A three-dimensional scene grid model simplification method and system based on iterative search

Abstract

The present application belongs to the technical field of mesh model simplification, and particularly relates to a three-dimensional scene mesh model simplification method and system based on iterative search. The method comprises the following steps: selecting a mesh to be simplified; calculating a single shrinkage weight of each edge in the mesh to be simplified based on a shrinkage quadratic error and curvature; calculating a final shrinkage weight of each edge in the mesh to be simplified based on the single shrinkage weight of each edge in the mesh to be simplified through iterative search; selecting an edge with the minimum final shrinkage weight in the mesh to be simplified as a collapse edge to gradually simplify the mesh to be simplified until the compression rate of the mesh to be simplified meets the requirement; and reselecting the mesh to be simplified and repeating the above steps until the compression rates of all meshes meet the requirement. The present application can simplify the mesh while retaining the visual features of the three-dimensional scene mesh model.

Description

Technical Field

[0001] This invention belongs to the field of mesh model simplification technology, specifically relating to a method and system for simplifying 3D scene mesh models based on iterative search. Background Technology

[0002] 3D models, as data sets of points, faces, and other information, have important applications in film, games, medicine, architecture, and other fields. In recent years, with the continuous improvement of computer-aided modeling technology in the film and manufacturing industries, the number of faces in 3D models can reach the millions. While high-resolution models are necessary in some scenarios, for speed considerations in data network transmission and real-time rendering, it is necessary to reduce the number of triangles in the mesh. Therefore, how to reduce the number of triangles in the mesh while preserving as much model information as possible is an important issue.

[0003] One of the most common methods for simplifying mesh models is iterative edge shrinking. To simplify the mesh, an edge is iteratively selected and folded into a single unit, and this process is repeated until the number of vertices or faces in the model is reduced to the desired amount. For example, the quadratic error metric algorithm proposed by Garland and Heckbert can simplify meshes quickly and reliably, but it cannot interpret the key properties of the mesh itself; Michaud et al. used an error metric algorithm based entirely on curvature. However, most of these methods fail to preserve the most obvious visual features of the model. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and system for simplifying 3D scene mesh models based on iterative search. It utilizes shrinkage quadratic error to optimize vertex positions and considers discrete curvature, prioritizing the simplification of flat planes and regions while maintaining the number of faces in areas with details and key features. This approach can preserve the visual characteristics of the 3D scene mesh model while simplifying it.

[0005] To address the shortcomings of existing technologies, the technical solution provided by this invention is as follows:

[0006] A method for simplifying 3D scene mesh models based on iterative search includes,

[0007] S1: Select the grid to be simplified;

[0008] S2: Calculate the single-time shrinkage weight of each edge in the grid to be simplified based on the shrinkage quadratic error and curvature, and calculate the final shrinkage weight of each edge in the grid to be simplified through iterative search based on the single-time shrinkage weight of each edge in the grid to be simplified.

[0009] S3: Select the edge with the smallest final shrinkage weight within the mesh to be simplified as the collapsed edge and simplify the mesh to be simplified;

[0010] S4: Determine whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If yes, proceed to step S5; otherwise, repeat steps S2 to S3 until the compression ratio of the mesh to be simplified meets the requirement.

[0011] S5: Select a new mesh to be simplified and repeat steps S2 to S4 until the compression ratio of all meshes meets the requirements.

[0012] Preferably, the step of calculating the single-shrinkage weight of each edge of the mesh to be simplified based on the shrinkage quadratic error and curvature includes:

[0013]

[0014] in, Let e ​​be the single contraction weight. Let v1 and v2 be the quadratic error of the contraction of edge e; v1 and v2 are the two vertices of edge e. For the optimal point of the collapsed edge e, K e Let e ​​be the Gaussian curvature of edge e; S be the sigmoid function; K ... Gaussian curvature of edge e; S be the Gaussian curvature of edge e; K be the Gaussian curvature of edge e; S be the Gaussian curvature of edge e; S be the Gaussian cur e The formulas for calculating S are as follows:

[0015]

[0016]

[0017] Let v1 be the Gaussian curvature. Let d1 be the Gaussian curvature of point v2, and d1 be the distance from point v1 to the optimum. The distance d2 is the distance from point v2 to the optimum. The distance.

[0018] Preferably, the final shrinkage weight of each edge within the grid to be simplified is calculated through iterative search based on the single-step shrinkage weight of each edge within the grid to be simplified, including:

[0019] S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight;

[0020] S32: For each edge e = {v1, v2}, try to merge v1, v2 into And shrink all edges connected to v1 and v2 to

[0021] S33: Recalculate all... The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage is selected as the collapsed edge for shrinkage.

[0022] Perform step S32 once, and step S33 K-1 times. The sum of the single-time shrinkage weight in step S32 and the single-time shrinkage weight in step S33 K-1 times is used as the final shrinkage weight of edge e.

[0023] Preferably, the formula for calculating the compression ratio of the mesh is as follows:

[0024]

[0025] Among them, t i Let be the compression ratio of the (i+1)th grid, i = 0, 1, ..., N-1, where N is the total number of grids; t is the original compression ratio of the grid; d i c represents the second ratio of the number of faces in the (i+1)th grid to the sum of the number of faces in all grids. i It represents the first proportion of the number of faces in the (i+1)th grid relative to the sum of the number of faces in all grids;

[0026] d i The calculation formula is as follows:

[0027]

[0028] c i The calculation formula is as follows:

[0029]

[0030] Where N[i] is the number of faces in the (i+1)th grid, N[j] is the number of faces in the (j+1)th grid, and j = 0, 1, ..., N-1.

[0031] A 3D scene mesh model simplification system based on iterative search includes a selection module and a mesh simplification module; the mesh simplification module includes a shrinkage weight calculation module and an edge simplification module.

[0032] The selection module is used to select the grid to be simplified and trigger the shrinkage weight calculation module;

[0033] The shrinkage weight calculation module is used to calculate the single shrinkage weight of each edge in the grid to be simplified based on the shrinkage quadratic error and curvature, and to calculate the final shrinkage weight of each edge in the grid to be simplified through iterative search based on the single shrinkage weight of each edge in the grid to be simplified, thereby triggering the edge simplification module.

[0034] The edge simplification module is used to select the edge with the smallest final shrinkage weight in the mesh to be simplified as the collapsed edge to simplify the mesh. It determines whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If so, the selection module is triggered until the compression ratio of all meshes meets the requirement; otherwise, the shrinkage weight calculation module is triggered.

[0035] Preferably, the shrinkage weight calculation module is specifically used to calculate the single-time shrinkage weight of each edge of the mesh to be simplified using the following formula:

[0036]

[0037] in, Let e ​​be the single contraction weight. Let v1 and v2 be the quadratic error of the contraction of edge e; v1 and v2 are the two vertices of edge e. For the optimal point of the collapsed edge e, K e Let e ​​be the Gaussian curvature of edge e; S be the sigmoid function; K ... Gaussian curvature of edge e; S be the Gaussian curvature of edge e; K be the Gaussian curvature of edge e; S be the Gaussian curvature of edge e; S be the Gaussian cur e The formulas for calculating S are as follows:

[0038]

[0039]

[0040] Let v1 be the Gaussian curvature. Let d1 be the Gaussian curvature of point v2, and d1 be the distance from point v1 to the optimum. The distance d2 is the distance from point v2 to the optimum. The distance.

[0041] Preferably, the shrinkage weight calculation module is specifically used to calculate the final shrinkage weight of edge e according to the following steps:

[0042] S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight;

[0043] S32: For each edge e = {v1, v2}, try to merge v1, v2 into And shrink all edges connected to v1 and v2 to

[0044] S33: Recalculate all... The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage is selected as the collapsed edge for shrinkage.

[0045] Perform step S32 once, and step S33 K-1 times. The sum of the single-time shrinkage weight in step S32 and the single-time shrinkage weight in step S33 K-1 times is used as the final shrinkage weight of edge e.

[0046] Preferably, it also includes a compression ratio calculation module, which is used to calculate the compression ratio of the mesh according to the following formula:

[0047]

[0048] Among them, ti d represents the compression ratio of the (i+1)th grid; i = 0, 1, ..., N-1, where N is the total number of grids; t represents the original compression ratio of the grid; d i c represents the second ratio of the number of faces in the (i+1)th grid to the sum of the number of faces in all grids. i It represents the first proportion of the number of faces in the (i+1)th grid relative to the sum of the number of faces in all grids;

[0049] d i The calculation formula is as follows:

[0050]

[0051] c i The calculation formula is as follows:

[0052]

[0053] Where N[i] is the number of faces in the (i+1)th grid, N[j] is the number of faces in the (j+1)th grid, and j = 0, 1, ..., N-1.

[0054] The beneficial effects of this invention are:

[0055] The present invention provides a 3D scene mesh model simplification method based on iterative search. It comprehensively considers the shrinkage weight of the edges based on the discrete curvature of the model and the shrinkage quadratic error, takes into account the planar curvature and other characteristics of the mesh itself, prioritizes the simplification of flat areas and preserves areas with obvious changes and key features, and simulates multiple iterations before shrinking each edge. The final shrinkage weight of the multiple iterations is used to select which edge to simplify. The local iterative search algorithm with backtracking is used. Compared with the traditional greedy selection algorithm, it can guarantee the global optimality during simplification and has a better visual compression effect.

[0056] This method takes into account the number of faces of each mesh and adaptively applies different compression rates to meshes with different numbers of faces, which can effectively maintain the visual characteristics of geometries with fewer faces. Attached Figure Description

[0057] Figure 1 A flowchart of the method for simplifying a 3D scene mesh model based on iterative search provided by the present invention. Detailed Implementation

[0058] The present invention will be further described below with reference to the embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0059] This invention provides a method for simplifying 3D scene mesh models based on iterative search. See [link to relevant documentation]. Figure 1 This includes the following steps:

[0060] S1: Calculate the compression ratio of all meshes and select the mesh to be simplified.

[0061] The compression ratio of different meshes is adaptively and dynamically adjusted based on the number of faces. The calculation process of the mesh compression ratio is as follows:

[0062] Count the number of faces of all meshes in the 3D scene mesh model and store them in a list. The total number of meshes in the 3D scene mesh model is N, and the value of N[i] is equal to the number of faces of the (i+1)th mesh, i = 0, 1, ..., N-1.

[0063] For the (i+1)th grid, calculate the first ratio of its face count to the sum of the face counts of all grids. For each N[i], take the square root and calculate the second ratio of its face count to the sum of the face counts of all grid cells. The value of N[j] is equal to the number of faces of the (j+1)th grid, where j = 0, 1, ..., N-1.

[0064] Compression ratio of the (i+1)th grid t represents the original compression ratio of the mesh. The original compression ratio t is a constant. This invention adaptively and dynamically adjusts the compression ratio of different meshes according to the number of faces, which can effectively maintain the visual characteristics of geometries with a small number of faces.

[0065] S2: For the triangular mesh model, the single-shrinkage weight of each edge within the mesh to be simplified is calculated based on the shrinkage quadratic error and curvature, including:

[0066] Calculate the quadratic error of the contraction of each edge e. The optimal point of the collapsed edge e

[0067] For an edge e = {v1, v2}, calculate the Gaussian curvature of each vertex v1 and v2. And from vertices v1 and v2 to the optimal point The distances d1 and d2.

[0068] Calculate the Gaussian curvature K of edge e e The calculation formula is as follows:

[0069]

[0070] The single-cycle contraction weight of edge e is calculated by combining the contraction quadratic error and Gaussian curvature. The calculation formula is as follows:

[0071]

[0072] Where S is the sigmoid function, calculated as follows:

[0073]

[0074] S3: The final shrinkage weight of each edge in the grid to be simplified is calculated through iterative search based on the single shrinkage weight of each edge in the grid to be simplified.

[0075] S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight;

[0076] S32: For each edge e = {v1, v2}, try to merge v1, v2 into And shrink all edges connected to v1 and v2 to

[0077] S33: Recalculate all values ​​related to the optimal point. The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage (i.e., the vertex of the min-heap) is selected as the collapsed edge for shrinkage.

[0078] Perform step S32 once, and step S33 K-1 times. The sum of the single-time contraction weight in step S32 and the single-time contraction weight in step S33 K-1 times is the final contraction weight of edge e. K can be selected considering factors such as computational cost and compression effect, such as 3, 5, 7, etc.

[0079] S4: Select the edge with the smallest final shrinkage weight in the mesh to be simplified as the collapsed edge to simplify the mesh. After simplification, update the mesh. After the update, determine whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If yes, go to step S5. If no, repeat steps S2 and S3 to obtain the edge with the smallest final shrinkage weight in the mesh to be simplified again and use this edge as the collapsed edge to simplify the mesh. Simplify the mesh to be simplified step by step until the compression ratio of the mesh to be simplified meets the requirement.

[0080] S5: Select a new mesh to be simplified and repeat steps S2 to S4 until the compression ratio of all meshes meets the requirements.

[0081] This invention also provides a 3D scene mesh model simplification system based on iterative search, including a selection module and a mesh simplification module; the mesh simplification module includes a shrinkage weight calculation module and an edge simplification module;

[0082] The selection module is used to select the grid to be simplified and trigger the shrinkage weight calculation module;

[0083] The shrinkage weight calculation module is used to calculate the single shrinkage weight of each edge in the grid to be simplified based on the shrinkage quadratic error and curvature. Based on the single shrinkage weight of each edge in the grid to be simplified, the final shrinkage weight of each edge in the grid to be simplified is calculated through iterative search, triggering the edge simplification module.

[0084] The edge simplification module is used to select the edge with the smallest final shrinkage weight in the mesh to be simplified as the collapsed edge to simplify the mesh. It determines whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If so, the selection module is triggered until the compression ratio of all meshes meets the requirement; otherwise, the shrinkage weight calculation module is triggered.

[0085] The shrinkage weight calculation module is specifically used to calculate the single-shrinkage weight of each edge of the mesh to be simplified using the following formula:

[0086]

[0087] in, Let e ​​be the single contraction weight. Let v1 and v2 be the quadratic error of the contraction of edge e; v1 and v2 are the two vertices of edge e. For the optimal point of the collapsed edge e, K e Let e ​​be the Gaussian curvature of edge e; S be the sigmoid function; K ... Gaussian curvature of edge e; S be the Gaussian curvature of edge e; K be the Gaussian curvature of edge e; S be the Gaussian curvature of edge e; S be the Gaussian cur e The formulas for calculating S are as follows:

[0088]

[0089]

[0090] Let v1 be the Gaussian curvature. Let d1 be the Gaussian curvature of point v2, and d1 be the distance from point v1 to the optimum. The distance d2 is the distance from point v2 to the optimum. The distance.

[0091] The shrinkage weight calculation module is specifically used to calculate the final shrinkage weight of edge e according to the following steps:

[0092] S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight;

[0093] S32: For each edge e = {v1, v2}, try to merge v1, v2 into And shrink all edges connected to v1 and v2 to

[0094] S33: Recalculate all... The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage is selected as the collapsed edge for shrinkage.

[0095] Perform step S32 once, and step S33 K-1 times. The sum of the single-time shrinkage weight in step S32 and the single-time shrinkage weight in step S33 K-1 times is used as the final shrinkage weight of edge e.

[0096] The 3D scene mesh model simplification system based on iterative search also includes a compression ratio calculation module, which calculates the mesh compression ratio using the following formula:

[0097]

[0098] Among them, t i d is the compression ratio of the (i+1)th grid; i = 0, 1, ..., N-1, where N is the total number of grids; t is the original compression ratio of the grid; d i c represents the second ratio of the number of faces in the (i+1)th grid to the sum of the number of faces in all grids. i It represents the first proportion of the number of faces in the (i+1)th grid relative to the sum of the number of faces in all grids;

[0099] d i The calculation formula is as follows:

[0100]

[0101] c i The calculation formula is as follows:

[0102]

[0103] Where N[i] is the number of faces in the (i+1)th grid, N[j] is the number of faces in the (j+1)th grid, and j = 0, 1, ..., N-1.

[0104] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0105] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0108] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

[0109] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for simplifying a 3D scene mesh model based on iterative search, characterized in that, include, S1: Select the grid to be simplified; S2: Calculate the single-time shrinkage weight of each edge in the grid to be simplified based on the shrinkage quadratic error and curvature, and calculate the final shrinkage weight of each edge in the grid to be simplified through iterative search based on the single-time shrinkage weight of each edge in the grid to be simplified. S3: Select the edge with the smallest final shrinkage weight within the mesh to be simplified as the collapsed edge and simplify the mesh to be simplified; S4: Determine whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If so, proceed to step S5. Otherwise, repeat steps S2 to S3 until the compression ratio of the mesh to be simplified meets the requirements; S5: Select a new mesh to be simplified and repeat steps S2 to S4 until the compression ratio of all meshes meets the requirements; The calculation of the single-shrinkage weight of each edge of the mesh to be simplified based on the shrinkage quadratic error and curvature includes: in, For the edge The single contraction weight, For the edge The second error of contraction; For the edge The two vertices, For the collapsed edge The best advantage, For the edge Gaussian curvature; It is the sigmoid function; and The calculation formula is as follows: For point Gaussian curvature, For point Gaussian curvature, For point To the optimal point distance, For point To the optimal point The distance; The single-step shrinkage weight based on each edge within the grid to be simplified is calculated through iterative search to obtain the final shrinkage weight for each edge within the grid to be simplified, including: S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight; S32: For each edge Try to merge arrive and all with The connected edges shrink to ; S33: Recalculate all... The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage is selected as the collapsed edge for shrinkage. Perform step S32 once, then proceed to step S33. Next, the single-shrinkage weight in step S32 and the weight in step S33 are combined. The sum of the single contraction weights is used as the edge weights. The final shrinkage weight.

2. The method for simplifying a 3D scene mesh model based on iterative search according to claim 1, characterized in that, The formula for calculating the compression ratio of the mesh is as follows: in, For the first Compression ratio of each grid, , The total number of grid cells; The original compression ratio of the mesh; For the first The number of faces in this grid is the second largest proportion of the total number of faces in all grids. For the first The number of faces in a given grid is the first proportion of the sum of the number of faces in all grids; The calculation formula is as follows: The calculation formula is as follows: in, For the first The number of faces in a grid. For the first The number of faces in a grid. .

3. A system for simplifying 3D scene mesh models based on iterative search, characterized in that, It includes a selection module and a mesh simplification module; the mesh simplification module includes a shrinkage weight calculation module and an edge simplification module; The selection module is used to select the grid to be simplified and trigger the shrinkage weight calculation module; The shrinkage weight calculation module is used to calculate the single shrinkage weight of each edge in the grid to be simplified based on the shrinkage quadratic error and curvature, and to calculate the final shrinkage weight of each edge in the grid to be simplified through iterative search based on the single shrinkage weight of each edge in the grid to be simplified, thereby triggering the edge simplification module. The edge simplification module is used to select the edge with the smallest final shrinkage weight in the mesh to be simplified as the collapsed edge to simplify the mesh. It determines whether the current compression ratio of the mesh to be simplified meets the compression ratio requirement of the mesh. If so, the selection module is triggered until the compression ratio of all meshes meets the requirement; otherwise, the shrinkage weight calculation module is triggered. Specifically, the shrinkage weight calculation module is used to calculate the single-shrinkage weight of each edge of the mesh to be simplified using the following formula: in, For the edge The single contraction weight, For the edge The second error of contraction; For the edge The two vertices, For the collapsed edge The best advantage, For the edge Gaussian curvature; It is the sigmoid function; and The calculation formula is as follows: For point Gaussian curvature, For point Gaussian curvature, For point To the optimal point distance, For point To the optimal point The distance; Specifically, the shrinkage weight calculation module is used to calculate the edge weight according to the following steps. Final shrinkage weights: S31: Construct a min-heap for all edges in the grid to be simplified according to the size of the single shrinkage weight; S32: For each edge Try to merge arrive and all with The connected edges shrink to ; S33: Recalculate all... The weight of each connected edge is shrunk once and the min-heap is reconstructed. The edge with the smallest weight in the current single shrinkage is selected as the collapsed edge for shrinkage. Perform step S32 once, then proceed to step S33. Next, the single-shrinkage weight in step S32 and the weight in step S33 are combined. The sum of the single contraction weights is used as the edge weights. The final shrinkage weight.

4. The 3D scene mesh model simplification system based on iterative search according to claim 3, characterized in that, It also includes a compression ratio calculation module, which calculates the compression ratio of the mesh using the following formula: in, For the first Compression ratio of each grid; , The total number of grid cells; The original compression ratio of the mesh; For the first The number of faces in this grid is the second largest proportion of the total number of faces in all grids. For the first +1 grid faces represent the first proportion of the total number of faces in all grids; The calculation formula is as follows: The calculation formula is as follows: in, For the first The number of faces in a grid. For the first The number of faces in a grid. .

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