Proceedings on Mathematics of surfaces II
Algorithm for algebraic curve intersection
Computer-Aided Design
Developable rational Be´zier and B-spline surfaces
Computer Aided Geometric Design
Arbitrarily precise computation of Gauss maps and visibility sets for freeform surfaces
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A Parametric Solution to Common Tangents
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A subdivision algorithm for computer display of curved surfaces.
A subdivision algorithm for computer display of curved surfaces.
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This paper develops a robust dual representation for the tangent space of a rational surface. This dual representation of tangent space is a very useful tool for visibility analysis. Visibility constructs that are directly derivable from the dual representation of this paper include silhouettes, bitangent developables and kernels.It is known that the tangent space of a surface can be represented by a surface in dual space, which we call a tangential surface. Unfortunately, a tangential surface is usually infinite. Therefore, for robust computation, the points at infinity must be clipped from a tangential surface. This clipping requires two complementary refinements, the first to allow clipping and the second to do the clipping. First, three cooperating tangential surfaces are used to model the entire tangent space robustly, each defined within a box. Second, the points at infinity on each tangential surface are clipped away while preserving everything that lies within the box. This clipping only involves subdivision along isoparametric curves, a considerably simpler process than exact trimming to the box. The isoparametric values for this clipping are computed as local extrema from an analysis using Sederberg's piecewise algebraic curves.A construction of the tangential surface of a parametric surface is outlined, and it is shown how the tangential surface of a Bézier surface can be expressed as a rational Bézier surface.