A Method for Obtaining Intersection Lines of Complex Plane Slices

Abstract

The invention relates to a seeking method for intersection sections of complex planar chips. The basic thought is as follows: an intersection result of two complex planar chips is composed of a plurality of line segments. The seeking method comprises the following steps: firstly, acquiring a theoretic intersection section which is long enough according to a plane equation of the two planar chips; acquiring a point of intersection of a lateral line segment and the theoretic intersection section on each planar chip; ranking the points of intersection according to the magnitudes of projection coefficients of the points of intersection; forming one intersection section by each pair of points of intersection, thereby acquiring a set of the intersection sections on each planar chip; and lastly, acquiring the intersection of the sets of the intersection sections of the two planar chips, namely, the intersection sections of two complex planar chips. The seeking method provided by the invention has the advantages of simple, easy operation, strict algorithmic logic, perfect geometric completeness, small calculated amount of algorithm, and the like, and is applicable to the geometric modeling in the fields of CAD (Computer-Aided Design), CAM (Computer-Aided Manufacturing), CAE (Computer-Aided Education), virtual reality, 3D (Three Dimensional) printing, and the like.

Description

technical field [0001] The invention belongs to the technical field of computer graphics, and relates to a method for obtaining intersection segments of complex plane slices, which can be used for computer-aided teaching of geometric modeling and descriptive geometry in the fields of CAD, CAM, CAE, virtual reality, 3D printing, etc. . Background technique [0002] With the rapid development of modern science and technology, computer virtual reality, animation simulation and other technologies are becoming more and more mature. Real-time drawing of graphics and natural scene simulation have become an urgent desire of human beings. Boolean operations have become one of the most important technologies. At present, the three-dimensional geometric model is becoming more and more complex, and the scale of the virtual environment is getting larger and larger. At the same time, people's demand for real-time interaction and real scenes is getting higher and higher, which also poses ...

AI Technical Summary

Problems solved by technology

The document "Descriptive Geometry and Mechanical Drawing" (Shaanxi Science and Technology Press, July 2002, author: Northwestern Polytechnical University Engineering Drawing Teaching and Research Office) introduces the use of straight lines and planes to find intersection points to find two plane slices without inner rings. The method of intersecting line segment, which is a method for obtaining the intersecting line segment by drawing with ruler and compass on two known projections of a plane sheet; document "Computer Graphics" (Tsinghua University Press, August 1995, author: Sun Jiaguang ) provides four steps of the intersection algorithm for two polygons with inner rings (respectively denoted as A and B): ① intersect all sides of polygon A with polygon B to obtain all valid intersection points; Intersect all sides with polygon A to find all effective intersection points; ③Sort all intersection points according to y first, and then sort according to the size of x; ④Check the inclusion of the midpoint of each pair of intersection points with A and B, if the middle point The point is both in A and in B, then the pair of intersections defines an intersection segment; the document "Computer Graphics Geometry Tool Algorithm Detailed Explanation" (Electronic Industry Press, January 2005, author: Philip J.Schneider, David H .Eberly, translated by Zhou Changfa) introduced the method of calculating the theoretical intersection line from the equations of two planes, but there is a conceptual error in using the linear combination of two plane normal vectors to represent a point on the intersection line, because the spatial point can only be used Vector representation, vectors cannot represent spatial points

It can be seen that the existing research results have the following problems: (1) The algorithm is relatively complex and difficult to implement

There are a large number of points in the detection of polygons in the algorithm, this work first needs to convert the spatial points and polygons into two-dimensional points and polygons, which requires a certain amount of calculation, and the detection itself has a large amount of calculation; (3) the algorithm exists Completeness problems, such as when the x and y coordinates of all intersection points are equal, it will be invalid to sort the intersection points with x and y coordinates; (4) the efficiency of the algorithm is not high, which is reflected in the fact that there are many It is useless to intersect edges and faces, and it is also useless to detect points within polygons. It is also inefficient to sort intersection points twice

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