Triangular mesh subdivision method based on vertex normal interpolation calculation

Abstract

The invention discloses a triangular mesh subdivision method based on vertex normal interpolation calculation. The method comprises the following steps: S1, coding and storing all points, lines and surfaces; s2, calculating protrusion indexes of all surfaces; s3, inputting a subdivision threshold degree a, and inputting subdivision intensity b; s4, determining all surfaces needing to be subdivided according to the subdivision threshold degree a; s5, subdivision calculation is carried out; s6, circulating all the to-be-subdivided surfaces, and performing subdivision calculation; s7, carrying out topological optimization again; and S8, carrying out coding storage on points, lines and surfaces of the graph after topological optimization. By calculating and optimizing the triangular patch model, the subdivision smoothing processing of the abrupt area of the model is realized, so that after the model is optimized, the surface of the model is smoother, a better display effect is kept, the operation performance of the model is greatly improved, and the effect display and fluency of live-action three-dimensional rendering and demonstration are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of triangular facet model optimization in three-dimensional models, and in particular to a triangular mesh subdivision method based on vertex normal interpolation calculation. Background Art

[0002] In 3D modeling and scene rendering, especially for the construction and visualization of large-scale scenes, triangular facet models are widely used to represent complex 3D surface structures. Facet rendering uses normal-based smooth shading to achieve smooth display of models. However, when the number of meshes in an object is very small, the smooth shading effect is very poor. Therefore, it is necessary to subdivide the object before smooth shading.

[0003] However, general subdivision is to subdivide all faces, which will cause the number of faces to become very high, resulting in an exponential growth in the number of faces, affecting the use of the model. Summary of the Invention

[0004] In order to solve the existing problems, the present invention provides a triangular mesh subdivision method based on vertex normal interpolation calculation, the specific scheme is as follows:

[0005] A triangular mesh subdivision method based on vertex normal interpolation calculation includes the following steps:

[0006] S1, encode and store all points, lines, and surfaces;

[0007] S2, calculate the protrusion index of all surfaces;

[0008] S3, input the subdivision threshold degree a and the subdivision strength b;

[0009] S4, subdivision threshold degree a determines all faces that need to be subdivided;

[0010] S5, subdivision calculation;

[0011] S6, loop all the faces to be subdivided and perform subdivision calculations;

[0012] S7, retopology optimization;

[0013] S8, encoding and storing the points, lines, and surfaces of the topology-optimized graphics.

[0014] Preferably, calculating the protrusion index of all surfaces in step S2 means sequentially calculating the weighted average of the angle between each selected surface and the adjacent surface multiplied by the line length to obtain the protrusion index of each selected surface.

[0015] Preferably, the subdivision threshold a in step S3 is used to screen the surfaces to be subdivided, and its value range is greater than 0 and less than 1; the subdivision strength b is used to select the distance between the selected point and the original surface during subdivision, and its value range is greater than 0 and less than 1.

[0016] Preferably, the subdivision strength b in step S3 is the ratio of the length of the line segment between the interpolation point and the midpoint of the line to the modulus length of the interpolation vector.

[0017] Preferably, the subdivision calculation in step S5 is specifically as follows:

[0018] S51, calculating the surface normals around the current surface, with the direction inward, and calculating the surface normal of the current surface, with the direction outward;

[0019] S52, calculating the vertex normal of the current triangle based on the above two calculations;

[0020] S53, calculating the interpolation vector of the vertex normal to obtain the interpolation normal, taking the midpoint of the edge as the starting point, and combining it with the subdivision strength b to obtain the interpolation point;

[0021] S54, generates new topological triangles and the subdivision is completed.

[0022] The present invention also discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is run, any of the above methods is executed.

[0023] The present invention also discloses a computer system, including a processor and a storage medium, wherein a computer program is stored on the storage medium, and the processor reads and runs the computer program from the storage medium to execute any of the methods described above.

[0024] The beneficial effects of the present invention are:

[0025] In terms of subdivision and smooth shading optimization in large-scale scene rendering, this invention combines the concepts of normal interpolation and edge refinement. By controlling vertex normals and interpolation to achieve refinement, it optimizes smoothing without significantly increasing the number of facets. Compared with traditional subdivision methods, this method has the following beneficial effects:

[0026] 1. Normal interpolation combined with subdivision

[0027] Instead of simply subdividing all faces, this method optimizes the surface by inserting a vector and using normal interpolation. Compared with traditional subdivision methods, this subdivision method based on normal interpolation can significantly reduce the number of patches and reduce the computational burden.

[0028] Traditional subdivision algorithms, such as Catmull-Clark or Loop subdivision, typically uniformly subdivide all triangles, resulting in a dramatic increase in the number of facets. This method, however, uses normal interpolation to locally optimize facets, avoiding unnecessary subdivisions, keeping the facet count low, and improving surface smoothness.

[0029] 2. Reduce redundant patches

[0030] This method effectively reduces the increase in redundant facets when refining edges, a challenge faced by traditional subdivision methods. By not fully subdividing all faces and instead controlling detail only through normal interpolation, the rate at which the number of facets increases can be slowed, avoiding a sharp drop in performance in large-scale scenes.

[0031] 3. Local topology optimization

[0032] This method refines edges by retopologically refining them, which can be understood as refining and reorganizing the local mesh. This local topology optimization approach combines the advantages of global and local refinement, ensuring rendering quality while avoiding unnecessary global subdivision overhead.

[0033] 4. Normal interpolation and visual effect improvement

[0034] During normal interpolation, the focus is on improving mesh smoothness, not just subdividing the model. Traditional smooth shading relies on interpolating vertex normals, but this can lead to noticeable visual stair-stepping when the mesh is not detailed enough. This method enhances the smoothness of normal transitions by interpolating intersections and retopologically reconstructing triangles.

[0035] 5. Application potential in large-scale scenarios

[0036] When rendering large-scale scenes, especially when dealing with complex surfaces, it is crucial to reduce the number of redundant facets while maintaining good rendering quality. This method, by thinning edges, can improve rendering quality while maintaining a low facet count, showing great potential for application.

[0037] 6. Innovations in Calculating the Surface Protrusion Index

[0038] For faces that need to be refined, the weighted calculation of the angle with the surrounding faces and the connecting lines is calculated to obtain the face protrusion index after weighted calculation. This protrusion index is related to the length of the common edge. The longer the length, the higher the weighted index. The length of the common edge between the facets (that is, the length of the edge shared between adjacent facets) will affect the visual protrusion effect. The longer the common edge, the more significant the protrusion effect. Therefore, a higher weight can be given to the long edge in the weight calculation. In this way, areas with longer common edges and larger angles will be subdivided first to enhance the performance of the protrusion area. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 is a flow chart of the method of the present invention;

[0041] Figure 2 is a coding diagram of the initial triangular model structure in an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of the initial triangular model structure in an embodiment of the present invention;

[0043] Figure 4 FIG1 is a subdivision calculation diagram in an embodiment of the present invention;

[0044] Figure 5 FIG2 is a subdivision calculation diagram in an embodiment of the present invention;

[0045] Figure 6 FIG3 is a diagram showing the subdivision calculation in an embodiment of the present invention

[0046] Figure 7 FIG4 is a subdivision calculation diagram in an embodiment of the present invention;

[0047] Figure 8 The graph after retopology according to an embodiment of the present invention;

[0048] Figure 9 Schematic diagram of subdivision of all surfaces in an embodiment of the present invention;

[0049] Figure 10 This is a subdivided model diagram of an embodiment of the present invention;

[0050] Figure 11 4 is a comparison diagram before and after segmentation of an embodiment of the present invention. DETAILED DESCRIPTION

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0052] In traditional facet refinement algorithms, all facets of the model are refined. Some originally straight connected facets do not need to be refined. Traditional Catmull-Clark or Loop subdivision subdivides all facets. The present invention adopts triangular facet model subdivision optimization based on vertex normal interpolation, and realizes smoothing of the abrupt areas of the model according to different thresholds, while not processing the non-abrupt areas. Therefore, after the model is optimized, the protrusions of abnormal points on the model are reduced, the redundancy of the facets is reduced, and a better display effect is maintained. The running performance of the model is greatly improved, and the display effect and smoothness of real-scene 3D rendering and demonstration are guaranteed.

[0053] Specifically, the present invention adopts vertex normal interpolation to interpolate a vector between each two adjacent vertex normals in the triangular face that exceeds the face protrusion index threshold. According to the set subdivision threshold, this vector takes the middle point of the two vertices of the two vertex normals as the starting point, and the length generates a new vertex according to the subdivision threshold. The three vertices of the triangular face will produce three such new vertices. These three vertices are re-topologically combined with the original triangle vertices to achieve the purpose of targeted refinement, which will produce the effect of refined edges. Then, by using smooth shading, a relatively excellent smooth display effect can be achieved.

[0054] like Figure 1 , a triangular mesh subdivision method based on vertex normal interpolation calculation, comprising the following steps:

[0055] S1, encode and store all points, lines, and surfaces. Vertex numbers are named as capital letters P + serial number; line numbering rules are English letters L + "point 1-point 2"; surface numbering rules are capital letters F + "point 1-point 2-point 3". The final encoding effect is as follows Figure 2 As shown, the initial triangle model structure diagram is as follows Figure 3 shown.

[0056] S2, calculate the protrusion index T of all surfaces F Calculating the protrusion index of all faces refers to sequentially calculating the weighted average of the angles between each selected face and the adjacent faces multiplied by the line length to obtain the protrusion index of each selected face.

[0057] Specifically, take one of the faces, F1-2-3, as an example, and calculate the protrusion index of the face as follows:

[0058] S21. Calculate the normals of all faces by taking the cross product of any two line vectors on the face to get the face normal. Specifically, points P1, P2, and P3 are the vertices of F1-2-3. The three points P1 (x1, y1, z1), P2 (x2, y2, z2), and P3 (x3, y3, z3) can be obtained by subtracting their coordinates to get the following vectors:

[0059] vector

[0060] vector

[0061] vector

[0062] Can be vector and The cross product of , we can find the normal vector of this face F1-2-3 for:

[0063]

[0064] S22, calculate the face normal to get the face angle, F1-3-4 is an adjacent face of F1-2-3, the same as step S21, the normal vector of F1-3-4 can be calculated similarly,

[0065] S23. Calculate the angle F1-3-4 as the angle θ between F1-2-3 using the vector dot product formula:

[0066]

[0067]

[0068] in, is the dot product between the normal vectors, and is the modulus (length) of the normal vector

[0069] S24, normalized angle index, the angle θ ranges from 0° (completely coplanar) to 180° (completely opposite), and is normalized using a sine function, with the normalized value = sinθ, representing the angle index.

[0070] When θ = 90°, the normalized value is 1, which means the two planes are perpendicular. When θ = 0° or θ = 180°, the normalized value is 0, which means the two planes are parallel.

[0071] S25, angle sinθ and common side length are used to calculate the side length weighted angle index

[0072] The three sides of F1-2-3 are L1-2, L2-3, and L1-3, and their lengths can be obtained by calculating the vector modulus. The lengths are l L1-2 、l L2-3 、l L1-3 The overall angle index can be calculated, which is the protrusion index T of this surface. F1-2-3 .

[0073]

[0074] S3, input the subdivision threshold degree a, and input the subdivision strength b.

[0075] Among them, the subdivision threshold a is used to: filter the faces that need to be subdivided, and the value range is greater than 0 and less than 1;

[0076] The subdivision strength b is the ratio of the length of the line segment between the interpolation point and the midpoint of the line to the modulus of the interpolation vector. The subdivision strength b is used to: when subdividing, the distance of the selected point from the original surface, and the value range is greater than 0 and less than 1.

[0077] S4, the subdivision threshold a determines all the faces that need to be subdivided. For example, if the threshold is set to sin45°, the protrusion index T of face F1-2-3 is F1-2-3 If it is greater than the threshold (sin45°), it needs to be subdivided. F1-2-3 If the angle is less than sin45°, no subdivision is required.

[0078] S5, detailed calculation. Specifically:

[0079] S51, calculating the surface normals around the current surface, with the direction inward, and calculating the surface normal of the current surface, with the direction outward;

[0080] S52, calculating the vertex normal of the current triangle based on the above two calculations;

[0081] S53, calculating the interpolation vector of the vertex normal to obtain the interpolation normal, taking the midpoint of the edge as the starting point, and combining it with the subdivision strength b to obtain the interpolation point;

[0082] S54, generates new topological triangles and the subdivision is completed.

[0083] Example: Calculate the normals of the surrounding faces (inward) and the current face normal (outward). The direction of the vertex normal calculated in this way is toward the inside of the triangle, preventing the subdivision direction from diverging. Calculate the current triangle vertex normal based on the above two face normals.

[0084] like Figure 4 As shown, the vertex normal is calculated as the average of the adjacent face normals. In this method, the normals of the surrounding faces (inward) are used to calculate the current face normal (outward). For example,

[0085] The vertex normal vector is interpolated to obtain the interpolated normal, starting from the edge midpoint and combined with the subdivision strength b to obtain the interpolated point. Figure 5 As shown. Vertex normal N P2 With N P3 The interpolation vector is N P2-P3 , N P2-P3 Move the starting point to P2-3 , we get point PN2-3, which is the interpolation point. The same process is used to get points PN1-2 and PN1-3.

[0086] Generate new topological triangles, such as Figures 6 to 8 As shown, the subdivision of F1-2-3 is completed.

[0087] S6, loop all the faces to be subdivided and perform subdivision calculations. Figure 9 shown.

[0088] S7, re-topology optimization, e.g. Figure 10 shown.

[0089] S8, encoding and storing the points, lines, and surfaces of the topology-optimized graphics.

[0090] like Figure 11 As shown, you can clearly see the comparison before and after segmentation.

[0091] This method uses interpolation of normals from the vertices of triangles in a 3D model to calculate new boundary points. This new boundary points are then retopologically optimized with the original model. This smoothing optimization is performed on areas with larger angles in the model, achieving targeted subdivision and achieving optimal smooth shading. This method, when applied to 3D model scenes, allows for low resource usage and optimal display quality. The benefits are as follows:

[0092] 1. Normal interpolation combined with subdivision

[0093] Instead of simply subdividing all faces, this method optimizes the surface by inserting a vector and using normal interpolation. Compared with traditional subdivision methods, this subdivision method based on normal interpolation can significantly reduce the number of patches and reduce the computational burden.

[0094] Traditional subdivision algorithms, such as Catmull-Clark or Loop subdivision, typically uniformly subdivide all triangles, resulting in a dramatic increase in the number of facets. This method, however, uses normal interpolation to locally optimize facets, avoiding unnecessary subdivisions, keeping the facet count low, and improving surface smoothness.

[0095] 2. Reduce redundant patches

[0096] This method effectively reduces the increase in redundant facets when refining edges, a challenge faced by traditional subdivision methods. By not fully subdividing all faces and instead controlling detail only through normal interpolation, the rate at which the number of facets increases can be slowed, avoiding a sharp drop in performance in large-scale scenes.

[0097] 3. Local topology optimization

[0098] This method refines edges by retopologically refining them, which can be understood as refining and reorganizing the local mesh. This local topology optimization approach combines the advantages of global and local refinement, ensuring rendering quality while avoiding unnecessary global subdivision overhead.

[0099] 4. Normal interpolation and visual effect improvement

[0100] During normal interpolation, the focus is on improving mesh smoothness, not just subdividing the model. Traditional smooth shading relies on interpolating vertex normals, but this can lead to noticeable visual stair-stepping when the mesh is not detailed enough. This method enhances the smoothness of normal transitions by interpolating intersections and retopologically reconstructing triangles.

[0101] 5. Application potential in large-scale scenarios

[0102] When rendering large-scale scenes, especially when dealing with complex surfaces, it is crucial to reduce the number of redundant facets while maintaining good rendering quality. This method, by thinning edges, can improve rendering quality while maintaining a low facet count, showing great potential for application.

[0103] 6. Innovations in Calculating the Surface Protrusion Index

[0104] For faces that need to be refined, the weighted calculation of the angle with the surrounding faces and the connecting lines is calculated to obtain the face protrusion index after weighted calculation. This protrusion index is related to the length of the common edge. The longer the length, the higher the weighted index. The length of the common edge between the facets (that is, the length of the edge shared between adjacent facets) will affect the visual protrusion effect. The longer the common edge, the more significant the protrusion effect. Therefore, a higher weight can be given to the long edge in the weight calculation. In this way, areas with longer common edges and larger angles will be subdivided first to enhance the performance of the protrusion area.

[0105] The present invention also discloses a computer-readable storage medium and a computer system, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed, it performs any of the methods described above. A computer system includes a processor and a storage medium, wherein the storage medium stores the computer program, and the processor reads and executes the computer program from the storage medium to perform any of the methods described above.

[0106] Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithmic steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of the two. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps are generally described above in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. A skilled person may implement the described functionality in different ways for each specific application, but such implementation decisions should not be interpreted as resulting in a departure from the scope of the present invention.

[0107] The various illustrative logic blocks, modules, and circuits described in conjunction with the embodiments disclosed herein may be implemented or performed using a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.

[0108] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read and write information from / to the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and storage medium may reside in a user terminal as discrete components.

[0109] In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functions may be stored on or transmitted via a computer-readable medium as one or more instructions or codes. Computer-readable media include both computer storage media and communication media, including any media that facilitates the transfer of a computer program from one location to another. A storage medium may be any available medium that can be accessed by a computer. By way of example and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Any connection is also properly referred to as a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwaves, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwaves are included in the definition of medium. As used herein, disk and disc include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc, where disks typically reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0110] The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0111] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A triangular mesh subdivision method based on vertex normal interpolation calculation, characterized in that: The following steps are involved: S1, encode and store all points, lines, and surfaces; S2, calculate the protrusion index of all surfaces; S3, input the subdivision threshold degree a and the subdivision strength b; S4, subdivision threshold degree a determines all faces that need to be subdivided; S5, subdivision calculation; S6, loop all the faces to be subdivided and perform subdivision calculations; S7, retopology optimization; S8, encoding and storing the points, lines, and surfaces of the topology-optimized graphics.

2. The method according to claim 1, wherein: Calculating the protrusion index of all surfaces in step S2 refers to sequentially calculating the weighted average of the angle between each selected surface and the adjacent surface multiplied by the line length to obtain the protrusion index of each selected surface.

3. The method according to claim 1, wherein: The subdivision threshold a in step S3 is used to screen the faces that need to be subdivided, and its value range is greater than 0 and less than 1; the subdivision strength b is used to determine the distance between the selected point and the original face during subdivision, and its value range is greater than 0 and less than 1.

4. The method according to claim 1, wherein: The subdivision strength b in step S3 is the ratio of the length of the line segment between the interpolation point and the midpoint of the line to the modulus length of the interpolation vector.

5. The method according to claim 1, wherein The detailed calculation in step S5 is as follows: S51, calculating the surface normals around the current surface, with the direction inward, and calculating the surface normal of the current surface, with the direction outward; S52, calculating the vertex normal of the current triangle based on the above two calculations; S53, calculating the interpolation vector of the vertex normal to obtain the interpolation normal, taking the midpoint of the edge as the starting point, and combining it with the subdivision strength b to obtain the interpolation point; S54, generates new topological triangles and the subdivision is completed.

6. A computer-readable storage medium, characterized in that: The medium stores a computer program, and after the computer program is run, the method according to any one of claims 1 to 5 is executed.

7. A computer system, characterized in that: The method comprises a processor and a storage medium, wherein the storage medium stores a computer program, and the processor reads and runs the computer program from the storage medium to execute the method according to any one of claims 1 to 5.

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