JP2006018513A - Method for generating set of cells and set of cells generated by the method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a set of cells allowed to be formed even in a mesh for forming a boundary part of substances or the neutral surface of a thin plate. <P>SOLUTION: A method for generating a set of cells comprises the following steps, i.e. a step (1) for searching a background cell having a tunnel side or a tunnel point in a set of background cells, a step (2) for adding a foreground cell to the position of the detected background cell. Furthermore the method may be provided with the following steps, i.e. a step (3) for searching a boundary cell from the set of cells and a step (4) for deleting the detected boundary cell. The set of cells is constituted of face cells and satisfies two following conditions, i.e. tunnel disablement (1) and thickness of 1 (2). <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a cell set generation method and a cell set generated thereby. The present invention particularly relates to a cell extraction method for generating a surface model from a volume model.

  In recent years, industrial X-ray CT (Computed Tomography) measurement has become widespread, and in addition to product inspection, a 3D shape model is generated from CT data, and this model is converted into CAD (Computer Aided Design) and CAE (Computer Aided Engineering). ) It has come to be used in the system.

  FIG. 1 shows an example of CT data. This figure is a cross-sectional image of the engine block. A large number of such cross-sectional images are taken at a certain interval to generate a three-dimensional image, a so-called volume model. A pixel of the volume model is called a voxel. A voxel has an image value, that is, a voxel value. In the case of CT, it has a real value or an integer value almost proportional to the density value of the object to be imaged at that location.

  Now, such a volume model is effective for observing the internal structure of the measurement object (for example, the “sink nest” of the cast product), but as described above, the volume model is not limited to CAD or CAE. The system cannot be used. Therefore, a polyhedron representing the shape of the object is generated from the volume model. As the polyhedron, a triangular mesh in which all faces are triangular is often used.

  FIG. 2 shows an example of a triangular mesh. Although FIG. (A) is a relatively simple example, FIG. (B) represents a three-dimensional shape with a small triangle. The latter type is generated from a volume model by X-ray CT, and the number of triangles can be from several million to tens of millions.

  As a method for generating a triangular mesh (hereinafter referred to as a mesh) from volume data in this way (hereinafter referred to as a surface generation method), there is an iso-surface generation (iso-surfacing). The most typical method is a method called marching cube method. The isosurface generation method will be described below.

(Isosurface generation method)
(Marching cube method)
Details of the marching cube method are described in Non-Patent Document 1 below. Since the volume model is obtained by superimposing a large number of cross-sectional images in which pixels are arranged in a two-dimensional grid, pixels (voxels) are arranged in a three-dimensional grid as a whole. Among these, a rectangular parallelepiped composed of eight voxels (a cube when all three lattice intervals are equal) is called a cell.

  Now, when an object is measured, the purpose of the marching cube method is to extract a portion corresponding to the surface of the object as a mesh. Since the density is different between the outside (background) of the object and the object, the voxel values of the voxels corresponding to each of the objects take different values. Therefore, a threshold value θ for distinguishing the voxel values of the background and the object is set.

  Then, the eight voxels of the cell can be divided into those having a voxel value larger than θ and those smaller than θ (except for the case where the voxel value is equal to θ for simplicity). And it turns out that the surface used as the boundary of a background and an object passes between voxels larger than (theta) and voxels smaller than (theta). So, for 12 sides of a cell, if one value of the voxels at both ends is greater than θ and the other is less than θ, the boundary will cut that side. The location to be cut can be obtained from the voxel values at both ends and θ from the internal division. Thus, the interference point between the boundary surface and the side is obtained, and then a triangle is generated in the cell according to the pattern of FIG. In consideration of the symmetry of the cell, it is known that the 14 patterns of FIGS. (A) to (n) are sufficient. This method has been extended a lot as described in Non-Patent Document 2, for example.

(Dual contouring)
The dual method is known as another method of generating isosurfaces. In this method, as shown in FIG. 4, a side at the center of four cells arranged in a 2 × 2 shape is considered. When one of the voxel values at both ends of the side is larger than θ and the other is smaller, a point is generated on the side in the same manner as the marching cube method. Furthermore, a triangle is generated by connecting the centers of the four cells around the side. This method is introduced in the following non-patent documents 3 and 4.

(Summary of isosurface generation method)
As described above, in the isosurface generation method for generating a triangular mesh from a volume model, a threshold value representing the boundary of an object is set for the voxel value of the volume model, and the cell unit (in the marching cube method, cell unit, dual unit) The triangle is generated in units of 4 cells in the method.

(Problems of isosurface generation)
(Problems of neutral plane generation in thin plate structure)
FIG. 5A shows an example of a thin plate structure such as an iron plate taken by X-ray CT, which is shown in two dimensions for simplicity. When the isosurface method is applied to this, a mesh as shown in FIG. 5B is generated. However, when designing a thin plate, it is often designed with a surface model representing the shape of a neutral surface as shown in FIG. In addition, a neutral surface shape is also required when performing analytical calculation by the finite element method or the like.

  Such a neutral plane cannot be extracted by setting a threshold for the volume model. Therefore, a cell set for generating a neutral plane and a generation method thereof are required.

(Problem of material interface generation of multi-media parts)
Many machine parts are composed of a plurality of materials. In the engine block of FIG. 1, the gray part is made of aluminum and the white part is made of iron, and there are three media in this image, together with the air. Naturally, there are a plurality of threshold values between different substances. With isosurface generation methods such as marching cubes, only one threshold value can be set. For example, when generating a mesh with aluminum and air threshold values to generate the outer shape of the engine block, the boundary between iron and air is used. Since the threshold is not correct, the mesh is not obtained correctly.

  FIG. 6 shows an outline of the generation of the boundary surface of the multimedia part. FIG. 6 schematically shows a state where three media of iron, aluminum, and air meet.

First, the voxels are classified into iron, aluminum, air, and two different medium boundaries, and further three medium boundaries (FIG. 6A). This can be done using voxel values or material boundary conditions. Next, for a cell at the boundary between two media, a threshold value between the two media is set, and a cell in which the voxel value sandwiches the threshold value is extracted (such that the voxel has a value larger and smaller than the threshold value). (FIG. 6B), so that a boundary surface can be generated for each of the two media using a threshold value between the two corresponding media. However, in a region where three media are gathered, the threshold value is not fixed, so that a cell for generating a surface cannot be extracted from the threshold value, and a surface cannot be generated.
WE Lorensen and HE Cline. Marching cubes: A high resolution 3d surface construction algorithm.In Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pages 163-169. ACM Press, 1987. LP Kobbelt, M. Botsch, U. Schwanecke, and H.-P. Seidel.Feature sensitive surface extraction from volume data.In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 57-66.ACM Press, 2001 . SF Frisken, RN Perry, AP Rockwood, and TR Jones.Adaptly sampled distance fields: a general representation of shape for computer graphics.In Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 249-254.ACM Press / Addison -Wesley Publishing Co., 2000. T. Ju, F. Losasso, S. Schaefer, and J. Warren.Dual contouring of hermite data.In Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pages 339-346.ACM Press, 2002.

  In isosurface generation methods such as the marching cube method and dual method, a surface is generated in units of cells or 2x2 cells. However, if the view is changed, a surface is generated from the entire cell using a threshold value. It can be seen that a power cell is being extracted. In the case of the aforementioned thin plate or multi-medium, such a cell set could not be extracted with the threshold value, but if it can be obtained by other methods, a surface can be generated there. It is done. Such a cell set is an appropriate cell set (a cell set near the neutral plane obtained by a process called skeletonization in the case of a thin plate, and a cell based on the aforementioned medium classification in the case of a multi-media boundary. It is possible to obtain a set by adapting it to a cell set that can generate a surface by applying the marching cube method or dual method (FIG. 6C). And if such a cell set is obtained, a code | symbol can be given to the voxel of the cell, and a surface can be produced | generated by applying a marching cube method (FIG. 6D). However, since a branch occurs in the mesh here, a non-manifold marching cube method is used.

  It is an object of the present invention to provide a cell set generation method capable of generating such a mesh and a cell set obtained thereby.

The cell set generation method according to the present invention comprises the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) A step of adding a foreground cell at the location of the found background cell.

  In the step (1), when a plurality of the background cells are found, the priority order can be determined using the evaluation function.

  It is also possible to repeat the steps (1) and (2) until the background cell can no longer be found.

The cell set generation method according to the present invention may be configured to include the following steps:
(1) searching for a boundary cell from the cell set;
(2) A step of deleting the found boundary cell.

  In this step (1), when a plurality of the boundary cells are found, the priority order can be determined using the evaluation function. Also, the steps (1) and (2) can be repeated until the border cell cannot be found.

  It is also possible to execute steps (1) and (2) in the latter generation method after executing steps (1) and (2) in the former generation method.

The cell set according to the present invention is composed of surface cells and satisfies the following two conditions:
(1) Unable to tunnel (2) Thickness is 1.

The cell set generation program according to the present invention is characterized by causing a computer to perform the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) A step of adding a foreground cell at the location of the found background cell.

The cell set generation program according to the present invention may be characterized by causing a computer to perform the following steps:
(1) searching for a boundary cell from the cell set;
(2) A step of deleting the found boundary cell.

The computer for generating a cell set according to the present invention is characterized by performing the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) adding a foreground cell to the location of the found background cell;
(3) searching for a boundary cell from the cell set;
(4) A step of deleting the found boundary cell.

The generation method according to the present invention is a method for generating a cell set capable of generating a polyhedron by an isosurface generation method, and may execute the following steps:
(1) A step of adding a cell to the cell set. (2) A step of deleting a cell from the cell set.

By executing these steps, it is possible to obtain a cell set characterized by being composed of plane cells and satisfying the following two conditions.
(1) Unable to tunnel (2) Thickness is 1.

  According to the present invention, it is possible to generate a “cell set capable of generating a desired mesh” by using “a set of cells representing an object”. A mesh can be generated by applying an appropriate isosurface generation method to this cell set.

  Hereinafter, an embodiment of the present invention will be described. First, organize the concepts necessary for explanation.

(Introduction of cell topology)
Here, the cells will be described first, and then the concept for expressing the relationship between the cells will be described.

(cell)
Volume model pixels are called voxels. A cell is a rectangular parallelepiped element having a voxel as a vertex. As shown in FIG. 7, each cell is composed of a surface, a side (ridge line), and a point (vertex), and shares a surface / side / point with an adjacent cell.

(Near points, sides, faces)
The 8 (4, 2) cells connected to a point (side, face) are called the neighborhood of the point (side, face).

(Foreground and background cells)
The cell to which the surface generation method is applied is called a foreground cell, and the other cells are called background cells.

  Hereinafter, the definition of the tunnel side and the tunnel point will be strictly performed.

(Cell adaptation)
Here, cell adaptation will be described. Cell adaptation refers to a process of converting to a cubic shell by adding / deleting a cell when an arbitrary foreground cell set is given as an input.

(Step Sa-3)
A foreground cell is added at the location of the highest priority background cell.

(Step Sb-3)
Delete the foreground cell with the highest priority.

  As described above, by applying the cell addition process and the cell deletion process, a cubic shell that cannot be tunneled and has a thickness of 1 is obtained.

(Example)
The cell generation method as described above can be executed by a computer and computer software. FIG. 14 shows a hardware configuration of a general computer. This computer includes a CPU 1, a memory 2, and a display unit 3. The memory 2 stores data necessary for processing (for example, pixel data) and a program for causing the computer to perform the processing. The CPU 1 executes the generation method as described above according to the program and outputs the result to the display unit 3. The user can visually recognize the result via the display unit 3. The display unit 3 is a printer or a display, for example.

The description of the embodiment is merely an example, and does not indicate a configuration essential to the present invention. The configuration of each part is not limited to the above as long as the gist of the present invention can be achieved.
Further, the functional blocks of the computer described above may be combined and integrated into one functional block. Further, the function of one functional block may be realized by cooperation of a plurality of functional blocks. Furthermore, the functional blocks described above only have to exist as functions, and any means such as hardware, computer software, or a combination thereof can be used as means for realizing the functions. One functional block may be realized by cooperation of hardware and computer software arranged at physically discrete positions.

It is a figure which shows an example of an industrial X-ray CT image. It is a figure which shows an example of a triangular mesh. It is explanatory drawing for demonstrating a marching cube method, Comprising: The figure (a) to the figure (n) show the example of the triangle produced | generated in a cell. It is explanatory drawing for demonstrating a dual method. It is explanatory drawing for demonstrating the necessity of the neutral surface production | generation in a thin-plate structure, Comprising: FIG. (A) is a schematic diagram of CT image of a thin-plate structure, FIG. (B) is the volume produced | generated by the marching cube method. The model, figure (C), is the necessary neutral plane. It is explanatory drawing for demonstrating the necessity of the neutral surface production | generation in a multimedia component, Comprising: (A) is a classification | category of multimedia components, (B) is a cell containing a threshold value between each two media. The extracted state, FIG. (C) is an adapted state, and FIG. (D) is a diagram showing the boundary surface between the media. It is explanatory drawing for demonstrating a cell and a surface, an edge | side, and a point. FIG. 4A is an explanatory diagram showing a plane cell, and FIG. 4B is an explanatory diagram showing a boundary cell in two dimensions for simplicity. It is explanatory drawing for demonstrating the state which cannot tunnel, Comprising: The figure (a) has shown the state which has a side tunnel, and the figure (b) has shown the state which has a point tunnel. It is explanatory drawing for demonstrating the state which has a tunnel, Comprising: The figure (a) has shown the state which has a side tunnel, and the figure (b) has shown the state which has a point tunnel. It is a figure which shows notionally the arrangement | positioning (2x2x2 cell) of the cell which does not satisfy | fill thickness 1. FIG. It is a flowchart for demonstrating the addition process of a cell. It is a flowchart for demonstrating the deletion process of a cell. It is a conceptual block diagram for demonstrating an example of the computer used for the production | generation method of a cell.

Explanation of symbols

1 CPU
2 Memory 3 Display

Claims (12)

A method of generating a cell set, characterized by comprising the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) A step of adding a foreground cell at the location of the found background cell.   2. The generation method according to claim 1, wherein, in the step (1), when a plurality of the background cells are found, a priority order is determined using an evaluation function.   The generation method according to claim 1 or 2, wherein the steps (1) and (2) are repeated until the background cell cannot be found. A method of generating a cell set, characterized by comprising the following steps:
(1) searching for a boundary cell from the cell set;
(2) A step of deleting the found boundary cell.   5. The generation method according to claim 4, wherein, in the step (1), when a plurality of the boundary cells are found, the priority order is determined using an evaluation function.   6. The generation method according to claim 4, wherein the steps (1) and (2) are repeated until the boundary cell cannot be found.   The method according to any one of claims 1 to 3, wherein the method according to any one of claims 4 to 6 is executed after the method according to any one of claims 1 to 3 is executed. A cell set composed of surface cells and satisfying the following two conditions:
(1) Unable to tunnel (2) Thickness is 1. A cell set generation program characterized by causing a computer to perform the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) A step of adding a foreground cell at the location of the found background cell. A cell set generation program characterized by causing a computer to perform the following steps:
(1) searching for a boundary cell from the cell set;
(2) A step of deleting the found boundary cell. A computer for generating a cell set, characterized by performing the following steps:
(1) searching for a background cell having a tunnel edge or a tunnel point for the background cell set;
(2) adding a foreground cell to the location of the found background cell;
(3) searching for a boundary cell from the cell set;
(4) A step of deleting the found boundary cell. A method for generating a cell set capable of generating a polyhedron by an isosurface generation method, wherein the cell set according to claim 8 is generated by executing the following steps:
(1) A step of adding a cell to the cell set. (2) A step of deleting a cell from the cell set.