CN114800965A - Method and device for automatically calculating adjacent area surfaces on same side of spatial polygon - Google Patents
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
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- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C45/00—Injection moulding, i.e. forcing the required volume of moulding material through a nozzle into a closed mould; Apparatus therefor
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Abstract
The invention discloses a method for automatically calculating adjacent area surfaces on the same side of a space polygon, and belongs to the technical field of surface area calculation. Which comprises the following steps: (1) geometrically ordering the sides of the space polygon and determining the direction of the polygon; (2) constructing direction vectors of the edges and constructing orientation vectors of the adjacent surfaces on the two sides of the edges; (3) and calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces, and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero. The method and the device judge which side of the edge the surface is positioned on through the three-vector mixed product, automatically calculate and identify the area surface of the hole boundary according to the closed boundary of the hole, and further solve the problem of automatic hole repairing during mold parting.
Description
Technical Field
The invention relates to the technical field of surface area calculation, in particular to a method and a device for automatically calculating adjacent area surfaces on the same side of a space polygon.
Background
The calculation of the area of the face has application in the aspects of feature identification, mold typing, CAM programming and the like. The surface area is generally divided into different continuous areas according to some rules, such as visibility by surface, boundary by boundary, etc., wherein the area division with a closed boundary is more applied. As in FIG. 1, for a regular geometric form, there are two and only two abutments per edge. Obviously, if the direction of the edge is specified, one abutment surface is to the left of the edge and the other is to the right of the edge. In a molding process, the two side surface regions sometimes have different meanings, and if the left side surface region of the parting line is defined as a cavity region, the right side surface is always a core region. Therefore, it is of significant value to determine on which side of the edge the abutment surface is located.
In the design process of the injection mold, the parting design is the first step, and the result has important influence on the mold structure. One of the parting operations is hole repairing, and the hole repairing of all the holes on the product model must be completed before the mold parting. The holes are common structures in a three-dimensional model of a product and mainly aim to meet the process requirements of the product. For simple holes, the existing CAD software can automatically repair, but the repair work of a large number of complex holes still depends on manual work, and according to practical experience, the repair time of the complex holes accounts for about 80% of the parting time, so that the repair work is a key factor influencing the design efficiency of the die. In the automatic repair of the open type hole, the key problem is the automatic judgment of the adjacent surface on the same side of the spatial polygon.
In SIEMENS NX software, open-type holes can be implemented using a "patch opening" tool. When using a "repair opening", two steps are required:
(1) selecting a reference surface of the hole boundary (actually, a region surface on the same side of the boundary);
(2) the closed boundary of the hole is selected.
Both steps need to be done manually. In the step (2), the parting tool automatically searches for the boundary of the hole in the step (2). However, for such holes, typing cannot find a matching repair method. Therefore, there is a need to develop an automatic repair tool to achieve automatic repair of such holes. But the key problem is to solve the automatic calculation of the area surface in the step (1) according to the closed boundary of the hole.
Disclosure of Invention
In view of the above, the present invention provides a method for automatically calculating surfaces of adjacent regions on the same side of a spatial polygon, which can quickly and accurately calculate the adjacent regions on the same side of the spatial polygon.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the method for automatically calculating the adjacent area surfaces on the same side of the space polygon comprises the following steps:
step (1): geometrically ordering the sides of the space polygon and determining the direction of the polygon;
step (2): constructing direction vectors of the edges and constructing orientation vectors of the adjacent surfaces on the two sides of the edges;
and (3): and calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces, and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero.
Further, in the step (1), in the sorting process, the direction of the polygon is sequentially searched and determined by taking the direction from the starting point to the end point of the first edge as the direction of the polygon and as the direction reference of the subsequent edge, and the method comprises the following steps:
s1: starting from any one edge, finding two end points, defining the first end point as a starting point, defining the second end point as an end point, setting the starting point as a polygon starting point, and setting the end point as a current point;
s2: if the remaining edge is empty, go to S4, otherwise, with the current point as the target, find the edge where the end point in the remaining edge coincides with the current point;
s3: taking the coincident point as the starting point of the edge and the other end point as the end point, updating the current point as the end point, subtracting 1 from the residual edge, and turning to S2;
s4: if the polygon starting point is coincident with the current point, the polygon is closed, otherwise, the polygon is not closed.
Further, in the step (2), the edges of any type are discretized, the starting point and the middle point of the edge are taken, and a direction vector is constructed in the direction from the starting point to the middle point.
Further, in the step (2), when constructing the orientation vector of the adjacent surface, a feature point on the edge pointing to the adjacent surface is taken as the orientation vector.
Further, the midpoint of the edge is taken as the starting point.
Further, the method for taking points on the adjacent surface comprises the following steps: and constructing a reference plane by using the midpoint of the edge and the direction vector of the edge, solving an intersection line of the reference plane and the adjacent surface, and taking the midpoint of the intersection line when the reference plane and the adjacent surface have one and only one intersection line.
Further, in step (3), the two adjacent surfaces of the edge are face1 and face2, respectively, and vecFwd is the direction vector of the edge;
the structural abutment surface orientation vectors vF1 and vF2 are direction vectors from the same point on the edge to a point pnt1 of the face1 and a point pnt2 of the face2 respectively;
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 the formula (1), the included angle between the vector direction of vF1 xvF 2 and vecFwd is larger than 90-180 degrees, and the two directions are basically opposite, then the face1 is judged to be the left side surface, and the face2 is judged to be the right side surface;
if the three vectors satisfy the formula (2), and the included angle between the vector direction of vF1 xvF 2 and vecFwd is 0-90 degrees, the two directions are basically consistent, then the face1 is the right side surface, and the face2 is the left side surface.
The device for automatically calculating the same-side adjacent area surface of the spatial polygon comprises:
the sorting module is used for geometrically sorting the sides of the space polygon;
the building module is used for building a direction vector of the edge and building orientation vectors of adjacent surfaces on two sides of the edge;
and the calculation and judgment module is used for calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero.
There is provided a computer readable storage medium storing a computer program which, when executed by a processor, implements a method of automatically computing a spatial polygon ipsilateral border region facet as claimed in any one of claims 1 to 7.
There is provided a computer device comprising a processor and a memory, wherein the processor executes a program corresponding to an executable program code by reading the executable program code stored in the memory to implement the method for automatically calculating the same-side adjacent area surface of a spatial polygon as set forth in any one of claims 1 to 7.
Compared with the prior art, the invention has the following beneficial effects:
according to the method, the sides of the space polygon are geometrically ordered, the direction of the polygon is determined, the direction vectors of the sides and the orientation vectors of the adjacent surfaces on the two sides of the sides are constructed, the three-vector mixed product of the side direction vectors and the orientation vectors of the two adjacent surfaces is calculated, and the orientations of the two adjacent surfaces are judged according to the relation between the three-vector mixed product and zero, so that the area surface of the hole boundary is automatically calculated and identified according to the closed boundary of the hole, and the problem of automatic hole repairing during mold parting is solved.
In addition, the invention adopts the starting point and the middle point of the edge, and the direction vector of the edge is constructed in the direction that the starting point points to the middle point, so that the unified calculation of different types of edges can be met; the invention solves the problem of ambiguous calculation of the orientation vector of the adjacent surface caused by improper point taking on the curved surface by utilizing the method of solving the intersection line between the constructed reference plane and the adjacent surface. By example verification, the method can quickly and accurately calculate the adjacent surface areas on the same side for different spatial polygons.
Drawings
FIG. 1 is a topological relationship diagram of regular geometric faces and edges in the background art;
FIG. 2 is a schematic view of the orientation of a spatial polygon in an embodiment of the present invention;
FIG. 3 is a diagram showing the positional relationship of points on the abutment surfaces in the embodiment of the present invention;
FIG. 4 is an orientation vector diagram of different point configurations in an embodiment of the invention;
FIG. 5 is a schematic illustration of a point on the abutment surface at a location proximate the edge in an embodiment of the present invention;
FIG. 6 is a schematic diagram of the discrimination principle of the three-vector mixture product in the embodiment of the present invention.
Detailed Description
In order to make the objects, 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 drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention, are within the scope of the invention.
In a planar simple polygon, it is generally specified that the counterclockwise direction is positive, when the point within the polygon is to the left, and vice versa. For the discrimination of the inner point and the outer point of the plane simple polygon, a classical ray method, a labeling method, a polygon inner point and outer point discrimination method based on a direction factor and a direction side and a plane conversion method are available.
For general spatial polygons, also called generalized polygons or spatial curved edge trapezoids, the main difference from planar simple polygons is that: (1) all the vertexes are not all in the same plane; (2) at least one side is a curve. Due to the complexity of the space polygon, a fixed normal direction is not provided, and the division between an inner point and an outer point is not provided, so that the judgment is difficult to be directly carried out by adopting a plane polygon method.
To this end, an embodiment of the present invention provides a method for automatically calculating a neighboring area surface on the same side of a spatial polygon, including the following steps:
the method comprises the following steps: geometrically ordering edges of a spatial polygon and determining the orientation of the polygon
To calculate the adjacent surface on the same side of the spatial polygon, the direction of the polygon must be determined first, and in order to simplify the calculation, the consistency of the directions of all sides is ensured without considering the positive and negative directions of the polygon. As shown in fig. 2, 6 sides of the spatial polygon ABCDEFA are connected end to end in sequence, arrows represent the direction of the polygon, and the directions of the arrows are connected end to end, which means that the directions of the polygon sides are consistent. Then, all side-abutting faces of the edges are divided into left and right regions with the polygon as a boundary.
Meanwhile, the edges need to be geometrically ordered in consideration that the input of the polygon edges is not necessarily in the order of their geometric positions. In the sorting process, the direction of the polygon is taken as the direction from the starting point to the end point of the first edge and taken as the direction reference of the subsequent edge, and the directions of the polygon are searched and determined in sequence, wherein the method comprises the following steps:
s1: starting from any one edge, finding two end points, defining the first end point as a starting point, defining the second end point as an end point, setting the starting point as a polygon starting point, and setting the end point as a current point;
s2: if the remaining edge is empty, go to S4, otherwise, find the edge whose end point in the remaining edge coincides with the current point as the target;
s3: taking the coincident point as the starting point of the edge and the other end point as the end point, updating the current point as the end point, subtracting 1 from the residual edge, and turning to S2;
s4: if the polygon starting point is coincident with the current point, the polygon is closed, otherwise, the polygon is not closed.
Step two: constructing direction vectors of edges, constructing orientation vectors of abutment surfaces on both sides of edges
For the direction vector of the edge, according to the type of the edge curve, there are 3 cases:
(1) a straight line edge, wherein the direction vector points to the end point as a starting point;
(2) in a general curve, the tangent vectors of the curve are different at each point, and any tangent vector direction can be taken;
(3) if the edge is a closed loop, such as a full circle curve, the start point and the end point of the edge coincide, and a direction vector cannot be constructed.
In order to solve the problem that the direction vector constructed by the closed edge curve fails, and simplify the calculation, a unified calculation method is adopted to disperse any type of edge, the starting point and the middle point of the edge are taken, and the direction vector is constructed in the direction from the starting point to the middle point.
When constructing the orientation vector of the adjacent surface, a feature point on the edge, which points to the curved surface, is taken as a vector. Specifically, the midpoint of the edge is taken as a starting point, and the orientation vector of the adjacent surface is taken as a point on the curved surface pointed by the starting point.
When constructing the orientation vector of the abutment surface, ambiguities may arise if points on the surface are not selected. As shown in fig. 3, the abutment surface F of the edge E 1 And F 2 On the surface F 1 Two different points P are respectively taken 11 And P 12 Flour F 2 Upper fetching point P 2 ，P 0 Is a point on edge E. As shown in FIG. 4, the direction of the edge eV is defined, and it is apparent that the plane F 1 On the left side, F 2 On the right side. From P 0 Point-structured orientation vector V of pointing surface 11 、V 12 、V 2 . Obviously, in the plane F 1 Get point P 11 Time, vector V 11 Relative eV at V 2 On the left side, the vector orientation relation is consistent with the relation of an actual surface; and on the surface F 1 Get point P 12 Time, vector V 12 Relative eV at V 2 On the right side, the vector orientation relationship is opposite to the relationship of the actual surface, which can cause the calculation error of the surface side and cause ambiguity.
To solve the computational ambiguity, a point which is as close to the edge as possible on the adjacent surface is considered, and the specific point taking method comprises the following steps: and constructing a reference plane by using the middle point of the edge and the direction vector of the edge, solving an intersection line of the reference plane and the adjacent surface, and taking the middle point of the intersection line when only one intersection line exists. As shown in fig. 5, the abutment surface F of the edge E 1 And F 2 Using the midpoint and direction vector of the edge E as the reference plane DP to calculate DP and F 1 、F 2 Cross line C of 1 、C 2 ，C 1 、C 2 Midpoint P of 1 、P 2 The point is the requested point. When the reference is flatThis method ensures that the appropriate point is reached when there is one and only one intersection between the surface and the abutment surface. Also, in the method, the midpoint of the edge is selected to form the reference plane to ensure that at least one line of intersection is created between the reference plane and each of the abutment surfaces.
Step three: calculating three-vector mixed product of side direction vector and two adjacent surface orientation vectors, and judging the orientation of two adjacent surfaces according to the relation between the three-vector mixed product and zero
As shown in FIG. 6, the two adjacent surfaces of the edge are face1 and face2, respectively, and vecFwd is the direction vector of the edge;
the structural abutment surface orientation vectors vF1 and vF2 are direction vectors from the same point on the edge to a point pnt1 of the face1 and a point pnt2 of the face2 respectively;
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 the formula (1), the included angle between the vector direction of vF1 xvF 2 and vecFwd is larger than 90-180 degrees, and the two directions are basically opposite, then the face1 is judged to be the left side surface, and the face2 is judged to be the right side surface;
if the three vectors satisfy the formula (2), the included angle between the vector direction of vF1 xvF 2 and vecFwd is 0-90 degrees, and the two directions are basically consistent, then face1 is the right side surface, and face2 is the left side surface;
in the mold parting, if the left side area of the parting line is defined as a cavity area, the right side area is a core area, and the left and right side areas of the parting line can be automatically calculated according to the method.
In order to implement the foregoing embodiment, an apparatus for automatically calculating a neighboring area surface on the same side of a spatial polygon is further provided in the embodiments of the present application, including a sorting module, configured to perform geometric sorting on edges of the spatial polygon;
the building module is used for building a direction vector of the edge and building orientation vectors of adjacent surfaces on two sides of the edge;
and the calculation and judgment module is used for calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero.
There is provided a computer readable storage medium storing a computer program which, when executed by a processor, implements the method for automatically calculating the same-side spatial polygon neighboring region surfaces of the above embodiments.
A computer device includes a processor and a memory, the processor executes a program corresponding to an executable program code by reading the executable program code stored in the memory, so as to implement the method for automatically calculating the same-side adjacent area surface of a spatial polygon in the above embodiment.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A method for automatically calculating the adjacent area surfaces on the same side of a space polygon is characterized by comprising the following steps:
step (1): geometrically ordering the sides of the space polygon and determining the direction of the polygon;
step (2): constructing direction vectors of the edges and constructing orientation vectors of the adjacent surfaces on the two sides of the edges;
and (3): and calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces, and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero.
2. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 1, wherein: in the step (1), in the sorting process, the direction of the polygon is sequentially searched and determined by taking the direction from the starting point to the end point of the first edge as the direction of the polygon and as the direction reference of the subsequent edge, and the method comprises the following steps:
s1: starting from any one edge, finding two end points, defining the first end point as a starting point, defining the second end point as an end point, setting the starting point as a polygon starting point, and setting the end point as a current point;
s2: if the remaining edge is empty, go to S4, otherwise, with the current point as the target, find the edge where the end point in the remaining edge coincides with the current point;
s3: taking the coincident point as the starting point of the edge and the other end point as the end point, updating the current point as the end point, subtracting 1 from the residual edge, and turning to S2;
s4: if the polygon starting point is coincident with the current point, the polygon is closed, otherwise, the polygon is not closed.
3. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 2, wherein: in the step (2), the edges of any type are dispersed, the starting point and the middle point of the edge are taken, and a direction vector is constructed in the direction of pointing to the middle point from the starting point.
4. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 3, wherein: in the step (2), when constructing the orientation vector of the adjacent surface, one point on the edge is taken to point to the characteristic point on the adjacent surface as the orientation vector.
5. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 4, wherein: the midpoint of the edge is taken as the starting point.
6. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 5, wherein: the method for taking points on the adjacent surface comprises the following steps: and constructing a reference plane by using the midpoint of the edge and the direction vector of the edge, solving an intersection line of the reference plane and the adjacent surface, and taking the midpoint of the intersection line when the reference plane and the adjacent surface have one and only one intersection line.
7. The method for automatically calculating the same side adjacent area surface of the spatial polygon as the claim 6, wherein: in the step (3), two adjacent surfaces of the edge are respectively face1 and face2, and vecFwd is a direction vector of the edge;
the structural abutment surface orientation vectors vF1 and vF2 are direction vectors from the same point on the edge to a point pnt1 of the face1 and a point pnt2 of the face2 respectively;
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 the formula (1), the included angle between the vector direction of vF1 xvF 2 and vecFwd is larger than 90-180 degrees, and the two directions are basically opposite, then the face1 is judged to be the left side surface, and the face2 is judged to be the right side surface;
if the three vectors satisfy the formula (2), and the included angle between the vector direction of vF1 xvF 2 and vecFwd is 0-90 degrees, the two directions are basically consistent, then the face1 is the right side surface, and the face2 is the left side surface.
8. An apparatus for automatically calculating the surfaces of adjacent regions on the same side of a spatial polygon, comprising:
the sorting module is used for geometrically sorting the sides of the space polygon;
the building module is used for building a direction vector of the edge and building orientation vectors of adjacent surfaces on two sides of the edge;
and the calculation and judgment module is used for calculating a three-vector mixed product of the side direction vector and the orientation vectors of the two adjacent surfaces and judging the orientations of the two adjacent surfaces according to the relation between the three-vector mixed product and zero.
9. A computer-readable storage medium, storing a computer program, which, when being executed by a processor, implements a method for automatically calculating the same-side adjoining area surfaces of a spatial polygon as set forth in any one of claims 1 to 7.
10. A computer device comprising a processor and a memory, wherein the processor executes a program corresponding to an executable program code by reading the executable program code stored in the memory to implement the method for automatically calculating the same-side adjacent area surface of a spatial polygon as set forth in any one of claims 1 to 7.
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| JPH0778254A (en) * | 1993-09-08 | 1995-03-20 | Hitachi Ltd | Graphic closed area extraction method |
| JP2009119716A (en) * | 2007-11-14 | 2009-06-04 | Fuji Xerox Co Ltd | Non-moldable portion detecting device, non-moldable portion detecting system, non-moldable portion detecting program, and non-moldable portion detecting method |
| CN101739493A (en) * | 2008-11-04 | 2010-06-16 | 本田技研工业株式会社 | Method of determining mesh data and method of correcting model data |
| JP5413532B1 (en) * | 2013-06-20 | 2014-02-12 | 富士ゼロックス株式会社 | PROJECTION DETECTION DEVICE, PROJECTION DETECTION SYSTEM, AND PROJECTION DETECTION PROGRAM |
| CN113056358A (en) * | 2018-11-22 | 2021-06-29 | 马自达汽车株式会社 | Resin member, mold for molding resin member, and method for producing resin member |
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- 2022-04-13 CN CN202210388311.4A patent/CN114800965A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0778254A (en) * | 1993-09-08 | 1995-03-20 | Hitachi Ltd | Graphic closed area extraction method |
| JP2009119716A (en) * | 2007-11-14 | 2009-06-04 | Fuji Xerox Co Ltd | Non-moldable portion detecting device, non-moldable portion detecting system, non-moldable portion detecting program, and non-moldable portion detecting method |
| CN101739493A (en) * | 2008-11-04 | 2010-06-16 | 本田技研工业株式会社 | Method of determining mesh data and method of correcting model data |
| JP5413532B1 (en) * | 2013-06-20 | 2014-02-12 | 富士ゼロックス株式会社 | PROJECTION DETECTION DEVICE, PROJECTION DETECTION SYSTEM, AND PROJECTION DETECTION PROGRAM |
| CN113056358A (en) * | 2018-11-22 | 2021-06-29 | 马自达汽车株式会社 | Resin member, mold for molding resin member, and method for producing resin member |
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