论文信息 - Rational bisectors of CSG primitives

Rational bisectors of CSG primitives

The bisector surface of two rational surfaces in R3 is non-rational, in general. However, in some special cases, the bisector surfaces can have rational parameterization. This paper classifies some of these special cases that are related to constructive solid geometry (CSG). We consider the bisector surfaces between points, lines, planes, spheres, cylinders, cones, and tori. Many cases are shown to yield rational bisector surfaces, while several other cases are still left as open questions.

Gershon Elber | Myung-Soo Kim

[1] Gershon Elber,et al. The bisector surface of freeform rational space curves , 1997, SCG '97.

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

[3] R. Farouki,et al. The bisector of a point and a plane parametric curve , 1994, Comput. Aided Geom. Des..

[4] Nicholas M. Patrikalakis,et al. An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids , 1996, IEEE Trans. Vis. Comput. Graph..

[5] Gershon Elber,et al. The bisector surface of rational space curves , 1998, TOGS.

[6] Christoph M. Hoffmann,et al. A dimensionality paradigm for surface interrogations , 1990, Comput. Aided Geom. Des..

[7] Rida T. Farouki,et al. Computing Point/Curve and Curve/Curve Bisectors , 1992, IMA Conference on the Mathematics of Surfaces.

[8] Rida T. Farouki,et al. Specified-Precision Computation of Curve/Curve Bisectors , 1998, Int. J. Comput. Geom. Appl..

[9] Debasish Dutta,et al. On the Skeleton of Simple CSG Objects , 1993 .

[10] Rajesh Ramamurthy. Voronoi diagrams and medial axes of planar domains with curved boundaries , 1998 .

[11] Damian J. Sheehy,et al. Shape Description By Medial Surface Construction , 1996, IEEE Trans. Vis. Comput. Graph..