Intersecting surfaces of special types

The paper reviews new approaches to computing the intersection curve of two surfaces of special types. We consider algorithms for intersecting a torus with a natural quadric or another torus. After that, we review a topological technique that computes the intersection curve of a sphere and a surface of revolution. Finally, we consider the intersection of two ruled surfaces.

[1]  Ramon F. Sarraga,et al.  Algebraic methods for intersections of quadric surfaces in GMSOLID , 1983, Comput. Vis. Graph. Image Process..

[2]  Gershon Elber,et al.  Bisector curves of planar rational curves , 1998, Comput. Aided Des..

[3]  Joshua Z. Levin.  Mathematical models for determining the intersections of quadric surfaces , 1979 .

[4]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[5]  Ron Goldman,et al.  Geometric Algorithms for Detecting and Calculating All Conic Sections in the Intersection of Any 2 Natural Quadric Surfaces , 1995, CVGIP Graph. Model. Image Process..

[6]  Gershon Elber,et al.  Ruled tracing , 1997, The Visual Computer.

[7]  Joshua Levin,et al.  A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces , 1976, CACM.

[8]  Les A. Piegl,et al.  Geometric method of intersecting natural quadrics represented in trimmed surface form , 1989 .

[9]  Ron Goldman,et al.  Using tangent balls to find plane sections of natural quadrics , 1992, IEEE Computer Graphics and Applications.

[10]  Myung-Soo Kim,et al.  Torus/Sphere Intersection Based on a Configuration Space Approach , 1998, Graph. Model. Image Process..

[11]  John K. Johnstone,et al.  Computing the intersection of a plane and a revolute quadric , 1994, Comput. Graph..

[12]  Rida T. Farouki,et al.  Automatic parsing of degenerate quadric-surface intersections , 1989, TOGS.

[13]  Chandrajit L. Bajaj,et al.  NURBS approximation of surface/surface intersection curves , 1994, Adv. Comput. Math..

[14]  John K. Johnstone.  A new intersection algorithm for cyclides and swept surfaces using circle decomposition , 1993, Comput. Aided Geom. Des..

[15]  Chandrajit L. Bajaj,et al.  Tracing surface intersections , 1988, Comput. Aided Geom. Des..

[16]  Nicholas M. Patrikalakis,et al.  Surface-to-surface intersections , 1993, IEEE Computer Graphics and Applications.

[17]  John K. Johnstone,et al.  Computing the intersection of a plane and a natural quadric , 1992, Comput. Graph..

[18]  Gershon Elber,et al.  The intersection of two ruled surfaces , 1999, Comput. Aided Des..

[19]  Ku-jin Kim,et al.  Computing All Conic Sections in Torus and Natural Quadric Intersections , 1998 .

[20]  James R. Miller,et al.  Geometric approaches to nonplanar quadric surface intersection curves , 1987, TOGS.

[21]  Itzhak Wilf,et al.  Quadric-surface intersection curves: shape and structure , 1993, Comput. Aided Des..