marching, and may be taken into account when constructing discrete or analytical representations of the container in the simulation pipeline. By explicitly supporting substantially cylindrical, polyhedral, prismatic, substantially spherical shapes and combinations thereof, the method may be deployed across diverse applications where container geometry is dictated by process, ergonomic or regulatory requirements rather than by the printing method itself. In one embodiment of the present disclosure, computing the projection data may comprise a step of performing ray tracing using an acceleration structure in the form of a Bounding Volume Hierarchy (BVH) constructed over a polygon mesh representation of at least the container, the Bounding Volume Hierarchy (BVH) being constructed using a Surface Area Heuristic (SAH) or another cost-based partitioning heuristic.

[0259] The container geometry may be represented as a polygon mesh obtained from a CAD model or from a 3D scanning process. The BVH may then be constructed over this mesh as a hierarchical tree of bounding volumes, such as axis-aligned bounding boxes, each enclosing a subset of the triangles of the container. During ray tracing, rays traversing the scene may first be tested against these bounding volumes to quickly discard large regions that cannot intersect a given ray, significantly reducing the number of triangle intersection tests required.

[0260] The use of the Surface Area Heuristic or another cost-based partitioning heuristic for building the BVH may improve traversal performance by producing a hierarchy that minimises an expected cost function for ray-triangle intersection queries. Alternative cost-based heuristics may consider additional factors, such as the expected distribution of ray directions, the refractive index distribution, or the presence of multiple media, and may be tuned to the specific optical configuration.

[0261] In some embodiments, the BVH may be constructed only over the container mesh, while the volume of the photosensitive medium and the object model may be handled by separate volumetric representations used in ray marching or volumetric simulation. Additionally, the BVH may be extended to also enclose other polygonal objects in the scene, such as support structures, optical windows, or internal components. The BVH can be rebuilt or refitted when the container geometry changes, for example when a different container is mounted in the system, or can be cached for commonly used container shapes. The combination of ray tracing and a BVH built with SAH or related principles may enable accurate modeling of refraction and reflection at the container boundaries with high computational efficiency, thereby improving the accuracy of the computed projection data without prohibitive computational cost. In one embodiment of the present disclosure, ray tracing may comprise determining a surface normal at ray-surface intersection points by interpolating vertex normals of triangles of the polygon mesh representation of the container. Each vertex of the polygon mesh representing the container may be assigned a vertex normal.

[0262] Interpolating vertex normals at ray-surface intersections may be advantageous for accurately modeling optical effects such as refraction and reflection according to Snell’s law and Fresnel equations. A purely face-normal-based approach treating each triangular facet as having a single constant normal may introduce discontinuities in the normal field at triangle boundaries, which can lead to artifacts in the simulated light paths and in the resulting dose distribution, particularly for containers that are intended to approximate smooth surfaces such as spheres or cylinders. By using vertex normal interpolation, the container surface can be treated as an approximation of a smooth underlying analytical surface, and the computed ray directions after refraction or reflection may more closely match the physical behaviour of light in the actual container.

[0263] Additionally, the vertex normals may be precomputed offline and stored as attributes in the polygon mesh, for example in a GPU buffer or other memory structure used by the ray-tracing engine. The interpolation of vertex normals at intersection points may be implemented in shader programs or compute kernels when the ray tracing is executed on a graphics processing unit.

[0264] In one embodiment of the present disclosure, the three-dimensional object may comprise a lattice structure and the projection data comprises projection images for a plurality of viewing directions including at least two non-parallel viewing directions aligned with respective faces of the container. The three-dimensional object to be printed may be defined as a lattice, for example a periodic or aperiodic network of struts, beams or walls forming pores or cells within the object volume. Such lattice structures may include cubic lattices, body-centred cubic lattices, octet lattices, gyroid-inspired structures, or other architected materials used for lightweight mechanical components, biomedical scaffolds or energy-absorbing structures. The container may in particular comprise a polyhedral or prismatic shape with planar faces, such as a substantially cubical container. In one embodiment of the present disclosure, the projection images may be generated for a subset of viewing directions comprising two substantially orthogonal viewing directions aligned with respective faces of the container. The system may select a reduced set of viewing directions, for example two main directions that are substantially orthogonal to one another, such as along the X- and Y-axes of a Cartesian coordinate system associated with a substantially cubical container. Each of these viewing directions may be aligned with a corresponding face of the container so that light enters through that face along a direction approximately normal to the face. As used herein, the term substantially orthogonal may be understood to encompass directions that deviate slightly from exact orthogonality due to practical constraints of the illumination system or container mounting, while remaining sufficiently orthogonal for the intended optical approximation.

[0265] Additionally, the subset of viewing directions comprising two substantially orthogonal directions may be combined with additional, secondary projection directions used only in selected regions or at certain stages of the printing process. For example, projections from the two main orthogonal directions may be used for bulk dose delivery, while one or more auxiliary directions may be activated to refine features in regions that are underexposed or difficult to access. The selection of which directions constitute the subset and the precise alignment with container faces may be determined based on a pre-analysis of the object geometry, the container configuration, and the optical characteristics of the resin. By basing the projection images on a subset of viewing directions with two substantially orthogonal directions aligned with faces of the container, the method may flexibly adapt to different application requirements and hardware configurations while maintaining efficient volumetric dose delivery.

[0266] In one embodiment of the present disclosure, the method may include computation of the projection data by ray marching comprises representing at least a portion of a curing volume as a set of discrete volume elements such as voxels, determining, for each ray, a plurality of volume elements intersected by the ray, computing for each intersected volume element a local light transmittance using an attenuation model based on at least one optical property of the photosensitive medium and a path length of the ray within the volume element, and determining a projection pixel value based on an aggregation of the local light transmittances along the ray. The curing volume may be discretized into a regular grid of cubic voxels or into another discrete volumetric structure, such as an octree, where each volume element represents a small region of the resin with approximately homogeneous properties. The object model and any spatially varying material properties may be mapped onto this grid so that each volume element is associated with relevant optical parameters.

[0267] Ray marching may then comprise determining, for each ray, which discrete volume elements are intersected by the ray and in which order.

[0268] This determination may be implemented using a voxel traversal algorithm, such as a digital differential analyzer method or other grid traversal schemes that step through the volume incrementally along the ray direction. For each intersected volume element, a local light transmittance may be computed using an attenuation model that depends on at least one optical property of the photosensitive medium, such as its absorption coefficient, scattering coefficient or extinction coefficient, and on the path length of the ray within that element. The attenuation model may, for example, be based on an exponential law describing how light intensity decays as a function of the product of absorption coefficient and path length.

[0269] After computing the local transmittances for all volume elements intersected by a ray, an overall transmittance or attenuation value along the ray may be obtained by aggregating the local contributions, such as by multiplying the transmittances or by summing optical depth values in a logarithmic domain. The projection pixel value associated with the ray may then be determined based on this aggregated measure, for example by setting the pixel intensity proportional to one minus the overall transmittance or to another function of the cumulative attenuation. This mapping may be chosen so that, when the resulting projection image is used in the illumination system, the delivered dose distribution in the curing volume approximates the target dose distribution. By representing the curing volume as discrete volume elements and computing projection pixels from aggregated local transmittances, the method may achieve a flexible and physically motivated framework for ray-marching-based dose computation that can be efficiently implemented on modern computing hardware.

[0270] In one embodiment of the present disclosure, the method is used for producing prosthetics, artificial limbs, implants, dental devices, pharmaceuticals, microfluidic devices, optical components, or combinations thereof. This embodiment highlights the versatility of the volumetric 3D printing method, highlighting its ability to produce objects across a wide range of applications that require high precision, intricate geometries, and tailored material properties. Each of these use cases benefits from the projection data, dynamic light control, and real-time feedback mechanisms inherent in the disclosed method.

[0271] For biomedical applications, such as prosthetics, implants, and dental devices, the ability to achieve high resolution and precise polymerization ensures that components fit accurately to patient-specific geometries. This level of customization can be useful in applications like dental crowns, hearing aids, or surgical implants, where anatomical compatibility and structural integrity can be important. The use of biocompatible photosensitive materials, combined with the method’s accuracy, makes it suitable for producing functional and safe medical devices.

[0272] In the field of microfluidic devices, the method’s capacity to produce complex internal channels and intricate features supports the manufacturing of advanced lab-on-a-chip systems for diagnostics or chemical processing. Similarly, in optical components, the uniform curing achieved by the projection data ensures high clarity and minimal distortion, which are critical for lenses, waveguides, or mirrors. Variations of this embodiment may involve specific material formulations optimized for the target application, further enhancing functionality and performance. By addressing diverse industrial needs, this method expands the applicability of volumetric 3D printing into areas demanding high precision, customization, durability, and reliability.

[0273] In a further aspect, the present disclosure relates to system for volumetric 3D printing of a three-dimensional object, comprising a computational unit comprising a processor, a power source and a non-transient memory, wherein the memory comprises instructions that when executed by a processor carries out the method as disclosed herein; and an illumination system configured to receive projection data, and to generate a series of projections for controlled polymerization of a photosensitive medium.

[0274] Here, the computational unit integrates light-propagation algorithms, projection data calculations, and optimization routines, enabling precise control over light delivery based on the object’s geometry and container design. This system facilitates the dynamic adjustment of light intensity, projection angles, and exposure patterns to achieve uniform curing and high-resolution outputs. The technical advantages of this system are rooted in its ability to combine advanced computation with responsive hardware. Unlike traditional systems that often rely on static light exposure or manual adjustments, this system dynamically adapts to realtime conditions, such as material inconsistencies or geometric complexities. The integration of the computational unit with the illumination system ensures seamless communication and rapid adjustments, significantly reducing defects like overcuring or undercuring. By enabling high fidelity and efficiency, the system represents a substantial improvement over existing technologies, making it highly applicable to fields requiring precision and customization, such as medical devices, optical components, and complex engineering prototypes.

[0275] The discloses system may be used to conduct any variation of or in combination with the method of the present disclosure.

[0276] Reference numeral list

[0277] 100 three-dimensional computer model of an object

[0278] 101 three-dimensional computer model of an object

[0279] 102 triangulations of various resin container geometries

[0280] 200 import 3D design

[0281] 201 GPU voxelization

[0282] 202 light source(s) configuration

[0283] 203 container characterization

[0284] 204 create ray tracing pipeline

[0285] 205 ray marching and iterative dose optimization

[0286] 206 real-time rendering of the final dose

[0287] 207 light source(s) configuration

[0288] 208 light source(s) coordinate(s)

[0289] 209 optical configuration (telecentric, non-telecentric)

[0290] 210 import 3D design

[0291] 211 GPU voxelization

[0292] 212 surface voxelization compute shader

[0293] 213 solid voxelization compute shader

[0294] 300 container characterization

[0295] 301 3D digital model (polygon mesh) 302 mathematical representation

[0296] 303 define material properties and size information

[0297] 304 load mesh data

[0298] 305 load material properties

[0299] 306 build acceleration structure

[0300] 400 solid voxelization of a three-dimensional computer model viewed as a two-dimensional projection

[0301] 401 surface voxelization of a three-dimensional computer model viewed as a slice along the z-axis

[0302] 402 surface voxelization of a three-dimensional computer model viewed as a slice along the y-axis

[0303] 403 surface voxelization of a three-dimensional computer model viewed as a slice along the x-axis

[0304] 404 solid voxelization of a three-dimensional computer model viewed as a slice along the z-axis

[0305] 405 solid voxelization of a three-dimensional computer model viewed as a slice along the y-axis

[0306] 406 solid voxelization of a three-dimensional computer model viewed as a slice along the z-axis

[0307] 500 container characterization

[0308] 501 mathematical characterization

[0309] 502 ray generation shader (considering light source configuration)

[0310] 503 ray-object intersection compute shaders

[0311] 504 ray traversal compute shaders (reflection, refraction, etc.)

[0312] 505 polygon mesh

[0313] 506 ray generation shader (considering light source configuration)

[0314] 507 ray-acceleration structure traversal

[0315] 508 any hit shader

[0316] 509 intersection

[0317] 510 miss shader

[0318] 511 closest hit shader (reflection, refraction, etc.)

[0319] 600 ray information from ray tracing pipeline

[0320] 601 forward ray marching compute shader

[0321] 602 backward ray marching compute shader

[0322] 603 optimization compute shader 604 save the final dose

[0323] 700 mathematical representation of a hemispherical container geometry 701 interface separating the inside from the outside of a container (700) as viewed in a top-down projection

[0324] 702 point of abrupt change in refractive index, from m via n2, to ns, causing a light ray to change direction

[0325] 703 mathematical representation of a box-shaped container geometry 704 interface separating the inside from the outside of a container (703) as viewed in a top-down projection

[0326] 705 light ray

[0327] 800 three-dimensional computer model of a cylindrical container

[0328] 801 three-dimensional computer model of an object

[0329] 802 computed light pattern using a cylindrical container (800)

[0330] 803 light intensity scale for the obtained dose distribution (802)

[0331] 804 simulated dose distribution using a cylindrical container

[0332] 900 three-dimensional computer model of a cylindrical container

[0333] 901 three-dimensional, high-fidelity computer model of an object

[0334] 902 computed light using a truncated cone-shaped container (900)

[0335] 903 light intensity scale for the obtained dose distribution (902)

[0336] 904 simulated dose distribution using a truncated cone-shaped container 1001 three-dimensional computer model of an arbitrary container with complex surface irregularities

[0337] 1002 octree voxelization of a three-dimensional computer model

[0338] 1003 computed light pattern using an arbitrary container with surface irregularities (1001)

[0339] Examples

[0340] The following examples illustrate some of the features, applications, and advantages of the disclosed method and system for volumetric 3D printing of three-dimensional objects. These examples are provided for illustrative purposes and are not intended to limit the scope of the present disclosure.

[0341] Structures with varying densities serve as compelling examples of challenges that arise when using a cylindrical container in volumetric 3D printing. For instance, in three-dimensional lattice structures, the void density within the lattice increases, making it difficult to manage light exposure and prevent overexposure in regions outside the target object. In such cases, cylindrical containers often exacerbate dose leakage into non-target areas, reducing the contrast between in-part and out-of-part regions, particularly along lateral dimensions, and compromising print fidelity. By contrast, a cubic container paired with a telecentric optical system can significantly reduce dose deposition in out-of-part regions, enhancing dose contrast. For example, a cubic container allows the lattice structure to be printed using only two orthogonal projections, whereas a cylindrical container would require projections from multiple angles, increasing dose buildup in non-target areas.

[0342] For objects containing fine details, cylindrical containers often lead to dose scattering due to tomographic projections of light patterns from various angles. This scattering causes excessive dose delivery to out-of-part regions, further degrading print fidelity. A hemispherical container, combined with a projector capable of moving freely along a hemispherical trajectory, allows light patterns to be projected from a broader range of arbitrary angles. This approach improves dose delivery to in-part voxels, reduces dose occlusion, and minimizes overexposure in non-target regions, resulting in enhanced print precision.

[0343] For example, as shown in FIG. 8 and FIG. 9, altering the container shape and allowing free movement of the light source significantly improves dose contrast for complex structures like the Eiffel Tower. Using a cylindrical container with traditional tomographic backprojection introduces significant dose smearing, where non-target regions receive unintended light exposure due to cumulative projections from multiple angles. In contrast, a truncated cone-shaped container paired with a spiral trajectory for the light source enhances dose contrast between in-part and out-of-part regions. This approach effectively reduces dose smearing and preserves intricate structural details of the Eiffel Tower model.

[0344] Another example involves printing dental models and appliances, including clearaligner models, surgical guides, splints, and denture bases. These workpieces are often large in lateral extent (e.g., a full-arch geometry) and are commonly produced in high throughput, which can drive the use of large containers holding substantial volumes of photopolymer resin. In conventional volumetric printing systems that employ a deep cylindrical container and a fixed orthogonal projection geometry, the projected light can be required to traverse relatively long optical path lengths through the resin. Over these extended path lengths, absorption and attenuation reduce the delivered dose at deeper voxels, while volumetric scattering broadens the effective point spread function (PSF) of the projected patterns. As a result, achieving the polymerization threshold throughout the intended dental workpiece may require increased exposure or dose compensation, which can in turn increase out-of-part dose deposition, blur fine anatomical details (e.g., margins, cusps, and guide features), and produce non-uniform polymerization that can adversely affect dimensional accuracy and mechanical uniformity. In contrast, in some implementations, the resin may be poured into an open-top vat or other shallow container, and the projector (or other light engine) may be moved freely relative to the vat to deliver light patterns directly through the free surface of the resin. By projecting through the resin surface and positioning the light source along a controlled trajectory (e.g., a hemispherical sweep, spiral, or other multi-degree-of-freedom path), the system reduces the optical depth that light must travel within the resin for a given set of projections. This reduced path length decreases absorption losses and scattering-induced blur, thereby improving dose contrast between in-part and out-of-part regions and enabling more uniform delivery of the target dose distribution across the dental geometry. In addition, because depthdependent PSF broadening is reduced, higher spatial-frequency features can be preserved, improving the accuracy and resolution of clinically relevant details such as interproximal contacts, occlusal anatomy, and guide sleeves. In many cases, this approach also reduces the total resin volume required for a given build envelope, lowering material usage while improving dose control and uniform polymerization of the workpiece.

[0345] In further implementations, the disclosed ray tracing and simulation pipeline may be used to model and compensate for refraction and surface effects at the resin-air interface (e.g., a meniscus, surface waviness, or dynamic surface disturbances), allowing the generated light patterns to be pre-distorted such that the intended volumetric dose distribution is still achieved within the resin despite these interface-related optical effects.

[0346] The disclosed ray tracing pipeline further facilitates compensation for surface irregularities or imperfections on the container when generating light patterns.

[0347] Containers often exhibit manufacturing imperfections, wear, or surface distortions over time, even in commonly used cylindrical designs. By incorporating these irregularities into simulations, the disclosed system corrects for potential optical distortions caused by the imperfections, ensuring accurate delivery of the intended dose distribution within the resin. For instance, in a container with subtle surface undulations, the system dynamically adjusts the light patterns to accommodate these irregularities, maintaining precise dose distribution and enhancing overall printing fidelity.

[0348] Items

[0349] 1. A method for volumetric 3D printing of a three-dimensional object, the method comprising:

[0350] • obtaining a model of the object and a model of a container;

[0351] • generating a target dose distribution based on the model of the object; • computing projection data based on the target dose distribution and the model of the container; and

[0352] • providing the projection data to an illumination system configured to generate a series of projections for controlled polymerization of a photosensitive medium.

[0353] 2. The method according to item 1, wherein the projection data is computed using one or more light-propagation algorithms.

[0354] 3. The method according to item 2, wherein the light-propagation algorithms comprises or consists of ray tracing.

[0355] 4. The method according to any one of items 2-3, wherein the light-propagation algorithms comprises or consists of ray marching.

[0356] 5. The method according to any one of items 2-4, wherein the light-propagation algorithms comprises or consists of volumetric simulation.

[0357] 6. The method according to any one of items 2-5, wherein the light-propagation algorithms comprise a simulation module configured to simulate scattering and refraction, such as to account for material properties of the photosensitive medium. 7. The method according to any one of items 2-6, wherein the light-propagation algorithm comprises or consist of one or more of ray tracing, ray marching, volumetric simulation, photon mapping, path tracing, Monte Carlo-based sampling, radiative transfer modeling, light scattering simulations, beam tracing, wavefront propagation, finite element analysis for light-propagation, bidirectional path tracing, point spread function modeling, discrete ordinates method, radiance caching, and / or combinations thereof.

[0358] 8. The method according to any one of the preceding items, wherein the projection data comprises a series of light projections, each defined as a pixel-wise light distribution specifying light intensity and spatial pattern, and wherein each projection is associated with one or more projection parameters.

[0359] 9. The method according to item 8, wherein the projection parameters comprise one or more of the following: the position of the light source relative to the container, the orientation angle of the light source, the focal plane of the projection, intensity modulation to adjust localized or overall light intensity, exposure duration to define the time a projection is delivered, position and / or orientation of the illumination system, and / or wavelength specifications to optimize curing for specific material properties

[0360] 10. The method according to any one of the preceding items, wherein the step of computing comprises optimizing the projection data through an iterative process employing an optimization algorithm.

[0361] 11. The method according to item 10, wherein said optimization algorithm minimizes a discrepancy between a target distribution, representing the desired light dose profile, such as for uniform curing, and a computed distribution iteratively generated by the optimization algorithm or the projection data.

[0362] 12. The method according to item 10-11, wherein the target dose distribution comprises a three-dimensional distribution in which the dose within voxels representing the object exceeds a curing threshold, and the dose in voxels outside the object remains below the curing threshold. 13. The method according to any one of items 10-12, wherein the target dose distribution defines the threshold-based curing region within the photosensitive medium, such that only voxels corresponding to the object’s geometry reach or exceed the curing threshold.

[0363] 14. The method according to any one of items 10-13, further comprising defining the target dose distribution to minimize exposure outside the object’s geometry by maintaining doses below the curing threshold in non-object voxels.

[0364] 15. The method according to any one of items 10-14, wherein the iterative process comprises adjusting the projection data based on discrepancies between the target dose distribution and the computed dose distribution across successive iterations.

[0365] 16. The method according to any one of items 10-15, wherein the optimization algorithm comprises or consists of a derivative-based method such as a gradient-based optimization, or a stochastic optimization, an evolutionary algorithm, or a heuristic method.

[0366] 17. The method according to any one of the preceding items, wherein the computing of the projection data is performed using a hierarchical or multiresolution approach.

[0367] 18. The method according to any one of the preceding items, further comprising dynamically adjusting the projection data based on feedback, such as real-time feedback, from one or more sensors monitoring the polymerization state within the photosensitive medium.

[0368] 19. The method according to item 18, wherein the sensors are configured to detect polymerization parameters including polymerization progress, temperature, scattering properties, or material density, and wherein feedback from the sensors is used to iteratively refine the projection data. The method according to any one of items 18-19, wherein the feedback is processed by a control system configured to evaluate differences between the actual polymerization state and an expected polymerization state, thereby informing adjustments to the projection data.

[0369] The method according to any one of items 18-20, wherein the control system operates as a closed-loop system, iteratively adjusting the projection data in response to variations in polymerization uniformity across the model, optimizing exposure for each projection cycle.

[0370] The method according to any one of the preceding items, wherein the projection data is configured to account for non-uniform or complex container geometries.

[0371] The method according to any one of the preceding items, wherein the projection data is computed based on geometric characteristics of the container, including convex, concave, or irregular surface features, to achieve consistent polymerization.

[0372] The method according to any one of the preceding items, wherein the model of the container is obtained by performing a 3D scan of the container.

[0373] The method according to any one of the preceding items, wherein the illumination system comprises at least one adjustable light source capable of being adjusted to different positions and angles relative to the container, and wherein the projection data includes information specifying, for each projection of the series of projections, associated positions and angles of the light source for generating the projection.

[0374] The method according to item 25, wherein the at least one adjustable light source is mounted on a motorized positioning apparatus, such as a robotic arm or gimbal, configured to dynamically adjust angles and positioning during the printing process.

[0375] The method according to any one of items 25-26, wherein the illumination system includes multiple independently controlled light sources, arranged to provide targeted illumination from multiple angles and / or positions, as directed by the projection data.

[0376] 28. The method according to any one of items 25-27, wherein the illumination system is configured to generate each projection, of the series of projections, from a position and at an angle, as specified by the associated position data and angular data.

[0377] 29. The method according to any one of items 25-28, wherein each light source is individually controlled based on the projection data.

[0378] 30. The method according to any one of the preceding items, wherein the method is computer-implemented.

[0379] 31. A computer-readable medium storing instructions that, when executed by one or more processing units, perform the method of any one of the preceding items.

[0380] 32. A method for producing a three-dimensional object, comprising:

[0381] • obtaining a computed projection data using the method of any one of items 1-31; and

[0382] • illuminating, by an illumination system, a container accommodating a curing volume, in a series of patterns of light determined by the projection data; thereby producing the three-dimensional object.

[0383] 33. The method according to item 32, wherein the illumination system comprises a light source which is oriented by a motorized arm or gimbal that adjusts position and / or orientation during the printing process.

[0384] 34. The method according to any one of the preceding items, wherein the method is used for producing prosthetics, artificial limbs, implants, dental devices, pharmaceuticals, microfluidic devices, optical components, or combinations thereof.

[0385] 35. A system for volumetric 3D printing of a three-dimensional object, comprising: • a computational unit comprising a processor, a power source and a nontransient memory, wherein the memory comprises instructions that when executed by a processor carries out the method of any one of items 1-34; and

[0386] • an illumination system configured to receive projection data, and to generate a series of projections for controlled polymerization of a photosensitive medium.

Claims

Claims1. A method for volumetric 3D printing of a three-dimensional object, the method comprising:• obtaining a model of the object and a model of a container configured to accommodate a photosensitive medium;• generating a target dose distribution based on the model of the object; • computing, using one or more light-propagating algorithms, projection data based on the target dose distribution and the model of the container, the projection data comprising a series of projections, each projection including a spatial light distribution and being associated with a respective position and / or orientation of at least one adjustable light source relative to the container; and• providing the projection data to an illumination system comprising the at least one adjustable light source and configured to generate each projection from the associated position and / or orientation for controlled polymerization of the photosensitive medium.

2. The method according to claim 1, wherein the light-propagation algorithms comprises or consists of ray tracing.

3. The method according to any to any one of the preceding claims, wherein the light-propagation algorithms comprises or consists of ray marching.

4. The method according to any one of the preceding claims, wherein the lightpropagation algorithms comprises or consists of volumetric simulation.

5. The method according to any one of the preceding claims, wherein the lightpropagation algorithms comprise a simulation module configured to simulate scattering and refraction, such as to account for material properties of the photosensitive medium.

6. The method according to any one of the preceding claims, wherein the lightpropagation algorithm comprises or consists of one or more of ray tracing, raymarching, volumetric simulation, photon mapping, path tracing, Monte Carlobased sampling, radiative transfer modeling, light scattering simulations, beam tracing, wavefront propagation, finite element analysis for light-propagation, bidirectional path tracing, point spread function modeling, discrete ordinates method, radiance caching, and / or combinations thereof.

7. The method according to any one of the preceding claims, wherein the projection data comprises a series of light projections, each defined as a pixelwise light distribution specifying light intensity and spatial pattern, and associated with one or more projection parameters.

8. The method according to claim 7, wherein the projection parameters comprise one or more of the following: the position of the light source relative to the container, the orientation angle of the light source, the focal plane of the projection, intensity modulation to adjust localized or overall light intensity, exposure duration to define the time a projection is delivered, and / or wavelength specifications to optimize curing for specific material properties.

9. The method according to any one of the preceding claims, wherein the step of computing comprises optimizing the projection data through an iterative process employing an optimization algorithm.

10. The method according to claim 9, wherein said optimization algorithm minimizes a discrepancy between a target distribution, representing the desired light dose profile for uniform curing, and a computed distribution iteratively generated by the optimization algorithm.

11. The method according to any one of claims 9-10, wherein the target dose distribution comprises a three-dimensional distribution in which the dose within voxels representing the object exceeds a curing threshold, and the dose in voxels outside the object remains below the curing threshold.

12. The method according to any one of claims 9-11, wherein the target dose distribution defines the threshold-based curing region within the photosensitivemedium, such that only voxels corresponding to the object’s geometry reach or exceed the curing threshold.

13. The method according to any one of claims 9-12, further comprising defining the target dose distribution to minimize exposure outside the object’s geometry by maintaining doses below the curing threshold in non-object voxels.

14. The method according to any one of claims 9-13, wherein the iterative process comprises adjusting the projection data based on discrepancies between the target dose distribution and the computed dose distribution across successive iterations.

15. The method according to any one of claims 9-14, wherein the optimization algorithm comprises or consists of a derivative-based method such as a gradient-based optimization, or a stochastic optimization, an evolutionary algorithm, or a heuristic method.

16. The method according to any one of the preceding claims, wherein the computing of the projection data is performed using a hierarchical or multiresolution approach.

17. The method according to any one of the preceding claims, further comprising dynamically adjusting the projection data based on feedback, such as real-time feedback, from one or more sensors monitoring the polymerization state within the photosensitive medium.

18. The method according to claim 17, wherein the sensors are configured to detect polymerization parameters including polymerization progress, temperature, scattering properties, or material density, and wherein feedback from the sensors is used to iteratively refine the projection data.

19. The method according to any one of claims 17-18, wherein the feedback is processed by a control system configured to evaluate differences between the actual polymerization state and an expected polymerization state, thereby informing adjustments to the projection data.

20. The method according to any one of claims 17-19, wherein the control system operates as a closed-loop system, iteratively adjusting the projection data in response to variations in polymerization uniformity across the model, optimizing exposure for each projection cycle.

21. The method according to any one of the preceding claims, wherein the projection data is configured to account for non-uniform or complex container geometries.

22. The method according to any one of the preceding claims, wherein the projection data is computed based on geometric characteristics of the container, including convex, concave, or irregular surface features, to achieve consistent polymerization.

23. The method according to any one of the preceding claims, wherein the model of the container is obtained by performing a 3D scan of the container.

24. The method according to any one of the preceding claims, wherein the projection data includes information specifying, for each projection of the series of projections, associated positions and angles of the light source.

25. The method according to any one of the preceding claims, wherein the at least one adjustable light source is mounted on a motorized positioning apparatus, such as a robotic arm or gimbal, configured to dynamically adjust angles and positioning during the printing process.

26. The method according to any one of the preceding claims, wherein the illumination system includes multiple independently controlled light sources, arranged to provide targeted illumination from multiple angles and / or positions, as directed by the projection data.

27. The method according to any one of claims 25-26, wherein each light source is individually controlled based on the projection data.

28. The method according to any one of the preceding claims, wherein the method is computer-implemented.

29. A computer-readable medium storing instructions that, when executed by one or more processing units, perform the method of any one of the preceding items.

30. A method for producing a three-dimensional object, comprising:• obtaining a computed projection data using the method of any one of claims 1-29; and• illuminating, by an illumination system, a container accommodating a curing volume, in a series of patterns of light determined by the projection data; thereby producing the three-dimensional object.

31. The method according to claim 30, wherein the illumination system comprises a light source which is oriented by a motorized arm or gimbal that adjusts position and / or orientation during the printing process.

32. The method according to any one of the preceding claims, wherein the container has a three-dimensional shape selected from a substantially cylindrical shape, a polyhedral shape, a prismatic shape, a substantially spherical shape, and combinations thereof.

33. The method according to any one of the preceding claims, wherein computing the projection data comprises performing ray tracing using an acceleration structure in the form of a Bounding Volume Hierarchy (BVH) constructed over a polygon mesh representation of at least the container, the Bounding Volume Hierarchy (BVH) being constructed using a Surface Area Heuristic (SAH) or another cost-based partitioning heuristic.

34. The method according to claim 33, wherein the ray tracing comprises determining a surface normal at ray-surface intersection points by interpolating vertex normals of triangles of the polygon mesh representation of the container.

35. The method according to any one of the preceding claims, wherein the three- dimensional object comprises a lattice structure and the projection data comprises projection images for a plurality of viewing directions including at least two non-parallel viewing directions aligned with respective faces of the container.

36. The method according to any one of the preceding claims, wherein the projection images are generated for a subset of viewing directions comprising two substantially orthogonal viewing directions aligned with respective faces of the container.

37. The method according to any one of the preceding claims, wherein the computation of the projection data by ray marching comprises representing at least a portion of a curing volume as a set of discrete volume elements such as voxels, determining, for each ray, a plurality of volume elements intersected by the ray, computing for each intersected volume element a local light transmittance using an attenuation model based on at least one optical property of the photosensitive medium and a path length of the ray within the volume element, and determining a projection pixel value based on an aggregation of the local light transmittances along the ray.

38. The method according to any one of the preceding claims, wherein the method is used for producing prosthetics, artificial limbs, implants, dental devices, pharmaceuticals, microfluidic devices, optical components, or combinations thereof.

39. A system for volumetric 3D printing of a three-dimensional object, comprising:• a computational unit comprising a processor, a power source and a nontransient memory, wherein the memory comprises instructions that when executed by a processor carries out the method of any one of items 1-38; and• an illumination system configured to receive projection data, and to generate a series of projections for controlled polymerization of a photosensitive medium.

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