TWI486907B - Free surface area computation system and method - Google Patents

Description

Free surface area calculation system and method

The invention relates to a computer aided design system and method, in particular to a free curved surface area calculation system and method.

In computer-aided design, the length and area are the most basic attributes of the primitive. For example, the length of the line and the area calculation of the plane figure can be completed by a simple four-step operation. The free-form surface is an abstract figure, which mainly describes the shape of the object by boundary points and control points. The area of the free-form surface cannot be obtained by conventional mathematical operations. At present, the calculation method for the free-form surface area is either high precision but slow, or fast but low precision.

In view of the above, it is necessary to provide a free-form surface area calculation system and method, which can quickly calculate the area of the free-form surface and improve the calculation accuracy of the free-form surface area.

A free-form surface area calculation system is applied to an electronic device. The system comprises: a boundary processing module, a triangular meshing module and a computing module. The boundary processing module is configured to obtain a contour surface composed of boundary points of the free surface, and obtain a polyline that approximates the contour surface in the parameter plane. The triangular meshing module is configured to set a sample point in the parameter plane, and construct an approaching the contour surface according to the set sample point, the vertices of the polyline, and the vertical line segment of the sample point or the intersection of the horizontal line segment and the polyline Polygon and said The polygon is triangulated. The calculation module is used to calculate the area of the free surface based on the triangle obtained by the triangular meshing.

A method for calculating a free-form surface area, the method comprising: (A) a boundary processing step of: obtaining a contour surface composed of boundary points of a free-form surface, and obtaining a polyline that approximates the contour surface in a parameter plane; (B) triangular meshing Step: setting a sample point in the parameter plane, and constructing a polygon approaching the contour surface according to the set sample point, the vertices of the polyline, and the vertical line segment passing through the sample point or the intersection of the horizontal line segment and the polyline, and The polygon is triangulated; and (C) the calculation step: calculating the area of the free surface from the triangle obtained by the triangular meshing.

Compared with the prior art, the free-form surface area calculation system and method provided by the invention can quickly calculate the area of the free-form surface and improve the calculation precision of the free-form surface area.

100‧‧‧Electronic devices

10‧‧‧ Free-form surface area calculation system

11‧‧‧Boundary Processing Module

13‧‧‧Triangular grid module

15‧‧‧Display module

17‧‧‧Computation Module

20‧‧‧Storage equipment

30‧‧‧ Processor

40‧‧‧Display equipment

1 is a functional block diagram of a preferred embodiment of a free-form surface area calculation system of the present invention.

2 is a flow chart of a preferred embodiment of a method for calculating a free curved surface area of the present invention.

FIG. 3 is a specific flowchart of step S201 in FIG. 2.

FIG. 4 is a specific flowchart of step S203 in FIG. 2.

FIG. 5 is a specific flowchart of step S205 in FIG. 2.

Figure 6 is a schematic diagram of the vertices of a polyline.

Figure 7 is a schematic diagram of sample points, polyline vertices, and intersection points in a parameter plane.

8 and 9 are schematic views of a connecting triangle.

1 is a functional block diagram of a preferred embodiment of the free-form surface area computing system 10 of the present invention. The freeform surface area computing system 10 is mounted and operates on the electronic device 100. The electronic device 100 further includes a storage device 20, a processor 30, and a display device 40. The electronic device 100 can be a computer or any other suitable device having data processing functions.

The storage device 20 is used to store the computerized code of the freeform surface area computing system 10. The storage device 20 may be a memory built in the electronic device 100 or a memory external to the electronic device 100.

The processor 30 executes the computerized code of the free-form surface area calculation system 10, converts the free-form surface into a triangle in the parameter plane, and calculates the sum of the converted triangle areas to obtain the area of the free-form surface.

The display device 40 is configured to display a triangle in a parameter plane obtained by converting the free-form surface and the free-form surface, and an area of the calculated free-form surface.

The free-form surface area calculation system 10 includes a boundary processing module 11, a triangular meshing module 13, a display module 15, and a computing module 17.

The boundary processing module 11 is configured to obtain a contour surface composed of boundary points of the free curved surface, and obtain a polyline that approximates the contour surface in the parameter plane (for details, please refer to the description of FIG. 3 below).

The triangular meshing module 13 is configured to set a sample point in the parameter plane, and construct the approximating the contour surface according to the set sample point, the vertices of the polyline, and the vertical line segment of the sample point or the intersection of the horizontal line segment and the polyline. Polygons and triangulate the polygons (see the description of Figure 4 below for details).

The display module 15 is configured to display the free-form surface and the free-form surface on the display device 40. The triangle in the parameter plane obtained after the change, and the area of the calculated free surface.

The calculation module 17 is configured to calculate the area of the free-form surface according to the triangle obtained by the triangular meshing (for details, please refer to the description about FIG. 5 below).

As shown in FIG. 2, it is a flow chart of a preferred embodiment of the free-form surface area calculation method of the present invention.

In step S201, the boundary processing module 11 obtains a contour surface composed of boundary points of the free-form surface, and obtains a polyline that approximates the contour surface in the parameter plane (refer to the description of FIG. 3 below for details). The display module 15 displays the free-form surface, the contour surface, and the polyline.

Step S203, the triangular meshing module 13 sets a sample point in the parameter plane, and constructs an approaching the contour according to the set sample point, the vertices of the polyline, and the intersection of the vertical line segment or the horizontal line segment passing through the sample line and the polyline. The polygon of the face, and the triangle is meshed (see the description of Figure 4 below for details). The display module 15 displays the parameter plane, the sample point, the vertices of the polyline, the intersection point, and the polygons before and after the triangle meshing.

In step S205, the calculation module 17 calculates the area of the free-form surface according to the triangle obtained by the triangular meshing (refer to the description of FIG. 5 below for details). The display module 15 displays the calculated area of the freeform surface.

As shown in FIG. 3, it is a specific flowchart of step S201 in FIG.

In step S301, the boundary processing module 11 reads a free surface from the storage device 20.

Step S303, the boundary processing module 11 connects the boundary points of the free-form surface to obtain a system. The contour of the freeform surface formed by the curves connected end to end.

In step S305, the boundary processing module 11 reads a curve constituting the contour surface.

In step S307, the boundary processing module 11 determines whether the curve is a rational curve. If the curve is a rational curve, the flow directly proceeds to step S321; if the curve is not a rational curve, the flow proceeds to step S309. In this embodiment, the rational curve is a B-spline curve. The curve forming the contour surface may be a straight line, an arc, an elliptical arc, and a rational curve, wherein the rational curve is closer to the contour line of the free surface.

In step S309, the boundary processing module 11 determines whether the curve is an elliptical arc. If the curve is an elliptical arc, the flow proceeds to step S311, and the boundary processing module 11 converts the elliptical arc into a rational curve. If the curve is not an elliptical arc, the flow advances to step S313.

In step S313, the boundary processing module 11 determines whether the curve is a straight line. If the curve is a straight line, the flow proceeds to step S315, and the boundary processing module 11 converts the straight line into a rational curve. If the curve is not a straight line, the flow advances to step S317.

In step S317, the boundary processing module 11 determines whether the curve is an arc. If the curve is an arc, the flow proceeds to step S319, and the boundary processing module 11 converts the arc into a rational curve. If the curve is not an arc, the flow proceeds to step S321.

In step S321, the boundary processing module 11 determines whether there is still a curve in the contour surface that is not read. If there are still curves in the contour plane that have not been read, the flow repeats from step S305 until all the curves in the contour plane are rational curves, and the flow advances to step S323.

In step S323, the boundary processing module 11 obtains a closed boundary curve composed of all rational curves. Converting all the curves that make up the contour surface into rational curves not only makes the closed boundary curve composed of rational curves more close to the contour surface of the free surface, but also the processing of a single type curve (ie, rational curve) can improve the processing speed.

In step S325, the boundary processing module 11 obtains the control points of the rational curves according to the parameter equations of the rational curves, and obtains the polyline that approximates the closed boundary curve according to the control points. Each rational curve has a corresponding parameter equation represented by parameters U and V. The range of U and V ranges from 0 to 1. According to the parameter equation, the control points of each rational curve can be obtained.

In step S327, the boundary processing module 11 uses a median interpolation method to obtain a series of vertices of the polyline in the parameter plane. In this embodiment, the level direction of the parameter plane is represented by U, the vertical direction is represented by V, and the coordinates of each point in the parameter plane may be represented by (U, V), which corresponds to the two-dimensional coordinate (X, Y), The values of U and V range from 0 to 1. For example, suppose the arc shown in FIG. 6 is the closed boundary curve, and the points A, B, C, and D on the arc are connected to obtain a polyline, but the polyline is not enough to fit the arc, that is, the The approximation accuracy error between the polyline and the arc is large. To improve the approximation accuracy, the midpoint of the arc segment between two adjacent vertices of the polyline may be taken, and the midpoint and the two vertices are respectively connected. For example, the midpoint A1 of the arc segment between the adjacent two vertices A and B of the polyline is connected to AA1 and A1B, respectively. By analogy, the more vertices of the polyline, the higher the approximation accuracy with the closed boundary curve. It should be noted that FIG. 6 to FIG. 9 only indicate the polyline with the connected line segments. In fact, the composition of the polyline may be a connected line segment or an arc.

In step S329, the boundary processing module 11 outputs a vertex queue composed of all the vertices of the polyline.

As shown in FIG. 4, it is a specific flowchart of step S203 in FIG.

In step S401, the triangular meshing module 13 sets samples in the parameter plane to obtain a sample queue in the parameter plane. As shown in FIG. 7, the triangular meshing module 13 divides the U-axis into 5 segments to obtain 6 uniformly distributed samples p1 to p6, and divides the V-axis into 4 segments to obtain 5 uniformly distributed samples p1. P7~p10. Thus, the six V-line segments passing through the samples p1~p6 Each sample (including the V-axis) is distributed with 5 samples (the sample points in the figure are indicated by open circles).

Step S403, the triangular meshing module 13 reads the vertices of the polyline in the parameter plane, the sample points falling into the polyline, and the U line segment or the V line segment passing through the sample point (the U line segment is taken when the number of U line segments is large, V The number of line segments is more than the intersection of the V-line segment and the polyline. As shown in FIG. 7, the black solid circle in the parameter plane represents the vertex of the polyline L, and the samples p16, p17, and p18 on the V line segment p5p14 fall into the polyline L, and the V line segment p5p14 and the polyline L have an intersection G1. G2.

In step S405, the triangular meshing module 13 forms a polygon in the parameter plane according to the read vertices, samples and intersections.

Step S407, the triangular meshing module 13 connects the vertices of the polyline, the sample points falling in the polyline, and the intersection to divide the polygon into a series of triangles. The connection principle is that there are no other vertices in the circumscribed circle of each triangle. . As shown in FIG. 8 , it is a partial schematic diagram of the polygon obtained in step S405 . The five points of the points Q5 to Q9 are the vertices of the polyline L, and the three points p16, p17 and p18 fall into the polyline L. In the sample point, the two points G1 and G2 are the intersections of the V line segment p5p14 and the polyline L. The triangular meshing module 13 connects the 10 points to obtain the 8 triangles shown in FIG.

In step S409, the triangular meshing module 13 filters out the triangles that fall outside the polyline. For example, if the points Q1, Q2, Q3, and Q4 in FIG. 7 are connected into two triangles, the two triangles fall outside the polyline L and are invalid triangles, which need to be filtered out.

In step S411, the triangular meshing module 13 outputs a triangular array of all valid triangles in the parameter plane.

As shown in FIG. 5, it is a specific flowchart of step S205 in FIG. 2.

In step S501, the calculation module 17 reads a triangle from the triangle array.

In step S503, the calculation module 17 calculates the lengths of the sides of the triangle according to the three vertex coordinates of the triangle.

In step S505, the calculation module 17 calculates the area of the triangle according to the length of each side of the triangle.

In step S507, the calculation module 17 determines whether there are still triangles in the triangle array that are not read. If there are still triangles in the triangle array that have not been read, the flow repeats from step S501 until all the triangle areas in the triangle array are calculated, and the flow advances to step S509.

In step S509, the calculation module 17 calculates the sum of the areas of all the triangles to obtain the area of the free-form surface.

The above is only the preferred embodiment of the present invention, and has been used in a wide range of applications. Any other equivalent changes or modifications which are not departing from the spirit of the present invention should be included in the following claims. Inside.

100‧‧‧Electronic devices

10‧‧‧ Free-form surface area calculation system

11‧‧‧Boundary Processing Module

13‧‧‧Triangular grid module

15‧‧‧Display module

17‧‧‧Computation Module

20‧‧‧Storage equipment

30‧‧‧ Processor

40‧‧‧Display equipment

Claims (8)

A method for calculating a free-form surface area is applied to an electronic device. The method includes: a boundary processing step: acquiring a contour surface composed of boundary points of a free-form surface, and obtaining a polyline that approximates the contour surface in a parameter plane, wherein the boundary processing step includes : reading a free-form surface from a storage device connected to the electronic device; connecting a boundary point of the free-form surface to obtain a contour surface of a free-form surface formed by a series of curves connected end to end; converting all curves constituting the contour surface into The rational curve obtains a closed boundary curve composed of all rational curves; the control points of each rational curve are obtained according to the parametric equations of each rational curve, and the polyline which approximates the closed boundary curve is obtained according to the control point; using the median interpolation method Obtaining a series of vertices of the polyline in the parameter plane; a triangle meshing step: setting a sample point in the parameter plane according to the set sample point, the vertices of the polyline, and the vertical line segment or the horizontal line segment passing through the sample point The intersection of the polylines constructs a polygon that approximates the contour plane and the polygon The meshing line; and calculating steps: calculating the area of a free curved surface according to the triangle of the triangular mesh obtained. The free-form surface area calculation method according to claim 1, wherein the triangular meshing step comprises: setting a sample point in the parameter plane; reading a vertex of the polyline in the parameter plane, and dropping the sample into the polyline And a horizontal line segment of the sample or an intersection of the vertical line segment and the polyline; the vertices, samples, and intersections read according to the above form a polygon in the parameter plane; and the vertices connecting the polylines and falling into the polyline The point and the intersection divide the polygon into a series of triangles. A method for calculating a free-form surface area as described in claim 2, wherein the triangular meshing step The step also includes filtering out the triangles that fall outside the polyline. The method for calculating a free-form surface area according to claim 3, wherein the calculating step comprises: calculating, according to a vertex coordinate of each triangle remaining after the filtering, a side length of each triangle remaining after filtering; according to remaining after filtering The side length of each triangle is calculated by the area of each triangle remaining after filtering; and the area of all the triangles remaining after all filtering is added to obtain the area of the free surface. A free-form surface area calculation system is applied to an electronic device, the system comprising: a boundary processing module, configured to acquire a contour surface composed of boundary points of a free-form surface, and obtain a polyline that approximates the contour surface in a parameter plane, wherein the boundary The processing module obtains a contour surface composed of boundary points of the free surface, and obtaining a polyline that approximates the contour surface in the parameter plane includes: reading a free surface from a storage device connected to the electronic device; connecting the boundary of the free surface Pointing to obtain a contour surface of a free-form surface composed of a series of curves connected end to end; converting all the curves constituting the contour surface into rational curves, and obtaining a closed boundary curve composed of all rational curves; a parametric equation according to each rational curve Obtaining control points of each rational curve, obtaining a polyline that approximates the closed boundary curve according to the control point; using a median interpolation method to obtain a series of vertices of the polyline in the parameter plane; a triangular meshing module for Set the sample point in the parameter plane, according to the set sample, the vertices of the polyline, and the sample a vertical line segment or a intersection of a horizontal line segment and a polyline to construct a polygon that approximates the contour plane, and triangulate the polygon; and a calculation module for calculating a free surface from the triangle obtained by the triangle meshing area. The free-form surface area calculation system of claim 5, wherein the triangular meshing module constructs a polygon that approximates the contour surface, and triangular meshing the polygon includes: Set the sample point in the parameter plane; read the vertices of the polyline in the parameter plane, the sample points falling within the polyline, and the intersection of the horizontal line segment or the vertical line segment and the polyline through the sample; according to the vertices read above, The sample points and intersections form a polygon in the parameter plane; and the vertices connecting the polylines, the samples falling within the polyline, and the intersections divide the polygon into a series of triangles. The free-form surface area calculation system of claim 6, wherein the triangular meshing of the polygon by the triangular meshing module further comprises: filtering out a triangle falling outside the polyline. The free-form surface area calculation system according to claim 7, wherein the calculating module calculates the area of the free-form surface according to the triangle obtained by the triangular meshing, including: calculating the remaining after filtering according to the vertices of the remaining triangles after filtering The side length of each of the lower triangles; the area of each triangle remaining after filtering is calculated based on the side lengths of the remaining triangles after filtering; and the area of all the triangles remaining after filtering is added to obtain the area of the free curved surface.