JP2004295258A - Surface detail extracting system and surface detail extracting program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To extract surface details in the state where reusability is high from a triangular mesh model having a detailed shape on its surface. <P>SOLUTION: A basic shape estimating part 11 applies a low-pass filter to a triangular mesh model to estimate a basic shape mesh whose surface is considered to have a detailed shape synthesized. A high-frequency component extracting part 12 regards the detailed shape as a high-frequency component and extracts the high-frequency component lost by the low-pass filter. A parameterization generating part 13 generates a parameterization having, on its basic plane, a phase structure for each apex of the estimated basic shape mesh. A surface detail generating part 14 imparts a height value based on the high-frequency component to each apex of the parameterization, thereby generating a surface detail mesh. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a surface detail extraction system and a surface detail extraction program for extracting a detailed shape from a triangular mesh model having a detailed shape on a surface.
[0002]
[Prior art]
In industrial products, there are many surface detailed composite shapes in which detailed shapes (surface details) such as characters and patterns composed of minute irregularities are synthesized on the surface of the basic shape on the surface of the shape. In a design design for such an industrial product, if the basic shape is a complicated curved surface, it is complicated and difficult to design surface details directly on the basic shape. Therefore, if the surface details and the basic shape are individually designed in the initial stage of the design, and the surface details can be accurately combined with the surface of the basic shape in the final stage, the design of the surface detailed composite shape can be realized easily and efficiently.
[0003]
The mesh model is a model in which an object shape is approximately represented as a polyhedron formed by a set of minute planes. Among them, in particular, those having all triangular surfaces are called triangular mesh models, which have been applied to various fields of shape representation because of their advantages such as easy operation of geometric operation and topology management, and high degree of freedom in shape representation. I have. In addition, a large-scale mesh model can be processed by improving computer resources, and the triangular mesh model is being used as a shape model of an application that requires a highly accurate shape representation. However, almost no triangular mesh modeling method has been proposed for designing the above-described detailed surface composite shape. Therefore, the inventors are researching a surface detail synthesis method for synthesizing the individually designed surface details to a local region of the basic shape surface with high accuracy for a triangular mesh model.
[0004]
By the way, if only the surface details can be extracted from the triangle mesh model of the existing surface detail composite shape, the reusability of the existing triangle mesh model can be improved by combining with the above-mentioned surface detail composition method, and the surface detail composite shape can be improved. Can be increased.
[0005]
There have been few studies on methods for extracting only surface details from surface detail composite shapes represented by triangular mesh models, and the only method for extracting surface details from mesh models with subdivision connectivity has been proposed ( Non-Patent Document 1). In this extraction method, a difference between a smooth curved surface obtained by fitting a subdivided curved surface from a coarse initial control mesh to an original mesh and an original shape is extracted as surface details. In this extraction method, the degree of surface detail extraction can be controlled with one parameter, and further interactive processing is possible.
[0006]
In addition, as an existing study that separately handles the surface details of a triangular mesh model from the basic shape, there is a study that holds detailed displacement of the shape surface as scalar displacement and expresses compact mesh data (Non-Patent Document See 2, 3). Prior art documents related to the invention of this application, including others, are as follows.
[0007]
[Non-patent document 1]
Henning Biermann, Ioana Martin, Fausto Bernardini, Denis Zorin, Cut-and-Paste Editing of Multisolution Solutions, proc. of SIGGRAPH 2002 Proceedings, pp. 312-321, 2002
[0008]
[Non-patent document 2]
I. Guskov, K .; Vidimce, W.C. Sweldens and P.S. Schroder: Normal Meshes, Proc. of SIGGRAPH2000, pp. 95-102, 2000
[0009]
[Non-Patent Document 3]
A. Lee, H .; Moreton and H.M. Hoppe: Displaced Subdivision Surface, Proc. of SIGGRAPH2000, pp. 85-94, 1999
[0010]
[Non-patent document 4]
G. FIG. Taubin: A Signal Processing Approach to Fair Surface Design, proc. of SIGGRAPH '95, pp. 351-358, 1995
[0011]
[Problems to be solved by the invention]
However, the extraction method of Non-Patent Document 1 cannot be applied to an arbitrary-phase mesh model. In addition, the extracted surface details are maps of minute vectors that are strictly associated with the subdivision connectivity, and are not effective from the viewpoint of individual management and visualization. The reusability was poor.
[0012]
The surface details separated by the methods of Non-Patent Documents 2 and 3 are maps of minute vectors strictly associated with the subdivision connectivity, similar to the method of Non-Patent Document 1, and include individual management and visual However, it is not effective from the viewpoint of formation, and is also inferior in reusability when synthesized on a surface of another basic shape.
[0013]
The present invention has been made in view of the above, and an object of the present invention is to provide a surface detail extracting system and a surface capable of extracting surface details from a triangular mesh model having a detailed shape on a surface in a highly reusable state. It is to provide a detailed extraction program.
[0014]
[Means for Solving the Problems]
According to a first aspect of the present invention, there is provided a surface detail extraction system comprising: a basic shape estimating unit configured to estimate a basic shape mesh by applying a low-pass filter to a triangular mesh model in which a detailed shape is synthesized on a surface; High-frequency component extraction means for extracting the extracted high-frequency component, parameterization generation means for generating parameterization having a topological structure of each vertex of the estimated basic shape mesh in a basic plane, and for each vertex of the parameterization Surface detail generation means for generating a surface detail mesh by giving a height value based on the high frequency component.
[0015]
According to the present invention, a low-pass filter is applied to a triangular mesh model to estimate a basic shape mesh that is considered to have a detailed shape synthesized on the surface, and the detailed shape is regarded as a high-frequency component and lost by the low-pass filter. Extracts the extracted high-frequency components, generates a parameterization with the topological structure of each vertex of the estimated basic shape mesh in the basic plane, and gives a height value based on the high-frequency component to each vertex of this parameterization Thereby, a surface detail mesh is generated. As a result, the surface detail mesh is reproduced on three-dimensional coordinates with the bottom as the basic plane, and is expressed in a format independent of the basic shape mesh, thereby facilitating individual management and visualization of the surface detail mesh. In this case, the reusability is improved when the detailed surface mesh is combined with the surface of another basic shape mesh.
[0016]
In the above surface detail extraction system, the basic shape estimating means applies a Taubin filter function using Laplacian defined for each vertex of the triangular mesh model.
[0017]
According to the present invention, by applying a Taubin filter function that can be set to control the filtering strength, filtering that flexibly corresponds to the shape of the surface details in the triangular mesh model is enabled.
[0018]
In the above-described surface detail extraction system, the basic shape estimating means is an Laplacian near n which is obtained by extending the Laplacian to vertices near n.
[0019]
In the present invention, the Laplacian in the Taubin filter function is extended to the Laplacian near n, so that a stronger low-pass filtering effect can be obtained.
[0020]
In the above-described surface detail extraction system, the high-frequency component extracting means obtains, as a high-frequency component, a moving amount of each vertex of the triangular mesh model by applying the low-pass filter.
[0021]
In the present invention, the amount of movement of each vertex of the triangle mesh model due to the application of the low-pass filter, that is, the difference between the estimated basic shape mesh and each vertex coordinate of the triangle mesh model, is lost by the low-pass filter. High frequency components can be extracted.
[0022]
In the above-described surface detail extraction system, the parameterization generation unit applies a linear piecewise mapping to a parameter plane to each vertex of the estimated basic shape mesh.
[0023]
In the present invention, by applying a linear piece mapping to each vertex of the estimated basic shape mesh, by appropriately designing the linear piece mapping, for example, on a triangular mesh model such as ridge length Specific metrics can be stored on parameterization.
[0024]
In the above-mentioned surface detail extraction system, the parameterization generating means solves each vertex so that a weighted sum of an evaluation function related to ridge line length conservation and an evaluation function for signed area conservation is minimized.
[0025]
In the present invention, by solving for each vertex the problem of minimizing the weighted sum of the evaluation function relating to the edge length conservation degree and the signed area conservation evaluation function, the edge length in the real space can be minimized on the parameter plane. It preserves and enables the construction of parameterization that does not cause surface interference.
[0026]
In the above-described surface detail extraction system, the surface detail generation unit gives a signed intensity defined by using a high-frequency component and a normal vector for each vertex of the parameterization as a height value to the vertex. I do.
[0027]
In the present invention, for each vertex of the parameterization, a signed value defined using a high-frequency component and a normal vector is given to each vertex as a height value, so that the unevenness of the detailed shape is set to a height value. A surface detail mesh is obtained.
[0028]
A surface detail extraction program according to a second aspect of the present invention includes a basic shape estimation process for estimating a basic shape mesh by applying a low-pass filter to a triangular mesh model in which a detailed shape is synthesized on a surface; High-frequency component extraction processing for extracting the extracted high-frequency component, parameterization generation processing for generating a parameterization having a topological structure of each vertex of the estimated basic shape mesh on a basic plane, and for each vertex of the parameterization. And a computer for executing a surface detail generation process of generating a surface detail mesh by giving a height value based on the high frequency component.
[0029]
According to the present invention, the basic shape estimation processing, the high-frequency component extraction processing, the parameterization generation processing, and the surface detail generation processing are executed by a program, so that the present method can be executed by a general-purpose computer on which the program is installed. It is possible to realize.
[0030]
BEST MODE FOR CARRYING OUT THE INVENTION
[Overview of extraction and synthesis of surface details]
As shown in the functional block diagram of FIG. 1, a surface detail extraction / synthesis system to which the surface detail extraction system according to one embodiment is applied includes a triangular mesh model (hereinafter, referred to as a “mesh model”) M representing a surface detail synthesized shape. A triangular mesh model (hereinafter referred to as “surface detail mesh”) M that represents a detailed shape such as characters and patterns composed of minute irregularities from the surface of_DAnd a surface detail mesh M extracted or individually designed_DDetail database (surface detail DB) 2 that stores and manages the data, and a triangular mesh model (hereinafter, referred to as “basic shape mesh”) M that represents a basic shape with no detailed shape combined_BShape database (basic shape DB) 3 that stores and manages the surface details mesh M read out from the surface details database 2_DIs the basic shape mesh M_BAnd a triangular mesh model (hereinafter referred to as “surface detailed composite mesh”) M_CIs provided with a surface detail synthesizing system 4 that outputs the following. The surface detail extracting system 1 and the surface detail synthesizing system 4 are configured by a computer, and the surface detail database 2 and the basic shape database 3 are configured by a large-capacity storage device.
[0031]
This surface detail extraction / synthesis system uses a surface detail mesh M in the initial stage of design._DAnd basic shape mesh M_BCan be individually designed, and in the final stage, the surface detail mesh M_DWith any basic shape mesh M_BIt is possible to synthesize with high precision on the surface of the. The triangular mesh modeling method of the detailed surface synthesized shape by the individual design and synthesis has the following advantages.
[0032]
1) Ease of design: The surface details can be independently designed as, for example, irregularities with respect to a plane, not on a complicated basic shape. Therefore, the design and correction of the surface details can be easily and efficiently performed.
[0033]
2) Improvement of data reusability: By individually designing and storing surface details and basic shapes, each shape data can be reused for another shape design.
[0034]
3) Improvement of shape design variation: It is possible to design a surface detail composite shape by combining various surface details and a basic shape, and the design design variation is improved.
[0035]
A detailed surface extraction system 1 applied to such a detailed surface extraction / synthesis system will be described below.
[0036]
[Basic concept of surface detail extraction]
There are the following two problems to extract only the surface detail mesh from the surface of the existing mesh model in which the surface detail has been synthesized, and to enable reuse by synthesis into another basic shape mesh.
[0037]
(1) Separation of basic shape estimation and surface details
The surface details are synthesized on the surface of a certain basic shape mesh. In order to extract the surface detail mesh, it is necessary to estimate a basic shape mesh for which the surface detail is considered to have been synthesized, and to separate the surface detail mesh.
[0038]
(2) Independent representation of surface details
Information on the surface detail mesh separated from the basic shape mesh should be capable of independent data management to improve its reusability, and should be expressed in a format independent of the basic shape mesh .
[0039]
In this extraction method, the irregular shape due to the surface details of the mesh model is regarded as a high-frequency component. As a result, the basic shape mesh in which the surface details are estimated to have been synthesized in the problem (1) can be obtained by low-pass filtering on the mesh model in which the surface details have been synthesized. Since the definition of the surface detail mesh to be extracted differs depending on the user, low-pass filtering needs to be able to flexibly control the strength. For example, there is a case where it is desired to selectively extract irregularities composed of large areas such as characters and patterns from irregularities composed of small areas such as the roughness of the shape surface. In this method, in order to meet such a demand, a method of Taubin et al., Which can make detailed settings for controlling the strength of filtering, is used (see Non-Patent Document 4). The information of the unevenness with respect to the basic shape mesh of the surface detail mesh is expressed as a difference between the shape after filtering and the original shape.
[0040]
On the other hand, with respect to the problem (2), in the present extraction method, the surface detailed mesh separated from the basic shape mesh is represented as a model having the irregularities of the detailed shape with respect to the basic shape mesh as height values of vertices. Resolve. The topological structure of the surface detail mesh uses the topological structure of the triangular mesh model before separation so as not to impair the degree of freedom in expressing shapes such as sharp edges. The height value representing the unevenness with respect to the basic shape mesh is represented by the intensity (norm) at each vertex of the high frequency component separated by the filtering. In addition, in order to define a basic plane having a topological structure of the triangular mesh model before separation, the method uses parameterization. The parameterization is a plane triangulation graph having vertices corresponding to the vertices of the triangular mesh model on a one-to-one basis on a parameter plane, as described later. To extract the surface detail mesh that preserves the metric on the basic shape mesh surface, construct a parameterization that preserves the metric regarding the estimated distance of the basic shape mesh surface. Lastly, the constructed parameterization is defined as a domain, and each vertex of the parameterization is modified based on the high-frequency component to obtain a detailed surface mesh M._DGenerate
[0041]
That is, in the present method, the high-frequency component lost by the low-pass filtering of the mesh model M is regarded as expressing the uneven shape of the surface detail mesh with respect to the basic shape mesh, and the high-frequency component is expressed on the basic plane having the phase structure of the basic shape mesh By giving the unevenness as a height value, the surface detail mesh M_DGenerate
[0042]
[Outline of surface detail extraction system]
As shown in the functional block diagram of FIG. 2, the detailed surface extraction system 1 according to the present embodiment has a configuration including a basic shape estimating unit 11, a high-frequency component extracting unit 12, a parameterization generating unit 13, and a detailed surface generating unit 14. is there.
[0043]
The outline of the processing in each unit is as follows. The basic shape estimating unit 11 applies a low-pass filter to the mesh model M expressing the surface detail composite shape, and outputs the basic shape mesh M without the surface details combined._BIs estimated. The high frequency component extraction unit 12 extracts high frequency components regarded as surface details from the surface of the mesh model M. The parameterization generation unit 13 generates parameterization for defining a basic plane having a topological structure for each vertex of the estimated basic shape mesh. The surface detail generation unit 14 gives a height value based on the high frequency component to each vertex of the parameterization, and generates a surface detail mesh M_DGenerate
[0044]
The processing in the basic shape estimating unit 11, high-frequency component extracting unit 12, parameterization generating unit 13, and surface detail generating unit 14 is executed by a surface detail extracting program installed in a computer. The surface detail extraction program may be installed, for example, by downloading it to a computer via a network, or by inserting a storage medium storing the program into a predetermined slot of the computer. Here, the storage medium refers to various storage media capable of storing programs, such as a magnetic disk, an optical disk, a magneto-optical disk, and a semiconductor memory.
[0045]
[Estimation of basic shape]
The basic shape estimating unit 11 uses, as a low-pass filter, a method of Taubin et al., Which can make detailed settings for controlling the strength of filtering (see Non-Patent Document 4). The method of Taubin et al. Can interpret the filtering based on the Fourier transform on the discrete signal as a generalization to the triangular mesh model based on the smoothing using the Gaussian function.
[0046]
The mesh model M is composed of n vertex strings (p₁, ..., p_n), First, the Laplacian Δp of the following equation (1)_iTo each vertex p of the mesh model M_iIs defined.
[0047]
ΔP_i= W_ij(P_j-P_i(1)
Where Σ is j∈i^*Shows the discrete integral at. i^*Is the set of vertices adjacent to vertex i, w_ijIs a weight of a positive value whose sum with j is 1. Weight w_ijHas several choices depending on the nature of the filtering required, but Taubin et al. Assume that the weight is the inverse of the number of adjacent vertices w_ij= 1 / | i^*| Is used. When equation (1) is expressed as a matrix, a matrix W = ｛w having weights as elements_ij｝, Unit matrix I, P = ｛p_iUsing 表, ΔP = − (I−W) P = −KP. K is a diagonal matrix having a diagonal component of 1 and a component corresponding to an adjacent vertex of -1/2. The matrix K is composed of n eigenvalues k_iAnd the eigenvector e that forms the basis_ihave. Eigenvector e of matrix K₁, ..., e_nIs considered as a natural vibration mode, and the corresponding eigenvalue k₁, ..., k_nCan be considered as the corresponding natural frequency. Since the matrix W is a probability matrix in which the sum of rows having two non-negative elements に in each row is 1, the eigenvalue is limited by an upper limit of 1. As a result, the eigenvalue k of the matrix K_iIs (0, 2) and the eigenvalue k_iIs sorted by its size, and 0 ≦ k₁≦… ≦ k_nWhen rewritten as ≦ 2, the eigenvector corresponding to a small eigenvalue is a periodic function having a low period, and the eigenvector corresponding to a large eigenvalue is a periodic function having a high period.
[0048]
Low-pass filtering is performed by repeatedly applying the following equation (2) using a matrix expression.
[0049]
P ′ = f (K) P = (I−μK) (I−λK) P (2)
Here, λ and μ are scaling factors (0 <λ <−μ).
[0050]
Applying equation (2) N times repeatedly results in an eigenvalue k of K representing the frequency._iEigenvector e for_i, A low-frequency component (small k) using the Taubin filter function of the following equation (3)._i).
[0051]
f_N(K) = {(1-μk) (1-λk)}^N    (3)
To actually perform the filtering, the passband frequency k_PB, Scaling factors λ and μ, and the number of calculation iterations N need to be appropriately determined. For example, the passband frequency k_PBIs f_N(K_PB) = 1, k_PB= 1 / λ + 1 / μ.
[0052]
Comparing the filter function in Gaussian filtering in FIG. 3A with the Taubin filter function in FIG. 3B, the filter function in FIG. 3A is f (k) = (1−λk). Since | 1−λk | <1, if the number N of computational iterations is increased, f is set at a value other than k = 0._N(K) = (1−λk)^Nと な り 0, which is not an ideal low-pass filter. In contrast, the Taubin filter function approaches an ideal low-pass filter as N increases, and the passband frequency k_PBIt was confirmed that only lower frequency components were passed.
[0053]
As described above, the basic shape estimating unit 11 estimates the basic shape in which surface details are not synthesized by repeatedly applying the equation (3) to the mesh model M N times. Hereinafter, the triangular mesh model of the estimated basic shape is referred to as an estimated basic shape mesh M ′.
[0054]
Note that the Taubin filter function used in the basic shape estimating unit 11 realizes low-pass filtering that does not cause shape degeneration, but since the calculation converges as the number N of calculation iterations increases, the filtering strength is reduced. Has certain limitations. For this reason, surface details composed of irregularities composed of several vertices can be sufficiently extracted. However, for example, when it is desired to extract surface details composed of several hundred vertices, a stronger low-pass filtering effect is required.
[0055]
Therefore, in order to extract a surface detailed mesh having a wider support (having a large number of components), i in the definition of Laplacian in Expression (1) is used.^*To the set near n of vertex i. Hereinafter, a Laplacian defined by using vertices in the vicinity of n is referred to as a Laplacian in the vicinity of n. Weight w_ijIs a non-negative sum of j with respect to j, the matrix W becomes a probability matrix, and the range of eigenvalues of K is still limited to 0 to 2. In this way, by extending the definition of Laplacian to the vicinity of n, the period of the base corresponding to the frequency passed for the same filter function becomes longer, and it is possible to filter irregularities having a longer period than that of one.
[0056]
FIG. 4 shows the result of filtering using the Laplacian near n. The filtering parameter is the passband frequency k_KB= 1.0, scaling factor λ = 0.5, and weight w_ijUsed the reciprocal of the number of vertices included in the neighborhood of n. From FIG. 4, it has been confirmed that the Laplacian near two can obtain a stronger low-pass filtering effect than the Laplacian near one at the same filtering parameter setting. This indicates that more supportable surface details can be extracted. Further, it was confirmed that when the vicinity was expanded to three or more, the effect of the smoothing did not change much.
[0057]
[Extraction of high frequency components]
The high-frequency component extraction unit 12 considers that the high-frequency components lost by the low-pass filter represent irregularities of the surface detail mesh with respect to the basic shape mesh surface, and uses the input mesh model M and the estimated basic shape mesh M ′. To extract the high frequency component H of the mesh model M. The high frequency component H of the mesh model M is the geometric information lost by the filtering, and is obtained by the following equation (4) as the movement amount of the vertex before and after the filtering.
[0058]
H = P−P ′ (P∈M, P′∈M ′) (4)
Where P = ｛p_i｝ Is a set of vertices of the mesh model M, P ′ = ｛p ’_i｝ Is a vertex set of the estimated basic shape mesh M ′ after filtering. The high-frequency component H is a surface detail mesh M for the estimated basic shape mesh M '._DH = ｛h_i｝.
[0059]
FIG. 5A shows an example of a mesh model M. FIG. 5B shows a vector of a high-frequency component obtained by applying Expression (4) to the mesh model M, It is the figure displayed as a starting point. Each vector h_iIs associated with the vertices of the estimated basic shape mesh M ′. In this state, since there is no spatial arrangement for other vectors in the high-frequency component H and no correspondence to other shapes, individual management is performed. It is not suitable for editing and editing, and it is also difficult to combine it with the surface of another basic shape mesh.
[0060]
[Generate parameterization]
Therefore, the parameterization generation unit 13 generates parameterization for defining a basic plane having a topological structure for each vertex of the estimated basic shape mesh M ′ so that irregularities of surface details can be managed independently. . As shown in FIG. 6, the parameterization of the mesh model M is a two-dimensional planar triangular graph G corresponding to the mesh model M on a one-to-one basis, and is described here as G (Q, К). Where Q = ｛q_i= (U_i, V_i) ∈R²| 1 ≦ i ≦ n｝ (parameter). To construct the parameterization, a piecewise linear map φ: | M | → R for the mesh model M shown in the following equation (5)²(| M | ⊂R³Is a set of points on the mesh model).
[0061]
φ (p_i) = Q_i    (5)
Any point p on the mesh model surface_mIs the point p_mIs defined by the following equation (6) using the parameters of the vertices of the triangle (i, j, k) including
[0062]
φ (p_m) = Λφ (p_i) + Μφ (p_j) + Νφ (p_k) (6)
Here, λ, μ, and ν are points p in the triangle (i, j, k)._m(Λ + μ + ν = 1). Also, since the mapping φ is a segmentation line mapping, its inverse mapping φ^-1: R²→ | M | is defined, and each vertex of the parameterization of the parameter plane has a one-to-one correspondence with each vertex of the triangular mesh model in the real space.
[0063]
As described above, the parameterization generation unit 13 generates the parameterization G ′ by applying the mapping onto the parameter plane to the estimated basic shape mesh M ′.
[0064]
Further, the parameterization generation unit 13 extracts a parameterization G ′ of the estimated basic shape mesh M ′ for the purpose of extracting a surface detail mesh capable of storing a metric related to a distance on the surface of the mesh model M that is the original composite shape. , Which have the property of preserving distance In this method, an evaluation function E relating to ridge length conservation shown in the following equation (7)_lenIs defined.
[0065]
E_len= Σ (‖p_i-P_j‖²−φ_B(P_ij))²/ Φ_B(P_ij) (7)
φ_B(P_ij) = ‖Φ (p_i) -Φ (p_j) ‖²
Here, Σ indicates a discrete integral in (i, j) ∈E. Equation (7) shows that the gradient for the parameters u, v is easily calculated, and p is calculated using the conjugate gradient method._iCan be solved for However, if the parameterization boundary or the mesh shape in the real space is complicated, the face is turned over and self-interference may occur, so that a single shot for the mesh model may not be constructed. Therefore, the evaluation function E of the signed area preservation of the surface shown in the following equation (8)_areTo solve the problem of self-interference.
[0066]
E_are= Σ ｛det [φ_B(P_ji)^Tφ_B(P_ki)^T] / 2-S_ijk｝²/ S_ijk    (8)
φ_B(P_ji) = Φ_B(P_j) -Φ_B(P_i)
φ_B(P_ki) = Φ_B(P_k) -Φ_B(P_i)
Here, Σ is a discrete integral in the plane (i, j, k) ∈F, and S_ijkIs the signed area of the surface segment (i, j, k) and S_ijk= ‖ (P_j-P_i) × (p_k-P_i) ‖ / 2. In the evaluation function of the equation (8), the gradient for the parameters u and v can be easily calculated, and p can be calculated using the conjugate gradient method._iCan be solved similarly.
[0067]
Finally, the parameterization G ′ of the estimated basic shape mesh M ′ for determining the domain of the surface detail mesh is a weighted sum of the evaluation functions of the equations (7) and (8) shown in the following equation (9). Can be constructed by solving using the conjugate gradient method.
[0068]
minimize (αE_len+ ΒE_are) (9)
Here, α and β are weighting factors that determine the strength of each property. By solving the equation (9), it is possible to save the real space and the ridge line length as much as possible on the parameter plane and realize the construction of the parameterization that does not cause the surface interference.
[0069]
FIG. 7 shows an example of the parameterization constructed according to the equation (9). In FIG. 7, for the sake of clarity, FIG. 7B shows the parameterization constructed by applying the above-described method to the local portion of the mesh model M shown in FIG. As a result of experiments on several mesh models, it was confirmed that by setting the weighting factors to α = 0.5 and β = 0.5, it was possible to construct a parameterization with no self-interference and little distance distortion. Was.
[0070]
[Generation of surface detail mesh]
In the surface detail generation unit 14, the surface detail mesh M whose domain is the parameterization G 'of the estimated basic shape mesh M'_DGenerate This is the vertex position q of the parameterization G '_i= (U_i, V_i) Is performed by operating based on the high-frequency component H obtained by the filtering. Element h of high frequency component H_i= (X_hi, Y_hi, Z_hi) Represents the irregularities of the surface details from each vertex of the estimated basic shape mesh._iSigned strength s of_iIs given as an attribute to each vertex of the parameterization G ′.
[0071]
s_i= Sign (h_i・ N_i) ｛(X_hi)²+ (Y_hi)²+ (Z_hi)²｝^1/2      (10)
Here, sign (x) is a function that is 1 when the sign of x is positive and −1 when the sign of x is negative._iIs the normal vector at vertex i. As shown in FIG. 8, each vertex p of the parameterization G 'shown in FIG._iInformation about (u_i, V_i, S_i) At the coordinates (x) in the real space shown in FIG._i, Y_i, Z_i), The surface detail mesh M in which the unevenness of the surface detail in the mesh model M is set to the height value z._DGenerate
[0072]
[Application result of this extraction method]
The estimated basic shape mesh obtained by applying the filtering to the mesh model of the surface detailed composite shape shown in each of FIGS. 9 to 11A is shown in FIG. It is shown in FIG. Each figure (d) is a figure in which the height value of the extracted surface detailed mesh is represented by shading. 9A and 10A have 6,962 face fractions, and the mesh model of FIG. 11A has 15,842 face fractions. The setting of the filtering parameters used for the basic shape estimation is k_PB= 0.01, N = 200, near 1. The extraction processing time was about 10 seconds (Pentium (registered trademark) -3, 1 GHz, RAM 512 MB) in the model of FIG. From the application results, it was confirmed that the surface details considered to have been synthesized in the given mesh model were extracted as a mesh model having asperities relative to the basic shape as height values.
[0073]
Therefore, according to the present embodiment, the basic shape estimation unit 11 applies a low-pass filter to the mesh model M to estimate a basic shape mesh regarded as having a detailed shape synthesized on the surface, and extracts a high-frequency component. The high-frequency component lost by the low-pass filter is extracted by the unit 12, the parameterization generation unit 13 generates a parameterization having the topological structure of each vertex of the estimated basic shape mesh on the basic plane, and the surface detail generation unit 14 generates the parameterization. A surface detail mesh is generated by giving a height value based on the high frequency component to each vertex of the rise. As a result, the surface detail mesh extracted from the mesh model M is reproduced on three-dimensional coordinates having the bottom as a basic plane, and is expressed in a form independent of the basic shape mesh. Therefore, the reusability when synthesizing the detailed surface mesh with the surface of another basic shape mesh can be improved. As a result, it is possible to increase the efficiency of design work and increase design variations in design design using triangular mesh modeling.
[0074]
According to the present embodiment, the basic shape estimating unit 11 flexibly responds to the shape of the surface detail in the triangular mesh model by applying the Taubin filter function that can be set for controlling the filtering strength. Filtering can be enabled.
[0075]
According to the present embodiment, the basic shape estimating unit 11 extends the Laplacian in the Taubin filter function to the Laplacian near n, so that a stronger low-pass filtering effect can be obtained. Such a large-scale surface detail mesh can be extracted with high accuracy.
[0076]
According to the present embodiment, the parameterization generation unit 13 solves, for each vertex, the problem of minimizing the weighted sum of the evaluation function related to the degree of conservation of the ridge length and the evaluation function of the preservation of the signed area for each vertex, so that the Length can be preserved as much as possible on the parameter plane, and parameterization that does not cause surface interference can be constructed.
[0077]
【The invention's effect】
As described above, according to the surface detail extraction system and the surface detail extraction program according to the present invention, individual management and visualization of the extracted surface details are easy, and the surface details are combined with the surface of another basic shape. The reusability at the time of performing can be improved.
[Brief description of the drawings]
FIG. 1 is a functional block diagram illustrating an entire configuration of a detailed surface extraction / synthesis system according to an embodiment.
FIG. 2 is a functional block diagram illustrating an overall configuration of a detailed surface extraction system according to one embodiment.
FIG. 3A shows a filter function in Gaussian filtering, and FIG. 3B shows a Taubin filter function.
FIG. 4 is a diagram showing an example of strong smoothing using n-nearby laprasin.
FIG. 5A is an example of a mesh model, and FIG. 5B is a diagram in which a vector of a high-frequency component obtained for the mesh model is displayed with a corresponding vertex as a starting point.
FIG. 6 is a diagram showing a correspondence relationship between a mesh model and parameterization by a piecewise linear mapping.
FIG. 7A is an example of a mesh model, and FIG. 7B is a diagram showing parameterization of a local portion of the mesh model.
8A is a diagram showing parameterization, and FIG. 8B is a diagram showing a detailed surface mesh.
9A and 9B are diagrams showing the application result of the present surface detail extraction method. FIG. 9A shows an input mesh model, FIG. 9B shows an estimated basic shape mesh, and FIG. The extracted detailed surface mesh, FIG. 6D is a diagram in which the height value of the detailed surface mesh is represented by shading.
10A and 10B are diagrams showing another application result of the present surface detail extraction method, wherein FIG. 10A shows an input mesh model, FIG. 10B shows an estimated basic shape mesh, and FIG. Is a surface detail mesh extracted, and FIG. 4D is a diagram showing the height value of the surface detail mesh in shades.
11A and 11B are diagrams showing still another application result of the present surface detail extraction method. FIG. 11A shows an input mesh model, FIG. 11B shows an estimated basic shape mesh, and FIG. ) Is an extracted surface detailed mesh, and FIG. 4D is a diagram in which the height value of the surface detailed mesh is represented by shading.
[Explanation of symbols]
1. Surface detail extraction system
2. Surface detail database
3… Basic shape database
4: Surface synthesis system
11 Basic shape estimation unit
12 high frequency component extraction unit
13 ... Parameterization generator
14 Surface detail generation unit

Claims (14)

Basic shape estimating means for estimating a basic shape mesh by applying a low-pass filter to a triangular mesh model in which a detailed shape is synthesized on a surface;
High-frequency component extraction means for extracting high-frequency components lost by the low-pass filter,
A parameterization generating means for generating parameterization having a topological structure of each vertex of the estimated basic shape mesh in a basic plane,
Surface detail generation means for generating a surface detail mesh by giving a height value based on the high-frequency component to each vertex of the parameterization,
A surface detail extraction system comprising: 2. The surface detail extraction system according to claim 1, wherein the basic shape estimating unit applies a Taubin filter function using Laplacian defined for each vertex of the triangular mesh model. 3. The surface detail extraction system according to claim 2, wherein the basic shape estimating unit sets the Laplacian to an n-neighborhood Laplacian that is extended to vertices near n. 4. The surface detail extraction system according to claim 1, wherein the high-frequency component extracting unit obtains, as a high-frequency component, a moving amount of each vertex of the triangular mesh model by applying the low-pass filter. 5. The surface detail extraction system according to claim 1, wherein the parameterization generation unit applies a linear piecewise mapping to a parameter plane for each vertex of the estimated basic shape mesh. The method according to any one of claims 1 to 5, wherein the parameterization generating means solves each vertex so that a weighted sum of an evaluation function related to ridge line length conservation and an evaluation function for signed area conservation is minimized. The described surface detail extraction system. 7. The method according to claim 1, wherein the surface detail generation unit gives a signed intensity defined using a high-frequency component and a normal vector to each vertex of the parameterization as a height value. The surface detail extraction system according to any one of the above. A basic shape estimation process of estimating a basic shape mesh by applying a low-pass filter to a triangular mesh model in which a detailed shape is synthesized on a surface;
High-frequency component extraction processing for extracting high-frequency components lost by the low-pass filter,
A parameterization generation process for generating a parameterization having a topological structure of each vertex of the estimated basic shape mesh in a basic plane;
Surface detail generation processing for generating a surface detail mesh by giving a height value based on the high frequency component to each vertex of the parameterization,
A computer program for causing a computer to execute the method. 9. The computer-readable storage medium according to claim 8, wherein the basic shape estimation process applies a Taubin filter function using Laplacian defined for each vertex of the triangular mesh model. 10. The computer-readable storage medium according to claim 9, wherein the basic shape estimating process is performed on the Laplacian near n by expanding the Laplacian to vertices near n. 11. The computer-readable storage medium according to claim 8, wherein the high-frequency component extraction process obtains, as a high-frequency component, a moving amount of each vertex of the triangular mesh model by applying the low-pass filter. 12. 12. The computer-readable storage medium according to claim 8, wherein the parameterization generation process applies a linear piecewise mapping to a parameter plane for each vertex of the estimated basic shape mesh. 13. The method according to claim 8, wherein the parameterization generation process solves each vertex so that a weighted sum of an evaluation function related to ridge line length conservation and an evaluation function for signed area conservation is minimized. The detailed surface extraction program described. 14. The method according to claim 8, wherein the surface detail generation processing gives a signed intensity defined by using a high-frequency component and a normal vector to each vertex of the parameterization as a height value to each vertex. A surface detail extraction program according to any of the above.

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