CN114800965A - Method and device for automatically calculating adjacent area surfaces on same side of spatial polygon - Google Patents

Abstract

The invention discloses a method for automatically calculating an adjacent area surface on the same side of a spatial polygon, and belongs to the technical field of surface area calculation. It includes the following steps: (1) geometrically sort the edges of the spatial polygon to determine the direction of the polygon; (2) construct the direction vector of the edge, and construct the orientation vector of the adjacent surfaces on both sides of the edge; (3) calculate the edge direction vector and the two The three-vector mixture product of the azimuth vectors of the adjacent surfaces, and the orientation of the two adjacent surfaces is judged according to the relationship between the three-vector mixture product and zero. The invention determines which side of the edge the surface is located on by the three-vector mixed product, realizes automatic calculation and identification of the area surface of the hole boundary according to the closed boundary of the hole, and solves the problem of automatic repair of the hole during mold parting.

Description

A method and device for automatically calculating the adjacent area surfaces on the same side of a spatial polygon

technical field

The invention relates to the technical field of surface area calculation, in particular to a method and a device for automatically calculating the adjacent area surfaces on the same side of a spatial polygon.

Background technique

The calculation of the surface area has applications in feature recognition, mold parting, CAM programming, etc. Generally, the surface area is divided into different continuous areas according to certain rules, such as by the visibility of the surface, by the boundary, etc., among which the area divided by the closed boundary is used more. As shown in Figure 1, for regular geometry, each edge has one and only two adjacent faces. Obviously, if the direction of the edge is specified, one adjoining face is to the left of the edge and the other is to the right of the edge. In engineering, the two side areas sometimes have different meanings. For example, in mold parting, if the left side area of the parting line is defined as the cavity area, the right side must be the core area. Therefore, it is of great value to determine which side of the edge the adjoining face is located on.

In the process of injection mold design, parting design is the first step, and the result has an important influence on the mold structure. One of the parting work is to fill holes. Before the mold parting, all the holes on the product model must be repaired. The hole is a common structure in the 3D model of the product, mainly to meet the technological requirements of the product. For simple holes, the existing CAD software has been able to automatically repair, but the repair work of a large number of complex holes still relies on manual labor. According to practical experience, the repairing time of complex holes accounts for about 80% of the parting time, which affects the efficiency of mold design. The key factor. In the automatic repair of open holes, the key problem is the automatic identification of the adjacent surfaces on the same side of the spatial polygon.

In SIEMENS NX software, for open holes, you can use the "Repair Opening" tool to achieve. When using Patch Openings, two steps are required:

(1) Select the reference surface of the hole boundary (actually the area surface on the same side of the boundary);

(2) Select the closed boundary of the hole.

Both of the above steps need to be done manually. In the mold parting automatic repair hole, the parting tool will automatically search for the hole boundary, which is the above step (2). But for these kinds of holes, the typing work has not been able to find a matching repair method. Therefore, it is necessary to develop an automatic repair tool to realize the automatic repair of such holes. But the key problem is to solve the automatic calculation of the area surface in the above step (1) according to the closed boundary of the hole.

SUMMARY OF THE INVENTION

In view of this, the present invention aims at the deficiencies of the prior art, and provides a method for automatically calculating the same-side adjacent area surface of a spatial polygon, which can quickly and accurately calculate the same-side adjacent surface area of a spatial polygon.

In order to solve the above-mentioned technical problems, the technical scheme adopted by the present invention is:

Provided is a method for automatically calculating the same-side adjacent area surface of a spatial polygon, comprising the following steps:

Step (1): geometrically sort the edges of the spatial polygon to determine the direction of the polygon;

Step (2): construct the direction vector of the edge, and construct the azimuth vector of the adjacent surfaces on both sides of the edge;

Step (3): Calculate the three-vector mixture product of the edge direction vector and the orientation vectors of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixture product and zero.

Further, in step (1), in the sorting process, take the starting point of the first side to the end point as the direction of the polygon, and use it as the direction reference of the subsequent sides, and sequentially search to determine the direction of the polygon, the method is as follows:

S1: Starting from any edge, find two endpoints, define the first endpoint as the starting point, the second endpoint as the ending point, set the starting point as the polygon starting point, and set the ending point as the current point;

S2: If the remaining side is empty, go to S4, otherwise, take the current point as the target, and find the side whose endpoint in the remaining side coincides with the current point;

S3: Take the coincident point as the starting point of the edge, and the other end point as the end point, update the current point as the end point, subtract 1 from the remaining side, and go to S2;

S4: If the starting point of the polygon coincides with the current point, the polygon is closed, otherwise it is not closed.

Further, in step (2), any type of edge is discretized, the starting point and the midpoint of the edge are taken, and a direction vector is constructed from the direction from the starting point to the midpoint.

Further, in step (2), when constructing the azimuth vector of the adjoining surface, take a point on the edge pointing to the feature point on the adjoining surface as the azimuth vector.

Further, take the midpoint of the edge as the starting point.

Further, the method of taking points on the adjacent surface is: construct the reference plane with the midpoint of the edge and the direction vector of the edge, and find the intersection line between the reference plane and the adjacent surface. When the reference plane and the adjacent surface have one and only one intersection line , take the midpoint of the intersection.

Further, in step (3), the two adjacent faces of the edge are face1 and face2 respectively, and vecFwd is the direction vector of the edge;

Construct the adjacent face orientation vectors vF1 and vF2, which are the direction vectors from the same point on the edge to the point pnt1 of face1 and the point pnt2 on face2;

The mathematical relationship of the three vectors is as follows:

(vF ₁ ×vF ₂ )·vecFwd≤0 (1)

(vF ₁ ×vF ₂ )·vecFwd>0 (2)

If the three vectors satisfy formula (1), the angle between the vector direction of vF1×vF2 and vecFwd is greater than 90°～180°, and the two directions are basically opposite, it can be determined that face1 is the left side and face2 is the right side;

If the three vectors satisfy formula (2), the vector direction of vF1×vF2 and the angle between vecFwd and vecFwd are between 0° and 90°, and the two directions are basically the same, then face1 is the right side and face2 is the left side.

Provided is a device for automatically calculating the adjacent area surfaces on the same side of a spatial polygon, including:

Sorting module for geometrically sorting the edges of spatial polygons;

The building block is used to construct the direction vector of the edge and the azimuth vector of the adjacent faces on both sides of the edge;

The calculation and judgment module is used to calculate the three-vector mixture product of the edge direction vector and the orientation vector of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixture product and zero.

A computer-readable storage medium is provided, which stores a computer program, and when the computer program is executed by a processor, implements the method for automatically calculating the same-side adjacent area surface of a spatial polygon according to any one of claims 1-7.

A computer device is provided, comprising a processor and a memory, the processor executes a program corresponding to the executable program code by reading the executable program code stored in the memory, so as to realize the execution of claims 1-7 A method for automatically calculating the same-side adjacent area surface of a spatial polygon as described in any one of.

Compared with the prior art, the beneficial effects of the present invention are as follows:

The invention determines the direction of the polygon by geometrically sorting the sides of the spatial polygon, constructs the direction vector of the side, and the azimuth vectors of the adjacent surfaces on both sides of the side, calculates the three-vector mixed product of the side direction vector and the azimuth vectors of the two adjacent surfaces, and According to the relationship between the three-vector mixed product and zero, the orientation of the two adjoining surfaces is judged, so as to realize the automatic calculation and identification of the area surface of the hole boundary according to the closed boundary of the hole, and then solve the problem of automatic repair of the hole during mold parting.

In addition, the invention adopts the starting point and midpoint of the edge, and constructs the direction vector of the edge from the direction from the starting point to the midpoint, which can satisfy the unified calculation of different types of edges; , which solves the problem of ambiguity in the calculation of the azimuth vector of the adjacency surface due to improper point selection on the surface. It is verified by examples that the method can quickly and accurately calculate the adjacent surface area on the same side for different spatial polygons.

Description of drawings

Fig. 1 is the topological relation diagram of regular geometry face and edge in the background technology;

2 is a schematic diagram of the orientation of a spatial polygon in an embodiment of the present invention;

Fig. 3 is a positional relationship diagram of points on adjacent surfaces in an embodiment of the present invention;

Fig. 4 is the azimuth vector relation diagram of different point structures in the embodiment of the present invention;

5 is a schematic diagram of a point-taking point at a position close to an edge on an adjoining surface in an embodiment of the present invention;

FIG. 6 is a schematic diagram of a three-vector mixed product discrimination principle in an embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, embodiments of the present invention. Based on the described embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art fall within the protection scope of the present invention.

In a plane simple polygon, it is generally specified that the counterclockwise direction is positive, and the points in the polygon are on the left side, and vice versa. For the discrimination of the inner and outer points of a plane simple polygon, there are the classical ray method and the labeling method, the method of judging the inner and outer points of the polygon based on the direction factor and the direction edge, and the method based on the plane transformation.

For general spatial polygons, also known as generalized polygons or spatial curved-sided trapezoids, the main differences from plane simple polygons are: (1) Not all vertices are in the same plane; (2) At least one edge is a curve. Due to the complexity of spatial polygons, there is no fixed normal direction, and there is no distinction between inner and outer points, so it is difficult to directly use the method of plane polygons to judge.

To this end, an embodiment of the present invention proposes a method for automatically calculating the same-side adjacent area surface of a spatial polygon, including the following steps:

Step 1: Geometrically sort the edges of the spatial polygon to determine the direction of the polygon

To calculate the adjoining surfaces on the same side of a spatial polygon, the orientation of the polygon must first be determined. In order to simplify the calculation, the forward and inverse directions of the polygon are not considered, and only the consistency of the directions of each side is guaranteed. As shown in Figure 2, the six sides of the spatial polygon ABCDEFA are connected end-to-end in sequence, the arrows represent the direction of the polygon, and the direction of the arrows is connected end-to-end, which means that the directions of the polygon edges are consistent. Then, taking the polygon as the boundary, divide all the side adjoining faces of the edge into a left area and a right area.

At the same time, considering that the input of polygon edges is not necessarily in the order of their geometric positions, it is necessary to geometrically sort the edges. In the sorting process, take the direction of the starting point of the first edge to the end point as the direction of the polygon, and use it as the direction reference of the subsequent edges, and sequentially search to determine the direction of the polygon. The method is as follows:

S1: Starting from any edge, find two endpoints, define the first endpoint as the starting point, the second endpoint as the ending point, set the starting point as the polygon starting point, and set the ending point as the current point;

S2: If the remaining side is empty, go to S4, otherwise, take the current point as the target, and find the side whose endpoint in the remaining side coincides with the current point;

S3: Take the coincident point as the starting point of the edge, and the other end point as the end point, update the current point as the end point, subtract 1 from the remaining side, and go to S2;

S4: If the starting point of the polygon coincides with the current point, the polygon is closed, otherwise it is not closed.

Step 2: Construct the direction vector of the edge, and construct the azimuth vector of the adjacent faces on both sides of the edge

For the direction vector of the edge, according to the type of edge curve, it can be divided into three cases:

(1) Straight line side, the direction vector is the starting point to the end point;

(2) For general curves, the tangent vector of the curve is different at each point, and any direction of the tangent vector can be taken;

(3) If the edge is a closed loop, such as a full-circle curve, and the start and end points of the edge coincide, the direction vector cannot be constructed.

In order to solve the problem that the closed edge curve fails to construct the direction vector, and to simplify the calculation, a unified calculation method is used to discretize any type of edge, the starting point and midpoint of the edge are taken, and the direction vector is constructed from the starting point to the midpoint.

When constructing the azimuth vector of the adjoining surface, take a point on the edge pointing to the feature point on the surface as the vector. Specially, the midpoint of the edge is taken as the starting point, and the point from this point to a point on the surface is taken as the azimuth vector of the adjacent surface.

When constructing the adjacency vector, ambiguity may arise if the point on the surface is not selected properly. As shown in Figure ₃ , the adjacent faces F1 and F2 _of edge E, take _two different points _P11 and _{P12 on} face F1 respectively, take point P2 _on face F2, and P0 is a point _on edge E . As shown in Figure 4, the direction eV of the edge is defined, obviously, the face F1 is _on the left and F2 is _on the right. Orientation vectors V ₁₁ , V ₁₂ , V ₂ are constructed from the points of the P ₀ pointing plane. Obviously, when the point _P11 is taken on the plane F1, the vector V11 is _on the left side of V2 relative to eV, and the azimuth relationship _of the vector is consistent with that of the actual plane; and when the point _P12 is taken _on the plane F1, the vector _V12 relative to eV is _on the left side of the vector V12. On the right side of V ₂ , the vector azimuth relationship is opposite to that of the actual surface. At this time, the calculation of the surface side will be wrong and there will be ambiguity.

In order to solve the calculation ambiguity, consider taking the point as close as possible to the edge on the adjoining surface. The specific point selection method is: construct the datum plane with the midpoint of the edge and the direction vector of the edge, and find the intersection of the datum plane and the adjacent surface. When an intersecting line is found, take the midpoint of the intersecting line. As shown in Figure ₅ , the adjacent faces F1 and _{F2 of} edge E, take the midpoint _of edge E and the direction vector as the reference plane DP, and find the intersection lines _C1 , _C2 , _C1 , The midpoints P ₁ and P ₂ of C ₂ are the desired points. This method can ensure that the appropriate point is obtained when the reference plane and the adjacent surface have one and only one intersection. At the same time, in this method, the midpoint of the edge is selected to construct the datum plane, in order to ensure that at least one intersection line is generated between the datum plane and each adjacent surface.

Step 3: Calculate the three-vector mixed product of the edge direction vector and the orientation vector of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixed product and zero

As shown in Figure 6, the two adjacent faces of the edge are face1 and face2, respectively, and vecFwd is the direction vector of the edge;

Construct the adjacent face orientation vectors vF1 and vF2, which are the direction vectors from the same point on the edge to the point pnt1 of face1 and the point pnt2 on face2;

The mathematical relationship of the three vectors is as follows:

(vF ₁ ×vF ₂ )·vecFwd≤0 (1)

(vF ₁ ×vF ₂ )·vecFwd>0 (2)

If the three vectors satisfy formula (1), the angle between the vector direction of vF1×vF2 and vecFwd is greater than 90°～180°, and the two directions are basically opposite, it can be determined that face1 is the left side and face2 is the right side;

If the three vectors satisfy formula (2), the vector direction of vF1×vF2 and the angle between vecFwd and vecFwd are between 0° and 90°, and the two directions are basically the same, then face1 is the right side and face2 is the left side;

In mold parting, if the area on the left side of the parting line is defined as the cavity area, the right side must be the core area. According to the above method, the left and right areas of the parting line can be automatically calculated.

In order to realize the above-mentioned embodiment, the embodiment of the present application also proposes an apparatus for automatically calculating the adjacent area surfaces on the same side of a spatial polygon, including a sorting module, which is used for geometrically sorting the edges of the spatial polygon;

The building block is used to construct the direction vector of the edge and the azimuth vector of the adjacent faces on both sides of the edge;

The calculation and judgment module is used to calculate the three-vector mixture product of the edge direction vector and the orientation vector of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixture product and zero.

A computer-readable storage medium is provided, which stores a computer program, and when the computer program is executed by a processor, realizes the method for automatically calculating the adjacent area surface on the same side of a spatial polygon according to the above embodiment.

A computer device, comprising a processor and a memory, the processor runs a program corresponding to the executable program code by reading the executable program code stored in the memory, so as to realize the automatic calculation space of the above embodiment Method for contiguous area faces on the same side of a polygon.

The above are the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. It should be regarded as the protection scope of the present invention.

Claims (10)

1. a method for automatically calculating the same side adjacent area surface of a spatial polygon, is characterized in that, comprises the following steps: Step (1): geometrically sort the edges of the spatial polygon to determine the direction of the polygon; Step (2): construct the direction vector of the edge, and construct the azimuth vector of the adjacent surfaces on both sides of the edge; Step (3): Calculate the three-vector mixture product of the edge direction vector and the orientation vectors of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixture product and zero. 2. The method for automatically calculating the same side adjacent area surface of a spatial polygon as claimed in claim 1, characterized in that: in step (1), in the sorting process, the starting point of the first side points to the direction of the end point as the direction of the polygon , and as the direction reference of the subsequent edges, search and determine the direction of the polygon in turn, the method is as follows: S1: Starting from any edge, find two endpoints, define the first endpoint as the starting point, the second endpoint as the ending point, set the starting point as the polygon starting point, and set the ending point as the current point; S2: If the remaining side is empty, go to S4, otherwise, take the current point as the target, and find the side whose endpoint in the remaining side coincides with the current point; S3: Take the coincident point as the starting point of the edge, and the other end point as the end point, update the current point as the end point, subtract 1 from the remaining side, and go to S2; S4: If the starting point of the polygon coincides with the current point, the polygon is closed, otherwise it is not closed. 3. the method for automatically calculating space polygon same side adjacent area surface as claimed in claim 2, is characterized in that: in step (2), carry out discretization to any type side, take the starting point and midpoint of side, point to the middle by starting point The direction of the point constructs the direction vector. 4. the method for automatically calculating space polygon same side adjoining area surface as claimed in claim 3 is characterized in that: in step (2), when constructing adjoining surface azimuth vector, take a point on the edge to point to the feature point on adjoining surface as Azimuth vector. 5. The method for automatically calculating the same-side adjacent area surface of a spatial polygon as claimed in claim 4, wherein the midpoint of the side is taken as the starting point. 6. the method for automatically calculating the space polygon same side adjacent area surface as claimed in claim 5 is characterized in that: the method for taking point on the adjacent surface is: construct the reference plane with the midpoint of the side and the direction vector of the side, seek The intersection line of the base plane and the adjacent surface, when there is only one intersection line between the base plane and the adjacent surface, the midpoint of the intersection line is taken. 7. the method for automatically calculating space polygon same side adjacent area surface as claimed in claim 6, is characterized in that: in step (3), two adjacent surfaces of side edge are respectively face1 and face2, and vecFwd is the direction vector of side ; Construct the adjacent face orientation vectors vF1 and vF2, which are the direction vectors from the same point on the edge to the point pnt1 of face1 and the point pnt2 on face2; The mathematical relationship of the three vectors is as follows: (vF ₁ ×vF ₂ )·vecFwd≤0 (1) (vF ₁ ×vF ₂ )·vecFwd>0(2) If the three vectors satisfy formula (1), the angle between the vector direction of vF1×vF2 and vecFwd is greater than 90°～180°, and the two directions are basically opposite, it can be determined that face1 is the left side and face2 is the right side; If the three vectors satisfy formula (2), the vector direction of vF1×vF2 and the angle between vecFwd and vecFwd are between 0° and 90°, and the two directions are basically the same, then face1 is the right side and face2 is the left side. 8. A device for automatically calculating the adjacent area surface on the same side of a spatial polygon, comprising: Sorting module, used to geometrically sort the edges of spatial polygons; The building block is used to construct the direction vector of the edge and the azimuth vector of the adjacent faces on both sides of the edge; The calculation and judgment module is used to calculate the three-vector mixture product of the edge direction vector and the orientation vector of the two adjacent surfaces, and judge the orientation of the two adjacent surfaces according to the relationship between the three-vector mixture product and zero. 9. A computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by the processor, the automatic calculation of the spatial polygon ipsilateral adjacent area surface as described in any one of claims 1-7 is realized. method. 10. A computer device comprising a processor and a memory, wherein the processor executes a program corresponding to the executable program code by reading the executable program code stored in the memory, so as to achieve the following: The method for automatically calculating the adjacent area surfaces on the same side of a spatial polygon according to any one of claims 1-7.

Images