JPH02236677A - Shape conversion method and device - Google Patents

Abstract

PURPOSE:To automatically divide an arbitrary form into finite elements by providing a means which transforms a straight line segment into a segment parallel to the coordinate axis. CONSTITUTION:When the two-dimensional form (a) is inputted from a graphic input part 1 or a graphic read part 7 to an arbitrary form setting part 8, a form (b), which is obtained by approximating the curved part of the form by the straight line, is generated. The respective line segments constituting the form (b) are allocated in parallel with an (x) axis or a (y) axis, and the form (b) is transformed into an approximate model such as a form (c). Thus the arbitrary form can be transformed into a graphic composed only of the straight lines in parallel with the coordinate axes, a grating is combined with the approx imate model, a curvilinear coordinate transformation method can be applied, and the arbitrary form can be automatically divided into the finite elements.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a shape conversion method and apparatus by computer used in fields such as CAE, and in particular, to modeling and meshing that require shape classification and identification. This article relates to a shape conversion method and device suitable for segmentation. [Prior art] In CAE, a boundary shape is expressed by structural data that connects each point on a surface, as well as component data such as equations of surfaces and lines and coordinates of points. Conventionally, the most commonly used shape recognition methods based on these data are the four-division method (two-dimensional) and the eight-division method (three-dimensional). Improved quadripartite method for J Mark A. Ely and Mark S. Shepherd IE
EE CG&A January 1983 P39-4 6
(A Modified Quadtree Appr.
oach to Finite E1am+ant
Mesh Generator Mark A
．． Yerry and Mark S. Shaph
ard IEE CO&A January
It is also explained in detail in 1983).

Here, in order to simplify the explanation, the 2
This method will be explained using a dimensional shape as an example. First, place this figure in a standard square (reference square) and set an integer coordinate system such that the length of one side of this square is 2n. Then, divide the reference square into four small squares, and classify the relationship between each area and the boundary line forming the figure as follows. (1) The square is inside the boundary line. (2) The square is outside the boundary line. (3) The square includes the boundary line. Here, only the squares determined as (3) are divided into four again, Perform the above checks. Continue these operations until the level corresponds to an appropriate shape resolution. The result of dividing the square until one side becomes 1/8 of the reference square is shown in Figure 17B, and the corresponding tree structure is shown in Figure 17C.
Also. When the resolution is increased by one rank, it becomes as shown in Figure 17D. In shape recognition, the general characteristics of the shape are determined based on the tree structure shown in FIG. 17C. The numbers written in Fig. 17C indicate the relationship between the divided square areas and the boundary line forming the target figure, and correspond to the three categories mentioned above. [Problems to be Solved by the Invention] In the above-mentioned conventional technology, it is difficult to grasp the overall graphical characteristics of the shape itself, and as the shape becomes distorted from the registered figure (the figure to be compared), the recognition rate progressively increases. There was a drawback that the performance decreased. Furthermore, when creating an approximate model, there is no unified theory regarding which coordinate axes to make each side of the target shape parallel to, and there is a lot of ambiguity involved. The problem of the present invention is to transform an arbitrary shape into an approximate model that can preserve the graphical characteristics and facilitate classification. (Means for solving the problem) The above problem is achieved by using a shape conversion device that is equipped with a means for converting an arbitrary shape into a shape consisting only of straight line segments, and converting the straight line segments into line segments parallel to the coordinate axes. The shape conversion device according to claim 1, wherein the means for converting a straight line segment into a line segment parallel to the coordinate axes includes an ambiguous operation unit that performs an operation using a membership function. In addition, in the above task, a boundary line or ridge line of an arbitrary shape is approximated by multiple straight line segments, and the degree of approximation of each line segment to the coordinate axis is expressed as a variable between 0 and 1. This can also be achieved by a shape transformation method that globally modifies the variables, assigns each line segment parallel to one of the coordinate axes, and finally converges to one approximate model.

Shape transformation also involves approximating a boundary line or ridgeline of an arbitrary shape with multiple straight line segments, and converting the line segments so that adjacent line segments are on a straight line or perpendicular to each other to form a shape. It can also be used as a method. In addition, a boundary line or ridge line of an arbitrary shape is approximated by multiple straight line segments, the angle that each line segment makes with the coordinate axis is calculated, and the calculated angle and a membership function based on a preset ambiguity rule are used to A shape conversion method may be used in which a line segment is assigned parallel to one of the coordinate axes to create an approximate model of the arbitrary shape. In addition, the ambiguity rule requires that a line segment is assigned as much as possible in the direction of the coordinate axis that has the smallest angle with the line segment, and that two adjacent line segments are assigned as much as possible as the angle between them is smaller than a certain angle. The shape conversion method according to claim 5 may include the step of assigning different directions to the same direction as the angles formed are larger than a certain angle. In addition, after independently creating an approximate model of the boundary surface or boundary line of a given shape and an approximate model of the hole included in the boundary surface or boundary line, A shape conversion method characterized by forming a smooth lattice and determining the relative position of the hole in the approximate model with respect to the boundary shape based on which lattice points correspond to the vertices forming the hole in the actual shape. Good too. Furthermore, it may be a shape conversion method characterized by converting the length of a line segment constituting the approximate model to the minimum integral multiple of the unit length while maintaining the topological characteristics of the shape of the approximate model. ．． [Operation] The arbitrary shape is transformed into a shape consisting only of straight line segments, and the straight line segments are further transformed to be parallel to one of the coordinate axes, so that the arbitrary shape is composed only of straight lines parallel to the coordinate axes. It will be converted into a shape. The fuzzy calculation part, which performs calculations using membership functions, selects which coordinate axis each line segment should be transformed parallel to, according to predetermined fuzzy rules. When creating an approximate model of an arbitrary shape, first, all the edges (in the case of a three-dimensional shape) or boundary lines (in the case of a two-dimensional shape) of the arbitrary shape are approximated by straight line segments,
The angle between each line segment and the coordinate axes (XyytZ axes) is calculated. Next, when assigning which coordinate axis each line segment should be parallel to, at least the following two basic fuzzy rules are used. ■Each line segment is assigned as far as possible to the direction of the coordinate axis that forms the smallest angle.

■The smaller the angle between two adjacent sides is than a certain angle, the more they are assigned to different coordinate axes, and the larger the angle that they form, the more they are assigned to the same direction. Membership functions in fuzzy theory are used to express the ambiguity of this rule.
First, the degree of approximation of each line segment to the coordinate axis is expressed from 0 to 1. In this case, the closer the angle to the coordinate axis is to 0 degrees, the closer the degree of approximation is to 1, and the closer the angle to the coordinate axis is to 90 degrees, the closer the degree of approximation is to 0. Furthermore, for two adjacent sides, the degree of same direction is expressed from -1 to 1 based on the angle formed by the two sides. In this case, 2
The closer the angle between the sides is to 180 degrees, the closer the degree of same direction is to 1, changes to -1 by 90 degrees, and remains constant at -1 below 90 degrees. Next, for two adjacent sides, the degree of influence on each other is calculated based on the degree of approximation to the coordinate axes and the degree of same direction. In this case, if the degree of co-direction is positive, for example, the degree of approximation in the X direction of the influencing side will work to increase the degree of approximation in the X direction of the affected side, and decrease the degree of approximation in the Y and Z directions. In addition, if the same direction is negative, for example, the Y-direction approximation of the influencing side is lower than the Y-direction approximation of the affected side < b, x, z
It works to increase the degree of directional approximation. Then, this degree of influence is expressed as a quantity, and depending on this degree of influence, x of each side is
, y, and z coordinate axes are corrected. Once all edges have been corrected, the degree of influence is calculated for two adjacent sides in the same way based on the corrected degree of approximation, and the degree of approximation to the coordinate axes is thereby corrected again. Such calculations are repeated, and when the degree of approximation in one direction to each coordinate axis for all sides approaches 1, the direction assignment of each side is determined with that state as a convergence state. Ru.

Once the direction assignment of each side is determined, the length of each side on the approximate model is determined for each loop (figure). At this time, the following method is used as a basic method for determining line length. As shown in Figure 15, if a two-dimensional figure is composed only of line segments parallel to the coordinate axes, the orientation of each line segment can be classified into four directions if a loop is followed. Therefore, the sum for each direction of the line segment length of each direction component of the line segment of the real shape corresponding to each line segment is calculated, and the line segment length of the line segment corresponding to direction 1 and direction 2 in the real shape is calculated. The average value of the sum is set to the sum of the line segment lengths of the line segments with direction 1 and direction 2 on the approximate model,
The same operation is performed for directions 3 and 4. Once the total value of the line segment lengths of line segments in the same direction on the approximate model is determined, this total value is calculated for each straight line segment assigned parallel to the coordinate axis according to the ratio of the line segment lengths in the actual shape. The length is distributed proportionally, and the length is determined on the approximate model of each side. In this way. An approximate model consisting only of line segments parallel to the coordinate axes is created, preserving the geometric and topological properties as much as possible. After an approximate model is constructed for each constituent unit (boundary shape and hole included in the shape), an appropriate unit length is set, and all sides are modified so that they are integral multiples of this unit length. , based on this unit length, a grid is created independently for the boundary shape and hole shape. Then, if a grid can be placed on the boundary shape of the approximate model, this grid is mapped to the real shape without considering holes using the curve coordinate transformation method. Here, the curve coordinate conversion method is a mathematical method of forming a uniform grid in an arbitrary shape based on an orthogonal grid, as shown in FIG.

If a grid can be drawn inside the boundary of the actual shape, the grid points closest to the feature points of the hole are found, and correspondence is taken on the grid drawn inside the boundary of the approximate model, and the boundary of the approximate model of the hole is calculated. The relative position of the shape relative to the approximate model is optimized, and an overall approximate model including holes is constructed.

Once the overall approximate model is created, as shown in Figure 16, assuming that the phase state of the approximate model is maintained,
A recognition model is constructed in which each side is transformed so that it takes the minimum integer value. Each edge of this recognition model is given the length of each edge of the corresponding approximate model as an attribute. Recognition of the recognition model is performed in the following steps.

■Classification by the size of the recognition model (NX, NY) ■Classification by the shape of the recognition model ■Comparison based on the line length of the corresponding line segment on each side Using the above three-step recognition procedure, the original arbitrary shape can be created. A corresponding registered figure is selected.

〔Example〕

FIG. 1 is a block diagram showing the overall configuration of an embodiment of the present invention. A keyboard 2. is connected to the arbitrary shape setting section 8. A graphic input unit 1 is provided in which a user directly inputs a shape from components such as a tablet 3 and a mouse 4, and the graphic input unit 1 further includes a CR having a display control unit 6.
Connected to T display 5. A shape reading section 7 is further connected to the input side of the arbitrary shape setting section 8,
On the output side of the arbitrary shape setting section 8, there is a shape that calculates the degree of approximation of each side to the coordinate axes and the degree of same direction of two adjacent sides based on the information obtained from the curve conversion section 9 and the geometric calculation section 10. An information generation unit 11 is connected. The shape information generation section 11 is further connected to an approximate model generation section 15, and the geometric operation section 10 generates the shape information generation section 11 and the approximate model from the generation section 1.
5. The approximate model generating section 15 is further connected to an overall approximate model generating section 18 , and the overall approximate model generating section 18 is connected to a recognition model generating section 19 . The recognition model generation section 19 is connected to a recognition result display section 22, and the recognition result display section 22 is further connected to the CRT display 5. The shape information generation section 11 further includes a curve conversion section 9 for linearly approximating the ridgeline (boundary line) of an arbitrary shape, and the direction assignment of the coordinate axes of each side determined by performing fuzzy calculations to generate the shape topologically. A matching confirmation unit 14 is connected to confirm whether or not the following holds true.

The approximate model generation unit 15 is connected to the fuzzy calculation unit 13 that corrects the degree of approximation of each side to the coordinate axes according to the ambiguity rule based on the shape information, and the consistency confirmation unit 14. , is connected to an ambiguous rule setting section 12 that sets various rules for performing shape conversion. The approximate model generation unit 15 constructs an approximate model based on the geometric data obtained from the geometric calculation unit 10 and the topological data obtained from the fuzzy calculation unit 13.
is connected to a mapping calculation unit 16 that generates a grid in a real shape using a curved coordinate transformation method based on a square grid stretched on an approximate model, and the mapping calculation unit 16 uses this grid to calculate the shape of the hole. Relative position calculation unit 1 that detects the relative position with respect to the boundary shape
7, it is connected to the overall approximate model generation section 18. Further, a recognition calculation unit 2.0 is provided which is connected to the recognition model generation unit 19 that converts an approximate model into a recognition model and performs matching with figures registered in the basic figure database 2l based on the recognition model. A basic figure database 21 in which basic figures are registered is connected to the recognition calculation unit 20. The recognition calculation unit 2o also includes the recognition calculation unit 2
It is connected to a recognition result display section 22 that displays the calculation result of 0. The geometric calculation section calculates the angles formed by each straight line, coordinate axes, and adjacent sides, and calculates the length of each side of an approximate model based on the actual shape. The overall approximate model generation section 18 constructs an overall approximate model by combining the boundary shape and hole approximate models based on the information provided from the approximate model generation section 15 and the relative position calculation section 17. Said CR
The T display 5 is also connected to an arbitrary shape setting section 8. The above-mentioned fuzzy rule setting unit 12 and fuzzy calculation unit 13 form a fuzzy calculation unit 30A, and the fuzzy calculation unit 30A, the geometric calculation unit 10, the shape information generation unit 11, the consistency confirmation unit 14, and the approximate model The generation unit 15 constitutes means 30 for converting a straight line segment into a line segment parallel to the coordinate axes. Next, the operation of the above embodiment will be explained. When the two-dimensional shape a shown in FIG. 2 is input to the arbitrary shape setting section 8 from the figure input section 1 or the figure reading section 7, the curved portion of the shape is linearly approximated by the curve conversion section 9. b is generated. Each line segment constituting shape b is assigned to a direction parallel to the X-axis or y-axis, and converted into an approximate model such as shape C in FIG. 2.

We will explain how to construct this approximate model. First, the following four basic rules are used as ambiguous rules regarding the generation of the phase information of the approximate model (information on which of the X+Y axes parallel to which each line segment is assigned). Rule 1: Each line should be parallel to the direction of the coordinate axis that makes the smallest angle. Rule 2: Regarding two adjacent sides, the smaller the angle they make is smaller than a separately determined fixed angle, the more they are assigned to different coordinate axes, and the larger the angle is larger than the fixed angle, the more they are assigned to the same coordinate axes. It will be done. Rule 3: Groups of lines with a small rate of change in slope are assigned to one direction as much as possible. Rule 4: Parallel #I groups are allocated in the same direction as much as possible. Rule 1 is realized by initializing the degree of approximation to the coordinate axes, which is obtained based on the angle that each line segment makes with the coordinate axes. The degree of approximation to the X-axis and y-axis is determined by the angle (Ox,
θy), and the degree of approximation P in the X-axis direction or y-axis direction is plotted on the vertical axis.
It is represented by a membership function that takes x, Py (0≦Px≦1, 0≦Py≦1). It is defined that the closer the angle a line segment makes with any coordinate axis is 0 degrees, the closer the degree of approximation is to 1, and the closer the angle it makes to 90 degrees, the closer the degree of approximation is to 0. Further, Rule 2 is realized by modifying the degree of approximation of each side to the coordinate axis based on the degree of approximation and the degree of same direction, which is the relationship between two adjacent sides. Same direction of two adjacent sides PR
is the third C, where the horizontal axis is the angle θB formed by the two adjacent sides, and the degree of same direction PR (-1≦Pyt≦1)1) is the vertical axis.
It is represented by a membership function as shown in the figure. In this case, the degree of same direction approaches 1 as the angle between the two sides approaches 180 degrees, changes to -1 as the angle approaches 90 degrees from 180 degrees, and below 90 degrees, - It is constant at 1. Regarding the correction of the degree of approximation, the two line segments shown in Figure 4
Let's explain using an example. First, according to Figure 3A, line segment ■
The X-axis approximation degree Px and y-axis approximation degree py are respectively 0.8,
0.2, the x and y axis approximations of line segment ■ are 0.4 and 0.4, respectively.
0.6, and the angle formed by the two sides is 108 degrees, so according to Figure 3C, the degree of same direction PR of the line segment ■■ is -0.6
, which means that the strength assigned to the coordinate axes of the two sides in different directions is 0.6. Therefore, based on these values, first, the degree of influence from the line segment to the line segment ■ is calculated. Note that the degree of influence is defined as indicating the degree to which the degree of approximation is modified. Calculating the degree of influence is achieved by calculating the following four items. (i) Degree of influence from the X-axis of the line segment ■ to the X-axis of the line segment , deny the X-likeness of line segment ■. As shown in Fig. 5A, the degree of approximation in the X-axis direction of the glandular segment ■ is 0.
8. Since the degree of approximation in the non-X-axis direction of line segment ■ is 0.6, the degree of influence Q x x from the X-axis of line segment ■ to the X-axis of line segment ■ is calculated by the following formula (1). ．． Qxx - (approximation degree of gland segment ■ in the X-axis direction) × (non-X of line segment ■
Axial direction approximation) X (same direction) ・・・・・・(1) = 0.8
Influence degree Qyx from the y-axis of the line segment ■ to the X-axis of the line segment
The y-likeness of , affirms the X-likeness of the line segment ■. As shown in Figure 5B, the degree of approximation of the line segment ■ in the y-axis direction is 0.2, and the degree of approximation in the X-axis direction of the line segment ■ is 0.4. The degree of influence Qyx on the axis is calculated using equation (2) below. Qyx = (approximation degree of line segment ■ in y-axis direction) × (approximation degree of line segment ■ in X-axis direction) × (degree of same direction X (-1))...
...(2) =0.2x0.4x(-0.6)X(-1)=0.04
8 (nu) Degree of influence Q from the X-axis of the gland segment ■ to the y-axis of the line segment ■
The two sides consisting of the xy line segment ■■ have a negative degree of same direction, so the line segment ■■
The X-likeness of the line segment ■ affirms the y-likeness of the line segment ■. As shown in Figure 5C, the degree of approximation in the X-axis direction of line segment ■ is 0.8, and the degree of approximation in the y-axis direction of line segment ■ is 0.6. The degree of influence Qxy on the y-axis is calculated by the following equation (3). Qxy=(approximation degree of line segment ■ in the X-axis direction)
× (degree of approximation in the y-axis direction of the gland)
))・・・・・・(3) =0.8X0.6(-0.6)X(-1)=0.288
(~) Influence degree Qyy from the y-axis of the line segment ■ to the y-axis of the line segment Denies the y-likeness. As shown in Figure 5D, the degree of approximation in the y-axis direction of the gland segment ■ is 0.2, and the y-axis direction of the line segment ■
Since the degree of approximation in the axial direction is 0.4, the degree of influence Qyy from the y-axis of the line segment ■ to the y-axis of the line segment ■ is calculated by the following equation (4). Qyy = (degree of approximation in y-axis direction of line segment ■) × (degree of approximation in non-y-axis direction of gland segment ■) × (degree of same direction) ...... (4) = 0.2X0, 4X (-0 .6)=-0.048(i)
Based on the calculation of ~(), the influence of line segment ■ on the degree of approximation in the X-axis direction is: Qxx+Qyx=-0.288+0.048=-0.2
The influence of the 4 line segments ■ on the degree of approximation in the y-axis direction is Qxy+Qyy"-0.288-0.048=0.24
becomes. The degree of approximation is corrected by adding (degree of influence x calculation constant) to the degree of approximation calculated in FIGS. 3A and 3B. For example, when the calculation constant is 0.1,
The degree of approximation in the X-axis direction of line segment ■ decreases from 0.4 to 0.4 + (-0.24) 0.2 4
) x O. 1 = 0.6 2 4, and the direction assignment of the line segment ■ is tilted in the y-axis direction. Similarly, by calculating the degree of influence from line segment ■ to line segment ■, a result is obtained in which the direction assignment of line segment ■ is tilted toward the X-axis direction. The above calculation is performed on all pairs of two adjacent sides of the figure (shape b in Figure 2) obtained by linear approximation of the curved part of the target figure, and the degree of approximation is corrected overall.
Next, the degree of influence is calculated based on the corrected degree of approximation, and the degree of approximation is corrected again. By repeating these operations, the degree of approximation of each side (line segment) will generally be the degree of approximation in one direction (
For example, the degree of approximation in the X-axis direction) converges to 1, and the degree of approximation in other directions (for example, the degree of approximation in the y-axis direction) converges to O. and,
By adopting the direction assignment in this convergence state, as shown in the transformation from shape b to shape C in Figure 2,
It is possible to generate phase information for approximate models. Regarding two-dimensional figures, -(XF)F)X(xty
), the degree of approximation is corrected by four operations, but for three-dimensional figures, (xt yt z) × (X,)'t
Z), the degree of approximation is corrected through nine calculations.

Also, as mentioned above, there are four basic ambiguous rules. In addition, as shown in the example in Figure 6, the constituent line segments of two line groups with approximately the same distance from each other are all assigned the same direction, and there are three directions assigned to one three-dimensional surface. There are auxiliary rules such as ``must not'', and by setting these rules appropriately, an approximate model can be generated efficiently. Next, a method for determining whether a shape is established topologically based on the direction assignment obtained by the above method will be explained using FIGS. 7A and 7B as an example. A shape that is a linear approximation of the curved part of the target figure f of an arbitrary shape is generated,
Assign the direction of each line segment to generate an approximate model from the shape, and the direction of the line segment when tracing the shape counterclockwise! +#'／"*X-t Y-expressed.x",
y+ is a line parallel to the X-axis and y-axis, respectively, in the direction in which the numerical value increases, and X'''', y- is a line parallel to the X-axis and y-axis, respectively, in the direction in which the numerical value decreases. Indicates the minute. The shape gel in Figure 7A shows an example of the direction of the line segment assigned to the shape f, and the difference between the shape g and the shape i is that in the shape g, the upper left line segment is assigned X-. In contrast, in shape i, the corresponding line segment is at the point assigned y+. When each figure is approximated as a model using line segments parallel to the assigned X-axis and y-axis, the shape g becomes the shape h, and the shape i becomes the shape j. When tracing a figure made up of only line segments parallel to the X and Y axes in a counterclockwise direction, the way around the angle made up of each line segment is
It will be one of the eight types shown in Figure B, and each corner will be given the corner number written on each corner in Figure 7B. The numbers written on each corner of shapes h and j are the corner numbers.

If the assigned line segment direction is topologically consistent, if the assigned line segment is traced counterclockwise, the sum of the corner numbers will be 1o, and if the assigned line segment is traced clockwise. In this case, there is a property that the sum of the included numbers is -10.
As shown in FIG. 7A, based on this property, it is determined whether or not the topological matching of the figures formed by the assigned line segment directions is achieved. One countermeasure when topological consistency cannot be obtained is to refer to past calculation results, change the current direction assignment starting from the edge with the highest degree of ambiguity, and search for an assignment pattern that achieves consistency. There is. Next, we will explain the generation of geometric information for the approximate model (determining the length of each side). As shown in shape m in Figure 8, if the loop (boundary IX that forms the figure) is traced in one direction, the orientation of each side of the approximate model is classified into four directions from ■ to ■ in the figure, and the ■ direction The sum of the lengths of the sides classified in the ■ direction is equal to the sum of the lengths of the sides classified in the ■ direction. Regarding the real shape shown in shape n in Figure 8, take the average value of the total value of the sides in the ■ direction and the total value of the sides in the ■ direction, and use this as the average value of the sides classified in the ■ and ■ directions of the approximate model. Set as the total length value. The same applies to the ■ direction and ■ direction. This determines the total length of the sides in each direction in the approximate model, so for each direction, based on the ratio of the lengths of each side in the actual shape,
The total length is divided proportionally and set as the length of each side of the approximate model, and an approximate model for each loop is completed as shown in shape O in Figure 8. Here, we will describe an application example of this approximate model. First, we will explain the curve coordinate transformation method. The curve coordinate conversion method is, as shown in Figure 9, when an arbitrary shape p and a lattice shape γ consisting only of straight lines parallel to the corresponding coordinate axes are set, an arbitrary shape can be transformed by performing a mapping operation. This is a method to obtain a shape q that generates a uniform grid. Therefore, when an arbitrary shape is set, an approximate model is created using the present invention, the shape is modified so that each side of the approximate model is an integral multiple of the unit length, and based on this unit length, If you set up a grid and set it as a grid shape, and apply the curve coordinate transformation method to this, automatic division into finite elements of arbitrary shapes will be performed. FIG. 10 shows an example of automatic division of two-dimensional and three-dimensional figures.

Next, we will explain how to create an approximate model of a shape that includes holes. First, as shown in Figure 11A, the shape of the approximate model is modified so that each side is an integral multiple of the unit length independently of the boundary shape and hole shape, and a grid is created based on this length. ．． Next, as shown in Figure 11B, a grid is generated on the boundary shape of the actual shape using the curve coordinate transformation method based on this grid, and it is determined to which grid the feature point of the hole is closest.
Correspondence is taken on a grid stretched over the boundary shape of the approximate model. Then, as shown in Figure 11C, move the hole-shaped approximate model with a lattice on the lattice stretched over the boundary shape of the approximate model until the sum of the differences between corresponding points is minimized. The position is found, the relative position of the hole shape to the boundary shape is determined, and an overall approximate model as shown in FIG. 11D is created. Using this method, it is possible to automatically create a lattice shape with holes in an arbitrary shape, and as a result, finite element division of arbitrary shapes with holes as shown in Figure 12 can also be automated. Next, we will explain how to construct a Shida Sensei model based on the approximate model,
We will explain the recognition method using this. Once the overall approximate model is created, as shown in FIG. 13A, a recognition model is constructed in which each side is transformed to take the minimum integer value on the premise that the phase state of the approximate model is maintained. Each edge of this recognition model is given the length of the edge of the corresponding approximate model as an attribute.

In addition, in order to express the relative position of the hole, as shown in Figure 13B, the point with the smallest Y coordinate belonging to the leftmost side is detected independently of the boundary shape and hole shape of the approximate model, and The distance between the corresponding point and the corresponding point of each hole shape in the actual shape is set as an attribute. Then, recognition is performed according to the following three steps based on the recognition model.

(1) As shown in Figure 13C, the size of the recognition model (N
Classified by X, NY). NX and NY are the summed values of the attribute values given to each side of the recognition model in the X-axis direction and the y-axis direction, respectively.

(it) Classification based on the shape of recognition models (m) Comparison based on attributes given to models (length of corresponding line segments, relative position of holes!!) An example of application of this recognition method is explained below. Consider the case where two-dimensional shapes So and to are given as shown in FIG. First, regarding the shape So, various shape deformations are possible as shown in FIG. 14, S1 and S, by changing the viewpoint position, but these are all replaced by the same recognition model shown in FIG. 14, 83. In addition, the shape to is also replaced with the same recognition model, but as shown in FIG.
It is clearly distinguished from o. In this way, by using this invention, figure recognition is performed that is less susceptible to the effects of distortion from the original shape. The above explanation deals with two-dimensional figures, but in the case of three-dimensional figures, the edges of the figure are first approximated to straight line segments, and then the same method is applied. Conventionally, when creating an approximate model, it was impossible to create it using a uniform mathematical method, but according to this example, by using membership functions, various transformation rules related to shape transformation can be created. Mathematical expression has become possible, and a universal shape conversion method has been established that reflects human judgment, including ambiguity.
In addition, when determining the relative position of the hole shape to the boundary shape, the negative effects of boundary shape distortion were reduced by generating a uniform grid using the curved coordinate transformation method. Furthermore, by performing figure recognition using a recognition model converted from an approximate model, it is possible to obtain recognition results that are less affected by deformation even if a certain recognized shape is deformed from the original shape, and also to By dividing the procedure into three stages, recognition work has been made more efficient. [Effects of the Invention] According to the present invention, an approximate model consisting of straight lines parallel to the coordinate axes is automatically generated for any shape, so a grid can be placed on this approximate model and a curved coordinate transformation method can be applied. This has the effect of making it possible to automatically divide an arbitrary shape into finite elements.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing the general configuration of a shape conversion device that is an embodiment of the present invention, Fig. 2 is a plan view showing an example of the conversion procedure to an approximate model, and Figs. 3A to 3C are members. A graph showing an example of the ship function, Fig. 4 is an explanatory diagram showing an example of the angle between a straight line segment and a coordinate axis, Figs. A plan view showing an example of ambiguity processing, Figures 7A and 7B are explanatory diagrams showing an example of a method for confirming phase matching of an approximate model, and Figure 8 is a plane view showing a method for determining the length of each line segment of an approximate model. Figure 9 is a plan view showing an example of the curve coordinate transformation method, Figures 10 and 12 are plan views showing an example of finite element division of a figure, and Figure 11A is a plan view showing an example of the curve coordinate conversion method.
Figures 11D to 11D are plan views showing the procedure for creating an approximate model of a shape with a hole, Figures 13A to 13C are plan views showing the procedure for creating a recognition model, and Figure 14 is a figure recognition procedure using the approximate model. FIG. 15 is a plan view illustrating the direction of the line segments that make up the approximate model, and FIG. 16 is a plan view illustrating the change from the approximate model to the recognition model.
Figures 17A to 17D are diagrams showing examples of conventional figure recognition methods. 30... Means for converting a straight line segment into a line segment parallel to the coordinate axes, 30A... Ambiguous calculation unit. Figure 1

Claims (1)

[Scope of Claims] 1. A shape converting device equipped with means for converting an arbitrary shape into a shape consisting only of straight line segments, comprising means for converting the straight line segments into line segments parallel to coordinate axes. Characteristic shape conversion device. 2. The means for converting a straight line segment into a line segment parallel to the coordinate axes is
2. The shape conversion device according to claim 1, further comprising an ambiguous operation section that performs an operation using a membership function. 3. Approximate a boundary line or ridgeline of an arbitrary shape with multiple straight line segments, express the degree of approximation of each line segment to the coordinate axis as a variable between 0 and 1, and modify the variable as a whole using an ambiguous rule. to assign each line segment parallel to one of the coordinate axes,
A shape conversion method that ultimately converges to one approximate model. 4. Shape transformation in which a boundary line or ridge line of an arbitrary shape is approximated by a plurality of straight line segments, and the line segments are transformed so that adjacent line segments are on a straight line or perpendicular to each other to form a shape. Method. 5. Approximate a boundary line or ridgeline of an arbitrary shape with multiple straight line segments, calculate the angle that each line segment makes with the coordinate axis, and use the membership function based on the calculated angle and a preset ambiguity rule to A shape conversion method that creates an approximate model of the arbitrary shape by assigning line segments parallel to one of the coordinate axes. 6. The ambiguity rule is that the line segment is assigned as much as possible in the direction of the coordinate axis that has the smallest angle with the line segment, and that the angle between two adjacent line segments is smaller than a certain angle, the more the line segment is assigned as possible. 6. The shape conversion method according to claim 5, further comprising the step of assigning different directions to the same direction as the angles formed are larger than a certain angle. 7. After independently creating an approximate model of the boundary surface or boundary line of a given shape and an approximate model of the hole included in the boundary surface or boundary line, A shape conversion method characterized by forming a smooth lattice and determining a relative position of a hole in an approximate model with respect to a boundary shape based on which lattice point corresponds to a vertex forming a hole in the actual shape. 8. A shape conversion method characterized by converting the lengths of line segments constituting the approximate model to the minimum integral multiple of the unit length while maintaining the topological characteristics of the shape of the approximate model.