3D mesh reconstruction method based on T-spline subdivision wavelet transform

Abstract

The invention relates to the technical field of spline surface modeling, in particular to a T-spline subdivision wavelet transform-based 3D mesh reconstruction method, which comprises the following steps of: S1, reading a T-spline three-dimensional mesh model which comprises a normal mesh, a special mesh and a mesh with T-shaped nodes; and S2, analyzing the patches in the grid, and dividing the nodes in the grid into normal points, first-class T-shaped nodes, second-class T-shaped nodes and special grid points according to the isometric property and resolution layer number difference of common edges of adjacent patches. According to the method, a globally unified subdivision wavelet transform framework is constructed by introducing a progressive interpolation principle and a spline technology, adaptive adjustment of the sharpness of a grid feature region is realized by using adjustable control parameters, the reconstruction error of the three-dimensional grid is reduced, and the reconstruction precision of the three-dimensional grid is improved. And the multi-resolution drawing quality and the reconstruction precision are effectively guaranteed while the model compression efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of spline surface modeling technology, and in particular to a 3D mesh reconstruction method based on T-spline subdivision wavelet transform. Background Technology

[0002] In digital geometry processing, subdivision surface technology is often used to generate smooth and continuous model surfaces. Among them, T-spline technology, because it allows T-shaped nodes in the control mesh, breaks the limitation of traditional B-splines that must satisfy rectangular topology, and can express complex geometric shapes with fewer control points. Combined with wavelet analysis theory, the subdivision wavelet transform method based on T-splines constructs a multi-resolution hierarchical structure of the model by decomposing the 3D mesh into a low-resolution base mesh and a series of detail coefficients. This multi-scale representation method plays a fundamental and crucial role in application scenarios such as geometric compression, progressive transfer, real-time rendering, and detail editing of 3D models.

[0003] Existing technologies mostly directly adopt the traditional Catmull-Clark subdivision wavelet transform algorithm, lacking a globally unified optimization framework based on the principle of progressive interpolation and spline technology. Furthermore, they do not introduce control parameters that can adaptively adjust the sharpness for the feature regions of the mesh, resulting in large reconstruction errors when performing multi-resolution decomposition and reconstruction of T-spline 3D meshes. This makes it difficult to effectively maintain the geometric feature fidelity and rendering quality of the model while achieving high-efficiency compression. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a 3D mesh reconstruction method based on T-spline subdivision wavelet transform. It aims to improve the existing technology in T-spline mesh wavelet transform, which lacks a unified feature-sensitive optimization framework and adjustable parameters, resulting in large model reconstruction errors and difficulty in maintaining geometric feature fidelity under high compression ratios.

[0005] This invention provides the following technical solution: a 3D mesh reconstruction method based on T-spline subdivision wavelet transform, comprising:

[0006] S1. Read the T-spline 3D mesh model, which includes normal mesh, special mesh, and mesh with T-shaped nodes;

[0007] S2. Analyze the patches in the grid, and classify the nodes in the grid into normal points, first type T-shaped nodes, second type T-shaped nodes, and special grid points based on the equal length of the common edge of adjacent patches and the difference in the number of resolution layers.

[0008] S3. For the normal points, based on the principle of asymptotic interpolation and CB splines, the coefficients of vertices, edges and faces in the Catmull-Clark subdivision scheme are orthogonally calculated.

[0009] S4. For the first type of T-shaped node, it is further divided into four types according to its geometric structure: aggregated edge, exterior angle, shared exterior angle and interior angle, and updated by applying the corresponding subdivision formula respectively;

[0010] S5. For the second type of T-shaped node, keep its common edge vertex unchanged, and perform an update operation on the vertex associated with the specific mesh structure consisting of one long edge and two short edges that is adjacent to the common edge.

[0011] S6. For the special grid point, keep its corner points unchanged and update its top edge face points according to a predefined order;

[0012] S7. Integrate the processing results of the normal points, the first type of T-shaped nodes, the second type of T-shaped nodes, and the special grid points, and execute the global T-spline grid wavelet decomposition and reconstruction algorithm to realize the multi-resolution representation of the three-dimensional grid model.

[0013] Preferably, the step of analyzing the patches in the mesh and classifying the nodes in the mesh into normal points, first-type T-shaped nodes, second-type T-shaped nodes, and special mesh points based on the equal length of the common edges of adjacent patches and the difference in the number of resolution layers specifically includes:

[0014] First, determine whether the common edge of two adjacent facets is of equal length;

[0015] If the common edges are of equal length, then it is further determined whether the resolution layer number of adjacent patches differs by 1. If so, the node is marked as a first-type T-shaped node. If the resolution layer number is the same, it is marked as a normal point.

[0016] If the common edges are of unequal length, further determine whether the resolution layer number of adjacent patches differs by 1. If so, mark the mesh at that location as a special mesh point. If the resolution layer number is the same, mark it as a second type T-shaped node.

[0017] Preferably, the orthogonalization calculation of vertex, edge, and face coefficients in the Catmull-Clark subdivision scheme for normal points, based on the principle of asymptotic interpolation and CB splines, specifically includes:

[0018] Based on the aforementioned progressive interpolation principle and CB splines, feature-sensitive control parameters and shape control parameters are introduced to determine the calculation coefficients of vertices, edges, and faces in the Catmull-Clark subdivision scheme.

[0019] Based on the calculated coefficients and vertex valences, orthogonalization is performed to obtain orthogonalized vertex coefficients, edge coefficients, and face coefficients.

[0020] During wavelet decomposition, the orthogonalized edge coefficients and face coefficients are used to update the vertices, and the edge points are updated and scaled according to predefined rules.

[0021] During wavelet reconstruction, the orthogonalized edge coefficients and face coefficients are applied in reverse to update the vertices, and the edge coefficients are merged and updated according to predefined rules.

[0022] Based on the orthogonalized vertex coefficients, the regular vertices are then subjected to final normalization.

[0023] Preferably, for the first type of T-shaped node, it is further divided into four types according to its geometric structure: converging edges, exterior angles, shared exterior angles, and interior angles, and the corresponding subdivision formulas are applied for updating each type. Specifically, this includes:

[0024] Identify the local geometry of the first type of T-shaped node, and classify it into aggregated edge, external angle, shared external angle or internal angle type based on the number and positional relationship of high-resolution and low-resolution patches around the node;

[0025] Specifically, if a node is surrounded by one high-resolution patch and one low-resolution patch, it is determined to be a converged edge; if it is surrounded by one high-resolution patch and three low-resolution patches, it is determined to be an external angle; if it is surrounded by two high-resolution patches and two low-resolution patches that are intersecting, it is determined to be a shared external angle; and if it is surrounded by three high-resolution patches and one low-resolution patch, it is determined to be an internal angle.

[0026] Based on the identified type, select the subdivision formula applicable to that type;

[0027] During wavelet decomposition, based on the selected subdivision formula, the edge points, vertices, and face points associated with this type of T-type node are updated and calculated in a predetermined logical order.

[0028] During wavelet reconstruction, based on the selected subdivision formula, the face points, vertices, and edge points associated with this type of T-shaped node are updated in reverse order according to a predetermined logical sequence.

[0029] Preferably, for the second type of T-shaped node, keeping its common edge vertices unchanged and performing an update operation on the vertices associated with the specific mesh structure consisting of one long edge and two short edges adjacent to the common edge specifically includes:

[0030] A sharp edge handling strategy is adopted to identify the common edge where the second type of T-shaped node is located, and to keep all vertices on the common edge unchanged in the vertex transformation step;

[0031] Identify a specific mesh structure that is adjacent to the common edge and consists of one long edge and two short edges;

[0032] During wavelet decomposition, for the vertices associated with the specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values.

[0033] During wavelet reconstruction, for the vertices associated with the specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values.

[0034] Preferably, for special grid points, keeping their corner points unchanged and updating their top edge face points according to a predefined order specifically includes:

[0035] Identify the special grid points and confirm their geometric features, such as unequal lengths of common edges between adjacent faces and a difference of 1 in the number of resolution layers.

[0036] During the subdivision wavelet transform process, the corner positions of the special grid points are kept unchanged;

[0037] During wavelet decomposition, the long side value and short side value of the common edge are distinguished, and the proportional relationship between the long side and the short side in the parameter domain is calculated to determine the geometric position parameter. Based on the geometric position parameter, the top edge face point associated with the special grid point is interpolated and updated according to a predefined order.

[0038] During wavelet reconstruction, based on the geometric position parameters, the top edge face points associated with the special grid points are calculated and updated according to a predefined order.

[0039] Preferably, the integration of the processing results for the normal points, the first type of T-shaped nodes, the second type of T-shaped nodes, and the special grid points, and the execution of the global T-spline grid wavelet decomposition and reconstruction algorithm specifically includes:

[0040] During wavelet decomposition, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to calculate the low-resolution grid and detail coefficients.

[0041] During wavelet reconstruction, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to reverse-fuse the detail coefficients and restore the high-resolution mesh.

[0042] By iteratively executing the decomposition and reconstruction process, a continuous representation of the three-dimensional mesh model at different resolution levels is generated.

[0043] The present invention has the following beneficial effects:

[0044] 1. In this invention, a globally unified subdivision wavelet transform framework is constructed by introducing the principle of progressive interpolation and spline technology. Adjustable control parameters are used to achieve adaptive adjustment of the sharpness of the mesh feature region, which reduces the reconstruction error of the three-dimensional mesh, improves the model compression efficiency, and effectively ensures the quality and reconstruction accuracy of multi-resolution rendering.

[0045] 2. In this invention, the second type of T-shaped nodes with unequal common edge lengths but the same number of resolution layers are included in the unified processing scope. For these nodes, which are often located in important geometric feature regions, a special vertex preservation and reverse recovery strategy is designed, thereby effectively avoiding the feature smoothing loss problem caused by the traditional algorithm ignoring such nodes, and enhancing the algorithm's ability to preserve the key geometric features of the model.

[0046] 3. In this invention, various T-shaped nodes are processed by extending the subdivision formula, and special quadrilateral meshes and special edges connecting different resolution levels are also taken into account. This comprehensive unified algorithm framework ensures the continuity and smoothness of the T-spline mesh surface during decomposition and reconstruction, providing robust and reliable technical support for the efficient compression and progressive transmission of 3D models. Attached Figure Description

[0047] Figure 1 This is a flowchart of a 3D mesh reconstruction method based on T-spline subdivision wavelet transform proposed in this invention.

[0048] Figure 2 This is a flowchart illustrating the processing of the T-spline mesh proposed in this invention.

[0049] Figure 3 This is a schematic diagram illustrating four topological classifications of the first type of T-shaped node based on the distribution of high and low resolution patches in an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of a local mesh structure of the second type of T-shaped node in an embodiment of the present invention;

[0051] Figure 5 This is a schematic diagram of a local mesh structure without T-shaped points in an embodiment of the present invention. Detailed Implementation

[0052] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] Please see Figures 1-5This invention provides a 3D mesh reconstruction method based on T-spline subdivision wavelet transform, comprising the following steps:

[0054] S1. Read the T-spline 3D mesh model, which includes normal mesh, special mesh, and mesh with T-type nodes;

[0055] Specifically, the T-spline mesh originates from the Catmull-Clark mesh, and the two share a natural structural similarity. The read T-spline 3D mesh model is denoted as M, and this model consists of a normal quadrilateral mesh portion M. norm Special quadrilateral grid section M S and T-spline mesh part M T The components together constitute a mathematical relationship:

[0056] M = M norm +M S +M T ;

[0057] Among them, the normal quadrilateral grid M norm This refers to a quadrilateral mesh region conforming to a conventional topological structure, which will be processed using the Catmull-Clark subdivision wavelet algorithm. The special quadrilateral mesh M... S This refers to a grid region containing two adjacent quadrilateral faces with unequal common side lengths and a difference of 1 in their resolution layer number. (T-spline grid, M) T This refers to a grid region containing T-shaped nodes. This region encompasses first-type T-shaped nodes with equal common edge lengths and a resolution layer number difference of 1, and second-type T-shaped nodes with unequal common edge lengths but the same resolution layer number. By reading this topology information, a data foundation is provided for subsequently adopting differentiated subdivision strategies for different regions.

[0058] S2. Analyze the patches in the grid, and classify the nodes in the grid into normal points, first type T-shaped nodes, second type T-shaped nodes, and special grid points based on the equal length of the common edge of adjacent patches and the difference in the number of resolution layers.

[0059] Furthermore, the mesh is analyzed, and based on the equal length of the common edges of adjacent meshes and the difference in resolution layers, the nodes in the mesh are classified into normal points, first-type T-shaped nodes, second-type T-shaped nodes, and special mesh points. The specific steps include:

[0060] First, determine whether the common edge of two adjacent facets is of equal length;

[0061] If the common edges are of equal length, then it is further determined whether the resolution layers of adjacent patches differ by 1. If so, the node is marked as a first-type T-shaped node; otherwise, it is marked as a normal point.

[0062] If the common edges are of unequal length, further determine whether the resolution layers of adjacent patches differ by 1. If so, mark the mesh at that location as a special mesh point; otherwise, mark it as a second type of T-shaped node.

[0063] Specifically, a node type index is established by traversing the faces in the mesh and their adjacency relationships. The determination process is as follows:

[0064] First, determine if the geometric lengths of the common edges of two adjacent faces are equal:

[0065] 1. If the length of the common edge is equal, further check whether the number of resolution layers of adjacent patches differs by 1:

[0066] If the number of resolution layers does not differ by 1, then the node is marked as a normal point;

[0067] If the resolution layers differ by 1, the node on the common edge is identified as a first-type T-shaped node and denoted as T1. To accurately match the subsequent subdivision formula, this step further counts the number and positional distribution of high-resolution and low-resolution patches around the node, performing the following fine-grained classification:

[0068] If a node is surrounded by one high-resolution patch and one low-resolution patch, it is considered an aggregated edge.

[0069] If a node is surrounded by one high-resolution patch and three low-resolution patches, it is determined to be an outer corner;

[0070] If a node is surrounded by two high-resolution patches and two low-resolution patches, and the two are intersecting, it is determined to be a shared outer corner;

[0071] If a node is surrounded by 3 high-resolution faces and 1 low-resolution face, it is determined to be an interior corner.

[0072] 2. If the lengths of the common edges are unequal, further check whether the number of resolution layers of adjacent patches differs by 1:

[0073] If the resolution layer number differs by 1, then that grid region is marked as a special grid point and assigned to M. s For example, a combination of facets with a resolution of 4, 3, and 3, which have different common edges but different levels, belongs to this category.

[0074] If the resolution and number of layers are the same, the node at that point is identified as a second type of T-type node and denoted as T2. This type of node is usually located in important geometric feature areas such as sharp corners or edges of the model. For example, for a combination of facets with a resolution of 4, 4, 4, although the common edges are of different lengths, the layers are the same, which belongs to this type.

[0075] The above classification logic ensures that all types of grid structures are fully covered and the correct indexes are established, providing a basis for subsequent steps to call the corresponding subdivision parameters.

[0076] like Figure 5 As shown, during the traversal, the system identifies topological relationships based on the face index. Taking face number 49 and face number 59 in the figure as an example, they share a vertical common edge. The system reads the resolution parameters of both faces. In this example, face 49 and face 59 are at the same resolution level or satisfy the continuity condition. Therefore, the vertices on this common edge are determined to be "no T-shaped points," i.e., "normal points." Such nodes do not require special T-shaped correction and directly enter the orthogonalization update process in the subsequent S3 step.

[0077] S3. For normal points, based on the principle of asymptotic interpolation and CB splines, the coefficients of vertices, edges, and faces in the Catmull-Clark subdivision scheme are orthogonally calculated.

[0078] Furthermore, for normal points, based on the principle of asymptotic interpolation and CB splines, the orthogonalization calculation of the vertex, edge, and face coefficients in the Catmull-Clark subdivision scheme specifically includes:

[0079] Based on the principle of asymptotic interpolation and CB splines, the calculation coefficients of vertices, edges, and faces in the Catmull-Clark subdivision scheme are determined.

[0080] The calculated coefficients are orthogonalized to obtain orthogonalized vertex coefficients, edge coefficients, and face coefficients.

[0081] During wavelet decomposition, orthogonalized edge and face coefficients are applied to update vertices, and edge points are updated and scaled according to predefined rules.

[0082] In the wavelet reconstruction process, the orthogonalized edge and face coefficients are applied in reverse to update the vertices, and the edge points are merged and updated according to predefined rules.

[0083] Based on the orthogonalized vertex coefficients, the regular vertices are then subjected to final normalization.

[0084] Specifically, based on the node type classification index table generated in step S2, for the regions marked as "normal points," that is, regions with continuous mesh topology and no resolution abrupt changes, this embodiment uses an improved Catmull-Clark subdivision rule for processing.

[0085] To overcome the limitations of traditional subdivision algorithms in shape control, this invention integrates the mathematical properties of asymptotic interpolation, shape control, and CB splines to derive a novel set of subdivision transformation formulas containing shape adjustment parameters. The limit point V in the subdivision transformation formula... ∞ The calculation is as follows:

[0086]

[0087] In the formula, V0 is the central vertex, V 2i-1 and V 2i Let a1(n), b1(n), and c1(n) be the ordered set of vertices within a ring neighborhood surrounding the central vertex; a1(n), b1(n), and c1(n) are weighted coefficients dependent on the vertex valence n, and their specific calculation expressions are as follows:

[0088]

[0089] First, define the control parameter angle α as ranging from 0 to π, and let the characteristic sensitive control parameter C... k =cosα, used to adjust the sharpness of the subdivision. To improve the efficiency of the algorithm, this embodiment pre-constructs an orthogonalization coefficient lookup table based on asymptotic interpolation and CB spline techniques, instead of solving the system of equations in real time at runtime.

[0090] For the surface wavelet and edge wavelet in the Catmull-Clark subdivision wavelet transform, with the control parameter α = 60°, i.e., C k With a typical setting of 0.5, the orthogonalization coefficients corresponding to different vertex valences are shown in Table 1 and Table 2, respectively:

[0091] Table 1. Orthogonalization coefficients for pre-calculated wavelet surface points (α = 60 degrees)

[0092]

[0093]

[0094] Table 2. Pre-calculated orthogonalization coefficients of edge point wavelets

[0095] <![CDATA[n0]]> <![CDATA[η0]]> <![CDATA[η1]]> <![CDATA[η2=η5]]> <![CDATA[η3=η4]]> σ 3 -0.214697 -0.149156 -0.038677 -0.024242 1.978194 4 -0.159232 -0.159232 -0.039555 -0.039555 1.921071 5 -0.128644 -0.164696 -0.040361 -0.046130 1.891928 6 -0.108991 -0.168099 -0.040917 -0.050113 1.874716 7 -0.095285 -0.170399 -0.041314 -0.052811 1.863500 8 -0.085158 -0.172053 -0.041611 -0.054754 1.855655 9 -0.077344 -0.173300 -0.041844 -0.056221 1.849865 10 -0.071107 -0.174276 -0.042031 -0.057370 1.845411 11 -0.065993 -0.175063 -0.042185 -0.058298 1.841868 12 -0.061707 -0.175713 -0.042315 -0.059065 1.838972

[0096] Based on the principle of asymptotic interpolation, the update of normal points follows a new subdivision formula with shape control parameters:

[0097]

[0098] Where V is the old vertex, e i For the old edge point, f i For traditional pastries, n is the price. The coefficients a1(n), b1(n), c1(n) are related to the shape parameter λ and the control parameter C.k There is a specific mapping relationship, and it is derived from the pre-calculated values ​​in Tables 1 and 2.

[0099] For all normal edge points on non-T-shaped edges, execute the update formula:

[0100]

[0101] Then the scaling formula is executed:

[0102] e i * = 2;

[0103] e in the formula i ' represents the i-th edge point to be updated, C k For the aforementioned control parameters, n represents the valence of the vertex associated with the edge, f' represents the face adjacent to the edge, and the modulo operation in the subscript is used to index adjacent face points in the topological ring.

[0104] For a regular vertex V on 3DMesh, the coefficients corresponding to the valence n in Tables 1 and 2 are applied for updating, and the update formulas are as follows:

[0105] V-=Y n *e' and V-=Z n *f';

[0106] Finally, normalization is performed:

[0107]

[0108] In the formula, V represents the coordinates of the vertex currently being processed, e' and f' are the edge and face points in the neighborhood of that vertex, respectively, and X... n Y n and Z n These represent the vertex weight coefficient, edge weight coefficient, and face weight coefficient after orthogonalization. These coefficients are obtained by linear combination of the original parameters λ, ω, η, etc. in the table above, in order to ensure the continuity and approximation accuracy of the subdivided surface.

[0109] S4. For the first type of T-type node, it is further divided into four types according to its geometric structure: aggregated edge, exterior angle, shared exterior angle and interior angle, and the corresponding subdivision formula is applied to update them respectively.

[0110] Furthermore, for the first type of T-shaped node, based on its geometric structure, it is further divided into four types: converging edges, exterior angles, shared exterior angles, and interior angles, and each is updated using corresponding subdivision formulas, specifically including:

[0111] Identify the local geometry of the first type of T-type node and classify it into aggregated edge, exterior angle, shared exterior angle, or interior angle type;

[0112] Based on the identified type, select the subdivision formula applicable to that type;

[0113] During wavelet decomposition, based on the selected subdivision formula, the edge points, vertices, and face points associated with this type of T-type node are updated and calculated in a predetermined logical order.

[0114] During wavelet reconstruction, based on the selected subdivision formula, the face points, vertices, and edge points associated with this type of T-shaped node are updated in reverse order according to a predetermined logical sequence.

[0115] Specifically, based on the classification results determined in step S2, which are based on the number and position distribution of surrounding high-resolution and low-resolution patches, update rules are defined for their corresponding edge points t, vertices T or V, face points f, and G-type edge points g:

[0116] 1. For cases where the edge is determined to be of the aggregated edge type (i.e., the node is surrounded by one high-resolution patch and one low-resolution patch), the edge update formula is:

[0117] and

[0118] The vertex update formula is:

[0119]

[0120] and its scaling factor

[0121] as well as and its scaling factor

[0122] The formula for updating pastry recipes is:

[0123] and

[0124] 2. For cases classified as external corners (i.e., the node is surrounded by one high-resolution patch and three low-resolution patches), the edge point update formula is:

[0125] and

[0126] The vertex update formula is:

[0127] and its scaling factor

[0128] as well as and its scaling factor

[0129] The formula for updating pastry recipes is:

[0130]

[0131] and

[0132] 3. For cases where the node is identified as having a shared outer corner (i.e., the node is surrounded by two high-resolution patches and two low-resolution patches arranged in an intersecting pattern), the edge point update formula is as follows:

[0133] and

[0134] The vertex update formula is:

[0135] and its scaling factor

[0136] as well as and its scaling factor

[0137] The formula for updating pastry recipes is:

[0138] and

[0139] 4. For cases where the node is identified as an interior corner (i.e., the node is surrounded by 3 high-resolution patches and 1 low-resolution patch), the edge point update formula is:

[0140] and

[0141] The vertex update formula is:

[0142] and its scaling factor

[0143] as well as and its scaling factor

[0144] The formula for updating pastry recipes is:

[0145]

[0146] and

[0147]

[0148] S5. For the second type of T-shaped node, keep its common edge vertices unchanged, and perform update operations on the vertices associated with the specific mesh structure consisting of one long edge and two short edges that are adjacent to the common edge.

[0149] Furthermore, for the second type of T-shaped node, keeping its common edge vertices unchanged, and performing update operations on the vertices associated with the specific mesh structure consisting of one long edge and two short edges adjacent to the common edge, specifically includes:

[0150] Identify the common edge containing the second type of T-shaped nodes, and keep all vertices on the common edge unchanged during the vertex transformation step;

[0151] Identify a specific mesh structure that is adjacent to a common edge and consists of one long edge and two short edges;

[0152] In the wavelet decomposition process, for the vertices associated with a specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values;

[0153] In the wavelet reconstruction process, for vertices associated with a specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values.

[0154] Specifically, for the second type of T-shaped node T2 identified in step S2, i.e., adjacent patches with unequal common edge lengths but the same number of resolution layers, such as a connection region with a resolution of 4, 4, 4, this embodiment adopts a reference sharp edge point processing strategy to maintain the geometric features of this region from undergoing unexpected smooth deformation. The processing includes:

[0155] 1. Anchor point locking: The long side vertex and the short side vertex on the unequal length common edge are regarded as feature anchor points. During the vertex update process of wavelet transform, their geometric coordinate values ​​are forced to remain unchanged, thereby fixing the skeleton structure of the mesh.

[0156] 2. Adjacent Vertex Update: For vertices on edges directly adjacent to the common edge, exhibiting a topology of one long edge corresponding to two short edges, a strategy of first regular update and then reverse recovery is adopted. That is, during the calculation process, the temporary position is first calculated using the regular subdivision formula in step S3, and then a reverse calculation is performed using a reverse operator based on sharp edge constraints to eliminate the over-smoothing effect caused by regular subdivision, thus obtaining the final vertex position that conforms to the geometric characteristics of the second type of T-shaped node. This process ensures that even in special regions with consistent resolution levels but inconsistent geometric subdivisions, the mesh can still maintain the tightness of topological connections and the accuracy of geometric representation.

[0157] S6. For special grid points, keep their corner points unchanged and update their top edge points according to a predefined order;

[0158] Furthermore, for special grid points, keeping their corner points unchanged and updating their top edge points according to a predefined order specifically includes:

[0159] Identify special grid points and confirm their geometric features, such as unequal lengths of common edges between adjacent faces and a difference of 1 in the number of resolution layers.

[0160] During the subdivision wavelet transform process, the corner positions of special grid points are kept unchanged;

[0161] During wavelet decomposition, the top edge face points associated with special grid points are calculated and updated according to a predefined order;

[0162] During wavelet reconstruction, the top edge points associated with special grid points are calculated and updated according to a predefined order.

[0163] Specifically, for the special grid points identified in step S2, namely the regions where the lengths of the common edges of adjacent patches are unequal and the difference in the number of resolution layers is 1, they are assigned to M. S Within this scope, the following processing strategy is adopted in this embodiment:

[0164] 1. Corner point position locking: During the subdivision process, the geometric coordinates of the corner points of this special mesh area are forcibly kept unchanged to maintain the stability of the mesh boundary;

[0165] 2. Obtaining geometric position parameters: First, identify the long and short sides of the common edge, and obtain their geometric length values ​​L respectively. long and L short Calculate the geometric position parameter γ = L short / L long This parameter is used to quantify the relative position of the top edge face point in the parameter domain;

[0166] 3. Update during wavelet decomposition: Based on a predefined order, prediction and updates are performed on the top edge face points using the geometric position parameter γ, and the detail coefficient d is calculated using the following formula:

[0167] p predict = (1-γ)×f left +γ×f right ;

[0168] d = f real -p predict ;

[0169] Where f real f represents the currently existing top edge facet point. left and f right p represents two reference points adjacent to this point. predict The predicted value is calculated based on geometric proportions, and d represents the saved high-frequency detail information;

[0170] 4. Update during wavelet reconstruction: During inverse reconstruction, the top edge points are also recovered based on the geometric position parameter γ, as shown in the formula.

[0171] f recon = (1-γ)×f left ′+γ×f right ′+d;

[0172] Where f recon For the reconstructed pasta, f left 'and f right ' represents the adjacent reference face point at the low-resolution level, and d represents the loaded detail coefficient.

[0173] By introducing the weighted interpolation calculation based on the γ value, it is ensured that the newly generated facets can accurately reflect the continuous transition of the geometry at complex boundaries where the mesh resolution changes abruptly and the geometric dimensions do not match, thus avoiding cracks or unnatural distortions.

[0174] S7. Integrate the processing results of normal points, first-type T-shaped nodes, second-type T-shaped nodes, and special grid points, and execute the global T-spline mesh wavelet decomposition and reconstruction algorithm to realize the multi-resolution representation of the three-dimensional mesh model.

[0175] Furthermore, by integrating the processing results for normal points, first-type T-shaped nodes, second-type T-shaped nodes, and special grid points, the global T-spline mesh wavelet decomposition and reconstruction algorithm is executed, specifically including:

[0176] During wavelet decomposition, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to calculate the low-resolution grid and detail coefficients.

[0177] During wavelet reconstruction, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to reverse-fuse the detail coefficients and restore the high-resolution mesh.

[0178] By iteratively executing the decomposition and reconstruction process, a continuous representation of the 3D mesh model at different resolution levels is generated.

[0179] Specifically, the local update results of the above-mentioned nodes are integrated into the global algorithm, and the G-shaped edges connecting different resolution levels are processed first:

[0180] If the G-shaped edge is not connected to an interior corner point, then execute:

[0181]

[0182] If the G-shaped edge is connected to an interior corner point, then execute:

[0183]

[0184] Where g1' is a G-type edge vertex, and V0 to V6 and T1 are the topological neighbor vertices surrounding this edge; then, wavelet detail coefficients are calculated and extracted, and the following is performed on all edges:

[0185] t' = m t and e' = m e ;

[0186] Where t' and e' are T-shaped edge points and ordinary edge points, respectively, and m t With m e These are the high-frequency detail coefficients obtained from the decomposition.

[0187] During the reconstruction phase, the inverse operation of the above process is performed, first by:

[0188] t′=t+m t e′=e+m e ;

[0189] The edge data is recovered, and then the G-type edges, face points, and vertices are processed in reverse order of decomposition. This includes the reverse recovery operation for T2 type points, as well as the addition update and coefficient multiplication recovery of edge points. In this way, the original high-resolution 3D model is accurately reconstructed from the low-resolution base mesh.

[0190] like Figure 4 As shown in the figure, a complex adjacent region is formed by facet 80 and faces 63 and 21. Here, due to specific differences in resolution level between facet 80 and faces 63 and 21 (e.g., a level difference greater than 1 or a specific geometric distribution), nodes on their common boundary cannot be interpolated using conventional methods, thus forming a second type of T-shaped node. In specific processing, the system will lock... Figure 4 The key corner points shown are used as feature anchor points. First, a global subdivision update is performed on the region. Then, the reverse recovery operator is used to force the anchor point positions back to the initial geometric state, thereby eliminating the need for mesh densification. Figure 4 The diagram shows the potential for geometric tearing at complex boundaries.

[0191] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A 3D mesh reconstruction method based on T-spline subdivision wavelet transform, characterized in that, include: S1. Read the T-spline 3D mesh model, which includes normal mesh, special mesh, and mesh with T-shaped nodes; S2. Analyze the patches in the grid, and classify the nodes in the grid into normal points, first type T-shaped nodes, second type T-shaped nodes, and special grid points based on the equal length of the common edge of adjacent patches and the difference in the number of resolution layers. S3. For the normal points, based on the principle of asymptotic interpolation and CB splines, the coefficients of vertices, edges and faces in the Catmull-Clark subdivision scheme are orthogonally calculated. S4. For the first type of T-shaped node, it is further divided into four types according to its geometric structure: aggregated edge, exterior angle, shared exterior angle and interior angle, and updated by applying the corresponding subdivision formula respectively; S5. For the second type of T-shaped node, keep its common edge vertex unchanged, and perform an update operation on the vertex associated with the specific mesh structure consisting of one long edge and two short edges that is adjacent to the common edge. S6. For the special grid point, keep its corner points unchanged and update its top edge face points according to a predefined order; S7. Integrate the processing results of the normal points, the first type of T-shaped nodes, the second type of T-shaped nodes, and the special grid points, and execute the global T-spline grid wavelet decomposition and reconstruction algorithm to realize the multi-resolution representation of the three-dimensional grid model.

2. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, The analysis of the patches in the mesh, based on the equal length of the common edges of adjacent patches and the difference in resolution layers, classifies the nodes in the mesh into normal points, first-type T-shaped nodes, second-type T-shaped nodes, and special mesh points, specifically including: First, determine whether the common edge of two adjacent facets is of equal length; If the common edges are of equal length, then it is further determined whether the resolution layer number of adjacent patches differs by 1. If so, the node is marked as a first-type T-shaped node. If the resolution layer number is the same, it is marked as a normal point. If the common edges are of unequal length, further determine whether the resolution layer number of adjacent patches differs by 1. If so, mark the mesh at that location as a special mesh point. If the resolution layer number is the same, mark it as a second type T-shaped node.

3. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, The orthogonalization calculation of vertex, edge, and face coefficients in the Catmull-Clark subdivision scheme for normal points, based on the principle of asymptotic interpolation and CB splines, specifically includes: Based on the aforementioned progressive interpolation principle and CB splines, feature-sensitive control parameters and shape control parameters are introduced to determine the calculation coefficients of vertices, edges, and faces in the Catmull-Clark subdivision scheme. Based on the calculated coefficients and vertex valences, orthogonalization is performed to obtain orthogonalized vertex coefficients, edge coefficients, and face coefficients. During wavelet decomposition, the orthogonalized edge coefficients and face coefficients are used to update the vertices, and the edge points are updated and scaled according to predefined rules. During wavelet reconstruction, the orthogonalized edge coefficients and face coefficients are applied in reverse to update the vertices, and the edge coefficients are merged and updated according to predefined rules. Based on the orthogonalized vertex coefficients, the regular vertices are then subjected to final normalization.

4. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, For the first type of T-shaped node, based on its geometric structure, it is further divided into four types: aggregated edges, exterior angles, shared exterior angles, and interior angles, and updated using corresponding subdivision formulas. Specifically, this includes: Identify the local geometry of the first type of T-shaped node, and classify it into aggregated edge, external angle, shared external angle or internal angle type based on the number and positional relationship of high-resolution and low-resolution patches around the node; Specifically, if a node is surrounded by one high-resolution patch and one low-resolution patch, it is determined to be a converged edge; if it is surrounded by one high-resolution patch and three low-resolution patches, it is determined to be an external angle; if it is surrounded by two high-resolution patches and two low-resolution patches that are intersecting, it is determined to be a shared external angle; and if it is surrounded by three high-resolution patches and one low-resolution patch, it is determined to be an internal angle. Based on the identified type, select the subdivision formula applicable to that type; During wavelet decomposition, based on the selected subdivision formula, the edge points, vertices, and face points associated with this type of T-type node are updated and calculated in a predetermined logical order. During wavelet reconstruction, based on the selected subdivision formula, the face points, vertices, and edge points associated with this type of T-shaped node are updated in reverse order according to a predetermined logical sequence.

5. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, For the second type of T-shaped node, keeping its common edge vertices unchanged and performing update operations on the vertices associated with the specific mesh structure consisting of one long edge and two short edges adjacent to the common edge specifically includes: A sharp edge handling strategy is adopted to identify the common edge where the second type of T-shaped node is located, and to keep all vertices on the common edge unchanged in the vertex transformation step; Identify a specific mesh structure that is adjacent to the common edge and consists of one long edge and two short edges; During wavelet decomposition, for the vertices associated with the specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values. During wavelet reconstruction, for the vertices associated with the specific mesh structure, a regular vertex update operation is first performed, followed by a reverse operation to restore their initial values.

6. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, The specific steps for keeping the corner points unchanged and updating the top edge points according to a predefined order for special grid points include: Identify the special grid points and confirm their geometric features, such as unequal lengths of common edges between adjacent faces and a difference of 1 in the number of resolution layers. During the subdivision wavelet transform process, the corner positions of the special grid points are kept unchanged; During wavelet decomposition, the long side value and short side value of the common edge are distinguished, and the proportional relationship between the long side and the short side in the parameter domain is calculated to determine the geometric position parameter. Based on the geometric position parameter, the top edge face point associated with the special grid point is interpolated and updated according to a predefined order. During wavelet reconstruction, based on the geometric position parameters, the top edge face points associated with the special grid points are calculated and updated according to a predefined order.

7. The 3D mesh reconstruction method based on T-spline subdivision wavelet transform according to claim 1, characterized in that, The integration of the processing results for the normal points, the first type of T-shaped nodes, the second type of T-shaped nodes, and the special grid points, and the execution of the global T-spline grid wavelet decomposition and reconstruction algorithm specifically includes: During wavelet decomposition, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to calculate the low-resolution grid and detail coefficients. During wavelet reconstruction, the subdivision formulas and update rules corresponding to each point type are called in a predetermined logical order to reverse-fuse the detail coefficients and restore the high-resolution mesh. By iteratively executing the decomposition and reconstruction process, a continuous representation of the three-dimensional mesh model at different resolution levels is generated.

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