Geometric structure generation method and apparatus

Abstract

An embodiment of the present disclosure provides a geometry generation method and device, comprising: obtaining a three-dimensional model; marking a starting growth region on the surface of the three-dimensional model and determining a corresponding starting growth attribute value; determining a control attribute value on the surface of the three-dimensional model based on the starting growth attribute value through iterative diffusion calculation, the control attribute value representing a degree of each region being reached by the spread; and performing noise modulation on the normal direction of the surface of the three-dimensional model based on the control attribute value, and performing geometry extrapolation processing along the modulated normal direction to generate a geometry structure with thickness. In this way, the control attribute value is determined based on the starting growth attribute value through iterative diffusion calculation, and the geometry extrapolation processing is performed in combination with the noise-modulated normal direction, which helps to generate a geometry structure with real thickness and natural density decay on the model surface, improves the generation efficiency and morphology controllability of the directional growth structure, and helps to reduce the data processing load in the complex geometry generation process.

Description

Technical Field

[0001] This disclosure relates to the field of computer technology, and more particularly to methods and apparatus for generating geometric structures. Background Technology

[0002] In the field of 3D digital content creation, it is often necessary to generate surface spike structures with directional growth characteristics on the model surface. Related technologies typically employ methods such as noise displacement, particle instantiation, or physical simulation to simulate the organic changes in surface morphology by applying spatial noise functions, distributing prefabricated geometry, or solving morphology generation equations on the model surface.

[0003] However, the above methods still have shortcomings. Noise displacement methods typically only produce surface height changes, making it difficult to generate geometric entities with realistic thickness and independent topology. Furthermore, the spike density is uniformly controlled by the noise frequency, making it difficult to achieve differentiated distribution in local areas. Particle instantiation methods discretize pre-made geometries on the surface, resulting in a lack of topological continuity between instances and a tendency for interpenetration and suspension. Physical simulation methods involve a large number of iterative calculations and data conversions, leading to high data processing loads and lengthy geometry transformation processes, making it difficult to balance generation efficiency and structural quality. In addition, the above methods typically cannot control the growth orientation along a specified direction, failing to simulate the natural growth process spreading outward from a specific starting region. Summary of the Invention

[0004] This disclosure provides a method, apparatus, computer-readable storage medium, and electronic device for generating geometric structures, to at least partially solve the aforementioned problems existing in the related art.

[0005] According to one aspect of this disclosure, a method for generating a geometric structure is provided, comprising: acquiring a three-dimensional model; marking initial growth regions on the surface of the three-dimensional model and determining corresponding initial growth attribute values; determining control attribute values ​​on the surface of the three-dimensional model based on the initial growth attribute values ​​through iterative diffusion calculation, wherein the control attribute values ​​represent the degree to which each region is spread; and performing noise modulation on the normal direction of the surface of the three-dimensional model based on the control attribute values, and performing geometric extrapolation processing along the modulated normal direction to generate a geometric structure with thickness.

[0006] According to one aspect of this disclosure, a geometric structure generation apparatus is provided, comprising: an acquisition module for acquiring a three-dimensional model; a first determination module for marking initial growth regions on the surface of the three-dimensional model and determining corresponding initial growth attribute values; a second determination module for determining control attribute values ​​on the surface of the three-dimensional model based on the initial growth attribute values ​​through iterative diffusion calculation, wherein the control attribute values ​​represent the degree to which each region is reached by diffusion; and a generation module for performing noise modulation on the normal direction of the surface of the three-dimensional model based on the control attribute values ​​and performing geometric extrapolation processing along the modulated normal direction to generate a geometric structure with thickness.

[0007] According to one aspect of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements any of the above methods.

[0008] According to one aspect of this disclosure, an electronic device is provided, including a processor and a memory, the memory for storing a computer program and the processor for executing the computer program to implement any of the above methods.

[0009] One embodiment of this disclosure provides a method for generating geometric structures, including: acquiring a three-dimensional model; marking initial growth regions on the surface of the three-dimensional model and determining corresponding initial growth attribute values; determining control attribute values ​​on the surface of the three-dimensional model based on the initial growth attribute values ​​through iterative diffusion calculation, wherein the control attribute values ​​represent the degree to which each region is reached by the diffusion; and performing noise modulation on the normal direction of the surface of the three-dimensional model based on the control attribute values, and performing geometric extrapolation along the modulated normal direction to generate a geometric structure with thickness. Thus, determining control attribute values ​​through iterative diffusion calculation based on the initial growth attribute values, and performing geometric extrapolation in conjunction with the noise-modulated normal direction, helps to generate geometric structures with realistic thickness and natural density decay on the model surface, improving the generation efficiency and morphological controllability of directional growth structures, and helping to reduce the data processing load in the process of generating complex geometry. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this disclosure, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 A schematic diagram of a system architecture is shown in one exemplary embodiment of this disclosure. Figure 2 A flowchart illustrating a method in one exemplary embodiment of this disclosure is shown; Figure 3 A schematic diagram of a three-dimensional model in one exemplary embodiment of this disclosure is shown; Figure 4 A schematic diagram of a pretreated surface in one exemplary embodiment of the present disclosure is shown; Figure 5 A schematic diagram of the initial growth region in one exemplary embodiment of this disclosure is shown; Figure 6 A schematic diagram showing control attribute values ​​in one exemplary embodiment of this disclosure is shown; Figure 7 A schematic diagram of a multi-layered stepped transition structure is shown in one exemplary embodiment of the present disclosure; Figure 8 A schematic diagram of the initial growth region in one exemplary embodiment of this disclosure is shown; Figure 9 This diagram illustrates an apparatus configuration in one exemplary embodiment of the present disclosure. Figure 10 A schematic diagram of the structure of an electronic device is shown in one exemplary embodiment of the present disclosure. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0013] It is understood that before using the technical solutions disclosed in the various embodiments of this disclosure, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in this disclosure in an appropriate manner in accordance with relevant laws and regulations, and user authorization should be obtained.

[0014] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this disclosure, "a plurality of" means two or more, unless otherwise expressly specified.

[0015] It should be noted that the information (including but not limited to: user input information, such as information entered by the user into an input box), data (including but not limited to data used for analysis, stored data, and displayed data, such as context code, all code of the current project, service pressure corresponding to operations performed on all code of the current project, and code development status of the current project), and signals involved in the embodiments of this disclosure are all authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards. For example, the context code, operations performed on all code of the current project, and the service pressure and code development status involved in the operations in the embodiments of this disclosure are all obtained under full authorization.

[0016] According to one embodiment of the geometric structure generation method of this disclosure, such as Figure 2 As shown, the method may include: Step S210: Obtain the 3D model; Step S230: Mark the initial growth region on the surface of the 3D model and determine the corresponding initial growth attribute value; Step S250: Based on the initial growth attribute value, determine the control attribute value on the surface of the three-dimensional model through iterative diffusion calculation. The control attribute value represents the degree to which each region is reached by the diffusion. Step S270: Based on the control attribute value, noise modulation is performed on the normal direction of the surface of the three-dimensional model, and geometric extrapolation is performed along the modulated normal direction to generate a geometric structure with thickness.

[0017] According to one embodiment of this disclosure, the control attribute value is determined by iterative diffusion calculation based on the initial growth attribute value, and geometric extrapolation is performed in combination with the noise-modulated normal direction. This helps to generate a geometric structure with real thickness and natural density decay on the model surface, improves the generation efficiency and morphological controllability of the directional growth structure, and helps to reduce the data processing load in the process of generating complex geometry.

[0018] The embodiments of this disclosure will now be further described.

[0019] In step S210, a three-dimensional model is acquired. This provides a continuously computable geometric surface for subsequent flame spread simulation, enabling growth properties to be accurately transferred across the topology and ensuring that spike generation has a stable input carrier. For example, the operator can directly read the input model to be processed from the Digital Content Creation (DCC) software environment. This input model can be a regular topological cuboid or sphere, or a scanned character model with a complex surface structure. During the reading process, the system automatically records the spatial position information and normal direction information of each vertex on the model surface, thereby providing a continuously computable basic geometric surface for subsequent flame spread simulation.

[0020] Optionally, the 3D model can be a basic geometry or a preprocessed polygonal mesh, used to carry out the growth calculations of surface spikes. For example... Figure 3 The diagram illustrates a three-dimensional model. Optionally, the aforementioned three-dimensional model can be a polygonal mesh with arbitrary topology directly read from the current working scene in a Digital Content Creation (DCC) software environment, such as a cuboid with a regular hexahedral topology, a sphere used to simulate a spherical covering surface, or a scanned character model or scene asset model imported from an external source. This three-dimensional model serves as the geometric carrier for subsequent flame spread simulation; its surface vertices must carry position and normal information to provide a continuous and computable spatial reference for marking the initial growth region and the spread of growth attributes. It should be noted that the three-dimensional model can be an unprocessed basic geometry or an organic surface preprocessed by noise displacement deformation or voxelization fusion. This disclosure does not intend to limit the source of the three-dimensional model or its preprocessing state.

[0021] In an optional implementation, after obtaining the 3D model, the process further includes: applying noise displacement deformation to the surface of the 3D model to obtain a deformed 3D model; obtaining a guiding direction curve and extruding the guiding direction curve along its direction into a thin-faceted geometry; converting the deformed 3D model and the thin-faceted geometry into voxel distance fields respectively; performing an expansion operation on the voxel distance fields to merge the deformed 3D model and the thin-faceted geometry in voxel space; and then converting the merged voxel distance field back into a polygonal mesh to obtain a pre-processed surface; wherein, the guiding direction curve is used to define the guiding direction. In this way, by applying noise deformation to the base model and merging it with guiding thin-faceted voxels, a trend base conforming to the user's intention is pre-established, allowing subsequent spikes to extend naturally along the preset guide, thus improving the structural consistency and artistic controllability of the generated result.

[0022] In one implementation, a sphere is first acquired as the base geometry. Simplex noise is used to deform the sphere along its vertex normal, with an amplitude of 0.25 and a noise element size of 1.0, creating natural surface undulations. Simultaneously, a user-drawn spatial guide curve is acquired and extruded along the curve to form a thin-faceted geometry. Subsequently, the deformed sphere and thin-faceted geometry are converted into voxel distance fields (VDBs, a sparse voxel data structure). A signed distance field (SDF) is generated using a voxel size of 0.05, and this distance field undergoes four dilation iterations to create a smooth transition between the two in voxel space. Finally, the fused voxel distance field is converted back into a polygon mesh, resulting in a preprocessed surface with organic contours. This surface will be used for subsequent initial growth region marking and spike generation processes.

[0023] Optionally, noise displacement deformation is used to apply spatial noise position offset along the normal direction of the base geometry surface to generate morphological changes with natural organic undulations.

[0024] Optionally, the aforementioned noise displacement deformation can be the result of Simplex noise or a lattice-based spatial noise function acting on the vertex positions. Considering the low efficiency and difficulty in batch reuse of hand-carved surface undulations, as a possible implementation, this step applies displacement along the normal direction of each vertex of the base geometry, causing the surface to generate random undulations while maintaining the original topological connectivity; wherein, the noise amplitude parameter can be set to 0.25, and the noise element size can be set to 1.0, thereby controlling the overall amplitude and fineness of the undulations. It should be noted that the above parameter values ​​are only examples. In practical applications, they can also be adaptively adjusted according to the overall size of the base geometry and the density requirements of subsequent spike growth to obtain a base undulation effect that better matches the artistic expectations. In addition, the seed value or offset used for noise displacement can also be dynamically changed to generate diverse but statistically consistent organic surfaces in the same process.

[0025] Optionally, the guide direction curve is used to define the directional growth trend of the spike structure. It can be a user-drawn spatial curve or a parameterized path generated by the program. Optionally, the guide direction curve can be manually created by the user in the 3D viewport using an interactive brush or curve drawing tool, or it can be automatically extracted by the system based on the guide direction field. The direction of this curve in space directly determines the macroscopic guidance followed by subsequent spike growth. For example, in a scenario simulating ice crystals spreading downwards from the mountain surface, the user can draw a curve following the ridgeline, ensuring that the overall orientation of the subsequently generated ice spikes is consistent with this trend. It should be noted that the guide direction curve is not limited to a single continuous curve; it can also be a group of curves composed of multiple segmented curves. Smoothing interpolation can be used between segments to eliminate abrupt changes in direction. In actual implementation, the user can also finely control the degree of local distortion after the thin-surface geometry is extruded by adjusting the control point density or tangent continuity of the curve, thereby indirectly affecting the deflection gradient of the final spike structure.

[0026] Optionally, in addition to serving as the path reference for geometric extrusion, the guide direction curve can also include spatially varying adjustment parameters. For example, different sections of the curve can map different combing intensities or spike densities, resulting in denser growth near the curve's origin and sparser growth further away. Before voxel fusion, the curve's radius of curvature can be smoothed or resampled to reduce self-intersections or overstretching of thin-faceted geometries. After the guide direction curve is converted into a thin-faceted geometry, its voxel distance field in voxel space can intersect and merge with the noise-displaced base geometry, thus providing a composite base with both undulations and trend guidance for subsequent flame spread simulation, achieving unified control of macroscopic trends and microscopic details.

[0027] Optionally, the thin-faceted geometry is a planar structure extruded along the guiding direction curve, used to merge with the base geometry in voxel space to form a trend-guided surface. Optionally, the thin-faceted geometry can be obtained by extruding a strip of surface of a specified width along the guiding direction curve. Its cross-sectional width can be set according to the coverage requirements of subsequent spike growth, for example, set to 0.1 to 0.5 world units. As a possible implementation, the thin facet does not directly participate in the final spike morphology, but rather serves as an auxiliary geometry for trend guidance, merging with the main model at the voxel level via Boolean fusion. This results in the pre-processed surface after fusion exhibiting a bulging trend towards the guiding direction in the region near the thin facet. It should be noted that the extrusion direction of the thin-faceted geometry can strictly follow the normal plane of the curve, or additional upward or outward offsets can be introduced to generate a composite trend with a certain angle. Furthermore, its subdivision level can be dynamically adjusted according to the accuracy of the fused voxels and the smoothness of the target surface to avoid step-like sampling defects during voxelization due to excessively sparse surface patches.

[0028] Optionally, a voxel distance field is used to convert polygonal meshes into volume representations to support the continuous fusion of two independent geometries in 3D space. Optionally, the voxel distance field can be constructed based on VDB (a sparse voxel data structure), generating a signed distance field (SDF) by performing voxelization sampling on the input polygonal mesh, where positive values ​​indicate voxels are located outside the surface, and negative values ​​indicate voxels are located inside the surface. Considering that direct Boolean operations between polygonal meshes can easily produce non-manifold intersection boundaries, as a possible implementation, this step first converts the deformed base geometry and thin-faceted geometry into independent voxel distance fields, so that both have continuously differentiable field function representations in the same sparse voxel space. It should be noted that the voxel size is a key parameter affecting fusion accuracy and computational efficiency. It can be set smaller (e.g., 0.05) in scenarios where subtle surface undulations need to be preserved, while it can be appropriately increased in scenarios where fast preview is desired. The converted voxel distance field not only enables geometric fusion through distance field dilation operations but also provides a unified volume operation environment for subsequent edge smoothing and shape transitions.

[0029] Optionally, the dilation operation extends the voxel distance field by a signed distance value domain extension, allowing the two geometries to meet in voxel space and achieve a natural transition.

[0030] Optionally, the dilation operation can perform multiple iterative expansions on the outer side of the zero isosurface of the voxel distance field. The number of iterations can be set according to the initial spacing between the geometries to be fused, for example, four times. As one possible implementation, each dilation iteration expands the field value outward by one voxel unit along the gradient direction, causing the voxel distance fields of the base geometry and the thin-faceted geometry to gradually overlap in the boundary region, forming a continuous fusion region. It should be noted that the degree of dilation is not limited to a fixed number of iterations. The number of iterations can be increased in areas with large geometries, while the number of iterations can be reduced or skipped in areas where there is sufficient contact. Furthermore, the dilation operation can be combined with median smoothing or anisotropic filtering for post-processing to eliminate the blocky transition traces caused by voxelization, ensuring that the de-voxelized polygon mesh has a smooth and natural appearance.

[0031] Optionally, the preprocessed surface is a fused polygonal mesh carrier, possessing both the organic undulations of the basic geometry and the guiding trend of the thin surface, serving as the computational basis for subsequent spread simulations. For example... Figure 4The diagram illustrates a preprocessed surface. Optionally, the preprocessed surface exhibits a unified manifold structure resulting from the voxel fusion of the basic geometry and thin-faceted geometry. It displays a natural bulge trend in the thin-faceted intersection region, while retaining the undulating details caused by noise displacement in regions far from the thin-faceted surfaces. Considering the high requirements for mesh connectivity and surface normal consistency in subsequent flame propagation simulations, as a possible implementation, the preprocessed surface can undergo topology cleaning and normal unification processing after generation to eliminate isolated vertices or degenerate patches that may be generated during voxelization-devoxelization. It should be noted that the surface density and vertex distribution of the preprocessed surface can be adaptively subdivided according to the neighborhood search radius of the subsequent propagation simulation. Higher surface density is retained in regions with large curvature changes to ensure that temperature properties diffuse continuously and uniformly along the surface during propagation. Furthermore, this surface can be reused as a common base for multiple different initial growth regions. By adjusting the propagation parameters corresponding to each region, spike communities with differences but conforming to the overall trend can be generated on the same surface.

[0032] In step S230, the initial growth region is marked on the surface of the 3D model, and the corresponding initial growth attribute value is determined. This allows users to flexibly specify the source location and range of spike growth through interactive drawing, providing precise initial conditions for subsequent flame spread simulation and effectively improving the controllability and artistic expressiveness of the generated results.

[0033] In one example, users can use the brush tool to draw continuous planar regions or scattered point regions on the model surface. The system generates scalar attributes with values ​​from 0 to 1 for the marked vertices as initial growth parameters. During the drawing process, users can adjust the brush radius, pressure sensitivity mapping, and decay curve to precisely control the shape and extent of the starting region.

[0034] Optionally, the initial growth region is used to define the growth source of the spike structure, which is determined by interactive drawing on the surface of the 3D model.

[0035] Optionally, the initial growth region can be a continuous planar region or a scattered point-like region, and its specific shape determines the overall spatial distribution pattern of the subsequent flame spread simulation. In one implementation, the user can use an interactive attribute drawing tool to draw on the surface of the 3D model with a brush. This drawing tool supports real-time adjustment of brush radius, pressure sensitivity mapping, and attenuation curve, allowing the outline boundary of the initial region to present a natural, soft, or irregular shape. Considering that the spike generation process requires a clear spread source as an initial condition, after the aforementioned initial growth region is marked, the system will generate a scalar attribute with a value between 0 and 1 for the corresponding vertex. This attribute serves as the initial fuel input for the flame spread simulation and directly determines the propagation path and coverage of the subsequent temperature attribute in space. Furthermore, when the marked region is scattered point-like, independent spread centers can be formed between each point, producing a multi-focal parallel growth effect; when the marked region is a continuous planar region, it is easier to form a large-area continuous spike coverage area.

[0036] Optionally, the initial growth attribute value is used to quantify the initial spread intensity of the marked region, taking a scalar value between 0 and 1, and serves as input data for subsequent diffusion simulations. Optionally, the initial growth attribute value can be stored as a floating-point scalar, with its value range limited to a closed interval of 0 to 1. Vertices corresponding to the marked initial growth region can be assigned a maximum value of 1.0, while unmarked vertices are uniformly assigned a value of zero. In another implementation, this attribute value can also be non-linearly assigned through brush pressure-sensitive mapping, for example, dynamically changing between 0.3 and 1.0 according to the drawing pressure, thereby constructing an initial intensity distribution with a gradient within the same region. It should be noted that the above-mentioned limitation of the value range is only an example, and can be adaptively adjusted according to specific hardware precision or data format requirements in actual implementation. During the data stream conversion process, the aforementioned initial growth attribute value is converted into the initial temperature attribute for flame spread diffusion simulation. This conversion relationship ensures that only explicitly marked regions can participate as effective fuel in subsequent iterative diffusion calculations, helping to reduce the risk of passive spread causing the generated results to deviate from expectations.

[0037] In an optional implementation, marking the initial growth region on the surface of the 3D model includes: drawing the initial growth region on the surface of the 3D model, the initial growth region including a continuous planar region or a scattered point region; and determining a corresponding initial growth attribute value for the marked region, the initial growth attribute value ranging from 0 to 1. In this way, defining the initial growth region as a continuous planar region or scattered point region by drawing, and limiting the attribute value to 0 to 1, not only allows for flexible customization of the propagation source morphology, but also provides continuously adjustable initial input for subsequent iterative diffusion, thus balancing the controllability of the generation direction with natural randomness.

[0038] In one implementation, the user runs an interactive attribute drawing tool on the surface of the 3D model. By adjusting the brush radius and pressure sensitivity mapping, a continuous planar area is painted on the surface of the cuboid as the initial growth area, and the initial growth attribute value of 1.0 is uniformly set for the marked vertices in this area. In another implementation, the user can switch to a scattered point mode, randomly select multiple discrete positions on the surface of the sphere model, and assign the initial growth attribute values ​​of the corresponding vertices at each position to 0.4, 0.7, and 1.0, respectively. This allows the subsequent simulation to start synchronously from multiple discrete sources, forming a decentralized growth pattern that is different from continuous planar spread.

[0039] Optionally, the marking operation described above can be performed directly on the model surface using an interactive property drawing tool to flexibly set the location and extent of the spike growth source. Alternatively, the drawing operation can be completed using the interactive property drawing tool within a Digital Content Creation (DCC) software environment. This tool provides brush controls in a graphical user interface, allowing users to mark the initial growth area by dragging the mouse or using a pressure-sensitive pen to directly paint on the 3D model surface. The brush control supports parameter configurations such as radius adjustment, pressure mapping, and decay curves. The radius value determines the coverage area of ​​a single stroke, the pressure mapping converts the physical pressure of the input device into an intensity gradient of the property value, and the decay curve controls the property transition shape from the brush center to the edge. By combining these parameters, users can draw starting areas with soft edges or sharp boundaries on the model surface, ensuring that the initial fuel distribution for subsequent flame spread closely matches the creative intent, avoiding the mechanical feel of a uniform, hard-edged distribution.

[0040] Optionally, besides drawing directly on the model surface using an interactive brush, marking the initial growth region can also be achieved by reading an external 2D mask texture or performing procedural vertex selection. For example, the system maps the 2D unfolded coordinates of the model surface vertices to a grayscale texture, automatically converting areas with texture pixel brightness between 0 and 1 into corresponding initial growth attribute values; or the user can specify several faces on a polygon mesh using a selection tool, assigning a uniform initial growth attribute value to the selected faces. It should be noted that the above drawing methods are merely examples. In practical applications, any method that can write scalar attribute values ​​to a specified area on the model surface and meets the requirement of continuity of initial fuel distribution in subsequent flame spread simulation can be applied to this solution.

[0041] Optionally, the initial growth region can be a continuous planar region or a scattered point-like region, which determines whether the subsequent spread is a continuous expansion or a multi-point concurrent process. Optionally, when the initial growth region is set as a continuous planar region, the region covers a set of adjacent mesh patches or vertex clusters, whose boundaries geometrically constitute a connected domain. In this case, the flame spread simulation expands synchronously outward from the overall boundary of the connected domain, and the spread front exhibits a continuously advancing wavefront morphology. The final generated spike structure usually appears as a dense cluster distribution radiating outward from the same source region, which is suitable for simulating the visual effect of ice crystals condensing over a large area on a smooth surface or thorns continuously proliferating along the edge of a wound. When the initial growth area is set as a scattered point area, each marker point is spatially independent and the spacing is adjustable. Each point can be regarded as an independent ignition source. During the simulation, each point source independently spreads outward and generates its own temperature decay gradient, eventually forming multiple separate spike clusters on the model surface. This multi-point concurrent mode is particularly suitable for simulating the distribution characteristics of discrete spicules of coral branches or local rust pits on the rock surface.

[0042] Optionally, between continuous planar regions and scattered point-like regions, there exists a transitional form: patchy regions composed of clusters of small, closely spaced but not fully connected planar surfaces. In this form, the vertices within each patch have non-zero initial growth attribute values, while unmarked gaps remain between patches. This allows the propagation fronts of adjacent patches to naturally interrupt their extension into the gaps due to the cooling attenuation threshold, thus macroscopically forming an intermediate spike distribution between completely continuous and completely discrete. It should be noted that the above division of region morphology is not intended to strictly limit the geometric characteristics of the initial growth region. In actual implementation, users can mix and arrange continuous regions and scattered point-like regions in any proportion according to the topological structure of the model surface and the expected visual density, to balance the overall propagation trend with the rhythm of local blank spaces.

[0043] Optionally, the initial growth attribute value is represented by a normalized scalar from 0 to 1 to quantify the spread intensity of the marked region and provide continuous input for subsequent diffusion calculations. Alternatively, the initial growth attribute value is normalized and encoded using a closed-range scalar from 0 to 1, where a value of 1.0 represents a fully marked strong growth source, a value of 0 represents an unmarked inert region, and values ​​between 0 and 1 represent intermediate states of different intensities according to linear or nonlinear mapping rules. As an example, the user can directly map the pressure applied by the pressure-sensitive pen to this range: a light touch produces a weak mark of 0.2, and a heavy press produces a strong mark of 1.0, thus allowing for continuous spatial variation in the initial fuel intensity. In subsequent iterative diffusion stages, this normalized scalar is converted into an initial value for the temperature attribute. A higher temperature value means that the vertex can support more rounds of cooling decay during the reaction stage, thereby determining the depth of the source region's spread to the surrounding neighborhood. It should be noted that the above range of values ​​from 0 to 1 is only one normalization example. In other implementations, 8-bit grayscale or any floating-point range can also be used for encoding, as long as the system completes the mapping conversion to a unified analog dimension during the input stage.

[0044] In step S250, based on the initial growth attribute value, control attribute values ​​are determined on the surface of the 3D model through iterative diffusion calculation. These control attribute values ​​represent the extent to which each region is reached by the diffusion. This simulates the natural spread of attributes through iterative diffusion calculation, causing the control attribute values ​​to decay from the center to the edge, avoiding the harshness of artificial distribution and providing an organic and controllable density basis for subsequent spike generation. For example, firstly, the initial growth attribute value is converted into an initial control attribute value, with the marked region having the maximum value and the remaining regions having zero. Then, for each vertex, neighboring vertices are searched within a preset search radius. The attribute differences between the current vertex and its neighboring vertices are weighted and fused, and spatial noise is used to modulate the diffusion rate. After each iteration, a decay operation is performed; when the control attribute value of a vertex falls below a preset threshold, it is set to zero. Finally, the control attribute value covering the diffusion region is obtained. A higher value indicates a closer proximity to the starting region, while a lower value corresponds to the diffusion edge. Figure 6 The diagram shows a control attribute value, illustrating the gradual distribution from the starting region (red / high temperature) to the spreading edge (blue / low temperature) and the irregular shape of the spreading boundary.

[0045] Optionally, iterative diffusion calculation is used to perform neighborhood propagation and attenuation on surface properties, generating the distribution of control attribute values ​​for the overlay model. Optionally, the above iterative diffusion calculation can perform multiple rounds of propagation updates on attribute values ​​based on neighborhood topology relationships. In one implementation, the calculation searches for a set of neighboring vertices within a preset search radius for each vertex on the surface of the 3D model. By weighted superposition of the attribute differences between the current vertex and its neighboring vertices, the attribute values ​​are naturally flowed from high-density areas to low-density areas. The weighting coefficients used in the weighted superposition are not only related to the spatial distance between vertices, but can also be dynamically determined based on the mesh edge connection relationship or area weight. Considering that uniform diffusion at a fixed rate is difficult to simulate the irregular boundaries affected by material differences in real flame spread, as a possible implementation, spatial noise modulation can be applied to the above diffusion rate. For example, a diffusion rate correction factor can be calculated based on a cell-pattern noise function for each location, causing random differences in the actual spread speed of different regions, thereby forming an organic morphology with uneven edges at the macroscopic level. It should be noted that the above descriptions regarding the neighborhood search radius, the number of neighboring vertices, and the noise type are merely examples, and this disclosure is not intended to limit the implementation of iterative diffusion calculations. In actual implementation, a diffusion strategy based on surface neighborhoods or a finite difference method on a voxel mesh can also be used for solving the problem, and the number of iterations and modulation method can also be determined according to the specific application.

[0046] Optionally, the control attribute value is used to quantify the extent to which each region is reached by the spread, serving as the basis for density control in subsequent extrapolation processing. Optionally, the control attribute value can be represented as a scalar field distributed across the entire surface of the 3D model. In one implementation, the attribute value reaches its maximum value in the initial growth region, gradually decreasing with increasing distance from the initial region, and returning to zero in the edge regions not reached by the spread. Considering that geometric extrapolation processing requires surface-level density modulation, as a possible implementation, vertex-level control attribute values ​​can be aggregated and increased to surface-level attribute values ​​through averaging. In this case, the larger the surface attribute value, the longer the corresponding extrapolation distance, and vice versa, thus achieving a natural decay of spike height from the center to the edge. It should be noted that, in addition to mapping to extrapolation distance, the control attribute value can also be used to calculate the number of extrapolations or noise amplitude; the specific application can be determined according to the actual scenario. Furthermore, its physical meaning can be mapped to deposition thickness or damage depth, etc., depending on the scenario; the specific implementation method can be flexibly adjusted according to requirements.

[0047] In an optional implementation, control attribute values ​​are determined on the surface of the 3D model based on the initial growth attribute values ​​through iterative diffusion calculations. This includes: converting the initial growth attribute values ​​into initial control attribute values, where the initial control attribute value corresponding to the marked region is the maximum value, and the initial control attribute value corresponding to the unmarked region is zero; performing neighborhood diffusion calculations on the control attribute value of each vertex, fusing the control attribute value of the current vertex with the control attribute values ​​of neighboring vertices, and applying noise modulation to the diffusion rate during the diffusion process; and performing a decay operation on the diffused control attribute values, setting the control attribute value of a vertex to 0 when it falls below a preset threshold. Thus, by establishing a binarized initial field before diffusion and introducing neighborhood fusion, rate perturbation, and cooling truncation mechanisms during the propagation phase, not only can the spike growth boundary exhibit a natural irregular shape, but the propagation distance and density gradient can also be effectively controlled. Figure 5 The diagram shows a starting growth region, with the starting growth region marked (highlighted in red) on the model surface and the remaining areas unmarked.

[0048] In one implementation, the system first converts the user-drawn initial growth attributes into initial control attribute values. Specifically, vertices corresponding to areas marked by the brush are assigned a maximum value of 1.0, while unmarked areas are strictly kept at 0, thus establishing clear diffusion boundary conditions on the model surface. Based on this, the system searches for up to 25 neighboring vertices within a search radius of 0.1 for each vertex, calculates the difference in control attribute values ​​between the current vertex and each neighboring vertex, and adds a weighted average of these differences to the current vertex, achieving gradual fusion and propagation of attributes. Simultaneously, the system introduces spatial noise during the diffusion process to multiply and modulate the diffusion rate, causing random differences in the actual spread rates of different regions. After each round of diffusion, the system performs cooling decay on the control attribute values ​​of all vertices. When the attribute value of a vertex falls below a threshold of 0.2 due to continuous decay, the control attribute value of that vertex is forcibly reset to zero, thereby clearly defining the effective spread range and the final boundary of spike growth.

[0049] Optionally, the initial control attribute value is used to characterize the diffusion initiation state, with the marked area corresponding to the maximum value and the unmarked area corresponding to zero value, to distinguish the diffusion initiation point from the non-spreading area. Optionally, the process of converting the initial growth attribute value into the initial control attribute value may include data type mapping and numerical remapping of the scalar attribute drawn by the user through an interactive brush. For example, when the initial growth attribute value is 0.8 at some vertices and 0.5 at others, it can be uniformly mapped to the same maximum value of 1.0 to eliminate the initial intensity unevenness caused by brush pressure differences and ensure that all marked areas have the same diffusion potential energy at the start of diffusion. As another implementation, the original initial growth attribute value can also be retained as the initial control attribute value, so that areas with higher brush pressure receive higher initial values, thereby forming a deeper or more persistent diffusion effect in subsequent diffusion. It should be noted that for unmarked areas, their initial control attribute value must be strictly kept at zero to form a clear diffusion boundary condition, prevent the attribute from spontaneously generating from non-initiation areas, thereby ensuring the causal determinism of the entire flame spread simulation, and ensuring that the subsequently generated spike structures strictly correspond to the growth initiation point specified by the user.

[0050] Optionally, the neighborhood diffusion calculation is used to find neighboring vertices and perform a fusion process on the control attribute values ​​of the current vertex and the neighboring vertices to achieve the gradual propagation of attributes on the model surface.

[0051] Optionally, in the above neighborhood diffusion calculation, the search range of neighboring vertices can be jointly limited by the search radius and the maximum number of neighboring vertices. For example, the search radius can be set to 0.05, 0.1, or 0.2, and the maximum number of neighboring vertices can be set to 15, 25, or 40; this disclosure is not limited to these. Considering that the subdivision density of the model surface may differ in different regions, as a possible implementation, in dense vertex regions, a smaller search radius can capture sufficient neighboring vertices to reflect the local surface curvature; in sparse vertex regions, the search radius needs to be appropriately expanded to ensure the continuity of diffusion. The above fusion process can specifically include: calculating the difference between the control attribute values ​​of the current vertex and each neighboring vertex, and superimposing the weighted average of the difference onto the control attribute value of the current vertex; wherein, the weight can be determined according to the spatial distance between the neighboring vertices and the current vertex, the closer the distance, the higher the fusion weight, thereby making the propagation of control attribute values ​​more consistent with the geometric continuity of the surface and avoiding abrupt changes in attributes at mesh boundaries.

[0052] Optionally, besides the weighted average fusion method based on spatial distance, the above fusion process can also employ other attribute fusion rules. For example, the maximum value of the control attribute of neighboring vertices can be assigned to the current vertex to accelerate the spread of attributes in a specific direction; or, a minimum value fusion rule can be used to ensure that the attribute value of the current vertex does not exceed the lowest level in the neighborhood range, thereby simulating a more conservative spread process. Furthermore, to adapt to the different characteristics of triangular meshes, quadrilateral meshes, or hybrid topologies, the method for finding neighboring vertices can be adjusted accordingly: for manifold meshes, one- or two-element nodes can be found directly through edge connectivity; for non-manifold meshes or surfaces with holes, a valid set of neighboring vertices can be determined by combining spatial distance search with topological connectivity filtering, thereby ensuring computational efficiency while avoiding erroneous attribute spread through non-existent surface connections.

[0053] Optionally, diffusion rate noise modulation is used to apply spatial noise during the diffusion process, causing differences in the actual diffusion rates of different regions, thereby forming an irregular diffusion boundary morphology.

[0054] Optionally, the noise modulation applied to the diffusion rate during the diffusion process can employ different spatial noise basis functions such as Wally noise, simplex noise, or Berlin noise. Furthermore, the noise computation domain can be normalized based on the three-dimensional spatial position of the vertices, or it can be mapped based on the texture coordinates or local tangent spatial coordinates of the vertices on the model surface. This disclosure does not limit the type of noise function or the computational space. Considering that real ice crystals or coral branches are often affected by the inhomogeneity of the local microenvironment during growth, as a possible implementation, multiplying the noise value with the diffusion rate can generate random acceleration or stagnation regions in the originally uniform theoretical diffusion process. This results in the final spike structure exhibiting a macroscopic attenuation trend from the starting region to the surrounding area, and a natural serrated and irregular shape at the microscopic boundary. It should be noted that the noise amplitude and element size can be adjusted independently: the larger the noise amplitude, the higher the irregularity of the diffusion boundary; the smaller the noise element size, the finer the serrations of the boundary. The two can be configured in conjunction according to the desired final organic morphological characteristics.

[0055] Optionally, in addition to using multiplication to change the diffusion rate, the noise modulation described above can also use addition to offset the neighborhood difference fusion result, or use the noise calculation result as a local correction factor for the diffusion iteration number, thereby causing some regions to end diffusion prematurely while others continue longer iterations. To avoid unwanted voids or breaks within the spread region due to overly discrete noise value distribution, as a possible implementation, the original noise can be smoothed or superimposed using octave bands, so that the noise spatially exhibits a distribution characteristic combining low-frequency gradation and high-frequency details; where low-frequency components control the spread differences in the macroscopic region, and high-frequency components control the fragmented and irregular shape of the boundary. Furthermore, the timing of noise modulation can also be dynamically changed at each stage of the diffusion iteration. For example, weaker noise can be applied in the first half of the iteration to ensure the overall spread trend, while stronger noise can be applied in the second half of the iteration to refine the boundary shape, thus making the distribution of control attribute values ​​both directional and organically varied.

[0056] Optionally, the decay operation is used to cool down and decay the control attribute value, and the preset threshold is used to determine the effective spread range, thereby controlling the growth boundary and density distribution of the spike structure.

[0057] Optionally, the cooling rate used in the above attenuation operation can be flexibly set according to the expected spread range. For example, the cooling rate can be set to different numerical levels such as 0.1, 0.2, or 0.3. The lower the cooling rate, the smaller the attenuation of the control attribute value in each iteration, the farther the attribute can spread on the model surface, and the larger the final spike coverage area. Conversely, the higher the cooling rate, the shorter the spread distance, and the more concentrated the spike distribution is near the starting area. As a possible implementation, the above preset threshold can be set to 0.15, 0.2, or 0.25. When the control attribute value of a vertex is lower than the preset threshold, it is forcibly set to zero, thereby clearing weak edge attributes in a hard truncation manner and avoiding the appearance of fragmented spike structures that are too low in height and almost invisible to the naked eye at the spread boundary. It should be noted that the cooling rate and the preset threshold can be adjusted in conjunction: when the cooling rate is low, the preset threshold can be appropriately increased to prevent the attribute from spreading too far and causing the spike density to be excessively diluted at the boundary; when the cooling rate is high, the preset threshold can be correspondingly decreased to retain more near-boundary details.

[0058] Optionally, in addition to using multiplicative attenuation at a fixed ratio per frame, the above attenuation operation can also employ distance-based function attenuation. For example, based on the geodesic or Euclidean distance between the current vertex and the nearest starting region center point, a gradient function can be calculated that accelerates attenuation with increasing distance, thus simulating the natural law that nutrients or energy are depleted more quickly when far from the source. Furthermore, the preset threshold can not be a fixed constant, but a spatially varying threshold field: a lower threshold is used at the core location near the starting growth region to retain more details, while a higher threshold is used at the edge location far from the starting region to truncate weak attributes in advance, forming a density distribution with clear boundaries and fine internal details. It should be understood that, whether it is a fixed threshold or a spatially varying threshold, the fundamental purpose is to transform the continuous distribution of control attribute values ​​into segmented regions with clear inner and outer boundaries, thereby providing a stable and reliable distance control basis for subsequent face-level attribute enhancement and polygon extrapolation.

[0059] In step S270, based on the control attribute values, noise modulation is applied to the normal direction of the 3D model surface, and geometric extrapolation is performed along the modulated normal direction to generate a geometric structure with thickness. This not only allows the spike height to exhibit natural random variations but also outputs a geometric structure with realistic topological volume along the normal direction, effectively solving the problem of insufficient thickness in simple displacement maps.

[0060] In one implementation, the system reads the surface-level temperature properties obtained through propagation simulation, multiplies and modulates these properties using alligator noise basis functions to obtain the extrapolation distance for each surface. Then, polygon extrapolation is performed along the surface normal direction, causing local regions of the preprocessed surface to extend outwards along the normal, generating a three-dimensional spike-like geometry. During this process, regions with higher temperature properties have larger extrapolation distances, resulting in a height distribution that gradually decreases from the starting region to the edge, outputting a surface spike structure with realistic volume and independent topological boundaries. Optionally, the aforementioned normal direction is used to determine the extrusion orientation of the geometric extrapolation, and it can be used for extrapolation distance control after noise modulation based on the surface-level control attribute value.

[0061] Optionally, the aforementioned normal direction can be a surface normal direction or a point normal direction. Considering the different directional accuracy requirements of the spike structure at different growth stages, as a possible implementation, in the basic extrapolation stage, the surface normal direction can be used as the unified extrusion direction, so that all vertices on the same surface are extrapolated in the same direction, thereby ensuring the neatness of the spike root and the structural stability; in the guiding extrapolation or detail extrapolation stage, the point normal direction can be used, so that each vertex is extrapolated independently according to its own combed normal direction, thereby allowing the spike tip to present natural bifurcation and orientation changes. It should be noted that the specific selection of the above normal direction is not intended to limit this disclosure. In actual implementation, one normal direction can be used alone, or the two can be used in combination, for example, using a surface normal at the root and gradually transitioning to a point normal direction at the top, to take into account both overall order and local randomness.

[0062] Optionally, the aforementioned geometric structure with thickness is generated by polygon extrapolation, and its cross-sectional profile is positively correlated with the noise-modulated control attribute value.

[0063] Optionally, the aforementioned geometry with thickness can be generated through polygon extrapolation. As one possible implementation, the main structure extrapolation uses a large base extrusion distance (e.g., 0.23), determining the actual extrapolation amount based on the noise-modulated surface-level temperature properties to generate the main body of the spikes. Supplementary extrapolation uses a smaller extrusion distance (e.g., 0.01), superimposing fine protrusions on top of the main body, giving the spike cross-section a natural profile from thick to thin. Furthermore, to avoid abrupt superposition between multiple layers, the same alligator noise basis function is used for temperature property modulation during the extrapolation process, but different amplitude and element size parameters can be used to introduce rich local variations while maintaining morphological harmony. This geometry has independent topological boundaries and realistic volume information, allowing direct use in subsequent rendering, baking, or 3D printing processes, rather than merely remaining a highly realistic visual fake.

[0064] In an optional implementation, the method further includes: directionally adjusting the normal direction of the geometric structure to deflect it towards a guiding direction, and performing polygon extrapolation along the adjusted normal direction to generate a structure with directional growth characteristics; wherein the guiding direction is determined by a guiding direction curve or a guiding direction field. In this way, by adjusting the direction to make the spikes grow along the guiding direction, not only is macroscopic directional propagation control achieved, but the limitation that the spike orientation can only rely on the surface normal is also effectively avoided, giving the final geometric structure a customizable growth path and stronger visual controllability.

[0065] In one implementation, for a geometry that has already completed temperature property propagation and base thickness extrapolation, the system can further adjust the direction of its normals; for example, based on a guide direction curve that the user has drawn in advance in the 3D view, spiraling upwards from the bottom of the model, the normal vector of the spike tip is gradually deflected along the tangent direction of the curve, and then polygon extrapolation is continued along these adjusted normal directions, thereby generating a spike shape with the tip growing upwards in a spiral direction on the original base structure.

[0066] The directional adjustment aims to progressively deflect the normal direction of the spike structure towards the guiding direction to control the extrusion orientation of subsequent outward extension, causing the generated surface spikes to spread and grow along a specified trend. Optionally, the directional adjustment uses a vector blending mechanism to progressively deflect the normal vector of each vertex towards the guiding direction vector, thereby achieving macroscopic control over the spike growth orientation. In one specific approach, the above operation can use a linear interpolation function to blend the original normal and the guiding direction vector. The blending ratio is controlled by a direction adjustment factor. When the direction adjustment factor approaches 1, the normal is almost completely aligned with the guiding direction, while when the factor approaches 0, the normal maintains the original surface orientation. Considering that a single round of normalizing might result in abrupt transitions over a large area, the aforementioned directional adjustments can be performed in multiple rounds. The first round uses a larger radius of action (e.g., 0.986) to coarsely adjust the overall normal field, causing a general shift in the orientation of the spike roots over a large area. The second round uses a smaller radius of action (e.g., 0.662) to finely correct local details, thus ensuring both consistency in the macroscopic orientation and preserving local organic variations. Furthermore, before directional adjustments, the surface of the geometry can be smoothed to eliminate local sharp noise, providing a continuous and stable normal field for normalizing and avoiding abnormal fluctuations in the normalizing results caused by uneven mesh subdivision.

[0067] Optionally, the orientation adjustment factor is not limited to a globally uniform value; it can be configured as a spatially varying adjustment factor field. In actual implementation, this factor can be dynamically calculated based on the spatial distance between each vertex and the guiding direction curve. For example, a larger first adjustment factor (e.g., 0.8) can be used in regions far from the guiding direction curve to make the spikes in that region more significantly tend toward the guiding direction, while a smaller second adjustment factor (e.g., 0.2) can be used in regions close to the guiding direction curve to retain more original surface features near the centerline. In addition to the distance-based gradient configuration mentioned above, the orientation adjustment factor can also be mapped according to temperature attributes, curvature attributes, or user-drawn masking attributes; this disclosure is not limited to these. To avoid the loss of volume due to completely parallel spike directions caused by excessive deflection in extreme cases, the above linear interpolation can also be replaced with spherical linear interpolation or a damped vector rotation. By limiting the maximum angle of a single deflection (e.g., not exceeding 45 degrees), it is ensured that while the spikes deflect toward the guiding direction, they still maintain a reasonable angle relationship with the base surface, thus balancing directional growth and structural stability.

[0068] The guiding direction field defines point-by-point changing guiding direction information in three-dimensional space, replacing or supplementing a single guiding direction curve, and providing a more flexible basis for directional control of spike growth. Optionally, the guiding direction field can be a three-dimensional vector field generated on the model surface or within the bounding box through vector field calculation nodes. Each field point stores a guiding direction vector, used to indicate the target orientation that the spike should deflect at the corresponding spatial location. Considering that a single guiding direction curve may be insufficient in describing large-scale, non-uniform directional changes, the guiding direction field can present a richer directional distribution, such as describing a radial vector distribution radiating outward from a core region, or describing a curl field rotating along the vortex axis. It should be noted that the guiding direction field and the guiding direction curve are not mutually exclusive. In actual implementation, a basic direction field can be generated first based on the guiding direction curve, and then a spatial noise function or gradient field can be superimposed for secondary modulation to obtain composite guiding information that combines macroscopic direction and local changes. In addition to the method of generating via procedural nodes as described above, the guiding direction field can also be drawn directly by the user in the 3D view using a brush, or mapped by importing external simulation data. This disclosure does not limit its generation source. By introducing the guiding direction field, even in scattered areas with complex surface topology or where guiding curves are difficult to cover, a consistent directional reference can be provided for normal routing, thereby ensuring that the spike structure can maintain the expected growth direction in different sub-regions.

[0069] Polygon extrapolation is used to extrude two-dimensional patches outward along the adjusted normal direction to give the spike structure solid thickness and a spatial extension shape driven by guiding trends. Optionally, polygon extrapolation differs from visual simulation methods based solely on shader displacement or texture normal mapping. It performs topological extrusion on existing patches along the normal direction, simultaneously generating new top and side geometry, thereby giving the spike structure a realistically measurable physical thickness and independent boundary contours. In one specific approach, the directionally adjusted normal direction is no longer the original surface normal, but a deflected normal that incorporates the user-specified guiding trend. Therefore, the extrusion path of polygon extrapolation will significantly deviate from the vertical direction of the original surface, causing the spikes to exhibit directional shapes such as oblique growth, spiral convergence, or radial extension. To avoid self-intersection or overlap of extruded patches due to abrupt changes in the normal direction, the polygon extrapolation operation can perform consistency constraints on the normal field before extrusion, such as limiting the maximum angle difference between the normals of adjacent vertices, or detecting and correcting patch flipping in real time during the extrusion process. It should be noted that the extrusion distance of polygon extrapolation can be set face-by-face differently according to the face-level control attributes (such as the temperature attribute after noise modulation). The higher the temperature of the face, the larger the extrusion distance, and the lower the temperature, the smaller the extrusion distance or even no extrusion. Thus, the growth density and geometric thickness are naturally driven by the same spread attribute.

[0070] In an optional implementation, before performing noise modulation on the normal direction of the 3D model surface based on control attribute values ​​and performing geometric extrapolation along the modulated normal direction, the method further includes: acquiring the mesh of the 3D model; performing edge sharpening on the mesh to increase the angle between normals of adjacent faces; acquiring vertex-level control attribute values ​​and aggregating and improving these vertex-level control attribute values ​​into face-level attribute values; wherein the aggregation and improvement uses an arithmetic mean or weighted average method, and the arithmetic mean or weighted average is used as the face-level attribute value of the corresponding face, and the face-level attribute value is used to control the extrapolation distance of the geometric extrapolation process. In this way, increasing the angle between normals of faces through edge sharpening enhances the clarity of the spike boundaries, and aggregating vertex attributes into face attributes uniformly controls the extrapolation distance, avoiding height inconsistencies caused by vertex-level fluctuations, and making the thickness distribution of the multi-layer spike structure more regular and controllable.

[0071] In one implementation, the system first acquires the mesh data of the current 3D model and performs edge sharpening processing on the mesh. By adjusting the vertex positions, the angle between the normals of adjacent faces is increased, thereby making the originally smooth transition boundary clearer. Subsequently, the system reads the control attribute values ​​on each vertex and uses the arithmetic mean method to aggregate the attribute values ​​of each vertex on the same face to calculate the face-level attribute value. For example, if the attribute values ​​of four vertices in a quadrilateral face are 0.8, 0.7, 0.6, and 0.5, then the face-level attribute value of the face is 0.65. This face-level attribute value will be directly used as the modulation reference for the extrusion distance of each face in the subsequent geometric extrapolation processing, so that the extrapolation height on the same spike side is consistent, avoiding local height breaks or unevenness caused by vertex-level attribute differences.

[0072] Optionally, edge sharpening increases the angle between the normals of adjacent faces by adjusting vertex positions, making the edges clear and sharp, providing a clear topological boundary for subsequent extrapolation. Optionally, the above edge sharpening can be directly applied to the surface of the polygonal mesh after the flame spread simulation. Its essence lies in enhancing the transition creases between adjacent faces through displacement adjustment, making the surface creases, which were originally in a gradual state due to numerical smoothing, tend to have clear edges. Considering that the spike structure needs to have a clear topological boundary in the subsequent multi-layer extrapolation process, if the original mesh edges are too smooth, the extrapolated sides are prone to adhesion or ambiguity in normal direction, which in turn leads to the cross-sectional contours of different spikes eroding each other. As a possible implementation, edge sharpening can adopt a crease edge detection and vertex crease weight allocation strategy based on dihedral angle threshold, or it can adopt an inverse operation based on Laplacian smoothing to increase the local curvature change rate. This disclosure does not limit the specific algorithm implementation. In one specific implementation, when the angle between the normals of adjacent facets is increased to a specified range, subsequent extrusion operations along the facet normal direction will generate independent side surfaces with clear boundaries, creating a sharp geometric transition between the spike body and the base surface. It should be noted that the degree of increase in the angle can be dynamically adjusted according to the stylistic requirements of the target spike. For example, a larger angle can be set when generating ice crystal-like structures to create sharp edges, while a relatively soft transition can be maintained when generating coral-like dendritic structures, thus accommodating the production needs of different visual styles.

[0073] Optionally, the surface-level attribute value is obtained by aggregating the attribute values ​​of all vertices on the same surface through an arithmetic or weighted average, serving as a unified control benchmark for the extrapolation distance of that surface. Optionally, considering that the vertex-level control attribute values ​​may exhibit a continuous gradual change after flame spread simulation, and that there are subtle temperature differences between different vertices of the same surface, directly driving extrapolation with vertex attributes could easily lead to inconsistent extrusion heights on the same spike side, resulting in jagged or torn geometric defects. As a possible implementation, the above aggregation and enhancement operation can be an arithmetic average of all vertex attribute values ​​constituting the surface, a weighted average based on the reciprocal of the distance between the vertex and the surface center, or an integral average based on area weights. This disclosure does not limit the specific aggregation formula. In one implementation, for a triangular surface, the system reads the temperature attribute values ​​of the three vertices respectively, calculates the arithmetic average, and writes it into the surface-level attribute channel of the surface. Subsequent noise modulation and extrapolation steps directly read this surface-level value, thereby ensuring that all points on the same surface obtain a completely consistent extrapolation benchmark. Furthermore, the purpose of this aggregation operation is to transform the discrete vertex-level spread results into a continuous surface-level density control field, ensuring that the spike structure exhibits a smooth gradient that naturally decays from the center to the edge on a macroscopic scale, rather than being constrained by the local jumps caused by the original mesh subdivision density.

[0074] Optionally, besides the arithmetic mean and weighted average, the above-mentioned aggregation enhancement can also employ other statistics that reflect the overall spread intensity of the patches. For example, a truncated average can be used to remove extreme vertex outliers caused by numerical noise in the neighborhood, or quantile statistics can be used to enhance the response to the core spread region. It should be noted that in the implementation of the weighted average, the weight coefficient can be related not only to spatial location but also to the vertex's normal direction, the number of convergence frames of that vertex in the flame spread iteration, or the local radius of curvature of that vertex. This automatically enhances or suppresses the extrapolation distance in high-curvature regions, allowing the spike thickness to better conform to the morphological characteristics of the base surface. In practical applications, if the subdivision density of the base mesh is uneven, the patch area in the lower resolution region will be larger. In this case, the information loss caused by sparse sampling can be compensated by increasing the attribute weight of the patch or using an area-based weighted average, avoiding distortion of the spike density distribution caused by mesh topology differences. It should be understood that, regardless of the aggregation method used, the purpose is to establish a stable mapping from vertex-level simulation data to face-level geometric operations, so that subsequent multi-level extrapolation has a unified and controllable input reference.

[0075] In an optional implementation, noise modulation is applied to the normal direction of the 3D model surface based on control attribute values, and geometric extrapolation is performed along the modulated normal direction. This includes: converting the control attribute values ​​into face-level control attribute values; multiplying or adding the face-level control attribute values ​​using a spatial noise function to obtain modulated attribute values; determining the extrapolation distance for each face based on the modulated attribute values, wherein the modulated attribute values ​​are positively correlated with the extrapolation distance; performing a first-layer polygon extrapolation along the face normal direction to generate a basic thickness structure; and performing a second-layer polygon extrapolation along the face normal direction, wherein the extrusion distance of the second layer is smaller than that of the first layer, forming a multi-layered stepped transition structure with progressively refined layers at the top. Thus, through differentiated multiplicative or additive noise modulation and layered polygon extrapolation, not only can the protruding cross-section escape the monotonous feel of a uniform columnar shape, but a natural stepped transition can also be formed at the top, significantly enhancing the organic realism of the geometric structure.

[0076] In one implementation, the system inputs the surface-level control attribute values ​​into the Alligator noise basis function and the Simplex offset noise for multiplication and addition modulation to obtain modulated attribute values. Then, the product of the modulated attribute values ​​and the base height of 0.23 is used to determine the first-layer extrapolation distance. First-layer polygon extrapolation is then performed along the surface normal direction to generate the base thickness structure, such as... Figure 6 The diagram illustrates a basic thickness structure. Further, a second layer of polygonal extrapolation is performed with an extrusion distance much smaller than the first layer (0.01). After the two layers are superimposed, a stepped transition is formed at the top of the spike, contracting from the main thickness towards the tip, ultimately presenting an organic outline resembling an ice crystal trunk surrounded by fine crystalline ridges; as shown... Figure 7 The diagram shows a multi-layered stepped transition structure.

[0077] Optionally, the noise modulation described above can perform multiplication or addition operations on the surface-level attribute values ​​to generate modulated attribute values ​​with spatially random variation characteristics. Optionally, multiplicative modulation multiplies the surface-level control attribute value with the output of the spatial noise function surface by surface, causing the originally continuous and smooth temperature field to produce varying degrees of enhancement or weakening in local areas; additive modulation adds a noise offset to the original attribute value, causing the surface-level attribute to produce details of up-and-down fluctuations while preserving the overall trend. It should be noted that the above multiplication or addition operations can be used alone or in combination: for example, multiplicative modulation can be performed first to widen the attribute differences between different regions, and then additive modulation can be performed to introduce micro-ripples within the same region. The purpose of these two modulation methods is to ensure that the extrapolation distance is no longer completely determined by the linearity of the spread temperature, but incorporates irregular variations with the characteristics of organic matter, thereby avoiding all spikes from exhibiting a uniform mechanical appearance. In actual implementation, the selected spatial noise function can be the Alligator noise basis function or other noise functions with continuous random characteristics; this disclosure does not limit this.

[0078] Optionally, the above extrapolation process can sequentially perform at least two layers of polygon extrapolation along the surface normal direction to construct a geometric structure with a base thickness and stepped transition on the surface. Optionally, the first layer of polygon extrapolation is performed along the surface normal direction with a first extrusion distance, which is determined by the product of the modulated attribute value and the first base height, thereby establishing a base thickness structure with topological closure from the root of the spike to the main body. Considering that a single uniform extrusion can easily produce a rigid contour similar to an artificial pipe, the first layer of extrapolation usually involves surface splitting on its sides while generating the main body volume to support the geometric connection of subsequent layers. It should be noted that the surface normal direction of the first layer of extrapolation is not limited to the original normal of the preprocessed surface, but can also be the combined normal direction after the aforementioned edge sharpening and noise modulation; when multiple adjacent surfaces are extrapolated at the same time, if their modulated attribute values ​​are different, the extrapolation distances of each surface will be different, so that the side of the same spike presents a natural wavy undulation rather than a pure cylindrical surface. In one possible implementation, the initial base height can be set to 0.23, or it can be dynamically adjusted according to the overall scale of the target model, as long as the extrusion distance of the subsequent second layer is significantly less than this value. Furthermore, the geometry generated by the extrapolation of the first layer will participate in the dilation and smoothing calculations as the main structure in the subsequent voxel fusion stage.

[0079] Optionally, the second layer of polygon extrapolation is performed after the base thickness structure is generated. Its second extrusion distance along the surface normal is significantly smaller than the first extrusion distance, thus forming only a thin, localized protrusion at the top of the spike. For example, when the first extrusion distance is set to 0.23 and the second extrusion distance is set to 0.01, the cross-section after the two layers are superimposed exhibits a stepped transition, gradually contracting towards the top from a base thickness of 0.24. Furthermore, if a finer crystal tip is required, a third or even more extrapolation layers can be added on top of the first two layers, each using a progressively decreasing extrusion distance, so that the spike tip eventually converges into a sharp ridge. To avoid topological cracks between layers, each extrapolation operation simultaneously generates side polygons connecting the old and new top surfaces while extruding a new top surface, thus maintaining the integrity of the mesh's manifold structure. It should be understood that the specific values ​​of the number of layers and the extrusion distance for each layer are not limited to two items; they can be increased or decreased in actual production according to the visual accuracy requirements of the target asset. This disclosure aims to cover all technical solutions for obtaining multi-layered stepped profiles through progressive extrusion.

[0080] In an optional implementation, at least one of the first and second polygonal extrapolations adopts a mixed direction of surface normals and point normals in its extrapolation direction. The mixed direction adopts surface normals at the root and gradually transitions to point normals at the top. In this way, the gradual mixing of surface normals at the root and point normals at the top ensures both the topological continuity between the base of the spike and the base surface, and allows the top to differentiate into an organic orientation guided by the vertex normals, thus balancing structural regularity and natural morphology.

[0081] In one implementation, the extrapolation of the first base layer thickness uses a hybrid direction of surface normals and point normals. Specifically, in the root region (i.e., the height segment near the original surface at the extrapolation starting point), the extrapolation direction is entirely surface normal to ensure a neat and topologically continuous connection boundary between the spike body and the base surface. As the extrapolation height increases, the extrapolation direction gradually transitions to point normals through linear interpolation, until it is entirely point normal in the top region (near the extrapolation endpoint). Since the point normal incorporates the orientation information of the vertex neighborhood, the extrusion direction of each point at the top will produce subtle differences, resulting in a differentiated shape where the spike tops naturally spread out or converge towards the guiding direction, avoiding a mechanical feel where all spike tops have completely uniform orientations. As another implementation, the above-mentioned hybrid transition can also be applied to the extrapolation of the second layer of fine protrusions, so that the second layer maintains surface normals at the root to support the structure of the first layer, while converting to point normals at the top to produce a more delicate orientation differentiation. For example, the switching point between using surface normals at the root and point normals at the top of the second layer can be set at 50% of its extrapolation height. This hybrid strategy allows for more dramatic changes in orientation of the top details, thereby generating an organic structure similar to ice crystal branches or coral twigs.

[0082] Optionally, point normals are intended to provide the local surface orientation at mesh vertices as a vertex-level orientation reference for geometric extrapolation. Optionally, point normals can be calculated by weighted averaging of the normals of adjacent faces sharing the target vertex, or estimated based on the geometric curvature distribution of the vertex neighborhood using least-squares fitting or spherical fitting. This disclosure does not limit the specific calculation method. During geometric extrapolation, face normals provide a unique and uniform orientation reference for the entire polygon face, suitable for basic extrapolation that requires maintaining cross-sectional consistency; while point normals carry the local orientation differences of the vertex neighborhood. When extrapolating spike structures to higher levels or apical regions, using point normals can cause subtle directional differentiation between adjacent vertices, thereby simulating the organic characteristics of naturally spreading tips of natural ice crystals or biological tissue. It should be noted that the above point normals can not only be used to characterize the geometric orientation of the original mesh, but can also be recalculated after normal sorting operations. At this time, the point normals have been affected by the deflection of the guiding direction vector, so the apical extrapolation direction will naturally tend towards the user-defined growth direction. In addition, point normals can also be associated with temperature attribute values. In the spread edge region with lower temperature attributes, the point normals between different vertices are more dispersed, thus making the spike tips in the low-density area present a more random and richer spreading effect.

[0083] Optionally, the blending direction is used to dynamically merge surface normals and point normals to balance root continuity with apical morphological diversity.

[0084] Optionally, the process of implementing the blending direction may include: establishing a blending factor based on the relative height between the current extrapolation position and the root reference plane. This blending factor has a value of 0 at the root and adopts the surface normal entirely, and a value of 1 at the top and adopts the point normal entirely. The intermediate segment is transitioned through linear interpolation or a smooth curve function. Considering that the topological regularity of the root has a direct impact on the subsequent voxel fusion effect, as a possible implementation, the above-mentioned root segment can be limited to the range of 0% to 30% of the total extrapolation height. Maintaining the surface normal direction within this range can effectively avoid gaps or overlapping of surfaces at the roots of adjacent spikes due to normal divergence. At the same time, the top segment transitions towards the point normal direction starting from 70% of the extrapolation height, so that the top of the spike gradually presents a differentiated orientation guided by the vertex normal during the extrusion process, thereby avoiding the defects of flat tops and lack of vividness caused by a single surface normal extrapolation. Furthermore, this mixing factor can also be multiplied and compounded with temperature attribute values. For example, in the core region with high temperature attribute, the proportion of the root surface normal remains unchanged, while the weight of the point normal is increased in the temperature edge region, so that the spikes in the low-density edge region produce a more random and natural tip spreading effect.

[0085] Optionally, in addition to a linear transition based on relative height, the blending direction can also employ a segmented switching logic based on the number of extrapolation layers. For example, in the extrapolation of the first layer's base thickness, surface normals are used throughout to ensure the regularity of the main structure; in the extrapolation of the second layer's fine protrusions, surface normals are used within the first 50% of the height at the root, while point normals are switched to the upper 50% of the height. That is, the above blending does not necessarily have to be a continuous gradual change within a single layer's extrapolation; it can also manifest as differences in directional strategies within different height ranges of the same layer or between different layers. This disclosure does not limit the specific granularity of the blending operation. It should be noted that in areas far from the guiding direction curve, the point normals in the blending direction can remain in their uncombed original state, causing the tips of the edge protrusions to randomly spread out, dominated by the model's original curvature; in areas close to the guiding direction curve, the point normals have undergone normal combing and are biased towards the guiding direction, while the tips of the protrusions uniformly grow towards the guiding direction, thus forming a biomimetic spreading morphology under the dual constraints of density and orientation. In addition to linear interpolation, transition functions can also employ power functions or smooth step functions to create sharp abrupt changes in direction or gentle, gradual deflections between the root and the apex.

[0086] In an optional implementation, directional adjustment includes: obtaining the surface normal vector of the geometry; smoothing the surface of the geometry to eliminate local sharp noise; determining the guiding direction vector based on the guiding direction; progressively deflecting the normal vector of each vertex toward the guiding direction vector, wherein the degree of deflection is controlled by a direction adjustment factor; and performing multiple rounds of directional adjustment operations, wherein the first round uses a larger radius of action for overall normal deflection, and the second round uses a smaller radius of action for fine-tuning local details. In this way, by first smoothing the surface normal and then progressively deflecting it, sharp noise interference can be eliminated, and by coordinating the overall and local growth directions through multiple rounds of differentiated radius adjustments, the accuracy and organic feel of the spike structure spreading along the guiding direction can be improved.

[0087] In one implementation, after the spike structure is generated by multi-layer polygon extrapolation, the system first obtains the surface normal vectors of each vertex and performs smoothing processing on the surface to eliminate local sharp noise generated by extrapolation, making the normal field more continuous and stable. Then, based on a pre-drawn guiding direction curve, a guiding direction vector is determined, and the normal vector of each vertex is progressively deflected toward this guiding direction vector, with the degree of deflection controlled by a direction adjustment factor. Further, the system performs two rounds of directional adjustment operations: the first round uses a larger radius of action to deflect the normal field over a large area, causing the overall growth direction of the spike group to tend toward the guiding curve; the second round uses a smaller radius of action to finely adjust local details, maintaining overall consistency while preserving the subtle differences in local random deflections.

[0088] Optionally, this vector is used to characterize the orientation of each vertex on the spike surface and serves as the basis input for subsequent directional adjustments. Optionally, the surface normal vector is used in the 3D mesh to describe the orientation of the surface where the vertex is located. In one embodiment of this scheme, the system reads the spike structure mesh after multi-layer extrapolation and obtains the surface normal vector of each vertex. Considering that the multi-layer polygon extrapolation process may produce small geometric jagged edges at the spike tip or side, causing a jump in the normal direction, the system further performs smoothing processing on the surface to eliminate local sharp noise. By setting a smoothing distance threshold, the angle between the normals of adjacent vertices tends to be gentler, thereby obtaining a continuous and stable normal field. It should be noted that the surface normal vector can be obtained after the multi-layer extrapolation is completed, or it can be obtained in stages between each extrapolation layer. This disclosure does not limit the execution node of a single acquisition. In addition, the distance threshold used for smoothing processing can be dynamically set according to the expected size of the spike. For example, a smaller threshold can be used for a dense thorn structure, and a larger threshold can be used for a robust ice spike structure, so as to achieve the effect of eliminating noise while preserving the macroscopic shape.

[0089] Optionally, this vector is used to define the expected growth orientation of the spike structure, determined by the tangent direction of the guide direction curve at the corresponding position. Optionally, to avoid the spike growth direction being completely dominated by the random surface curvature, resulting in a scattered overall shape, the system needs to constrain the normal according to the macroscopic orientation specified by the user. In one implementation, the guide direction vector can be obtained by spatially sampling the guide direction curve and calculating the tangent direction at each sampling point; the guide direction curve can be a three-dimensional spatial curve running through the model surface, or a segmented polyline. Further, the normal vector of each vertex is progressively deflected toward the guide direction vector, where the deflection is achieved using vector linear interpolation or spherical interpolation, so that the normal gradually approaches the guide direction while maintaining the original surface features. It should be noted that progressive deflection does not mean that all vertices are adjusted to a completely consistent orientation, but rather that a certain original normal component is retained under the control of the deflection degree parameter, so that the spike tips present natural directional differences while converging overall, avoiding mechanical neat arrangement. This can establish a unified growth trend at the macroscopic level and maintain organic randomness at the microscopic level, enhancing visual realism.

[0090] Optionally, this factor controls the degree to which the normal vector deflects in the guiding direction, and its value can be dynamically set between 0 and 1.

[0091] Optionally, considering that the degree of obedience of the spike structures to the guiding direction should vary in different regions, the orientation adjustment factor can be set as a uniform constant or configured as an adjustable field that varies with spatial location. In one implementation, when the orientation adjustment factor is 0, the normal vector of the vertex maintains its original orientation without deflection; when the orientation adjustment factor is 1, the normal vector is completely aligned with the guiding direction vector. In practical applications, this factor can be dynamically mapped based on the distance between the vertex and the guiding direction curve. For example, a smaller adjustment factor can be used near the guiding path to retain local randomness, while a larger adjustment factor can be used far from the guiding path to ensure consistent macroscopic orientation. Furthermore, the orientation adjustment factor can be combined with a noise function for spatial modulation, causing irregular differences in the deflection degree of adjacent spikes within the same region, thereby further enhancing the organic feel and natural variation of the growth morphology.

[0092] Optionally, this operation performs a progressive smoothing of the normal field from the overall to the local level by using differentiated action radii. Optionally, to balance the consistency of the macroscopic orientation of the spike group with the organic changes in microscopic details, the above directional adjustment can be performed in at least two rounds. In the first round, the system uses a larger action radius (e.g., 0.986) to smooth the normal field over a large area, causing the spikes in the large area to generally align in the guiding direction; in the second round, the system uses a smaller action radius (e.g., 0.662) to finely adjust the normals in the local area, correcting any loss of detail that may have been caused by oversmoothing in the first round. It should be noted that the action radius, adjustment factor, and number of iterations in each round of multi-round operations can be set independently, and are not limited to two rounds; they can also be extended to three or more rounds, for example, by adding a transition round with a medium radius between the two. This progressive approach, from the whole to the parts and from coarse to fine, not only avoids the loss of details caused by large-radius adjustments in a single round, but also prevents the limitation that small-radius adjustments in a single round cannot establish an overall direction. As a result, the final spike structure has both clear directional growth characteristics and retains natural and organic edge variations.

[0093] In an optional implementation, the direction adjustment factor is a spatially varying adjustment factor field. A first adjustment factor is used in regions far from the guiding direction curve, and a second adjustment factor is used in regions close to the guiding direction curve. The first adjustment factor is greater than the second adjustment factor. In this way, regionally differentiated deflection control is achieved through a spatially varying adjustment factor field. Strong deflection at the far end ensures the overall tendency to follow the guiding direction, while weak deflection at the near end preserves local details, balancing macroscopic guidance consistency with the naturalness of microscopic morphology.

[0094] In one implementation, the spatial distance from each vertex on the surface of the 3D model to the guide direction curve can be calculated first. For target vertices with a distance greater than 0.5 world units, their corresponding direction adjustment factor is set to 0.8 (i.e., the first adjustment factor), causing their normals to deflect significantly towards the guide direction. For target vertices with a distance less than or equal to 0.5 world units, the direction adjustment factor is set to 0.3 (i.e., the second adjustment factor), allowing them to retain more of their original normal direction. Accordingly, the root region of the spikes far from the guide direction curve is forcibly combed to the specified growth direction, while the tip region of the spikes close to the guide curve maintains a relatively natural random orientation. This ensures the overall trend is consistent while avoiding the top shape from appearing mechanically rigid due to excessive deflection.

[0095] Optionally, the orientation adjustment factor can be configured as a spatially varying scalar field, controlling normal deflection based on its proximity to the guide curve. Alternatively, the spatially varying adjustment factor field can be a set of floating-point scalars independently stored at each vertex of the 3D model surface. This set of scalars can be generated through continuous interpolation based on the geodesic or Euclidean distance from each vertex to the guide orientation curve. Furthermore, to avoid abrupt changes caused by distance calculations, the aforementioned adjustment factor field can be convolved using a smoothing kernel function, resulting in a gradual transition in adjustment factor values ​​between adjacent vertices. It should be noted that, in addition to being constructed using distance mapping, this scalar field can also be regionalized based on surface curvature, spike height, or user-drawn masks; the specific implementation method can be selected according to actual needs. In practical applications, elevating the orientation adjustment factor from a global constant to spatially varying field data not only allows for precise constraint on the macroscopic orientation of the spike group but also automatically reduces the combing intensity in sensitive areas near the guide curve, effectively preventing geometric interpenetration or morphological distortion caused by excessive deflection.

[0096] Optionally, the first adjustment factor is configured in a region far from the guide curve and has a large value, to apply a strong deflection to the normal in that region.

[0097] Optionally, the first adjustment factor can be a scalar coefficient uniformly applied across a spatial range far from the guide direction curve. Its numerical range can be dynamically determined based on the radius of curvature of the guide direction curve and the designed height of the spike. Considering that the region far from the guide curve typically corresponds to the root or main body of the spike, these regions require stronger directional constraints to ensure the overall growth trend aligns with the guide direction. Figure 1As one possible implementation, the first adjustment factor can be set to a floating-point value between 0.6 and 0.95. It should be noted that the above numerical range is only an example; in actual implementation, it can be adaptively modified according to the round of normal combing and the radius of effect. For example, when a larger radius of effect is used in the first round of combing, the corresponding first adjustment factor can be appropriately reduced to avoid excessive directional abrupt changes in the root region. The purpose of this differentiated configuration is to enhance the distal deflection weight, so that the spikes form a neat and uniform arrangement at the macroscopic level.

[0098] Optionally, the second adjustment factor is configured in a region close to the guide curve and has a small value, used to apply a weak deflection to the normal in that region. Optionally, the second adjustment factor can be a scalar coefficient applied within a spatial range close to the guide direction curve, and its value can be significantly lower than the first adjustment factor, for example, set as a floating-point value between 0.1 and 0.4. Considering that the region close to the guide curve is often located at the top or end of the spikes, if too strong a directional constraint is applied, it is easy to cause the top shape to tend to be uniform and lose the natural and organic variation characteristics. Therefore, by reducing the adjustment factor in this region, the random noise component in the original normal direction can be effectively preserved. Furthermore, the difference between the second adjustment factor and the first adjustment factor can be adjusted according to the required organic feel intensity of the final output; the larger the difference, the more fully the randomness of the top shape is preserved, and the smaller the difference, the stronger the overall directional consistency. One objective of this embodiment is to improve the natural realism of the generated structure by reducing the combing intensity at the proximal end, avoiding the visual effect of all spike tips being forced to point in the same direction and producing a mechanical arrangement.

[0099] In an optional implementation, the method further includes: obtaining a structure with directional growth characteristics; performing voxelization on the structure with directional growth characteristics to obtain a voxel distance field; performing dilation and smoothing on the voxel distance field; and generating the final geometric structure model by devoxing the processed voxel distance field. Thus, through the dilation and smoothing after voxelization, not only are the spikes naturally integrated in the voxel space and hard edges eliminated, but devoxing also outputs a final geometric entity with topological continuity and a stronger sense of organic structure.

[0100] In one implementation, the system acquires a spiked mesh structure with directional growth characteristics after normal combing and multi-layer extrapolation, and converts it into a sparse voxel signed distance field with a voxel size of 0.005. Then, it performs four voxel dilations to bring adjacent spikes closer together, followed by median smoothing with a radius of 1 to eliminate voxel jaggedness. Finally, it de-voxels the distance field back to a polygonal mesh, resulting in a final ice-crystal-like geometric model with naturally smooth transitions at the spike tips and seamless integration of the overall boundary. The de-voxelization step ensures efficient reconstruction from regular voxel data to a renderable continuous surface. Optionally, the dilation and smoothing of the voxel distance field aims to bring adjacent spikes closer together and create a smooth transition in voxel space.

[0101] Optionally, the dilation of the voxel distance field can be achieved by performing multiple iterative convolution operations on a 3D voxel mesh using a dilation kernel. This expands the zero isovalues ​​in the signed distance field outward by a specified distance, allowing previously separate spike geometries to intersect at the voxel level, laying the foundation for subsequent natural fusion and topological connectivity. After dilation is complete, smoothing can be performed on the dilated distance field data using neighborhood median filtering. The radius and number of iterations of the filtering kernel can be dynamically adjusted based on the original spike density and the desired degree of fusion. For example, a larger smoothing radius can be used in high-density spike clusters to promote more microscopic bridging, while the smoothing intensity can be reduced in sparsely distributed regions to preserve the independent morphology of the spikes. It should be noted that, in order to avoid excessive expansion of the spikes in the direction perpendicular to the growth direction and distortion of the main trend due to isotropic expansion, an anisotropic strategy can be adopted for expansion operation. That is, a larger expansion step size is applied in the growth axis along the guiding direction, while a smaller expansion step size is applied in the vertical direction. This can effectively maintain the directional growth trend of the spikes in the longitudinal extension while promoting the lateral bridging of the spikes and the smooth transition of the roots. This results in an organic form that has both a natural fusion boundary and a clear overall orientation feature.

[0102] Optionally, besides median-based smoothing, the smoothing of the voxel distance field can also employ Gaussian weighted convolution, bilateral filtering, or geometric diffusion methods based on curvature flow. This disclosure is not limited to any specific filtering strategy. For example, when it is necessary to preserve sharp ice crystal tips, bilateral filtering that preserves edge features can be used to smooth the sides of the spikes while avoiding excessive grinding of the sharp corners at the tips. When dealing with coral-like multi-branched structures, a curvature-adaptive filtering kernel can be introduced to automatically reduce the filtering influence range at bifurcation nodes with drastic curvature changes, and expand the smoothing range in the middle of branches with gentle curvature to promote a natural transition. Furthermore, the order of the above-mentioned expansion and smoothing processes can also be adjusted according to the actual art design requirements. A serial processing flow of expansion followed by smoothing can be used to ensure full volume integration, or an iterative method of alternating expansion and smoothing can be used to eliminate newly generated voxel noise immediately after each round of expansion, thereby obtaining a more delicate and controllable organic surface morphology in a multi-round progressive process.

[0103] Optionally, devoxization is used to restore the optimized voxel distance field to a continuous polygonal mesh, outputting a final geometric model with standard topology.

[0104] Optionally, the devoxification step can convert the regularized voxel distance field into a polygonal mesh representation using an isosurface extraction algorithm. This process is not limited to a specific mesh reconstruction strategy and can also adaptively adjust the facet density based on the distance field gradient. Specifically, in the region of spike tips with drastic curvature changes, the system can automatically increase the triangular facet subdivision density to accurately capture sharp geometric features; while at the base of the spikes and in the merging transition region, the number of faces can be appropriately reduced and coplanar triangle merging and small-angle edge folding optimization can be performed to control the output data scale while ensuring visual continuity. It should be noted that the devoxification process can also be combined with vertex normal smoothing and kerf repair strategies to eliminate the stepped defects and non-manifold edges caused by voxel discretization. This ensures that the reconstructed final geometric structure model not only has topologically correct and boundary-continuous closed surfaces, but can also be directly applied to the real-time rendering pipeline of game engines, film-grade offline lighting baking, or 3D printing slice path generation process without relying on additional material replacement effects, effectively connecting the downstream production links of digital content creation.

[0105] In an optional implementation, voxelization is performed on the structure with directional growth characteristics to obtain a voxel distance field. The voxel distance field is then dilated and smoothed, followed by inverse voxelization to generate the final geometric structure model. This includes: deleting intermediate attribute data from the structure with directional growth characteristics while retaining geometric position and topological information; converting the structure with retained geometric position and topological information into a first voxel distance field; performing a dilation operation on the first voxel distance field to obtain a second voxel distance field, in which structures are close to each other in voxel space. The dilation operation employs anisotropic dilation, with the degree of dilation in the growth direction being greater than that in the vertical direction; after smoothing the second voxel distance field, it is converted back to a polygonal mesh to obtain the final geometric structure model. In this way, anisotropic dilation causes the spikes to preferentially fuse along the guiding direction while remaining relatively independent in the vertical direction. This strengthens the coherence of the overall directional trend and avoids excessive lateral adhesion, significantly improving the organic hierarchy and structural readability of the final model. Figure 8 This is a schematic diagram of a final geometric structure model.

[0106] In practical applications, when the system acquires the spiked mesh after multi-layer extrapolation and normal sorting, it first removes intermediate data such as temperature attributes, initial growth attributes, and noise modulation parameters attached to vertices and faces, retaining only the vertex spatial coordinates and the topological index of the polygonal facets. Then, the cleaned mesh is converted into a first voxel distance field with a voxel size of 0.005, and anisotropic expansion is performed along the guiding direction—for example, expanding 2 voxel units along the tangent direction of the guiding curve in each iteration, while expanding only 1 voxel unit in the plane perpendicular to the tangent, thereby generating a second voxel distance field. After that, the field is smoothed and converted back into a polygonal mesh. Finally, each spike naturally connects into a ridge-like network along the guiding direction, while maintaining clear separation in the lateral direction, forming an organic surface structure with a clear sense of direction.

[0107] Optionally, anisotropic expansion performs directionally differentiated expansion on the oriented growth structure in voxel space, causing spikes to preferentially fuse along the guiding direction. Optionally, considering that the oriented spike structure, after multi-layer extrapolation, has a relatively consistent alignment along the guiding direction, if isotropic expansion is used, the spikes expand at the same rate in both the lateral and longitudinal directions, easily leading to premature adhesion of adjacent spike sidewalls, thus blurring the boundaries of individual spikes and losing directional hierarchy. As a possible implementation, the above-mentioned anisotropic expansion can establish a local coordinate system based on the guiding direction vector. In this coordinate system, the expansion kernel function is designed as an ellipsoid or an axially stretched cuboid, such that its semi-axial length or extension step length parallel to the guiding direction is greater than the corresponding dimension in the vertical direction. Furthermore, the above-mentioned expansion degree difference is not limited to a fixed ratio; it can also be dynamically adjusted according to the curvature of the guiding direction curve or the attenuation gradient of local temperature properties. In areas with large curvature or low temperature, the expansion difference ratio can be appropriately reduced to avoid excessive fusion and damage to local details. It should be noted that the above-mentioned guiding direction can be consistent with the guiding direction curve in the preprocessing surface generation step, or the user can re-specify an independent vector field in the post-processing stage. This disclosure does not limit its specific source.

[0108] Optionally, in another implementation of the anisotropic expansion described above, the spatial shape of the expansion kernel function, besides being ellipsoidal or a cuboid stretched along the axial direction, can also be a conical kernel function that gradually narrows along the guiding direction. This conical kernel function has a smaller transverse cross-section at the root and extends longer at the apex along the guiding direction, thus maintaining a compact aggregation at the root of the spikes in the region near the pre-treated surface, while allowing for more free fusion in the tip region far from the surface. In other words, the anisotropic expansion described above can not only be performed along a single fixed guiding direction vector, but can also dynamically adjust the expansion principal axis based on the mixed interpolation result of the local normal field and the guiding direction vector. In regions where the angle between the normal direction and the guiding direction is small, the expansion difference ratio is increased, while at locations where the angle is large or where topological abrupt changes occur, the expansion step size is contracted. It should be understood that the above dilation operation can be implemented using custom convolutional nodes of VDB (a sparse voxel data structure used to represent distance or density fields in three-dimensional space), or it can be directly reconstructed locally near the zero isosurface of SDF (signed distance field, which stores the signed distance from any point in space to the nearest surface; positive values ​​represent outside the surface, and negative values ​​represent inside the surface). This disclosure does not limit this approach. In this way, both the continuity of the macroscopic trend and the controllability of the microscopic topology can be taken into account.

[0109] Optionally, the first voxel distance field and the second voxel distance field correspond to the voxel states before and after expansion, to support staged directional fusion and geometric reconstruction.

[0110] Optionally, when converting the spike structure after normalization and multi-layer extrapolation into a voxel representation, it is necessary to clearly distinguish the distance field state before and after the dilation process so as to perform independent parameter control and state backtracking in subsequent steps. As a possible implementation, the first voxel distance field is directly obtained from the original spike mesh through voxelization, and its zero isosurface precisely corresponds to the initial geometric boundary of the spike surface. After performing anisotropic dilation on the first voxel distance field, the zero isosurface expands outward, and adjacent spikes approach each other or even partially overlap in the voxel space, thereby generating the second voxel distance field. Furthermore, the above two voxel distance fields can be stored as independent VDB (a sparse voxel data structure used to represent distance fields or density fields in three-dimensional space) data objects, or they can be embedded in the same data structure in the form of a time axis or hierarchical attributes. This disclosure does not limit its storage method. It should be noted that, in addition to direct voxelization conversion, the spike structure can also be baked into a high-density polygon mesh first, and then converted into the first voxel distance field through downsampling or adaptive subdivision to achieve a balance between accuracy and computational cost.

[0111] Optionally, intermediate attribute data can be deleted to clean up redundant information, retaining only geometric position and topological information to ensure the purity and stability of the voxelization reconstruction input.

[0112] Optionally, after the aforementioned steps, a large number of temporary scalar or vector attributes have accumulated on the mesh vertices and faces, such as temperature spread values, noise modulation coefficients, and normal deflection weights. If these attributes are directly input into the voxelization process without cleaning, some modeling platforms will write these attributes into the voxel data or cause an unnecessary increase in memory overhead during distance field calculation. As a possible implementation, the system can perform attribute filtering before entering the voxelization node, retaining only the three core geometric data types: vertex spatial coordinates, vertex normals, and face vertex index arrays. For normal attributes, if an implicit surface reconstruction algorithm is used in the subsequent voxel smoothing stage, the original normals can be further removed, retaining only the topological adjacency relationship, and the surface orientation can be recalculated from the voxelized distance field gradient. It should be understood that the above cleanup operation does not affect the final geometry, because at this stage, the macroscopic distribution and microscopic thickness of each spike have been completely determined through the previous steps. Deleting intermediate attributes is only to solidify the calculation results into a pure geometric description, thereby providing a minimum and sufficient input set for the VDB (a sparse voxel data structure used to represent distance fields or density fields in three-dimensional space) processing pipeline.

[0113] According to one embodiment of the geometric structure generation apparatus of this disclosure, such as Figure 9 As shown, the device may include: The acquisition module is used to acquire 3D models; The first determining module is used to mark the initial growth region on the surface of the 3D model and determine the corresponding initial growth attribute value; The second determination module is used to determine control attribute values ​​on the surface of the three-dimensional model based on the initial growth attribute values ​​through iterative diffusion calculations. The control attribute values ​​represent the extent to which each region is reached by the spread. The generation module is used to modulate the noise of the normal direction of the surface of the 3D model based on the control attribute value, and perform geometric extrapolation along the modulated normal direction to generate a geometric structure with thickness.

[0114] In this way, the control attribute values ​​are determined by iterative diffusion calculation based on the initial growth attribute values, and geometric extrapolation is performed in combination with the noise-modulated normal direction. This helps to generate geometric structures with real thickness and natural density decay on the model surface, improves the generation efficiency and morphological controllability of directional growth structures, and helps to reduce the data processing load in the process of generating complex geometry.

[0115] The specific details of each part of the above-mentioned device have been described in detail in the method section of the implementation plan. For any undisclosed details, please refer to the implementation plan of the method section, and therefore will not be repeated here.

[0116] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to exemplary embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0117] Figure 10 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this disclosure.

[0118] The following is a detailed reference. Figure 10 The diagram illustrates a structural schematic suitable for implementing an electronic device according to embodiments of the present disclosure. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 1201, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 1202 or a program loaded from memory 1208 into random access memory (RAM) 1203. The RAM 1203 also stores various programs and data required for the operation of the electronic device. The processor 1201, ROM 1202, and RAM 1203 are interconnected via a bus 1204. An input / output (I / O) interface 1205 is also connected to the bus 1204.

[0119] Typically, the following devices can be connected to I / O interface 1205: input devices 1206 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 1207 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 1208 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1209. Communication device 1209 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 10 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0120] In particular, according to one embodiment of this disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, one embodiment of this disclosure includes a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via communication device 1209, or installed from memory 1208, or installed from ROM 1202. When the computer program is executed by processor 1201, it performs the functions defined in the methods described above in various embodiments of this disclosure.

[0121] Figure 10 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0122] This disclosure also provides a computer-readable storage medium in which the methods described in this disclosure can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium after being downloaded over a network. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium may also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

[0123] A portion of this disclosure can be applied to computer program products, such as computer program instructions, which, when executed by a computer, can invoke or provide methods and / or technical solutions according to this disclosure through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, and installation package files. Accordingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions; the computer compiling the instructions and then executing the corresponding compiled program; the computer reading and executing the instructions; or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0124] Although embodiments of the present disclosure have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present disclosure, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for generating geometric structures, characterized in that, include: Obtain the 3D model; Mark the initial growth region on the surface of the three-dimensional model and determine the corresponding initial growth attribute value; Based on the initial growth attribute value, control attribute values ​​are determined on the surface of the three-dimensional model through iterative diffusion calculation. The control attribute values ​​represent the extent to which each region is reached by the diffusion. Based on the control attribute value, noise modulation is applied to the normal direction of the surface of the three-dimensional model, and geometric extrapolation is performed along the modulated normal direction to generate a geometric structure with thickness.

2. The method according to claim 1, characterized in that, Also includes: The normal direction of the geometric structure is directionally adjusted to deflect it toward a guiding direction, and polygon extrapolation is performed along the adjusted normal direction to generate a structure with directional growth characteristics; wherein the guiding direction is determined by a guiding direction curve or a guiding direction field.

3. The method according to claim 2, characterized in that, After obtaining the 3D model, the process also includes: Noise displacement deformation is applied to the surface of the three-dimensional model to obtain the deformed three-dimensional model. Obtain the guide direction curve, and extrude the guide direction curve along its direction into a thin-surface geometry; The deformed 3D model and the thin-faceted geometry are converted into voxel distance fields respectively. An expansion operation is performed on the voxel distance fields to merge the deformed 3D model and the thin-faceted geometry in voxel space. The merged voxel distance fields are then converted back into polygon meshes to obtain a preprocessed surface. The guiding direction curve is used to define the guiding direction.

4. The method according to claim 1, characterized in that, Marking the initial growth region on the surface of the three-dimensional model includes: A starting growth region is drawn on the surface of the three-dimensional model. The starting growth region includes a continuous planar region or a scattered point region. A corresponding initial growth attribute value is determined for the marked region, and the value of the initial growth attribute value ranges from 0 to 1.

5. The method according to claim 1, characterized in that, The process of determining control attribute values ​​on the surface of the 3D model based on the initial growth attribute values ​​through iterative diffusion calculations includes: The initial growth attribute value is converted into an initial control attribute value, wherein the initial control attribute value corresponding to the marked region is the maximum value, and the initial control attribute value corresponding to the unmarked region is zero. For each vertex, a neighborhood diffusion calculation is performed, and the control attribute value of the current vertex is fused with the control attribute values ​​of the neighboring vertices. During the diffusion process, noise modulation is applied to the diffusion rate. Perform a decay operation on the diffused control attribute values. When the control attribute value of a vertex is lower than a preset threshold, set the control attribute value of that vertex to 0.

6. The method according to claim 1, characterized in that, Before performing noise modulation on the normal direction of the 3D model surface based on the control attribute value, and then performing geometric extrapolation along the modulated normal direction, the method further includes: Obtain the mesh of the 3D model; The mesh is subjected to edge sharpening to increase the angle between the normals of adjacent faces; Obtain vertex-level control attribute values, and aggregate and promote these vertex-level control attribute values ​​to face-level attribute values; The aggregation enhancement adopts an arithmetic mean or weighted average method, and uses the arithmetic mean or weighted average as the face-level attribute value of the corresponding face. The face-level attribute value is used to control the extrapolation distance of the geometric extrapolation process.

7. The method according to claim 1, characterized in that, The step of modulating noise in the normal direction of the 3D model surface based on the control attribute value and performing geometric extrapolation along the modulated normal direction includes: Convert the control attribute values ​​into surface-level control attribute values; The surface-level control attribute values ​​are modulated by multiplication or addition using a spatial noise function to obtain modulated attribute values. The extrapolation distance of each face is determined based on the modulated attribute value, wherein the modulated attribute value is positively correlated with the extrapolation distance; Perform first-layer polygon extrapolation along the surface normal direction to generate the basic thickness structure; The second layer of polygons is extrapolated along the surface normal direction, where the extrusion distance of the second layer is smaller than that of the first layer, forming a multi-layered stepped transition structure at the top that is refined layer by layer.

8. The method according to claim 7, characterized in that, At least one of the first and second polygon extrapolation layers has an extrapolation direction that is a mixture of surface normals and point normals, wherein the mixture direction is a surface normal at the root and gradually transitions to a point normal direction at the top.

9. The method according to claim 2, characterized in that, The directional adjustment includes: obtaining the surface normal vector of the geometry; The surface of the geometry is smoothed to eliminate localized sharp noise; Determine the guiding direction vector based on the guiding direction; The normal vector of each vertex is progressively deflected toward the guiding direction vector, wherein the degree of deflection is controlled by a direction adjustment factor; Multiple rounds of directional adjustment operations are performed. In the first round, a larger radius of action is used to deflect the overall normal, and in the second round, a smaller radius of action is used to make fine adjustments to local details.

10. The method according to claim 9, characterized in that, The direction adjustment factor is a spatially varying adjustment factor field. A first adjustment factor is used in regions far from the guide direction curve, and a second adjustment factor is used in regions close to the guide direction curve. The first adjustment factor is greater than the second adjustment factor.

11. The method according to claim 2, characterized in that, Also includes: Obtain structures with directional growth characteristics; The structure with directional growth characteristics is subjected to voxelization to obtain the voxel distance field; Perform dilation and smoothing on the voxel distance field; The processed voxel distance field is devoxed to generate the final geometric structure model.

12. The method according to claim 11, characterized in that, The process of performing voxelization on structures with directional growth characteristics to obtain voxel distance fields, performing dilation and smoothing on the voxel distance fields, and then performing inverse voxelization to generate the final geometric structure model includes: Delete intermediate attribute data from the structure with directional growth characteristics, while retaining geometric position and topological information; The structure, which retains geometric position and topological information, is converted into a first voxel range field; An expansion operation is performed on the first voxel distance field to obtain a second voxel distance field. In the second voxel distance field, each structure is close to each other in the voxel space. The expansion operation adopts anisotropic expansion, and the expansion degree in the growth direction is greater than the expansion degree in the vertical direction. After smoothing the second voxel distance field, it is converted back to a polygonal mesh to obtain the final geometric structure model.

13. A geometric structure generation device, characterized in that, include: The acquisition module is used to acquire 3D models; The first determining module is used to mark the initial growth region on the surface of the three-dimensional model and determine the corresponding initial growth attribute value; The second determining module is used to determine control attribute values ​​on the surface of the three-dimensional model based on the initial growth attribute values ​​through iterative diffusion calculations. The control attribute values ​​represent the extent to which each region is reached by the diffusion. The generation module is used to perform noise modulation on the normal direction of the surface of the three-dimensional model based on the control attribute value, and to perform geometric extrapolation along the modulated normal direction to generate a geometric structure with thickness.

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