rational curves, hodograph, Bezier curves
Derivatives and normals of rational Bézier curves and surface patches are discussed. A non-uniformly scaled hodograph of a degree m x n tensor-product rational surface, which provides correct derivative direction but not magnitude, can be written as a degree (2m - 2) x 2n or 2m x (2n - 2) vector function in polynomial Bézier form. Likewise, the scaled normal direction is degree (3m - 2) x(3n - 2). Efficient methods are developed for bounding these directions and the derivative magnitude.
Original Publication Citation
T. Saito, G. Wang, and T. W. Sederberg,"Hodographs and normals of rational curves and surfaces", Computer Aided Geometric Design, 12, 417-43, 1995.
BYU ScholarsArchive Citation
Sederberg, Thomas W.; Saito, Takafumi; and Wang, Guo-Jin, "Hodographs and Normals of Rational Curves and Surfaces" (1995). All Faculty Publications. 1161.
Physical and Mathematical Sciences
© 1995 Elsevier. The original publication may be found at http://www.sciencedirect.com/science/journal/01678396.
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