The genetic algorithm and marching method are integrated into a novel algorithm to solve the surface intersection problem. By combining genetic algorithm with local searching method the efficiency of evolution is grea...The genetic algorithm and marching method are integrated into a novel algorithm to solve the surface intersection problem. By combining genetic algorithm with local searching method the efficiency of evolution is greatly improved. By fully utilizing the global searching ability and instinct attribute for parallel computation of genetic algorithm and the local rapid convergency of marching method, the algorithm can compute the intersection robustly and generate correct topology of intersection curves. The details of the new algorithm are discussed here.展开更多
The most difficult problem in surface intersection is to determinate all the initial tracing points. Collinear normal line is a power tool for solving this problem. A lemma about the existence of collinear normal line...The most difficult problem in surface intersection is to determinate all the initial tracing points. Collinear normal line is a power tool for solving this problem. A lemma about the existence of collinear normal line between two toil is presented, based on this lemma an algorithm for finding all the initial tracing points is implemented, numerical examples show that it is robust and efficient.展开更多
Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc....Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc.In practical applications,quadric surfaces,which are the most basic type of surfaces,are typically bounded surfaces trimmed by a sequence of planes.In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics.The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance.The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique.Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.展开更多
A brand new direct and adaptive slicing approach is proposed, which canapparently improve the part accuracy and reduce the building time. At least two stages are includedin this operation: getting the crossing contour...A brand new direct and adaptive slicing approach is proposed, which canapparently improve the part accuracy and reduce the building time. At least two stages are includedin this operation: getting the crossing contour of the cutting plane with the solid part anddetermining the layer thickness. Apart from usual SPI algorithm, slicing of the solid model has itsspecial requirements. Enabling the contour line segments of the cross-section as long as possible isone of them, which is for improving manufacturing efficiency and is reached by adaptively adjustingthe step direction and the step size at every crossing point to obtain optimized secant height. Thelayer thickness determination can be divided into two phases: the geometry-based thicknessestimation and the material-based thickness verifying. During the former phase, the geometrytolerance is divided into two parts: a variety of curves are approximated by a circular arc, whichintroduces the first part, and the deviation error between the contour line in LM process and thecircular arc generates the second part. The latter phase is mainly verifying the layer thicknessestimated in the former stage and determining a new one if necessary. In addition, an example usingthis slicing algorithm is also illustrated.展开更多
文摘The genetic algorithm and marching method are integrated into a novel algorithm to solve the surface intersection problem. By combining genetic algorithm with local searching method the efficiency of evolution is greatly improved. By fully utilizing the global searching ability and instinct attribute for parallel computation of genetic algorithm and the local rapid convergency of marching method, the algorithm can compute the intersection robustly and generate correct topology of intersection curves. The details of the new algorithm are discussed here.
基金Supported by National Science and Technology Major Project(No.2013ZX04011031)
文摘The most difficult problem in surface intersection is to determinate all the initial tracing points. Collinear normal line is a power tool for solving this problem. A lemma about the existence of collinear normal line between two toil is presented, based on this lemma an algorithm for finding all the initial tracing points is implemented, numerical examples show that it is robust and efficient.
基金supported in part by the National Natural Science Foundation of China under Grant No.61972368。
文摘Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc.In practical applications,quadric surfaces,which are the most basic type of surfaces,are typically bounded surfaces trimmed by a sequence of planes.In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics.The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance.The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique.Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.
基金This project is supported by National Natural Science Foundation of China (No.59975015, No.50275018) Doctoral Foundation of Ministry of Edu-cation of China (No.1999014102).
文摘A brand new direct and adaptive slicing approach is proposed, which canapparently improve the part accuracy and reduce the building time. At least two stages are includedin this operation: getting the crossing contour of the cutting plane with the solid part anddetermining the layer thickness. Apart from usual SPI algorithm, slicing of the solid model has itsspecial requirements. Enabling the contour line segments of the cross-section as long as possible isone of them, which is for improving manufacturing efficiency and is reached by adaptively adjustingthe step direction and the step size at every crossing point to obtain optimized secant height. Thelayer thickness determination can be divided into two phases: the geometry-based thicknessestimation and the material-based thickness verifying. During the former phase, the geometrytolerance is divided into two parts: a variety of curves are approximated by a circular arc, whichintroduces the first part, and the deviation error between the contour line in LM process and thecircular arc generates the second part. The latter phase is mainly verifying the layer thicknessestimated in the former stage and determining a new one if necessary. In addition, an example usingthis slicing algorithm is also illustrated.
