Large-scale periodic lattice porous structure real-time editing and rendering method and system based on spherical tracking

Abstract

The invention discloses a large-scale periodic lattice porous structure real-time editing and rendering method and system based on spherical tracking, and the method employs an enhanced spherical tracking method to carry out enhanced spherical tracking on each pixel, thereby determining the color which should be displayed, and achieving the rendering. The enhanced spherical surface tracking method is obtained by improving on the basis of spherical surface tracking and comprises the steps of solving intersection point information of light rays and an entity part in a shell and intersection point information of the light rays and a filling part in the shell for each pixel according to a pre-calculated hierarchical bounding volume (BVH), starting spherical surface tracking iteration, calculating a correction distance and a tracking distance of advancing of the light rays in each step of iteration, and calculating a correction distance and a tracking distance of advancing of the light rays. And returning a distance value required by spherical surface tracking according to the correction distance, the tracking distance and the type of the required Boolean operation, thereby completing ray casting, namely performing pixel coloring. The invention provides a method integrating rendering, editing and slicing and an overall framework, and an integrated additive manufacturing process from design to manufacturing of a large-scale periodic lattice porous structure is realized.

Description

Technical Field

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

[0002] A porous structure is a complex structure containing many cavities. It plays an important role in many fields such as materials science, aerospace technology, and biomedical engineering because of its material saving, light weight, high surface area, and controllable physical properties. A lattice is a porous structure composed of a large number of connected rod-like structures. Its properties are easy to control and its strength is high. It is one of the most concerned porous structures in academia and industry. A periodic lattice is a lattice composed of units arranged periodically in space. It is widely used in optical materials, aerospace, etc. Periodic lattices have the advantages of excellent mechanical properties, high thermal conductivity, and easy regulation. Its long-term order makes its physical properties (such as electronic band structure, thermal conductivity, optical properties, etc.) more predictable, which is crucial for material design.

[0003] Thanks to the development of Additive Manufacturing (AM), it is possible to manufacture models (Shell lattices) filled with complex lattice structures. There are many common processes for additive manufacturing, such as Fused Deposition Modeling (FDM), Stereo Lithography Apparatus (SLA), Selective Laser Sintering (SLS), Selective Laser Melting (SLM), etc. These additive manufacturing technologies all rely on the generation of model slices. When a large-scale periodic lattice is filled in an explicitly represented shell to form a Shell-lattice, how to efficiently generate slices at any angle is a major challenge. On the other hand, how to edit and visualize such complex Shell lattices in real time and efficiently in a computer is also a difficult problem.

[0004] The size of the lattices that industry can currently process is limited, and the U.S. Defense Advanced Research Projects Agency (DARPA) has also set the processing of such large-scale lattices as a major challenge in a report.

[0005] Conventional methods for visualizing and manufacturing porous models in additive manufacturing can be roughly divided into two categories: (1) explicit representation of the workflow (e.g. Figure 1(a)(b)); (2) implicitly represent the workflow (such as Figure 1 (c)).

[0006] According to the different representation types in the modeling stage, explicit representation can be further divided into parametric surface-based representation and mesh-based representation. Usually, the workflows under these two representations will generate results based on stereolithography (StereoLithography, STL) format in the final manufacturing stage for 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), its representative industrial software is Autodesk Fusion 360, Altair Inspire, and Siemens NX. The advantage of this modeling method is that it can accurately control and represent the shape and can perform complex geometric modifications. However, when facing large-scale lattice tasks, it may have problems of high computational complexity and high memory overhead: when a lattice with a large number of rods performs Boolean operations or smooth transitions with other parametric models, a large number of complex parametric surface intersection calculations will be involved; when there are hundreds of millions of rods, each rod usually requires multiple surfaces to represent it, and each surface requires a set of control vertex information.

[0008] Mesh is a relatively simpler way to explicitly represent lattice structures. Its advantages are that it is straightforward, easy to edit, and easy to render using a rasterization pipeline. However, this method also faces some problems when dealing with large-scale lattice structures. The most widely used is the pure explicit workflow, which has the same process as Figure 1 As shown in (a), the input is unified as Mesh. The representative software of this workflow is 3DXpert, Materialise Magics, TRUMPF TruTops, Materialise 3-matic, and Autodest Netfabb. Similar to parametric surface modeling, the memory overhead of this method increases as the lattice scale increases. At the same time, it is relatively difficult to solve the smooth transition between Mesh representations.

[0009] In order to exploit the robustness and efficiency of implicit representation in Boolean and smooth transition operations, Figure 1(b) shows another workflow that outputs results in STL format. Its modeling process is based on implicit representation, and the boundaries of the model are specified by isosurfaces of spatial scalar fields. Its advantage is that it can express some very complex models very lightly and supports robust and efficient Boolean and smoothing operations. Representative industrial software are nTopology and ParaMatters. This workflow uses the lattice structure of implicit input, and converts the shell into implicit representation, and converts the results of the Boolean / smooth transition of the two into STL format output. The common method for converting from implicit to explicit representation here is Marching Cubes. This workflow may require two format conversions, which will bring additional memory overhead and usually reduce the detailed features of the model. For large-scale periodic lattices, the lattice represented by the final output STL will also take up more storage resources.

[0010] On this basis, the pure implicit workflow further avoids the conversion from implicit to explicit representation and directly generates slice results from explicit representation. It has attracted the attention of many researchers in recent years. The process of this workflow is as follows Figure 1 (c) is shown, and its representative software is VoxelDance. However, in actual scenarios, most shell models are represented explicitly, and they often need to be converted to implicit representation. There are two common ways to do this conversion: (1) Use a discrete level set grid and sample implicit function values ​​at the grid points (usually using a signed distance function). When using this level set, the implicit function value of the query point that is not at the grid point is the trilinear interpolation of the eight adjacent grid points. This method is usually not easy to strike a balance between higher model accuracy and lower latency / memory overhead. (2) Calculate the implicit function value of the Mesh in real time during the rendering and slicing process. The problem with this method is that the amount of calculation is usually large.

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

[0012] In view of the above situation, the present invention provides a software system and workflow that can reasonably handle large-scale periodic shell-lattices, such as Figure 1(d) This workflow mixes implicit lattices and explicit shells without making complex conversions as much as possible, achieving seamless integration of shell-lattice from rendering, editing to slicing. Summary of the invention

[0013] The purpose of the present invention is to address the deficiencies of the prior art and provide a method and system for real-time editing and rendering of large-scale periodic lattice-like porous structures based on spherical tracking, which can realize real-time editing of additively manufactured periodic lattice porous structure models and realize rendering or slice generation.

[0014] The technical solution adopted by the present invention is as follows:

[0015] Real-time editing and rendering method of large-scale periodic lattice-like porous structures based on spherical tracking, including:

[0016] Determine the shell parameters of the parts required to render porous structures in additive manufacturing and the control parameters C of the periodic lattice l The shell includes an unfilled solid portion M s and the filling portion M to be filled in the periodic lattice f ;

[0017] An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel, so as to determine the color it should display and achieve rendering; the enhanced spherical tracing method is improved on the basis of spherical tracing, including solving the intersection information of the light and the solid part and the filled part in the shell according to the pre-calculated hierarchical bounding volume BVH for each pixel, starting the spherical tracing iteration, calculating the corrected distance and tracing distance of the light in each step of the iteration, returning the distance value required for spherical tracing according to the corrected distance, tracing distance and the type of required Boolean operation, thereby completing the ray projection and performing pixel coloring.

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

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

[0020] For the defined unit cell, the set of rods contained in it is B = {B[i], i = 1, ..., n b}, let N[i,j] denote the two nodes of the 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, consider the relationship between the nodes and the vertices, edges, and faces of the hexahedral unit, first, check whether there is a vertex located in the sphere corresponding to N[i,j]. If so, all 8 units around the vertex participate in the rendering of B[i], and B[i] is expanded to the other 7 vertices in the unit. Next, check whether there is an edge that intersects with the sphere corresponding to N[i,j]. If so, the 4 units around the edge participate in the rendering of B[i], and B[i] is expanded to the other 3 parallel edges in the unit. Finally, check whether there is a face that intersects with the sphere corresponding to N[i,j]. If so, the 2 units on both sides of the face participate in the rendering of B[i], and B[i] is expanded to the position of the face facing the face in the unit; get the set of all rods in the hexahedral unit after expansion The SDF value F of this unit b that is The minimum value of the SDF of all the rods in .

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

[0023] P l =(P g -V min )%S-0.5·S

[0024] Where V min is the minimum coordinate for generating a unit cell, % is the remainder, and S is the unit size;

[0025] By querying point mapping, in P g The SDF value of the unit cell is:

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

[0027] That is, mapping the query point from a cell to the unit cell, and mapping the cell rod from the unit cell to the global, the SDF value F generated in each iteration of spherical tracing b are equal;

[0028] A distance correction algorithm is used to correct the SDF value obtained in a single unit to a safe advance distance for the entire lattice; the distance correction algorithm is specifically:

[0029] When a ray enters a new cell, it must first stop at the common boundary between the current cell and the new cell and advance a small distance ∈ t , so that the distance the light reaches the boundary plus ∈t is the corrected distance, where ∈ t is taken to be equal to the termination threshold ∈ of spherical tracing; wherein the distance for the light to reach the boundary is the minimum distance required for the light to hit the plane where the boundary is located from three directions. The specific method for calculating these three distances is:

[0030] For the three coordinate axis directions, the distance required to advance from the query point to the plane where the unit boundary is located, which is perpendicular to the axis and located in the positive direction of the axis, is calculated respectively. If the distance is less than 0, the distance required to advance to the boundary plane, which is perpendicular to the axis and located in the negative direction of the axis, is calculated instead.

[0031] Furthermore, construct M s and M f Their respective BVHs, solving the rays and M s and M f The intersection information of M s , only the first intersection is recorded, and the hit face is recorded as I s , whose distance from the camera is t s , for M f , all intersection points need to be recorded, and the faces intersected by the light are sorted in ascending order of distance and recorded in list I f , the corresponding distance is recorded in list t f ;

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

[0033] Furthermore, the BVH is traversed using the pruning method, where:

[0034] For M s BVH traversal: When selecting two child nodes, always give priority to the child node close to the starting point of the light, and discard the child node whose closest distance to the camera is greater than the current ts Nodes;

[0035] For M f BVH traversal: Any distance to the camera greater than t s The nodes are directly discarded;

[0036] In addition, considering that the camera is from M f In the case of internal departure, for nodes whose maximum signed distance to the camera is less than 0, for M s and M f The BVH is directly discarded during traversal.

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

[0038] A large-scale periodic lattice-like porous structure real-time editing and rendering system based on spherical tracking, used to implement any of the above methods, comprising:

[0039] Large-scale processing module, with periodic lattice control parameters C l As input, through rod enhancement and correction of local distance, the corrected distance is obtained, which is used to complete the rendering of the entire lattice when only querying the SDF in a single unit cell;

[0040] Hybrid rendering module, with the entity part M in the shell parameter s and the filling part M f It is used as input to render the implicitly represented lattice and the explicitly represented shell simultaneously without representation conversion, and obtain the tracking distance for spherical tracking; and returns the distance value required for spherical tracking based on the corrected distance, the tracking distance, and the type of required Boolean operation, which is used to achieve rendering.

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

[0042] A computer-readable storage medium stores a program, wherein the program can be executed by a processor to implement any of the methods described above.

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

[0044] The model of porous structure parts in the field of additive manufacturing of the present invention provides a method and an overall framework for large-scale periodic lattices that integrates rendering, editing, and slicing, which realizes an integrated process from design to manufacturing of large-scale periodic lattice porous structures, facilitating the additive manufacturing process. In particular, this method can complete the correct rendering of the entire lattice by only querying the SDF in a single unit cell, greatly improving the rendering efficiency. In the test, the real-time rendering effect is also achieved for large-scale lattices, and the results obtained after Boolean operations of implicit representation and explicit representation can be efficiently rendered without performing representation conversion, avoiding the huge memory overhead, time cost and detail loss caused by representation conversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Comparison of the conventional process (a), (b), (c) for processing the periodic lattice filling structure Shell-lattice and the hybrid process (d) of the present invention;

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

[0047] Figure 3 Schematic diagram of the distance correction algorithm, where (a) and (b) are the spherical tracking process and results when no distance correction is used, and (c) and (d) are the spherical tracking process and results after using distance correction;

[0048] Figure 4 Schematic diagram of hybrid rendering Boolean operation, where (a) shows the process of post-processing Boolean intersection operation using Algorithm 3; (b) shows the process of post-processing Boolean union operation using Algorithm 4; (c) shows the process of traditional spherical tracking processing Boolean intersection; (d) shows the process of traditional spherical tracking processing Boolean union;

[0049] Figure 5 Rendering results with both internal and external smoothing applied to different unit types commonly used in industry;

[0050] Figure 6 Example plots of slice results for a lattice-filled model along different directions;

[0051] Figure 7 The figure is a schematic diagram of the overall and local rendering of a partial part of an assembly model after being filled with a lattice using the method of the present invention; in (c), the total number of rods contained in the lattice is about 5.686 billion. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0053] The real-time editing / rendering problem of large-scale periodic lattice filling structures in the field of additive manufacturing often faces the following challenges: 1) How to efficiently render large-scale internal periodic lattices and provide real-time feedback after the lattice properties are modified by the user to generate the modified results; 2) How to efficiently render the results after the implicit lattice and explicit shell Boolean / smooth transition, keeping the details of the lattice and shell themselves intact while taking into account memory and efficiency; 3) How to support the extension of lattice properties while solving the above two challenges, such as smooth blending, field-guided property distribution, deformation, etc.; 4) How to generate slices that are consistent with rendering for the above-mentioned large-scale periodic lattice filling structures, and achieve seamless integration of editing, rendering, and slicing.

[0054] In response to the above challenges, the present invention proposes an Augmented Sphere Tracing (AST) method to support real-time rendering and editing of large-scale periodic lattice filling structures (Shell-lattice). AST supports both implicit and explicit input, but avoids complex representation conversion as much as possible. This method does not actually generate a complete model structure of Shell-Lattice, but can obtain high-fidelity, Boolean-correct rendering results in screen space, as well as corresponding slices for manufacturing. The overall process is as follows: Figure 1 (d) as shown.

[0055] The real-time editing and rendering method of a large-scale periodic lattice-like porous structure based on spherical tracking of the present invention is as follows: Figure 2 As shown, it includes:

[0056] Determine the shell parameters of the parts required to render porous structures in additive manufacturing and the control parameters C of the periodic lattice l The shell includes an unfilled solid portion M s and the filling portion M to be filled in the periodic lattice f ;

[0057] An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel, so as to determine the color it should display and achieve rendering; the enhanced spherical tracing method is improved on the basis of spherical tracing, including solving the intersection information of the light and the solid part and the filled part in the shell according to the pre-calculated hierarchical bounding volume BVH for each pixel, starting the spherical tracing iteration, calculating the corrected distance and tracing distance of the light in each step of the iteration, returning the distance value required for spherical tracing according to the corrected distance, tracing distance and the type of required Boolean operation, thereby completing the ray projection and performing pixel coloring.

[0058] Specific:

[0059] 1. Overall framework of the program

[0060] The present invention considers a periodic lattice L(C) that is infinitely extended in three orthogonal directions. l ) is filled in the Mesh shell M, where C l is the control parameter of the lattice. Shell M = M f ∪M s ,satisfy Among them, M s represents the unfilled entity part, while M f represents the filling part, both of which are watertight and manifold. Therefore, the target Shell-Lattice structure is expressed as:

[0061] Ω(C l ,M)=L(C l )∩M f ∪M s . (1)

[0062] The present invention considers L(C l ) is very complex (including hundreds of millions of rods), and is designed to solve the real-time editing / rendering of such complex models and the generation of corresponding slices. Real-time editing is specifically reflected in that whenever C l The parameters of C are modified and the corresponding Ω is immediately rendered on the screen. l The specific content is shown in Table 1.

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

[0064]

[0065]

[0066] The system framework provided by the present invention may generally include three modules: a large-scale processing module, a hybrid rendering module and an expansion module.

[0067] The large-scale processing module supports efficient rendering of periodic lattices with billions of rods and arbitrary unit types. It includes a set of user-friendly unit cell definition rules and two algorithms: rod enhancement algorithm and distance correction algorithm. This module maps global query points to query points within the unit cell, and can correctly render the lattice while considering only a single lattice information at a time.

[0068] The hybrid rendering module is responsible for rendering the results of explicit shells and implicit lattice Booleans without model conversion. It first constructs a bounding volume hierarchy (BVH) for the Mesh, and performs ray-triangle intersection based on the BVH during the rendering process of each frame, and then extracts the distance value that can be used for the spherical tracing process in each iteration of spherical tracing based on the intersection sequence. This module also includes a method for pruning the BVH.

[0069] In addition to these two core algorithm modules, the present invention also includes an expansion module for a wider range of practical applications. Among them, slicing is achieved by 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 in the rendering stage; field-guided attributes, deformations, and region-specified unit types are achieved by adjusting unit and query point attributes when calculating SDF values.

[0070] 2. Core Methods

[0071] The two core modules of the AST algorithm proposed in the present invention are the large-scale processing module and the 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 accurate SDF values, but can be used to implement Boolean intersection / union operations by taking the maximum / minimum values ​​during spherical tracing like SDF values.

[0072] 2.1 SDF Query within a Single Cell

[0073] Correctly calculating the SDF value within a single unit is the basis for large-scale processing modules. Here, let the set of rods 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], so j = 0, 1. Without loss of generality, the algorithm assumes that the range of each coordinate component of the node is: N[i,j] ★ ∈[-1,1], where * = x, y, z. The SDF value of member 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], and r is the radius of the rod.

[0076] However, considering only user-defined rods in a cell is not sufficient to render the entire unit, because some rods in neighboring cells extend beyond their cell in volume into this cell, but they are not counted. Specifically, such rods appear when:

[0077]

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

[0079] Algorithm 1 is as follows:

[0080] Traverse all nodes N[i,j] in the unit, and consider the relationship between the nodes and the vertices, edges, and faces of the hexahedral unit. First, check whether there is a vertex located in the sphere corresponding to N[i,j]. The method of checking is to compare whether the distance between the node N[i,j] and the unit vertex in its quadrant is less than the radius r. If it is less than, there is a vertex located in the sphere corresponding to N[i,j]. All 8 units around the vertex participate in the rendering of B[i], so B[i] is expanded to the other 7 vertices in the unit (lines 4-16). Next, check whether there is an edge that intersects with the sphere corresponding to N[i,j]. The method of checking is to compare the distance between the node N[i,j] and the 12 edges of the current unit to see if any one of them is less than the radius r. If so, the 4 units around the edge participate in the rendering of B[i], so B[i] is expanded to the other 3 parallel edges in the unit (lines 18-35). Finally, check whether there is a face that intersects with the sphere corresponding to N[i,j]. The method of checking is to compare the distance between node N[i,j] and the six faces of the current unit to see if any distance is less than r. If so, the two units on both sides of the face participate in the rendering of B[i], so B[i] is expanded to the position of the face of the face object in the unit (lines 39-46).

[0081] Output in Algorithm 1 After that, the SDF value of the unit (denoted as F b )that is The minimum value of the SDF value of all the rods in is:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] 2.2 Local distance correction

[0088] Next we will show you how to query the distance of the entire lattice at a certain query point, which can be used for spherical tracking.

[0089] Direct calculation of the SDF of the lattice requires consideration of all the rods, which is an unacceptable amount of calculation. A common solution is to use the locality of the cell to limit the distance query to the adjacent 27 cells, or to further consider the relative position of the query point in the cell and limit the calculation to the adjacent 8 cells. However, the present invention proposes a method that only needs to consider a single cell.

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

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

[0092] Where V min is the minimum coordinate for generating the unit cell, and % means the remainder.

[0093] By querying point mapping, in P g The SDF value of the unit cell where the query is located is:

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

[0095] This equation can be interpreted as the F generated at each iteration of the sphere tracing by mapping the query point from a cell to the unit cell and mapping the rods of the cell from the unit cell to the global b are equal.

[0096] Because F b (P g ) considers only one unit cell, which is not the exact SDF of the entire lattice, such as Figure 3 (a). When the total volume of the rods in the unit is small and their distribution is not uniform, F b (P g ) may represent a distance that is too large, causing the ray to be lost or enter the rod it should be rendered directly after traveling this distance, resulting in rendering errors, such as Figure 3(b) as shown.

[0097] To solve this problem, the present invention proposes Algorithm 2 to reduce the distance that may be too aggressive to a just safe distance. Figure 3 As shown in (c), the basic idea is that when a ray enters a new cell, it must first stop at the common boundary between the current cell and the new cell and advance a small distance ∈ t . Calculate the three possible advance distances required for the ray to hit the cell boundary (lines 3-13) and take the minimum value (lines 6 and 10). ∈ t It ensures that the light enters the next unit. If it is too large, it will generally not solve the above problem, and if it is too small, the boundary of the unit will be rendered. t is taken to be equal to the termination threshold ∈ of spherical tracking.

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

[0099]

[0100] 2.3 Hybrid Rendering Module

[0101] The hybrid rendering module can render both the implicit (SDF) lattice and the explicit (Mesh) shell without any representation conversion, correctly accounting for Boolean relationships. This is achieved by replacing the SDF values ​​of the Mesh with an aggressive but safe tracking distance.

[0102] Given M s and M f , their respective BVHs are constructed separately before starting the rendering pipeline. Hybrid rendering consists of two steps: (1) calculating the intersection of the ray and the mesh before starting spherical tracing; (2) in each iteration of spherical tracing, extracting the advance distance from the intersection as the input of the iteration.

[0103] In the first stage, the present invention uses the standard BVH traversal process in ray tracing to obtain the intersection of the ray and the Mesh. s , the algorithm only records the first intersection point, since the ray never enters the solid shell. The face hit is recorded as I s , whose distance from the camera is t s In contrast, for M f , the algorithm needs to record a large number of intersections, because the porous structure makes M f The faces behind the first face hit by the ray may also be visible. The algorithm sorts these intersecting faces in ascending order of distance and records them in list I. f , the corresponding distance is recorded in list t f .

[0104] In the second stage, the present invention will f and t s The two conversions are respectively given by Algorithm 3 and Algorithm 4. These two algorithms respectively make the Boolean operation of intersection / union can be directly obtained by taking the maximum / minimum value of the input distance.

[0105]

[0106]

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

[0108]

[0109]

[0110] The situation in Algorithm 4 is more straightforward: when there is no intersection, the algorithm returns a large value to make tracing end quickly (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 working principle of these two algorithms is demonstrated. Their efficiency is reflected in two aspects: (1) the number of sphere tracing iterations is greatly reduced, especially near the surface of the mesh; (2) the time of each iteration is also greatly reduced compared to the method of accurately calculating the SDF of the mesh during the iteration process.

[0112] In addition to efficiency, another advantage of this algorithm is the accurate preservation of details. Some discrete transformation methods, such as Marching Cubes or sampled level sets, will lose these details, especially some sharp features such as corners / edges.

[0113] 2.4 BVH Pruning

[0114] For the BVH used in 2.3 above, the present invention provides a method for pruning when traversing it.

[0115] For Ms The pruning strategy of the present invention is as follows: (1) when selecting two child nodes, the child nodes that are close to each other are always preferred; (2) the child nodes whose closest distance to the camera is greater than the current t are discarded. s Node.

[0116] As for M f , the situation is different, because all intersections of it and the ray are potentially visible. Therefore, M f The traversal of t f But thanks to M s existence, and Based on the premise, the present invention proposes to use t s Come and prune M f I s and t s Will precede I f and t f is calculated. When traversing M f When the BVH is , any distance to the camera is greater than t s The nodes are directly discarded.

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

[0118] 3 Extension Modules

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

[0120] 3.1 Smooth transition.

[0121] In the lattice manufacturing scenario, proper smooth blending can provide better physical properties than direct Boolean. The smoothing here includes two categories: (1) internal smoothing, that is, smoothing between rods; (2) internal and external smoothing, that is, smoothing between lattices and M. f Smoothness between the complementary spaces of .

[0122] 3.1.1 Internal smoothing

[0123] Smoothing between SDFs only requires replacing the maximum and minimum operations in Boolean with the corresponding smoothing functions. The present invention chooses the KS function because it supports multiple inputs and is independent of the order of the inputs. Consistent with the method in 2.2, the present invention utilizes the locality of the unit and only calculates the smoothing in one unit cell:

[0124]

[0125] Where p represents the smoothness term, the smaller it is, the greater the degree of smoothness.

[0126] This method introduces minimal overhead on the basis of the original rendering and does not cause problems in most scenes, but may produce discontinuous results when the following two conditions are met: (1) p is too small, that is, the degree of smoothing is too large; (2) the symmetry constraints are not satisfied, that is, when the lattice units are connected in the * direction, the rods in each cell must be symmetric 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 is triggered. Most of the units used in periodic lattices in industrial scenarios do not meet condition (2), such as Figure 4 As shown. This means that in most cases, the present invention can use high-intensity smoothing for the unit. For the case where the symmetry is not satisfied, the present invention provides a range of p that will not cause obvious discontinuity in most cases, which is p≥30 / S★.

[0128] 3.1.2 Internal and external smoothing

[0129] Although the present invention provides the tracking distance of the Mesh that can complete spherical tracking without calculating the SDF of the Mesh in 2.3, this distance cannot be used for internal and external smoothing because the smoothing function requires that the input must be an SDF.

[0130] To solve this problem, the present invention proposes to use a fixed-resolution and low-resolution, pre-sampled level set, which is based on the fact that the smoothing operation will eliminate the model details. Although the level set method is difficult to balance satisfactory details and memory overhead, the intersection operation proposed in 2.3 will be responsible for preserving all the details of the Mesh. The present invention increases L(C l ) but keep M f The present invention uses a resolution of 128 3 The exact SDF values ​​of the level sets 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 around the query point.

[0132] Figure 5 Shows the camera from M fThe mixed rendering results of the inside and outside are obtained by starting from the inside. The units used for the test are typical units widely used in the field of additive manufacturing. Although the results are visually satisfactory, they are not completely accurate due to the use of level sets. The present invention eliminates this error in the final slicing stage.

[0133] 3.2 Replication with changes

[0134] In addition to conventional periodic lattices in which all units are exactly the same, the present invention can also support repetitions with differences and variations between units. The control parameters of these variations can be modified in real time.

[0135] To ensure continuity between adjacent elements, changes need to be applied in groups. Each group contains multiple rods, and a rod belongs to only one group. The user can freely specify the groups, but to ensure continuity, the present invention recommends that rods connected to each other at the node be placed in one group. In addition, the rods generated by the rod enhancement algorithm are always in the same group as the original rods.

[0136] 3.2.1 Field Guidance Attributes

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

[0138] Here, a trigonometric function field is used as an example to describe the method of rendering field-guided attributes of the present 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 triple attribute is:

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

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

[0141]

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

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

[0144] The field-guided cell size only requires replacing the cell size S in Equation (5) and Algorithm 2 with T tri (S,P g ). During this process, each query thinks it is rendering a grid with a constant cell size, but in fact each query point uses a different constant size. If the field changes too drastically, rendering errors may occur due to the ray traveling too fast. This can be solved by applying a falloff factor to the distance the ray travels.

[0145] 3.2.2 Lattice deformation

[0146] The deformed periodic lattice expands the geometrical limits on the basis of the conventional periodic lattice, thereby meeting a wider variety of physical and aesthetic requirements. In the deformed periodic lattice, different transformations are applied to each volume element, rather than at the node center. The present invention includes two different deformations: twisting and bending.

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

[0148] Twist is a deformation of the rod surface that keeps the position of each unit unchanged. In the present invention, to obtain the twist effect, R(ψ(P g )) -1 Acting on the local query point P l superior:

[0149] P l ′=R(ψ(P g )) -1 P l . (10)

[0150] In order to obtain the bending effect, R(ψ(P g)) -1 Acting on the 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 of the query point, for example, it is 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 the deformation effect.

[0155] 3.3 Area-specific unit types

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

[0157] The replication rules for cells are usually specified based on the cell index. For example, the user can specify that cells whose index components sum to an odd number use cell type A and cells whose index components sum to an even number use type B. For a given query point P g , the index of the unit to which it belongs is:

[0158]

[0159] To ensure structural integrity, the rods obtained by the rod enhancement algorithm will also be copied to other unit cells. In addition, the user needs to ensure that different unit types are continuous at the boundaries.

[0160] 3.4TPMS structure

[0161] Although the present invention is specifically provided for periodic lattices, the hybrid rendering module can also accept more 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, namely, the Primitive (P) type and the Gyroid (G) type, which are defined as:

[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 , and b is an isosurface constant. The present invention considers the TPMS as a single structure as a whole, rather than embedded in a tetrahedral unit. P and I G Essentially, it is not a standard SDF. The present invention multiplies a decay factor based on the TPMS function value during rendering to obtain a relatively conservative forward distance.

[0166] 3.5 Slice Generation

[0167] The slice generation method of the present invention is based on the rendering framework, which retains almost all the steps of rendering and only requires limited changes:

[0168] (1) The perspective projection used for rendering is changed to an orthographic projection; in a perspective projection, all light rays originate from the camera and radiate outward through different pixels in the image plane, while in an orthographic projection, all light rays originate from the pixel and are perpendicular to the viewing 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 the two being the thickness of the slice. In addition, the near plane is no longer located behind the viewing plane, but coincides with the viewing plane.

[0170] (3) When the inside and outside are opened smoothly, M f The SDF value is no longer approximated by the low-resolution level set, but reuses 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 screen boundary, thereby improving the pixel utilization rate.

[0172] (5) All calculations related to face normals and shading are removed.

[0173] Figure 6 The figure shows a part of the slices generated in different slice directions by the method of the present invention. The unit type is Body-centric Cubic.

[0174] The system provided by the present invention includes: a hybrid rendering module, a large-scale rendering module and an expansion module. The first two modules are the core modules of the algorithm. The hybrid rendering module uses the shell data M s and M f As input, the large-scale rendering module uses the lattice parameter C l As input. The two modules output the tracking distance and the correction distance respectively, which are used in the spherical tracking process, thereby forming the enhanced spherical tracking method proposed by the present invention. After each pixel goes through the enhanced spherical tracking process, it can be known that the color it should display is formed, thereby forming a rendered frame or slice. The third module, the expansion module, mainly acts on the large-scale rendering module, and is implemented by affecting the calculation of SDF values ​​to support a variety of practical application scenarios. According to an example of the present invention, the scheme of the present invention is implemented based on WebGPU, and the program implementation includes both the CPU and GPU ends. The CPU end is implemented based on Typescript and the VUE3 front-end framework, which is mainly responsible for interacting with the user through the UI component, translating the user input into the lattice configuration parameters and inputting them into the GPU end, calling the rendering task, and drawing the GPU rendering results in the Canvas component of the web page. The GPU end is implemented based on WebGPU and is responsible for parallelism at the pixel level, that is, each thread is responsible for drawing a single pixel.

[0175] All pixel-level algorithms run on the GPU, including Algorithm 2, Algorithm 3, Algorithm 4, and all extensions. And these algorithms run in real time during the rendering process. Algorithm 1 runs on the CPU and is directly implemented through the Typescript script. The reason for this design is that Algorithm 1 has a low degree of parallelism and does not need to be called when drawing each frame. The construction of BVH and the construction of low-resolution level sets are completed in advance, rather than calculated in real time. Complex data, such as M s and M f The data (vertices and faces), rod sets, BVH, etc. are all stored in WebGPU storage type memory. Lightweight data, such as other configurations except rod sets in Table 1, camera parameters, model transformation parameters, etc., are all stored in uniform type memory. This is because storage memory supports larger databases, but the efficiency is relatively low; while uniform type memory is more efficient, but the capacity is smaller and requires data to strictly comply with certain format requirements.

[0176] Whenever the user modifies a property of the lattice, such as radius, unit size, field parameters, etc., or changes the perspective or moves the model, the VUE3 framework will capture this modification through the monitoring mechanism, and let the renderer pass the updated data to the GPU and send a command to draw a new frame. When the user modifies the operation in Table 1, it will not trigger the recompilation of the shader, and there is no need for complex preprocessing.

[0177] The CPU part is relatively simple. It is a bridge for interaction between the user and the GPU module. It is responsible for informing the GPU of the user's edited information and displaying the GPU calculation results to the user. Specifically, in the present invention, all configuration information about the lattice is managed by the global Hooker. When the user modifies the data of a component (such as a text component, a slider component, a selection box component, 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 group of data consisting of a single or a few data. Its callback function will copy the modified data to the Buffer corresponding to the GPU and request a rendering. The callback function will be triggered when the listener detects the modification.

[0178] The GPU part is the core of the present invention, and its focus is on the task of each pixel. Specifically, each pixel (thread) needs:

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

[0180] (2) Solve the light and M based on the pre-calculated BVH s 、M f The intersection information of the BVH is traversed here by following the pruning method proposed in the present invention;

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

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

[0183] b) Calculate the tracking distance according to Algorithm 3 and Algorithm 4

[0184] c) Return the distance value required for spherical tracing according to the correction distance, tracing distance and the type of specific Boolean operation. d) Get the normal and intrinsic color of the hit body according to the type (Mesh or lattice), and color it according to the Phong shading model.

[0185] pass Figure 7 As shown in Table 2, some experimental analyses also confirm the ability of the present invention to accurately draw model structures and to render / edit large-scale periodic lattices in real time. Figure 7A more complex assembly model is 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 with internal smoothing and field-guided unit size enabled, while the yellow lattice uses the Octahedron cell type. Figure 7 In (c), the unit cell size of the yellow and red lattices is much smaller, and both use the Body-centricCubic unit cell (16 rods). 3 The red and yellow shells together account for 4.4425% of the total volume of the bounding box, and the total number of rods involved in this configuration reaches 5.686 billion. It can be seen that when the camera field of view (FoV) becomes smaller, the details of the corresponding lattice can be easily and clearly rendered.

[0186] Table 2 shows the frame rate difference of the present invention under different numbers of units and screen resolutions. It should be noted that due to the frame locking mechanism of the browser, the maximum frame rate can only reach about 60. It can be seen from the table that when the number of units is 6.28 billion, the method of the present invention still maintains a good efficiency.

[0187] Table 2 Frame rate test under different picture resolutions / unit numbers.

[0188]

[0189] The above-described embodiments are only some of the preferred solutions of the present invention, but they are not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A real-time editing and rendering method for large-scale periodic lattice-like porous structures based on spherical tracking, characterized in that: include: Determine the shell parameters of the parts required to render porous structures in additive manufacturing and the control parameters C of the periodic lattice l The shell includes an unfilled solid portion M s and the filling portion M to be filled in the periodic lattice f ; An enhanced spherical tracing method is used to perform enhanced spherical tracing on each pixel, so as to determine the color it should display and achieve rendering; the enhanced spherical tracing method is improved on the basis of spherical tracing, including solving the intersection information of the light and the solid part and the filled part in the shell according to the pre-calculated hierarchical bounding volume BVH for each pixel, starting the spherical tracing iteration, calculating the corrected distance and tracing distance of the light in each step of the iteration, returning the distance value required for spherical tracing according to the corrected distance, tracing distance and the type of required Boolean operation, thereby completing the ray projection and performing pixel coloring.

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

3. The real-time editing and rendering method of large-scale periodic lattice-like porous structure based on spherical tracking according to claim 2 is characterized in that: The rod strengthening process specifically includes: For the defined unit cell, the rod set B={B[i], i=1, … ,n b }, let N[i,j] denote the two nodes of the rod B[i], so j = 0,1, and the rod is a capsule-shaped rod with hemispherical surfaces at both ends; Traverse all nodes N[i,j] in the unit cell, consider the relationship between the nodes and the vertices, edges, and faces of the hexahedral unit, first, check whether there is a vertex located in the sphere corresponding to N[i,j]. If so, all 8 units around the vertex participate in the rendering of B[i], and B[i] is expanded to the other 7 vertices in the unit. Next, check whether there is an edge that intersects with the sphere corresponding to N[i,j]. If so, the 4 units around the edge participate in the rendering of B[i], and B[i] is expanded to the other 3 parallel edges in the unit. Finally, check whether there is a face that intersects with the sphere corresponding to N[i,j]. If so, the 2 units on both sides of the face participate in the rendering of B[i], and B[i] is expanded to the position of the face facing the face in the unit; get the set of all rods in the hexahedral unit after expansion The SDF value F of this unit b that is The minimum SDF value of all rods in .

4. The real-time editing and rendering method of large-scale periodic lattice-like porous structure based on spherical tracking according to claim 1 is characterized in that: The query point P located at any unit cell position of the lattice g Mapped to the query point P in the unit cell l In, it is: P l =(P g -V min )%S-0.5·S Where V min is the minimum coordinate for generating a unit cell, % is the remainder, and S is the unit size; By querying point mapping, in P g The SDF value of the unit cell is: F b (P g )=F b (P l ) That is, mapping the query point from a cell to the unit cell, and mapping the cell rod from the unit cell to the global, the SDF value F generated in each iteration of spherical tracing b are equal; A distance correction algorithm is used to correct the SDF value obtained in a single unit to a safe advance distance for the entire lattice; the distance correction algorithm is specifically: When light enters a new cell, it must first stop at the common boundary between the current cell and the new cell and advance a small distance. ∈t , so that the distance the light reaches the boundary plus ∈t is the corrected distance, where ∈t is taken to be equal to the termination threshold for spherical tracking ∈ ; The distance for the light to reach the boundary is the minimum distance required for the light to hit the plane where the boundary is located from three directions. The specific method for calculating these three distances is: For the three coordinate axis directions, the distance required to advance from the query point to the plane where the unit boundary is located, which is perpendicular to the axis and located in the positive direction of the axis, is calculated respectively. If the distance is less than 0, the distance required to advance to the boundary plane, which is perpendicular to the axis and located in the negative direction of the axis, is calculated instead.

5. The real-time editing and rendering method of large-scale periodic lattice-like porous structure based on spherical tracking according to claim 1 is characterized in that: Build M s and M f Their respective BVHs, solving the rays and M s and M f The intersection information of M s , only the first intersection is recorded, and the hit face is recorded as I s , whose distance from the camera is t s , for M f , all intersection points need to be recorded, and the faces intersected by the light are 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 Converted to distances for spherical tracking, specifically: for t s The conversion method is that when there is no intersection, an infinite value is returned to make the tracking end quickly. When there is an intersection but the query point is in M s In addition, the distance from the query point to the next intersection point is returned; for t f , the conversion method is, when the query point is in M f In addition, the distance from the query point to the next intersection point is returned. f or when leaving M f Stay at M f On the surface, it returns negative infinity when the ray is about to enter M f Stay at M f On the surface, return a value slightly smaller than the termination threshold ∈ of spherical tracking.

6. The real-time editing and rendering method of large-scale periodic lattice-like porous structure based on spherical tracking according to claim 5 is characterized in that: The BVH is traversed using the pruning method, where: For M s BVH traversal: When selecting two child nodes, always give priority to the child node close to the starting point of the light, and discard the child node whose closest distance to the camera is greater than the current t s Nodes; For M f BVH traversal: Any distance to the camera greater than t s The nodes are directly discarded; In addition, considering that the camera is f In the case of internal departure, for nodes whose maximum signed distance to the camera is less than 0, for M s and M f The BVH is directly discarded during traversal.

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

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

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

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

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