We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Th...We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.展开更多
Parametric surfacelsurface intersection methods are essential in a sculptured solid modelingsystem- To improve the robustness, accuracy and topological consistence, an algorithm extendedfrom ideas in [1] and in [3] is...Parametric surfacelsurface intersection methods are essential in a sculptured solid modelingsystem- To improve the robustness, accuracy and topological consistence, an algorithm extendedfrom ideas in [1] and in [3] is described in this paper. Including a new rnethod for obtaining the sur-face near points; an appropriate method for estimating the marching step length; and a reliablernethod for determining singular points. Furthermore, our algorithm can evaluate intersections between offset surfaces without offset approximation. These ideas are discussed and implemented in anintegrated CADICAM system. Tested by rnany typical examples , they have been proved to be robustand efficient. Some exarnples are provided.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
The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented, which use extrapolating acceleration technique, and have convergent precision o...The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented, which use extrapolating acceleration technique, and have convergent precision of order 2. Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive. Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.展开更多
文摘We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.
文摘Parametric surfacelsurface intersection methods are essential in a sculptured solid modelingsystem- To improve the robustness, accuracy and topological consistence, an algorithm extendedfrom ideas in [1] and in [3] is described in this paper. Including a new rnethod for obtaining the sur-face near points; an appropriate method for estimating the marching step length; and a reliablernethod for determining singular points. Furthermore, our algorithm can evaluate intersections between offset surfaces without offset approximation. These ideas are discussed and implemented in anintegrated CADICAM system. Tested by rnany typical examples , they have been proved to be robustand efficient. Some exarnples are provided.
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.
文摘The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented, which use extrapolating acceleration technique, and have convergent precision of order 2. Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive. Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.
