JP2006277712A - Fitting device, method and program for three-dimensional model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To generate an accurate, strong, and appropriate initial control mesh (ICM) of a loop subdivided curved surface at high speed for a group of high density measuring points having an intricate shape including a characteristic ridge line part obtained from scanning a three-dimensional model. <P>SOLUTION: The fitting device for a three-dimensional model inputs scanning data of the three-dimensional physics model, generates the group of high density measuring points, generates a volume base mesh by applying a marching cubes method for the group of high density measuring points, generates a high density mesh by further applying a shrink-wrapping method, conducting extraction processing of a characteristic boundary for the high density mesh, generates an initial control mesh seed storing the characteristic boundary by simplification of the high density mesh using the characteristic boundary, and generates a loop subdivided curved surface initial control mesh by conducting geometric improvement of the initial control mesh seed by quasi-interpolation. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a three-dimensional model fitting apparatus, method, and program.

  Reverse engineering (RE) is a method of measuring a 3D physical model by 3D scan or X-ray CT scan, etc., and generating a curved surface model that fits the obtained measurement point group. It is suitable for generating a curved surface model that is difficult to design directly, and for generating an analysis model having an internal structure.

  Conventionally, polygonal surface approximation models and quadrilateral parametric surfaces have been mainly used as fitting surface models in RE. However, the former has a problem that it takes a long time to perform geometric calculation because the surface fraction becomes enormous, and a smooth curved surface cannot be expressed. The latter has a problem that it is difficult to generate a smooth curved surface that fits a point group using only a single quadrangular curved surface patch, and the processing for smoothly connecting a plurality of patches is complicated.

  As a method for solving such problems, the document “Schroder, P .:“ Subdivision for modeling and animation. ”Course notes of SIGGRAPH 98. 1998” (Non-Patent Document 1) fitting a subdivision curved surface to a measurement point group A technique to be used as a curved surface model has been proposed. The subdivided curved surface has many attractive features as an RE fitting curved surface model such that a single smooth curved surface can be generated on a mesh having arbitrary connectivity. In recent years, there are many commercial 3D modeling software having a function for modeling a subdivided curved surface, and some mechanical CAD systems have a design design function using a subdivided curved surface.

  The RE problem of the subdivision curved surface can be defined as a problem of deriving an initial control mesh in which the subdivision limit curved surface fits the measurement point group. Due to the development of non-contact measuring instruments, in recent years, the RE problem of subdivided curved surfaces is required to have a high-performance fitting capability for large-scale and complex measurement data obtained from various sources. These function requests are the following four.

  The first functional requirement is a robust fitting for objects with complex geometric structures. Many design mockups made with style design include arbitrary and complex geometric shapes such as button holes and heat dissipation holes. In addition, an object measured by an X-ray CT scan may have a complicated internal structure such as a multiple shell or a cooling pipe. A complicated initial control mesh corresponding to such a case must be derived.

  The second function request is management of fitting errors. The fitting error must be controlled directly or indirectly in order to maintain the quality of the generated subdivision surface.

  The third function requirement is high-speed fitting to a huge measurement point group. It is desirable that the fitting process be completed in as short a time as possible even for an enormous measurement point group of about several million points.

  The fourth function requirement is high-precision fitting to the feature ridge line portion. In design mockups and 3D physical models of industrial products, there are many regions called “characteristic ridges” where the curvature of the surface changes abruptly. These regions do not exist as perfectly sharp edges, but actually as small radius fillets. Therefore, it recognizes these microradius fillets, derives an initial control mesh with an appropriate phase and geometry, and reproduces the feature ridges that exist as such fillets on the limit curved surface of the subdivision surface There is a need.

  Literature “Hoppe, H. et al .:“ Surface reconstruction from unorganized points. ”SIGGRAPH 92 Conference Proceedings, (1992) 71-78. (Non-Patent Literature 2), literature“ Hoppe, H. et al .: “Piecewise "SIGGRAPH 94 Conference Proceedings, (1994) 295-302." (Non-Patent Document 3) describes a typical technique of RE that generates a subdivision surface from a group of measurement points. This technique uses energy minimization to generate a loop subdivision surface tagged with ridgelines from a point cloud and applies different subdivision rules to the tagged ridgeline directions, resulting in a perfectly sharp Feature ridgeline can be expressed. Also, “Shingo Takeuchi, Hiromasa Suzuki et al .:“ Generation method of subdivision surfaces based on point cloud and polyhedron data ”, Journal of the Japan Society of Mechanical Engineers, C, 67, 653 (2001) 284-289” (Non-patent Document 4) ), Fitting is performed based on the initial control mesh with a simple geometric shape and a small number of surface fractions. The initial control mesh repeats the minimization of the error energy function and the insertion of control vertices to change its geometric / topological structure. A method for improving and adjusting the subdivision limit point so as to fit the measurement point group has been proposed. However, although this method is fast, there is a problem that an initial control mesh must be manually defined for accurate fitting.

  In the document "Joeng, W. et al .:" Direct reconstruction of displaced subdivision surface from unorganized points. "Pacific Graphics 01 Conference Proceedings, (2001) 160-168. (Non-Patent Document 5), Displaced from measurement points. It proposes the generation of subvision surface (DSS). DSS is a technique for expressing details of a model by superimposing a scalar displacement map on a smooth subdivision surface. In this method, Shrink-wrapping proposed in the document "Kobbelt, LP et al .:" A shrink wrapping approach to remeshing polygonal surfaces. "EUROGRAPHICS 99 Proceedings, (1999) 119-130. Techniques and Quadric error metrics proposed in the literature “Garland, M. et al .:“ Surface simplification using quadric error metrics. ”SIGGRAPH 92 Conference Proceedings, (1992) 209-216.” Although it is possible to generate the initial control mesh directly from the measurement point group using simplification based on the (QEM) technique, the subdivision surface cannot be fitted to the measurement point group of an object having an arbitrary genus. The literature “Razdan, A. et al .:“ Reverse Engineering Using a Subdivision Surface Scheme. ”3D Modeling 03 Proceedings (2003)” (non-patent document 8) proposes fitting for DSS, but this algorithm is highly The density mesh is used as an input and does not correspond to the measurement point group. In the document "Kanai, T: MeshToSS:" Converting Subdivision Surfaces from Dense Meshes. "6th International Fall Workshop on Vision, Modeling and Visualization 01 proceedings, (2001) 325-332. A method of generating by simplifying a high-density mesh based on QEM for the subdivision limit point has been proposed. However, this method can stably generate the initial control mesh from the high-density mesh, but the fitting from the measurement point group is not discussed, and the accurate fitting ability that recognizes the small fillet region There was a problem with its limitations.

The existing technologies as described above are excellent methods for generating subdivision surfaces from point clouds for the purpose of application to computer graphics, and satisfy all the above four functional requirements at the same time. There was nothing to get.
Schroder, P .: "Subdivision for modeling and animation." Course notes of SIGGRAPH 98 (1998). Hoppe, H. et al .: "Surface reconstruction from unorganized points." SIGGRAPH 92 Conference Proceedings, (1992) 71-78. Hoppe, H. et al .: "Piecewise smooth surface reconstruction." SIGGRAPH 94 Conference Proceedings, (1994) 295-302. Shingo Takeuchi, Hiromasa Suzuki et al., “Method of generating subdivision surface based on point cloud and polyhedron data”, Journal of the Japan Society of Mechanical Engineers, C, 67, 653, 2001, 284-289. Joeng, W. et al .: "Direct reconstruction of displaced subdivision surface from unorganized points." Pacific Graphics 01 Conference Proceedings, (2001) 160-168. Kobbelt, LP et al .: "A shrink wrapping approach to remeshing Polygonal Surfaces." EUROGRAPHICS 99 Proceedings, (1999) 119-130. Garland, M. et al .: "Surface simplification using quadric error metrics." SIGGRAPH 92 Conference Proceedings, (1992) 209-216. Razdan, A. et al .: "Reverse Engineering Using a Subdivision Surface Scheme." 3D Modeling 03 Proceedings (2003). Kanai, T: MeshToSS: "Converting Subdivision Surfaces from Dense Meshes." 6th International Fall Workshop on Vision, Modeling and Visualization 01 proceedings, (2001) 325-332.

  The present invention has been made in view of the above-described problems of the prior art, and can be applied to a high density measurement point group having a complicated shape including a characteristic ridge line portion obtained from scanning of a three-dimensional model. It is possible to generate an initial control mesh (ICM) of a loop subdivision curved surface that is accurate, robust, and suitable for high speed, and meets all the above four functional requirements, and is robust and accurate for complex and high-density measurement points. An object of the present invention is to provide a 3D model fitting technique capable of fitting a Loop subdivision curved surface at high speed.

  According to the first aspect of the present invention, there is provided a three-dimensional model fitting apparatus that receives scanning data of a three-dimensional physical model and generates a high-density measurement point group, and a high-density measurement generated by the high-density measurement unit. A high-density mesh constructing unit that generates a high-density mesh for the point group; a feature boundary extracting unit that performs a feature boundary extracting process on the high-density mesh generated by the high-density mesh constructing unit; and the feature boundary extraction An initial control mesh seed generating unit that generates an initial control mesh seed that preserves the feature boundary by simplifying the high-density mesh using the extracted feature boundary; and geometric improvement of the initial control mesh seed And an initial control mesh geometry improvement unit that generates and outputs a Loop subdivision curved surface initial control mesh.

  According to a second aspect of the present invention, in the three-dimensional model fitting apparatus according to the first aspect, the high-density mesh construction unit applies the Marching cubes method to the high-density measurement point group generated by the high-density measurement unit. A volume-based mesh is generated, and a high-density mesh is generated by applying a shrink-wrapping method to the volume-based mesh. The initial control mesh geometry improvement unit performs geometric improvement of the initial control mesh seed by quasi-interpolation. Thus, a loop subdivision curved surface initial control mesh is generated.

  According to a third method of fitting a three-dimensional model of the present invention, a high-density measurement step of inputting scanning data of a three-dimensional physical model to generate a high-density measurement point group, and a high-density measurement for the high-density measurement point group A high-density mesh generation step for generating a mesh, a feature boundary extraction step for performing feature boundary extraction processing on the high-density mesh, and a feature boundary obtained by simplifying the high-density mesh using the feature boundary An initial control mesh seed generating step for generating the initial control mesh seed, and an initial control mesh geometric improving step for generating a Loop subdivision curved surface initial control mesh by performing geometric improvement of the initial control mesh seed. .

  According to a fourth aspect of the present invention, in the three-dimensional model fitting method according to the third aspect, in the high-density mesh generation step, a volume-based mesh is generated by applying a Marching cubes method to the high-density measurement point group. Further, a high-density mesh is generated by applying a shrink-wrapping method to this, and in the initial control mesh geometric improvement step, the initial control mesh seed is geometrically improved by quasi-interpolation to perform loop subdivision curved surface initial control. It is characterized by generating a mesh.

  A three-dimensional model fitting program according to a fifth aspect of the present invention inputs a scanning data of a three-dimensional physical model and generates a high density measurement point group, and a high density for the high density measurement point group. A high-density mesh generation process for generating a mesh, a feature boundary extraction process for extracting a feature boundary for the high-density mesh, and a feature boundary by preserving the high-density mesh using the feature boundary The initial control mesh seed generating process for generating the initial control mesh seed and the initial control mesh geometric improving process for generating the loop subdivision curved surface initial control mesh by executing the geometric improvement of the initial control mesh seed are executed by the computer. Is.

  According to a sixth aspect of the present invention, in the three-dimensional model fitting program according to the fifth aspect, in the high-density mesh generation process, a volume-based mesh is generated by applying a Marching cubes method to the high-density measurement point group. In addition, a high-density mesh is generated by applying a shrink-wrapping method to this, and in the initial control mesh geometric improvement process, the initial refinement of the initial control mesh seed is performed by quasi-interpolation to perform loop subdivision curved surface initial control. It is characterized by generating a mesh.

  According to the present invention, the limit curved surface can express a single smooth curved surface with an arbitrary phase, and the subdivision calculation is simple because it only needs to generate the internal dividing point and update the vertex position. In addition, there is an advantage that the degree of detail (LOD) control is easy.

  In addition, according to the present invention, an appropriate phase structure is also applied to a feature ridge line portion that becomes a micro fillet based on a curvature evaluation on a mesh for a complex shape high density measurement point group including a hole and a feature ridge line. It is possible to provide a technique capable of estimating an initial control mesh and fitting to a loop subdivision surface with high accuracy and high speed.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram of a 3D model fitting apparatus according to an embodiment of the present invention, and FIG. 2 is a sequence diagram of a fitting process executed by the 3D model fitting apparatus.

The 3D model fitting apparatus according to the present embodiment has a 3D model measuring unit 101 such as a 3D scanner or 3DCT scanner that scans a 3D physical model, and inputs measurement data from the 3D model measuring unit 101. The high-density measurement unit 102 that generates the high-density measurement point group U, and the high-density mesh construction process using the three-dimensional voxel model are executed on the high-density measurement point group U from the high-density measurement unit 102 dense mesh construction unit 103, feature boundary extraction unit 104 performs the extraction processing of feature boundary for the high density mesh M ₁ to generate a high-density mesh construction unit 103, and stored the feature boundary due to simplification of dense mesh Initial control mesh seed generation unit 105 for generating an initial control mesh seed, Quasi-interpolation Relevant data by the initial control mesh geometry improvement unit 106 performs geometric improvement of initial control mesh outputs the Loop subdivision surface initial control mesh M ₃ and stores various data calculated in each section, and by reading from each component Is provided.

  A method for fitting a three-dimensional model by the three-dimensional model fitting apparatus of the present embodiment is as follows. This apparatus implements the method by installing a three-dimensional model fitting program for executing the following arithmetic processing in a computer system. Here, the processing will be described separately for each arithmetic processing.

  The three-dimensional model fitting method according to the present embodiment is a method of storing a feature boundary by constructing a high-density mesh using a voxel model (step SQ01), extracting a feature boundary (step SQ02), and simplifying the high-density mesh. It consists of four steps: generation of control mesh seed (step SQ03) and geometric improvement of the initial control mesh by Quasi-interpolation (step SQ04).

  Step SQ01 is a high-density mesh generation step. In order to fit a subdivision curved surface with high precision to a high-density measurement point group having a complex shape, which is scanned by the three-dimensional scanner 101 and generated from the scanning data by the high-density measurement unit 102, the shape of the point cloud is represented. It is necessary to stably generate an initial control mesh seed (initial control mesh estimated shape) having a small number of vertices, reflecting the topological structure and geometric features well. In the present embodiment, as a pre-process for seed generation, the high-density mesh construction unit 103 generates a high-density mesh by the following processing procedure.

FIG. 3 is an explanatory diagram of the outline of the Marching Cubes. As shown in FIG. 3A, the rough mesh generation by the Marching Cubes is performed by arranging a high-density measurement point group U to be input from the high-density measurement unit 102 in a voxel space having an interval, and the inside and outside of each voxel with respect to U. Make a decision. When the measurement point is included in a cubic space having a side length w centered on the voxel lattice point, the lattice point attribute value is set to 1 as shown in FIG. 3B, and the lattice point attribute is set to other lattice points. Assign 0 to the value. Thereafter, the grid points are further scanned in the x, y, and z directions, and the attribute values of the grid points in the space surrounded by the grid point group having the attribute value 1 are changed to 1, as shown in FIG. Based on the lattice attribute value pattern of each voxel, it is disclosed in the document "Lorensen, WE et al .:" Marching cubes: A high resolution 3D surface construction algorithm. "Computer Graphics, 21, 4 (1987) 163-169." By applying the Marching cubes method, a volume-based mesh M ₀ that correctly captures the shape of the point cloud is generated as shown in FIG. FIG. 4 shows a surface generation basic pattern table based on grid point attribute values used when generating the volume-based mesh.

Next, a high-density mesh M ₁ is generated from the volume mesh M ₀ using the Shrink wrapping method disclosed in Non-Patent Document 6. FIG. 5 is a sequence diagram showing an outline of this shrink wrapping method, and FIG. 6 shows its principle. Through the following four steps, each vertex of the high-density mesh M ₁ is located at the same position as a certain point in the measurement point group U, and the high-density mesh M ₁ is accurately fitted to the measurement point group U.

In step SQ11, mitigated by equation (1) the vertex position ν at each vertex v of the volume mesh M _0.

Here, nbhd (v) is a set of 1 neighbor vertices of each vertex v, _dj is the average of 1 neighbor ridge line length of v _j , α∈ [0, 1] is a relaxation coefficient, and α = 0 in this embodiment. .5.

In step SQ12, each vertex v is fitted to the measurement point group U. The vertex position of each vertex v is corrected to the position of the point u _near εU closest to the straight line in the average normal n _v direction of each vertex v in the volume mesh M ₀ .

In step SQ13, performs error judgment for the measurement point group U of the volume mesh _{M 0.} In the present embodiment, the error of the volume mesh M ₀ with respect to the measurement point group U is defined as the distance between each point in the measurement point group U and the surface on the volume mesh M ₀ closest to that point. As shown in FIG. 7, if the average error is smaller than the mesh generation tolerance τ _m , the volume mesh M ₀ is output as the high density mesh M ₁ . Otherwise, step SQ14 is executed. In this step SQ14, the volume mesh _{M 0} 1 times and Loop subdivision, repeat the step SQ12~SQ13. FIG. 8A shows a volume-based mesh image, and FIG. 8B shows a high-density mesh image generated by the Shrink Wrapping method.

Next, step SQ02 in the sequence of FIG. 2 executed by the feature boundary extraction unit 104 will be described. A large number of characteristic ridgelines exist on the surface of a three-dimensional physical model such as a design mockup or industrial product, and these ridgelines are actually realized as a fillet region having a minute radius. Therefore, the phase structure and geometric shape of the initial control mesh are appropriately derived so that the subdivision surface can be appropriately fitted to the measurement point group in such a region (feature region). 9 and 10 are explanatory diagrams of the feature boundary ridge line extraction processing. Dense mesh M ₁ as shown in FIG. 9 (a), since this surface fraction for use as initial control mesh is too large, it must be reduced surface fraction by simplified. As the simplification process proceeds as shown in FIG. 9B, the small triangular surface fraction on the feature region A0 decreases, and one feature region A0 is reduced to one feature ridge line A1. However, since the subdivision limit curved surface A2 obtained from the initial control mesh generated using such simplification is excessively smoothed around the feature ridge line A1, these sub-surfaces are shown in FIG. 9C. The fitting accuracy of the limit curved surface with respect to the point cloud at the periphery of the is reduced. To solve this problem, in this embodiment, one from the same high density mesh M ₁ shown in FIG. 10 (a), both ends of the feature region A0 in the results of simplified as shown in FIG. 10 (b) It is necessary to leave the feature boundary ridgeline B1 one by one. By saving the pair of feature boundary ridgelines B1 in this way, the fitting accuracy around the feature region A0 is improved as shown in FIG. 10C.

In this embodiment, the first characteristic boundaries on high density mesh M _1, and extracted by evaluating the curvature at the vertex of dense mesh M _1, ridge collapse operations based on the curvature, save the feature boundary B1 to simplify the dense mesh M ₁ while. This mesh simplification can be obtained an initial control mesh seed M ₂ with the appropriate feature boundary B1.

Features area A0 of dense mesh M _1, the maximum is greater than that of the other areas of dense mesh M ₁ of the absolute value of the principal curvatures. Therefore, it is possible to extract a feature region A0 of dense mesh M ₁ by assessing the curvature of each vertex of the dense mesh M _1. In this embodiment, this curvature evaluation is performed by the method proposed in the document “Alliez, P. et al .:“ Anisotropic polygonal remeshing. ”SIGGRAPH 03 Conference Proceedings, (2003) 485-493. Formula 3 curvature tensor

From the maximum absolute value of the eigenvalues and evaluation value k principal curvatures at the apex of the M ₁ v (v).

Here, B is a set of planes included in a sphere having a radius r centered on the vertex v, | B | is the sum of the areas of the planes included in B, and β (e) is two planes sharing the edge line e. Signed dihedral angle, | e∩B | is the ridge length of the part included in B of e,

Is a unit column vector in the same direction as e. Using principal curvatures evaluation value kappa (v), extracting features boundary edge B1 on dense mesh M ₁ by the following steps.

FIG. 11 is an explanatory diagram of the feature boundary line B1 extraction process based on the vertex curvature evaluation. Seeking kappa (v) for each vertex v of M ₁ as shown in FIG. 11 (a), comparing the curvature evaluation tolerance user defined tau _c and kappa (v) as in FIG. 11 (b), For each vertex v, an attribute value φ (v) is set using equation (5).

  Next, when all the vertices near one of the vertices v have the attribute value 1 (or all -1), change to φ (v) = 0, and as shown in FIG. A ridge line whose values are both 1 is defined as a feature boundary B1.

Next, step SQ03 of the initial control mesh seed generation process executed by the initial control mesh seed generation unit 105 of the present embodiment will be described. Since the obtained high density mesh M ₁ is the surface fraction is large, it is not effective to use it as an initial control mesh directly subdivision surface. Therefore, by simplifying the dense mesh M _1, to approximate the shape of the point group, and less surface fraction mesh, to generate the initial control mesh seed M _2. In this embodiment, a new edge collapse algorithm that evaluates the QEM and preserves the feature boundary B1 is adopted.

Simplification of meshes by edge collapse (EC) based on quadrature error metrics (QEM) is described in the document “Garland, M. et al .:“ Surface simplification using quadric error metrics. ”SIGGRAPH 92 Conference Proceedings, (1992) 209-216. .
Is proposed and is now widely used. In one EC, the ridge line (i, j) connecting the vertices i, j is the cost of Equation 6 for (i, j) as follows:

Is reduced to the vertex k.

Fundamental quadric represented by Q _i in Equation 7 for each vertex i

The elements A _i , V _i , and C _i are calculated using Equation (8).

Here, p _i is a column vector representing the position of the vertex i, n _f is a unit normal vector of the triangular surface segment f, and f ^* (i) represents a set of surface segments connected to the vertex i.

For each ridge line (i, j), the cost Q _ij (k) of Equation 6 for the ridge line degeneration (i, j) → k is calculated by Equation 9.

Here, _pk is a new vertex position and is expressed by the following equation (10).

The edge (i, j) with the smallest cost Q _ij (k) is degenerated to a new vertex k,

And Then, Equation 9 to Equation 11 are repeated.

The simplified by EC based on the above-described QEM, is no guarantee that feature boundaries on high density mesh M ₁ is stored. Therefore, in the present embodiment, a new EC algorithm for storing this is adopted.

  As shown in FIG. 12, the edge degeneration cost and the new vertex position in EC (i, j) → k are determined using the following rules.

(A) When the two vertices i and j of the ridge line (i, j) are not on the feature boundary and the ridge line (i, j) itself is not the feature boundary as in the ridge line shown in FIG. The reduction cost Q _ij (k) of the ridge line is a value of Expression 9, and the new vertex position is a value of Expression 10.

(B) When the ridge line (i, j) is a feature boundary as in the ridge line shown in FIG. 12B, the degeneration cost Q _ij (k) of the ridge line is the following cost including an error from the feature boundary. Change to

here

Is the unit direction vector of edge e which is the feature boundary,

Is a set of edges that are feature boundaries connected to the vertex i.

Instead of

Is used to calculate the cost from equation (9), and the new vertex position is calculated from equation (10).

  (C) When the ridge line as shown in (c) of FIG. 12, that is, the ridge line (i, j) is not a feature boundary but one of the two vertices i and j is on the feature boundary, the ridge line according to Equation 9 The degeneration cost of (i, j) is calculated, and the new vertex position is matched with the position of the vertex on the feature boundary of i, j.

  (D) When the ridge line as shown in FIG. 12D, that is, the ridge line (i, j) is not a feature boundary and the two vertices i and j are on different feature boundaries, the ridge line is not degenerated.

By applying these new EC operations, to generate the initial control mesh seed M ₂ which is kept plane fraction was stored characteristic boundary decreased.

Next, step SQ04 of the initial control mesh geometry improvement processing by the initial control mesh geometry improvement unit 106 will be described. FIG. 13 is an explanatory diagram of the geometric improvement processing of the initial control mesh according to the present embodiment. Doing Loop subdivision with respect to the initial control mesh M ₂ obtained in the above process, the limit surface does not pass through the measurement point group. Therefore, Quasi-interpolation described in the document "Levin, A. et al .:" Polynomial generation and quasi-interpolation in stationary non-uniform subdivision. "CAGD 03 proceedings, 20, 1 (2003) 41-60." subdivision limit point modifies the vertex position of the initial control mesh M ₂ so as to match the vertices of the initial control mesh M ₂ using (QI). QI back-calculates the vertex position of the initial control mesh at high speed from the vertex on the initial control mesh and the subdivision limit point position corresponding to the one neighboring vertex group by local calculation. Correction of the position of each vertex v of the initial control mesh M ₂ with QI is defined by the number 17 expression.

  Here, k is the valence of v, γ = −1 / (2k).

Those for the initial control mesh M ₂ was applied QI the initial control mesh M ₃ of Loop subdivision surface, which is the final output.

The experimental result of this Embodiment is shown. FIG. 14 shows a loop subdivision curved surface fitting result according to the present embodiment with respect to the measurement point group U obtained from the design mockup of the IT equipment housing. For the design mockup shown in the photograph of FIG. 14A, a high-density measurement point group U shown in FIG. FIG. 4C shows a volume base mesh M ₀ obtained from the measurement point group U, and FIG. 4D shows a high density mesh M ₁ . And FIG. (E) is the initial control mesh seed M _2, FIG. (F) is the initial control mesh M ₃ obtained therefrom. FIG. 5G shows a Loop subdivision curved surface. As shown in FIG. 14G, it can be seen that the minute fillet surface, which is the characteristic region, is correctly reproduced on the limit curved surface.

  FIG. 15A shows a fitting error distribution as a result of this embodiment, and FIG. 15B shows a fitting error distribution when EC based only on QEM is used as a simplification. It can be seen that the fitting accuracy around the feature region corresponding to the feature ridge is improved in this method.

  FIG. 16 shows the result of applying the present fitting method to the measurement point group obtained by sampling the surface of the CAD data on the front panel of the mobile phone. The model shown in FIG. 11A includes complex holes and feature regions. According to this embodiment, such a geometric shape of a point group is appropriately reflected as shown in FIG. It can be seen that the subdivision curved surface initial control mesh can be generated, and by using this, the limit curved surface can be correctly fitted as shown in FIG.

  FIG. 17 shows an application result of the present embodiment to the measurement point group U obtained from the CT scan of the turbine blade. This model contains a very complex cooling line inside, but the subdivision surface obtained properly reflects this.

The processing time required for the above three results was completed within 5 minutes using a Windows (registered trademark) PC (3 GHz Dual CPU, 2 GB RAM). FIG. 18 shows the number of points of the measurement point group, the surface fraction of the initial control mesh of the fitted subdivision surface, and the maximum / average of the normal surface fitting error of the limit surface (normalized by the diagonal length of the bounding box of the measurement point group) ). Fitting is possible with the initial control mesh having the number of vertices of about 1/100 to 1/500 while maintaining a normalization error of about 10 ⁻³ .

  As described above, according to the present embodiment, a high-density measurement point group having a complex shape including a hole and a characteristic ridge line is also appropriate for a characteristic ridge line portion that becomes a micro fillet based on the curvature evaluation on the mesh. The initial control mesh with a simple topological structure was estimated, and it was possible to perform fitting to a loop subdivision surface with high accuracy and high speed, and its effectiveness could be confirmed by computer experiments.

The block diagram of the fitting apparatus of the three-dimensional model of one embodiment of this invention. The sequence diagram of the fitting process of the three-dimensional model processed in the said embodiment. Explanatory drawing of the outline | summary of Marching Cubes. Explanatory drawing of the surface production | generation basic pattern table based on the lattice point attribute value used at the time of the production | generation of a volume base mesh. The sequence diagram of Shrink wrapping method. Explanatory drawing which shows the principle of Shrink wrapping method. Explanatory drawing of Shrink wrapping method. Volume-based mesh images and high-density mesh images generated by the Shrink Wrapping method. Explanatory drawing of the conventional feature boundary ridgeline extraction process. Explanatory drawing of the feature boundary ridge line extraction process by the said embodiment Explanatory drawing of the feature boundary line extraction process by the vertex curvature evaluation implemented in the said embodiment. Explanatory drawing about the method of determining the degeneration cost of a ridgeline in EC and a new vertex position. Explanatory drawing of the process of the geometric improvement of the initial control mesh implemented in the said embodiment. The figure which shows a Loop subdivision curved surface fitting result. The figure which shows fitting error distribution. The figure which shows the result of applying a fitting technique. The figure which shows the application result of this Embodiment with respect to the measurement point group obtained from CT scan of the turbine blade. The table | surface which shows the number of the measurement point group, the surface fraction of the initial control mesh of the subdivision surface fitted, and the maximum and average of the normalized fitting error of the limit surface.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 3D model measurement part 102 High density measurement part 103 High density mesh construction part 104 Feature boundary extraction part 105 Initial control mesh seed generation part 106 Initial control mesh geometry part

Claims (6)

A high-density measurement unit that inputs scanning data of a three-dimensional physical model and generates a high-density measurement point group,
A high-density mesh construction unit that generates a high-density mesh for the high-density measurement point group generated by the high-density measurement unit,
A feature boundary extraction unit that performs a feature boundary extraction process on the high density mesh generated by the high density mesh construction unit;
Using the feature boundary extracted by the feature boundary extraction unit, an initial control mesh seed generation unit that generates an initial control mesh seed that stores the feature boundary by simplification of the high-density mesh;
An apparatus for fitting a three-dimensional model, comprising: an initial control mesh geometry improvement unit that executes geometric improvement of the initial control mesh seed and generates and outputs a Loop subdivision curved surface initial control mesh. The high-density mesh construction unit generates a volume-based mesh by applying a Marching cubes method to the high-density measurement point group generated by the high-density measurement unit, and further applies a shrink-wrapping method to the volume-based mesh. Generate a dense mesh,
The 3D model according to claim 1, wherein the initial control mesh geometry improvement unit generates a Loop subdivision curved surface initial control mesh by performing geometric improvement of the initial control mesh seed by Quasi-interpolation. Fitting device. A high-density measurement step for inputting scanning data of a three-dimensional physical model and generating a high-density measurement point group;
A high-density mesh generation step for generating a high-density mesh for the high-density measurement point group;
A feature boundary extraction step for performing feature boundary extraction processing on the high-density mesh;
An initial control mesh seed generation step of generating an initial control mesh seed storing the feature boundary by simplification of the high-density mesh using the feature boundary;
A three-dimensional model fitting method comprising: an initial control mesh geometry improvement step of generating a loop subdivision curved surface initial control mesh by performing geometric improvement of the initial control mesh seed. In the high-density mesh generation step, a volume-based mesh is generated by applying a Marching cubes method to the high-density measurement point group, and further, a high-density mesh is generated by applying a shrink-wrapping method to the volume-based mesh.
4. The initial control mesh geometry improvement step includes generating a Loop subdivision curved surface initial control mesh by performing geometric improvement of the initial control mesh seed by Quasi-interpolation. Fitting method. High-density measurement processing that inputs scanning data of a three-dimensional physical model and generates a high-density measurement point group;
A high-density mesh generation process for generating a high-density mesh for the high-density measurement point group;
Feature boundary extraction processing for performing feature boundary extraction processing on the high-density mesh;
An initial control mesh seed generation process for generating an initial control mesh seed storing feature boundaries by simplification of the high-density mesh using the feature boundaries;
A three-dimensional model fitting program for causing a computer to execute an initial control mesh geometric improvement process for generating a loop subdivision curved surface initial control mesh by executing geometric improvement of the initial control mesh seed. In the high-density mesh generation process, a Marching cubes method is applied to the high-density measurement point group to generate a volume-based mesh, and a Shrink-wrapping method is further applied to generate a high-density mesh.
6. The initial control mesh geometric improvement process includes generating a Loop subdivision curved surface initial control mesh by performing geometric improvement of the initial control mesh seed by Quasi-interpolation. Fitting program.

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