Real-time editing and rendering method and system for large-scale periodic lattice-like porous structures based on spherical tracking

Abstract

This invention discloses a method and system for real-time editing and rendering of large-scale periodic lattice porous structures based on spherical tracing. The method employs enhanced spherical tracing to perform enhanced spherical tracing on each pixel, thereby determining its appropriate color and achieving rendering. The enhanced spherical tracing method is an improvement on spherical tracing, including solving for the intersection information of rays with the solid and infill portions of the outer shell for each pixel based on a pre-calculated hierarchical bounding volume (BVH). Iterative spherical tracing is initiated, and in each iteration, the correction distance and tracing distance for ray propagation are calculated. Based on the correction distance, tracing distance, and the type of the required Boolean operation, the required distance value for spherical tracing is returned, thus completing ray projection and enabling pixel shading. This invention provides a method and overall framework integrating rendering, editing, and slicing, realizing an integrated additive manufacturing process from design to manufacturing of large-scale periodic lattice porous structures.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design (CAD) and computer-aided manufacturing (CAM) technology, and relates to a method and system for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking. Background Technology

[0002] Porous structures are complex structures containing numerous cavities. Due to their material-saving, lightweight, high surface area, and controllable physical properties, they play a crucial role in many fields such as materials science, aerospace technology, and biomedical engineering. Crystal lattices are porous structures composed of numerous interconnected rod-like structures. Their properties are easily controlled, and they possess high strength, making them one of the most popular porous structures in academia and industry. Periodic lattices are crystal lattices composed of periodically arranged units in space, and they are widely used in optical materials, aerospace, and other fields. Periodic lattices possess advantages such as excellent mechanical properties, high thermal conductivity, and ease of control. Their long-term order makes their physical properties (such as electronic band structure, thermal conductivity, and optical properties) more predictable, which is crucial for materials design.

[0003] Thanks to advancements in additive manufacturing (AM) technology, it has become possible to create shell lattices filled with complex crystal structures. Additive manufacturing employs various common processes, such as fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering (SLS), and selective laser melting (SLM). These additive manufacturing techniques all rely on the generation of model slices. When large-scale periodic lattices fill an explicitly represented shell to form a shell-lattice, efficiently generating slices at arbitrary angles presents a significant challenge. Furthermore, the ability to edit and visualize these complex shell lattices in real-time and efficiently on a computer is also a difficult problem.

[0004] The scale of crystal lattices that industry can currently handle is still limited. The U.S. Defense Advanced Research Projects Agency (DARPA) has also identified the handling of such large-scale crystal lattices as a major challenge in a report.

[0005] Conventional methods for visualizing and fabricating porous models in additive manufacturing can be broadly classified into two categories: (1) explicit representation of the workflow (e.g. Figure 1(a)(b) shown); (2) Implicit representation of workflow (such as Figure 1 (c) is shown.

[0006] Depending on the type of representation used in the modeling stage, explicit representation can be further divided into parametric surface-based representation and mesh-based representation. Typically, workflows using either of these representations generate results in stereolithography (STL) format during the final manufacturing stage, which are then used by the 3D printing module to generate slices.

[0007] The workflow for modeling lattice structures using parametric surface representation is as follows: Figure 1 As shown in (a), representative industrial software includes Autodesk Fusion 360, Altair Inspire, and Siemens NX. The advantage of this modeling approach lies in its ability to precisely control and represent shapes, enabling complex geometric modifications. However, for tasks involving large-scale lattices, it may suffer from high computational complexity and memory overhead: when performing Boolean operations or smooth transitions between lattices with numerous bars and other parametric models, it involves a large number of complex parametric surface intersection calculations; when there are hundreds of millions of bars, each bar typically requires multiple surfaces to represent it, and each surface requires a set of control vertex information.

[0008] Mesh is a relatively simpler explicit representation of lattice structures, with advantages including ease of use, editing, and rasterization pipeline rendering. However, this method also faces some challenges when dealing with large-scale lattice structures. The most widely used approach is the purely explicit workflow, whose process is similar to... Figure 1 As shown in (a), the input is uniformly a mesh. Representative software for this workflow includes 3DXpert, Materialise Magics, TRUMPF TruTops, Materialise 3-matic, and Autodest Netfabb. Similar to parametric surface modeling, the memory overhead of this method increases with the lattice size. Furthermore, solving for smooth transitions between mesh representations is relatively difficult.

[0009] To leverage the robustness and efficiency of implicit representation in Boolean and smooth transition operations, Figure 1(b) illustrates another workflow for outputting results in STL format. Its modeling process is based on implicit representation, specifying the model's boundaries through isosurfaces of a spatial scalar field. Its advantage lies in its ability to lightweightly represent complex models and supports robust, efficient Boolean and smoothing operations. Representative industrial software includes nTopology and ParaMatters. This workflow uses an implicitly input lattice structure and converts the shell to an implicit representation as well, then unifies the Boolean / smoothed transition results into STL format output. A common method for implicit-to-explicit representation conversion here is Marching Cubes. This workflow may require two format conversions, which incur additional memory overhead and typically reduce the model's detail. For large-scale periodic lattices, the final STL-represented lattice output will also consume significant storage resources.

[0010] Building upon this, the purely implicit workflow further avoids the conversion from implicit to explicit representation, directly generating slice results from the explicit representation. It has attracted considerable attention from researchers in recent years. The workflow is as follows: Figure 1 (c) shows that the representative software is VoxelDance. However, in real-world scenarios, most shell models are explicitly represented and often need to be converted to implicit representations. There are two common ways to do this conversion: (1) Use a discrete level set mesh and sample implicit function values ​​at the grid points (usually using a directed distance function). When using this level set, the implicit function value of the query point that is not at a grid point is the trilinear interpolation of the 8 nearest grid points. This method is usually not easy to balance between high model accuracy and low latency / memory overhead. (2) Calculate the implicit function value of the Mesh on the fly during rendering and slicing. The problem with this method is that the computational cost is usually high.

[0011] In summary, existing workflows for processing large-scale periodic shell-lattice structures rely heavily on the conversion between implicit and explicit representations. This conversion process often leads to reduced efficiency, high memory consumption, or decreased accuracy. Furthermore, some workflows do not uniformly consider the seamless integration of shell-lattice structures from rendering and editing to slicing. For example, some methods directly generate STL results and then hand them over to other slicing software; others do not provide real-time rendering of large-scale periodic lattices, but only generate slices.

[0012] In view of the above situation, this invention provides a software system and workflow that can reasonably handle large-scale periodic shell-lattices, such as... Figure 1As shown in (d), this workflow blends implicit lattices and explicit shells with minimal complex transformations, achieving seamless integration of shell-lattice from rendering and editing to slicing. Summary of the Invention

[0013] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for real-time editing and rendering of large-scale periodic lattice porous structures based on spherical tracking. This method enables real-time editing of additive manufacturing periodic lattice porous structure models, and allows for rendering or slice generation.

[0014] The technical solution adopted in this invention is as follows:

[0015] A real-time editing and rendering method for large-scale periodic lattice-like porous structures based on spherical tracing includes:

[0016] Determine the shell parameters and periodic lattice control parameters C for the parts requiring porous structures to be rendered in additive manufacturing. l The outer casing includes an unfilled solid portion M. s and the filling portion M that needs to fill the periodic lattice f ;

[0017] An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel to determine the color it should display and achieve rendering. The enhanced spherical tracing method is an improvement on spherical tracing. It includes solving the intersection information of the light rays with the solid part and the filling part in the shell of each pixel according to the pre-calculated hierarchical bounding volume (BVH), starting spherical tracing iteration, calculating the correction distance and tracing distance of the light rays in each step of the iteration, and returning the distance value required for spherical tracing according to the correction distance, tracing distance and the type of Boolean operation required, thereby completing the ray projection and enabling pixel shading.

[0018] In the above technical solution, before calculating the correction distance of the light propagation, the set of rods contained in the unit cell defined in the periodic lattice control parameters is subjected to rod enhancement processing to obtain the enhanced and expanded set of rods in each background grid hexahedral unit, and the directed distance SDF value of the unit is determined.

[0019] Furthermore, the rod reinforcement process specifically includes:

[0020] For the set of rods contained within a defined unit cell, B = {B[i], i = 1, ..., n} b Let N[i,j] represent the two nodes of rod B[i], so j = 0, 1, and the rod is a capsule-shaped rod with hemispherical surfaces at both ends;

[0021] Traverse all nodes N[i,j] in the unit cell, considering the relationship between the nodes and the vertices, edges, and faces of the hexahedral elements. First, check if any vertex is located within the sphere corresponding to N[i,j]. If so, all 8 elements surrounding that vertex participate in the rendering of B[i], expanding B[i] to the other 7 vertices within the element. Next, check if any edge intersects the sphere corresponding to N[i,j]. If so, the 4 elements surrounding that edge participate in the rendering of B[i], expanding B[i] to the other 3 parallel edges within the element. Finally, check if any face intersects the sphere corresponding to N[i,j]. If so, the 2 elements on either side of that face participate in the rendering of B[i], expanding B[i] to the position of the face facing that face within the element. This yields the set of all rods within the hexahedral element after expansion. The SDF value F of this unit b that is The minimum SDF value of all rods in the middle.

[0022] Furthermore, the query point P located at any unit cell position in the crystal lattice... g Mapped to query point P within the unit cell l In the middle, it is:

[0023] P l =(P g -V min )%S-0.5·S

[0024] Where V min is the smallest coordinate of the generated unit cell, % is the remainder, and S is the unit cell size;

[0025] By querying the point mapping, at P g The SDF value of the cell containing it can be found at:

[0026] F b (P g ) = F b (P l )

[0027] The mapping of the query point from a certain unit cell to the unit cell, and the mapping of the bar of the unit cell from the unit cell to the global array, generate the SDF value F in each iteration of spherical tracing. b They are equal;

[0028] A distance correction algorithm is used to correct the SDF value obtained in a single cell to a forward distance that is safe for the entire lattice; the distance correction algorithm is specifically as follows:

[0029] When a ray of light enters a new cell, it must first pause at the boundary shared by the current cell and the new cell and then proceed a very small distance. t Add ∈ to the distance the light travels to the boundary.t That is, the corrected distance, where ∈ t The threshold value ∈ is taken as equal to the termination threshold of spherical tracing; wherein the distance for the ray to reach the boundary is the minimum forward distance required for the ray to hit the plane containing the boundary from three directions, and the specific method for calculating these three forward distances is as follows:

[0030] For each of the three coordinate axes, calculate the distance required to move from the query point to the plane containing the cell boundary that is perpendicular to the axis and located in the positive direction of the axis. If the distance is less than 0, then calculate the distance required to move to the boundary plane that is perpendicular to the axis and located in the negative direction of the axis.

[0031] Furthermore, construct M s and M f For each ray's BVH, solve for the ray's M. s and M f The intersection information, where: for M s Only the first intersection point is recorded; the face that is hit is denoted as I. s Its distance from the camera is t s For M f All intersection points need to be recorded, and the surfaces intersecting with the light rays should be sorted in ascending order of distance and recorded in list I. f The corresponding distances are recorded in list t. f ;

[0032] t s and t f Convert these to distances for spherical tracking, specifically: for t s The conversion method is to return an infinite value when there is no intersection to allow the tracing to end quickly, and to return an infinite value when there is an intersection but the query point is in M. s In addition, return the distance from the query point to the next intersection point; for t f The conversion method is that when the query point is M f In addition, return the distance from the query point to the next intersection point, when the query point is at M. f In or when leaving M f Staying at M f On the surface, it returns to negative infinity, as the light is about to enter M. f Staying at M f On the surface, return a value slightly smaller than the termination threshold ∈ of the spherical tracing.

[0033] Furthermore, a pruning method is used to traverse the BVH, where:

[0034] For M s BVH traversal: When selecting two child nodes, always prioritize the child node closer to the ray's origin and discard the child node whose nearest distance to the camera is greater than the current t.s Nodes;

[0035] For M f BVH traversal: any object whose nearest distance to the camera is greater than t s All nodes were discarded directly;

[0036] Furthermore, considering that the camera is from M f For nodes originating from within the system, where the maximum signed distance to the camera is less than 0, for M... s and M f During BVH traversal, all values ​​are directly discarded.

[0037] Furthermore, based on the method, slices of the model in additive manufacturing can be generated by adjusting the rendering pipeline. The adjustment includes making all light rays originate from pixels and be perpendicular to the view plane, making the distance between the far plane and the near plane equal to the slice thickness, and making the near plane coincide with the view plane.

[0038] A real-time editing and rendering system for large-scale periodic lattice-like porous structures based on spherical tracing, used to implement the method described in any of the above-mentioned embodiments, comprising:

[0039] Large-scale processing modules, using the control parameters C of periodic lattices l As input, the corrected distance is obtained through rod enhancement and correction of local distances, which is used to complete the rendering of the entire lattice by querying only the SDF within a single cell;

[0040] Hybrid rendering module, using the solid part M in the shell parameters s and filling part M f As input, it is used to simultaneously render the implicitly represented lattice and the explicitly represented shell without representation conversion, to obtain the tracking distance for spherical tracing; and returns the distance value required for spherical tracing based on the correction distance, tracking distance, and the type of the required Boolean operation, for rendering.

[0041] Furthermore, the system also includes extension modules for implementing smooth transitions at connections, lattice field-guided properties, lattice deformation, and region-specified unit cell types to cater to a wider range of practical applications.

[0042] A computer-readable storage medium having a program stored thereon, the program being executable by a processor to implement the method as described in any of the preceding claims.

[0043] The beneficial effects of the present invention are:

[0044] This invention provides a method and overall framework for rendering, editing, and slicing large-scale periodic lattices in the modeling of porous components for additive manufacturing. It achieves an integrated workflow from design to manufacturing of large-scale periodic lattice porous structures, facilitating the additive manufacturing process. In particular, this method can correctly render the entire lattice by querying only the SDF within a single unit cell, greatly improving rendering efficiency. In tests, it achieved real-time rendering for large-scale lattices and can efficiently render the results of implicit and explicit representations after Boolean operations without representation conversion, avoiding the huge memory overhead, time cost, and loss of detail caused by representation conversion. Attached Figure Description

[0045] Figure 1 A comparison of the conventional process (a)(b)(c) and the hybrid process (d) of the present invention for processing periodic lattice-filled shell-lattice structures;

[0046] Figure 2 This is a schematic diagram of the method flow of the present invention;

[0047] Figure 3 The diagram shows the distance correction algorithm, where (a) and (b) are the spherical tracking process and results without distance correction, and (c) and (d) are the spherical tracking process and results with distance correction.

[0048] Figure 4 The diagram illustrates the Boolean operations in hybrid rendering, where (a) represents the process of post-processing Boolean intersection using Algorithm 3; (b) represents the process of post-processing Boolean union using Algorithm 4; (c) represents the process of processing Boolean intersection using traditional spherical tracing; and (d) represents the process of processing Boolean union using traditional spherical tracing.

[0049] Figure 5 To simultaneously apply internal smoothing and external smoothing to rendering results under different unit types commonly used in industry;

[0050] Figure 6 Example diagrams showing the slicing results generated along different directions for a lattice-filled model;

[0051] Figure 7 The diagram shows the overall composition of an assembly model after some parts are filled with a lattice and a partial rendering using the method of this invention; in (c), the total number of bars contained in the lattice is approximately 5.686 billion. Detailed Implementation

[0052] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] In the field of additive manufacturing, the challenges of real-time editing / rendering of large-scale periodic lattice-filled structures often include: 1) How to efficiently render large-scale internal periodic lattices and provide real-time feedback after the lattice properties are modified by the user, generating the modified results; 2) How to efficiently render the results after the Boolean / smooth transition of the implicit lattice and the explicit shell, maintaining the details of the lattice and shell themselves while considering memory and efficiency; 3) How to support the expansion of lattice properties while solving the above two challenges, such as smooth blending, field-guided property distribution, deformation, etc.; 4) How to generate slices consistent with the rendering for the above large-scale periodic lattice-filled structures, achieving seamless integration of editing, rendering, and slicing.

[0054] To address the aforementioned challenges, this invention proposes an Augmented Sphere Tracing (AST) method to support real-time rendering and editing of large-scale periodic lattice-filled structures (Shell-lattice). AST supports both implicit and explicit inputs while minimizing complex representation transformations. This method does not actually generate the complete model structure of the Shell-Lattice, but it achieves high-fidelity rendering results with correct Boolean relationships in screen space, along with corresponding slices for fabrication. The overall workflow is as follows: Figure 1 As shown in (d).

[0055] The present invention provides a real-time editing and rendering method for large-scale periodic lattice-like porous structures based on spherical tracking, such as... Figure 2 As shown, it includes:

[0056] Determine the shell parameters and periodic lattice control parameters C for the parts requiring porous structures to be rendered in additive manufacturing. l The outer casing includes an unfilled solid portion M. s and the filling portion M that needs to fill the periodic lattice f ;

[0057] An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel to determine the color it should display and achieve rendering. The enhanced spherical tracing method is an improvement on spherical tracing. It includes solving the intersection information of the light rays with the solid part and the filling part in the shell of each pixel according to the pre-calculated hierarchical bounding volume (BVH), starting spherical tracing iteration, calculating the correction distance and tracing distance of the light rays in each step of the iteration, and returning the distance value required for spherical tracing according to the correction distance, tracing distance and the type of Boolean operation required, thereby completing the ray projection and enabling pixel shading.

[0058] Specifically:

[0059] 1. Overall framework of the plan

[0060] This invention considers a periodic lattice L(C) extending infinitely in three orthogonal directions. l The model obtained by filling the Mesh shell M, where C l These are the control parameters for the crystal lattice. The outer shell M = M f ∪M s ,satisfy Where M s This indicates the unfilled portion of the entity, while M... f The filling portion is represented by two elements, both of which are watertight and manifold. Therefore, the target's Shell-Lattice structure is represented as:

[0061] Ω(C l M)=L(C l )∩M f ∪M s (1)

[0062] This invention considers L(C) l This solution addresses highly complex models (containing hundreds of millions of links) and aims to solve the real-time editing / rendering of such complex models, as well as the generation of corresponding slices. Real-time editing is specifically manifested in the ability to edit and render complex models whenever C... l The parameters are modified, and the corresponding Ω is immediately rendered on the screen. C l The specific details are shown in Table 1.

[0063] Table 1C l Symbols and meanings of included parameters

[0064]

[0065]

[0066] The system framework provided by this invention can generally include three major modules: a large-scale processing module, a hybrid rendering module, and an extension module.

[0067] The large-scale processing module supports efficient rendering of periodic lattices with billions of bars and arbitrary cell types. It includes a user-friendly set of cell definition rules and two algorithms: a bar enhancement algorithm and a distance correction algorithm. This module maps global query points to query points within the cell, enabling correct lattice rendering even when considering only individual lattice information each time.

[0068] The hybrid rendering module is responsible for rendering the results of the explicit shell and the implicit lattice Boolean without performing model transformation. It first constructs a Bounding Volume Hierarchy (BVH) for the Mesh, and then performs ray-triangle intersections based on this BVH during the rendering of each frame. Finally, it extracts distance values ​​usable in the spherical tracing process for each iteration based on the intersection point sequence. This module also includes methods for pruning this BVH.

[0069] In addition to these two core algorithm modules, this invention also includes an extension module for broader practical applications. Slicing is achieved through fine-tuning the rendering pipeline; internal blending is achieved by limiting the blending function to a single unit; internal and external blending uses a fixed low-resolution level set during the rendering stage; field-guided attributes, deformation, and region-specified unit types are achieved by adjusting unit and query point attributes when calculating SDF values.

[0070] 2. Core Methodology

[0071] The two core modules of the AST algorithm proposed in this invention are a large-scale processing module and a hybrid rendering module. In each iteration of spherical tracing, these two modules generate the corrected distance and the tracing distance, respectively. These two distances are not exact SDF values, but they can be used like SDF values ​​during spherical tracing by taking the maximum / minimum values ​​to perform Boolean intersection / union operations.

[0072] 2.1 SDF query within a single cell

[0073] Accurately calculating the SDF value within a single cell is fundamental to large-scale processing modules. Here, let the set of bars contained in the user-defined unit cell be B = {B[i], i = 1, ..., n}. b Let N[i,j] represent the two nodes of rod B[i], therefore j = 0, 1. Without loss of generality, the algorithm assumes that the range of each coordinate component of a node is: N[i,j] ★ ∈[-1,1], where *=x,y,z. The SDF value of link B[i] at query point P is

[0074] F b,i (P)=F l,i (P)-r, (2)

[0075] Where F l,i (P) represents the distance from P to the line segment defined by N[i,0] and N[i,1], while r is the radius of the rod.

[0076] However, considering only user-defined bars within a unit cell is insufficient for rendering the entire cell, because some bars in adjacent cells may expand beyond their original cell and enter that cell, but these are not calculated. Specifically, such bars occur when:

[0077]

[0078] Based on the above observations, this invention provides a method that can fully consider all intersecting bars only when querying the current unit cell. The specific process is shown in Algorithm 1.

[0079] Algorithm 1 is as follows:

[0080] Iterate through all nodes N[i,j] in the cell, considering the relationships between the nodes and the vertices, edges, and faces of the hexahedral cells. First, check if any vertex lies within the sphere corresponding to N[i,j]. This is done by comparing the distance between node N[i,j] and the vertex of the cell in its quadrant with the radius r. If it is, then a vertex lies within the sphere corresponding to N[i,j], and all 8 cells surrounding this vertex participate in the rendering of B[i]. Therefore, B[i] is expanded to the other 7 vertices within the cell (lines 4-16). Next, check if any edge intersects the sphere corresponding to N[i,j]. This is done by comparing the distance between node N[i,j] and the 12 edges of the current cell, checking if any of them is less than the radius r. If so, the 4 cells surrounding this edge participate in the rendering of B[i]. Therefore, B[i] is expanded to the other 3 parallel edges within the cell (lines 18-35). Finally, check if any face intersects the sphere corresponding to N[i,j]. The method for checking is to compare the distances between node N[i,j] and the six faces of the current cell, and see if any of the distances is less than r. If so, the two cells on both sides of the face will participate in the rendering of B[i], so B[i] is expanded to the position of the face object within the cell (lines 39-46).

[0081] In the output of Algorithm 1 Then, the SDF value of this cell (denoted as F) b )that is The minimum SDF value of all rods, i.e.:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] 2.2 Local Distance Correction

[0088] Next, we will explain how to query the distance of the entire lattice at a given query point, which can be used for spherical tracing.

[0089] Directly calculating the SDF of a lattice requires considering all members, resulting in unacceptable computational complexity. Common solutions utilize cell locality, limiting the distance query to the nearest 27 cells, or further consider the relative position of the query point within the cell, limiting the calculation to the nearest 8 cells. However, this invention proposes a method that only requires considering a single cell.

[0090] Based on the distance lookup method for the unit cell in section 2.1, this invention establishes a mapping between arbitrary unit cells and the unit cell. Specifically, this invention maps the lookup point (denoted as P) located at any unit cell position in the lattice. g The mapping is to the query point within the unit cell (denoted as P). l In, rather than mapping the rods of the unit cell to other unit cells:

[0091] P l =(P g -V min )%S-0.5·S, (5)

[0092] Where V min It represents the minimum coordinates of the generated unit cell, and % indicates the remainder.

[0093] By querying the point mapping, at P g The query for the SDF value of the cell containing the given information is as follows:

[0094] F b (P g ) = F b (P l (6)

[0095] This equation can be interpreted as mapping the query point from a certain unit cell to the unit cell, and mapping the bar of the unit cell from the unit cell to the global coordinates, resulting in F in each iteration of spherical tracing. b They are equal.

[0096] Due to F b (P g Considering only a single unit cell, which is not the exact SDF of the entire lattice, such as... Figure 3 As shown in (a). When the total volume of the rods within the unit is small and their distribution is not uniform, F b (P g This might represent an excessively large distance, causing light rays to either be lost or enter the beam they should be rendering after traveling that distance, resulting in rendering errors, such as... Figure 3As shown in (b).

[0097] To address this problem, this invention proposes Algorithm 2 to reduce potentially overly aggressive distances to just safe levels. For example... Figure 3 As shown in (c), the basic idea is that when light enters a new unit, it must first stop at the common boundary between the current unit and the new unit and then advance a very small distance ∈ t Calculate the three possible travel distances required for the ray to hit the cell boundary (lines 3-13), and take the minimum of these (lines 6 and 10). ∈ t This ensures that light enters the next unit; if the light source is too large, it will largely fail to solve the aforementioned problem, while if it is too small, the unit boundaries will be rendered incorrectly. In this invention, ∈ t It is taken as equal to the termination threshold ∈ of spherical tracing.

[0098] The final rendered result is as follows Figure 3 As shown in (d).

[0099]

[0100] 2.3 Hybrid Rendering Module

[0101] The hybrid rendering module can simultaneously render implicit (SDF) lattice representations and explicit (Mesh) shell representations without representation conversion, correctly conveying Boolean relationships. This is achieved by replacing the SDF values ​​of the mesh with aggressive yet safe tracing distances.

[0102] Given M s and M f Each of their respective BVHs is built separately before the rendering pipeline is started. Hybrid rendering consists of two steps: (1) calculating the intersection of the ray and the mesh before spherical tracing begins; and (2) extracting the forward distance from the intersection as input for each iteration of spherical tracing.

[0103] In the first stage, this invention uses the standard BVH traversal process in ray tracing to obtain the intersection points of rays and meshes. For M s The algorithm only records the first intersection point because light rays never enter the solid shell. The hit face is denoted as I. s Its distance from the camera is t s In contrast, for M f The algorithm needs to record a large number of intersection points because the porous structure makes M... f The face that is first hit by the ray may also be seen. The algorithm sorts these intersecting faces in ascending order of distance and records them in list I. f The corresponding distances are recorded in list t. f .

[0104] In the second stage, the present invention will t f and t s The distances are converted into distances suitable for spherical tracking, as given by Algorithms 3 and 4 respectively. These two algorithms allow the Boolean operations for intersection / union to be directly obtained by taking the maximum / minimum value of the input distance.

[0105]

[0106]

[0107] In Algorithm 3, whenever a ray is about to enter or temporarily leave the mesh, the algorithm guides the ray to the next intersection (line 4). When a ray hits a face while in the mesh or leaving the mesh, the algorithm returns a negative number with a large absolute value (lines 6 and 13). When a ray hits a face before entering the mesh, the algorithm returns the normal of the face and records it, while also returning a value slightly less than ∈ (lines 10 and 11). Considering the camera is from M... f In the special case of starting from the inside, the algorithm takes n into account when making the internal and external judgments (lines 3 and 9).

[0108]

[0109]

[0110] Algorithm 4 is more straightforward: when there are no intersections, the algorithm returns a large value to quickly end the tracing (lines 1-2). When the ray has not yet entered the mesh, the algorithm quickly guides it to the first intersection (lines 3-4).

[0111] Figure 4 The operating principles of these two algorithms are demonstrated. Their efficiency is reflected in two aspects: (1) the number of spherical tracing iterations is greatly reduced, especially near the Mesh surface; (2) the time for each iteration is also greatly reduced compared to the method of accurately calculating the SDF of the Mesh during the iteration process.

[0112] Besides efficiency, another advantage of this algorithm is its precise preservation of detail. Some discrete transformation methods, such as Marching Cubes or sampled level sets, lose these details, especially sharp features such as corners / edges.

[0113] 2.4BVH Pruning

[0114] For the BVH used in 2.3 above, this invention provides a method for pruning it during traversal.

[0115] For Ms The pruning strategy of this invention is as follows: (1) When selecting two child nodes, always prioritize selecting child nodes that are close to each other; (2) Discard the child node whose nearest distance to the camera is greater than the current t. s The node.

[0116] And for M f The situation is different here, because all the points where it intersects with the light rays can be visible. Therefore, M f The traversal of t f Come and prune. But thanks to M s The existence of, and Based on this premise, the present invention proposes to use t s Come to prune M f I s and t s Will precede I f and t f Computed. When traversing M f At BVH, any distance to the nearest camera greater than t s All nodes were discarded directly.

[0117] Considering the camera from M f In the case of internal origins, this invention also prunes nodes whose maximum (signed) distance to the camera is less than 0. For M, these nodes... s and M f They were all discarded directly.

[0118] 3 expansion modules

[0119] The extension module enables the invention to support more lattice types for practical application scenarios, based on the core algorithm module.

[0120] 3.1 Smooth transition.

[0121] In lattice fabrication scenarios, appropriate smoothing provides better physical properties compared to direct Boolean energy. Smoothing here includes two categories: (1) internal smoothing, i.e., smoothing between bars; and (2) internal-external smoothing, i.e., smoothing between the lattice and M. f Smoothing between complementary spaces.

[0122] 3.1.1 Internal Smoothing

[0123] Smoothing between SDFs simply requires replacing the Boolean max and min operations with the corresponding smoothing functions. This invention chooses the KS function because it supports multiple inputs and is independent of the input order. Consistent with the method in 2.2, this invention utilizes cell locality to compute smoothing only within a single unit cell:

[0124]

[0125] Where p represents the smoothing term, the smaller the value, the greater the smoothness.

[0126] This method introduces minimal overhead on top of the original rendering and does not cause problems in most scenarios, but may produce discontinuous results when the following two conditions are met: (1) p is too small, that is, the smoothness is too great; (2) the symmetry constraint is not satisfied, that is: when the lattice units are connected in the * direction, the rods in each cell must be symmetrical about the plane perpendicular to the * direction and passing through the center of the cell.

[0127] This internal mixing works very effectively when neither of the above two conditions is triggered or only one condition is triggered. Most of the cells used in periodic lattices in industrial settings do not satisfy condition (2), such as... Figure 4 As shown. This means that in most cases, the present invention can use high-intensity smoothing on the elements. For cases where symmetry is not satisfied, the present invention provides a range of p that will not cause significant discontinuities in most cases: p ≥ 30 / S★.

[0128] 3.1.2 Internal and external smoothing

[0129] Although the present invention provides a tracking distance for a spherical tracing that can be completed without calculating the SDF of the mesh in section 2.3, this distance cannot be used for inner and outer smoothing because the smoothing function requires the input to be SDF.

[0130] To address this issue, this invention proposes using a pre-sampled level set with a fixed and low resolution, based on the fact that smoothing operations inherently eliminate model details. While the level set method struggles to balance satisfactory detail with memory overhead, the intersection operation proposed in section 2.3 is responsible for preserving all the details of the mesh. This invention increases L(C) by... l But retain M f The internal and external smoothing is achieved by keeping the resolution constant. This invention utilizes a resolution fixed at 128. 3 The level set, whose precise SDF values ​​are pre-sampled at the grid points.

[0131] Let the level set be The mixing function is F ∪I and The negative space, that is, For input. It is obtained by performing trilinear interpolation on the eight grid points surrounding the query point.

[0132] Figure 5 The camera was shown from M fThe rendering results, obtained from the internal model, are a blend of internal and external rendering. The cells used in the test are typical cells widely used in the field of additive manufacturing. Although the results are visually satisfactory, they are not entirely accurate due to the use of level sets. This invention eliminates this error in the final slicing stage.

[0133] 3.2 Replication with Changes

[0134] In addition to a conventional periodic lattice where all units are exactly identical, this invention can also support repetitions with differences and variations between units. The control parameters for these variations can be modified in real time.

[0135] To ensure continuity between adjacent units, changes need to be applied in groups. Each group contains multiple links, and a link belongs to only one group. Users can freely specify groups, but to ensure continuity, this invention recommends that links connected to each other at nodes be placed in the same group. Furthermore, links generated by the link enhancement algorithm are always in the same group as the original links.

[0136] 3.2.1 Field Guidance Attributes

[0137] In practical industrial applications, some physical parameters of porous models are typically specified by a global field. These fields usually come from simulation or modeling results and contain the physical properties that the filled model should satisfy. In the algorithm of this invention, each query point only needs to focus on the attribute values ​​within a local range.

[0138] This section uses a trigonometric function field as an example to describe the method for rendering field-guided attributes in this invention. Field-guided attributes include field-guided triples and field-guided scalars. Given a global query point P... g The ★ component of the field-guided triplet attribute is:

[0139] T tri (v ★ ,P g ;A,ω,φ)=v ★ +v ★ Acos(ωP g,＊ +φ), (8)

[0140] Where v, A, ω, and φ are the original triplet, amplitude, frequency, and phase, respectively. Taking v as the original scalar, the field-guided scalar is:

[0141]

[0142] Where A, Ω, and Φ are triplets representing amplitude, frequency, and phase, respectively.

[0143] In this invention, the radius / internal smoothness of the field guidance is obtained by directly applying a scalar of the field guidance to the radius / smoothing coefficient, denoted as T. sca(r,P g ) and T sca (p,P g The rendering result of field-guided rendering only requires replacing the original scalar with the field-guided scalar when calculating the SDF value during the rendering process. Since the radius of the field guide may cause rods that originally did not intersect with the cell boundary to now intersect with the cell boundary, when using the field guide attribute, r in lines 4, 20, and 40 of Algorithm 1 should be replaced with r(1+A). max ).

[0144] The cell size for field guidance simply requires replacing the cell size S in formula (5) and algorithm 2 with T. tri (S,P g In this process, each query point believes it is rendering a lattice with a constant cell size, but in reality, the constant size used by each query point is different. If the field changes too drastically, rendering errors may occur due to the light rays traveling too rapidly. This can be resolved by applying an attenuation factor to the distance the light rays travel.

[0145] 3.2.2 Lattice Deformation

[0146] Deformable periodic lattices broaden the geometric constraints of conventional periodic lattices, thereby satisfying a wider range of physical and aesthetic requirements. In deformable periodic lattices, different transformations are applied to each volume element, rather than at the node centers. This invention incorporates two distinct deformations: twisting and bending.

[0147] For ease of representation, R(ψ(P) is used here. g ) represents a function that returns a rotation matrix, corresponding to a rotation angle of ψ(P). g This matrix acts on the lattice, and the same effect can be achieved by applying R(ψ(P) to the query point. g )) -1 We have obtained the information. The description of the axis of rotation is omitted here because it is not the key point of the problem.

[0148] Torsion is a deformation at the rod level that maintains the position of each unit. In this invention, to achieve the tortuous effect, R(ψ(P) g )) -1 Acting on local query point P l superior:

[0149] P l ′=R(ψ(P g )) -1 P l (10)

[0150] To achieve the bending effect, R(ψ(P) g)) -1 Acting on global query point P g superior:

[0151] P′ g =R(ψ(P) g )) -1 P g (11)

[0152] The rotation angle can be a function related to the query point; for example, it can be proportional to some component of the query point.

[0153] ψ(P g )=αP g,★ (12)

[0154] Where α is a variable that the user controls to determine the deformation effect.

[0155] 3.3 Area-Specified Cell Type

[0156] This invention provides a method for supporting different unit cell types by specifying cell replication rules. This extension improves lattice diversity without introducing excessive overhead.

[0157] Cell replication rules are typically specified based on the cell index. For example, a user can specify that cells with an odd sum of indexed components use cell type A, while cells with an even sum use type B. For a given query point P... g The index of its cell is:

[0158]

[0159] To ensure structural integrity, the bars obtained by the bar reinforcement algorithm are also copied into other unit cells. Additionally, users need to ensure that different element types are continuous at adjacent boundaries.

[0160] 3.4 TPMS Structure

[0161] Although this invention is specifically designed for periodic lattices, the hybrid rendering module can also accept many other types of porous structures as input.

[0162] A typical example is the Triply Periodic Minimal Surface (TPMS). Two common TPMS types are introduced here: Primitive (P) and Gyroid (G), which are defined as follows:

[0163] I P (P)=cos(X)+cos(Y)+cos(Z)+b, (14)

[0164] I G (P)=sin(X)cos(Y)+sin(Z)cos(X)+sin(Y)cos(Z)+b, (15)

[0165] Where X = Θ x P x Y = Θ y P y Z = Θ z P z , b are isosurface constants. This invention considers the TPMS as a single, holistic structure, rather than embedded within tetrahedral elements. Because I P and I G It is not a standard SDF in nature. This invention multiplies the TPMS function value by a decay factor during rendering to obtain a relatively conservative forward distance.

[0166] 3.5 Slice Generation

[0167] The slice generation method of this invention is based on a rendering framework, retaining almost all the steps of rendering, requiring only a few limited modifications:

[0168] (1) The perspective projection used for rendering is changed to orthographic projection; in perspective projection, all light rays originate from the camera and radiate outward through different pixels of the image plane. In orthographic projection, all light rays originate from the pixels and are perpendicular to the view plane.

[0169] (2) The far plane is no longer located far behind the scene, but is very close to the near plane, with the distance between them being the thickness of the slice. In addition, the near plane is no longer located behind the view plane, but coincides with the view plane.

[0170] (3) When the inside and outside are smoothly opened, M f The SDF value is no longer approximated by the low-resolution level set, but instead reuses the M... f The BVH is calculated in real time during slicing.

[0171] (4) The width of the slice will be adjusted according to the height specified by the user so that its object boundary is consistent with the picture boundary, thereby improving the pixel capture rate.

[0172] (5) All calculations regarding face normals and shading have been removed.

[0173] Figure 6 The diagram shows a subset of slices generated using the method of this invention under different slicing orientations. The cell type is Body-centric Cubic.

[0174] The system provided by this invention includes: a hybrid rendering module, a large-scale rendering module, and an extension module. The first two modules are the core modules of the algorithm. The hybrid rendering module uses shell data M... s and M f As input, the large-scale rendering module uses lattice parameters C l The input consists of two modules, which output the tracking distance and the correction distance, respectively, for the spherical tracking process, thus forming the enhanced spherical tracking method proposed in this invention. Each pixel, after passing through the enhanced spherical tracking process, reveals its intended explicit color, thereby forming a rendered frame or slice. The third module, the extension module, primarily functions in the large-scale rendering module, influencing the calculation of the SDF value to support various practical application scenarios. According to an example of this invention, the solution is implemented based on WebGPU, with the program containing both CPU and GPU ends. The CPU end is implemented using Typescript and the VUE3 front-end framework, primarily responsible for user interaction through UI components, translating user input into lattice configuration parameters for input to the GPU end, invoking rendering tasks, and drawing the GPU rendering results onto the Canvas component of the webpage. The GPU end, implemented based on WebGPU, is responsible for pixel-level parallelism, i.e., each thread is responsible for drawing a single pixel.

[0175] All pixel-level algorithms run on the GPU, including Algorithms 2, 3, and 4, as well as all their extensions. These algorithms run in real-time during rendering. Algorithm 1, on the other hand, runs on the CPU, implemented directly using TypeScript. This design is because Algorithm 1 has low parallelism and doesn't need to be called every time a frame is drawn. The construction of the BVH and the low-resolution level set are pre-compiled, not calculated in real-time. Complex data, such as M... s and M f Data such as vertex and face representations, rod sets, and BVH (Browser-Vehicle-Head) are stored using WebGPU's storage type memory. Lightweight data, such as configurations other than rod sets in Table 1, camera parameters, and model transformation parameters, are stored using uniform type memory. This is because storage memory supports larger databases but is relatively inefficient; while uniform type memory is more efficient but has smaller capacity and requires data to strictly adhere to certain format requirements.

[0176] Whenever a user modifies a lattice property, such as radius, cell size, field parameters, or changes the viewpoint or moves the model, the Vue 3 framework captures this modification through a listening mechanism and instructs the renderer to send the updated data to the GPU, then sends a command to draw the new frame. When a user modifies Table 1, it does not trigger a recompilation of the shaders, nor does it require a complex preprocessing process.

[0177] The CPU portion is relatively simple; it acts as a bridge between the user and the GPU module, responsible for informing the GPU of user-edited information and displaying the GPU's calculation results to the user. Specifically, in this invention, all configuration information regarding the lattice is managed through a global Hooker. When the user modifies component data (e.g., text components, slider components, checkbox components, etc.), the global state changes accordingly. The renderer object maintains a series of listeners for these global states (configurations). Each listener is responsible for listening to a single piece of data or a group of a few pieces of data. Its callback function copies the modified data to the GPU's corresponding buffer and requests a rendering. The callback function is triggered when a listener detects a modification.

[0178] The GPU component is the core of this invention, focusing on the task of each pixel. Specifically, each pixel (thread) requires:

[0179] (1) Calculate the corresponding light information;

[0180] (2) Solve for the ray and M based on the pre-calculated BVH. s M f The intersection information is obtained by following the pruning method proposed in this invention when traversing BVH.

[0181] (3) Initiate spherical tracing iteration. Perform the following operation in each step of the iteration until the returned distance value is less than ∈:

[0182] a) Calculate the correction distance using Algorithm 2 and the method of the extended module.

[0183] b) Calculate the tracking distance based on Algorithm 3 and Algorithm 4

[0184] c) Return the distance value required for spherical tracking based on the correction distance, tracking distance, and the type of the specific Boolean operation. d) Obtain the normal and intrinsic color of the hit body (Mesh or Lattice), and perform coloring according to the Phong coloring model.

[0185] pass Figure 7 The experimental analysis shown in Table 2 also confirms the invention's ability to accurately draw model structures and its ability to render / edit large-scale periodic lattices in real time. Figure 7A relatively complex assembly model was shown. Figure 7 In (b), the red and yellow parts are filled with lattices of different configurations. The red lattice uses the Body-centric Cubic cell type and enables internal smoothing and field-guided cell size, while the yellow lattice uses the Octahedron cell type. Figure 7 In (c), both the yellow and red lattices have much smaller unit cell sizes, and both use a body-centric Cubic-like unit cell (16 bars). In this example, 2000 3 Each cell is filled within a bounding box, and the red and yellow shells together account for 4.4425% of the total volume of the bounding box. This configuration involves a total of 5.686 billion members. It can be seen that as the camera's field of view (FoV) decreases, the details of the corresponding lattice can be rendered easily and clearly.

[0186] Table 2 shows the frame rate differences of this invention under different numbers of units and screen resolutions. It should be noted that due to the browser's frame-locking mechanism, the maximum frame rate can only reach around 60. As can be seen from the table, even with 6.28 billion units, the method of this invention still maintains good efficiency.

[0187] Table 2 Frame rate test at different screen resolutions / number of units.

[0188]

[0189] The embodiments described above are merely some preferred embodiments of the present invention, and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracing, characterized in that, include: Determine the shell parameters and periodic lattice control parameters C for the parts requiring porous structures to be rendered in additive manufacturing. l The outer casing includes an unfilled solid portion M. s and the filling portion M that needs to fill the periodic lattice f ; An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel to determine the color it should display and achieve rendering. The enhanced spherical tracing method is an improvement on spherical tracing. It includes solving the intersection information of the light rays with the solid part and the filling part in the shell of each pixel according to the pre-calculated hierarchical bounding volume (BVH), starting spherical tracing iteration, calculating the correction distance and tracing distance of the light rays in each step of the iteration, and returning the distance value required for spherical tracing according to the correction distance, tracing distance and the type of Boolean operation required, thereby completing the ray projection and enabling pixel shading.

2. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 1, characterized in that, Before calculating the corrected distance for the light beam, the set of rods contained in the unit cell defined in the periodic lattice control parameters is subjected to rod enhancement processing to obtain the enhanced rod set in each background grid hexahedral unit and determine the directed distance SDF value of the unit.

3. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 2, characterized in that, The rod reinforcement process specifically includes: For the set of rods contained within a unit cell, B = {B[i], i = 1, ...} … ,n b Let N[i,j] represent the two nodes of rod B[i], so j = 0, 1. The rod is a capsule-shaped rod with hemispherical surfaces at both ends. Traverse all nodes N[i,j] in the unit cell, considering the relationship between the nodes and the vertices, edges, and faces of the hexahedral elements. First, check if any vertex is located within the sphere corresponding to N[i,j]. If so, all 8 elements surrounding that vertex participate in the rendering of B[i], expanding B[i] to the other 7 vertices within the element. Next, check if any edge intersects the sphere corresponding to N[i,j]. If so, the 4 elements surrounding that edge participate in the rendering of B[i], expanding B[i] to the other 3 parallel edges within the element. Finally, check if any face intersects the sphere corresponding to N[i,j]. If so, the 2 elements on either side of that face participate in the rendering of B[i], expanding B[i] to the position of the face facing that face within the element. This yields the set of all rods within the hexahedral element after expansion. The SDF value F of this unit b that is The minimum SDF value of all rods in the middle.

4. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 1, characterized in that, The query point P located at any unit cell position in the crystal lattice g Mapped to query point P within the unit cell l In the middle, it is: P l =(P g -V min )%S-0.5·S Where V min is the smallest coordinate of the generated unit cell, % is the remainder, and S is the unit cell size; By querying the point mapping, at P g The SDF value of the cell containing it can be found at: F b (P g )=F b (P l ) The mapping of the query point from a certain unit cell to the unit cell, and the mapping of the bar of the unit cell from the unit cell to the global array, generate the SDF value F in each iteration of spherical tracing. b They are equal; A distance correction algorithm is used to correct the SDF value obtained in a single cell to a forward distance that is safe for the entire lattice; the distance correction algorithm is specifically as follows: When light enters a new cell, it must first pause at the boundary shared by the current cell and the new cell and then travel a very small distance. ∈t Adding the distance the light travels to the boundary ∈t That is, the corrected distance, where ∈t The threshold value is set to be equal to the termination threshold of spherical tracking. ∈ The distance required for the light ray to reach the boundary is the minimum distance the light ray needs to travel from three directions to hit the plane containing the boundary. The specific method for calculating these three travel distances is as follows: For each of the three coordinate axes, calculate the distance required to move from the query point to the plane containing the cell boundary that is perpendicular to the axis and located in the positive direction of the axis. If the distance is less than 0, then calculate the distance required to move to the boundary plane that is perpendicular to the axis and located in the negative direction of the axis.

5. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 1, characterized in that, Construct M s and M f For each ray's BVH, solve for the ray's M. s and M f The intersection information, where: for M s Only the first intersection point is recorded; the face that is hit is denoted as I. s Its distance from the camera is t. s For M f All intersection points need to be recorded, and the surfaces intersecting with the light rays should be sorted in ascending order of distance and recorded in list I. f The corresponding distance is recorded in list t. f ; t s and t f Convert these to distances for spherical tracking, specifically: for t s The conversion method is to return an infinite value when there is no intersection to allow the tracing to end quickly, and to return an infinite value when there is an intersection but the query point is in M. s In addition, return the distance from the query point to the next intersection point; for t f The conversion method is that when the query point is M f In addition, return the distance from the query point to the next intersection point, when the query point is at M. f In or when leaving M f Staying at M f On the surface, it returns to negative infinity, as the light is about to enter M. f Staying at M f On the surface, return a value slightly smaller than the termination threshold ∈ of the spherical tracing.

6. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 5, characterized in that, The BVH is traversed using a pruning method, where: For M s BVH traversal: When selecting two child nodes, always prioritize the child node closer to the ray's origin and discard the child node whose nearest distance to the camera is greater than the current t. s Nodes; For M f BVH traversal: any object whose nearest distance to the camera is greater than t s All nodes were discarded directly; Furthermore, considering that the camera is from M f For nodes originating from within the system, where the maximum signed distance to the camera is less than 0, for M... s and M f During BVH traversal, all values ​​are directly discarded.

7. The method for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking according to claim 1, characterized in that, Based on the method, slices of models in additive manufacturing can be generated by adjusting the rendering pipeline. The adjustment includes making all light rays originate from pixels and be perpendicular to the view plane, making the distance between the far plane and the near plane equal to the slice thickness, and making the near plane coincide with the view plane.

8. A real-time editing and rendering system for large-scale periodic lattice-like porous structures based on spherical tracking, characterized in that, For implementing the method as described in any one of claims 1-7, comprising: Large-scale processing modules, using the control parameters C of periodic lattices l As input, the corrected distance is obtained through rod enhancement and correction of local distances, which is used to complete the rendering of the entire lattice by querying only the SDF within a single cell; Hybrid rendering module, using the solid part M in the shell parameters s and filling part M f As input, it is used to simultaneously render the implicitly represented lattice and the explicitly represented shell without representation conversion, to obtain the tracking distance for spherical tracing; and returns the distance value required for spherical tracing based on the correction distance, tracking distance, and the type of the required Boolean operation, for rendering.

9. The real-time editing and rendering system for large-scale periodic lattice-like porous structures based on spherical tracking according to claim 8, characterized in that, It also includes extension modules for implementing smooth transitions at connections, properties of field guidance within the lattice, lattice deformation, and region-specified unit cell types to cater to a wider range of practical applications.

10. A computer-readable storage medium, characterized in that, The medium stores a program that can be executed by a processor to implement the method as described in any one of claims 1-7.

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