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- W2089358519 abstract "An explicit representation for any irreducible rational Bézier curve and Bézier surface patch on the unit sphere is given. The extension to general quadrics (ellipsoids, hyperboloids, paraboloids) is outlined. The construction is based on an algebraic result concerning Pythagorean quadruples in polynomial rings and can be additionally interpreted as a generalized stereographic projection onto the sphere. This projection is shown to be the composition of a hyperbolic projection (a special net projection) with a stereographic projection. The investigation of its properties leads to new results for the biquadratic Bézier patch on the sphere. Further attention is payed to the interpolation of a given point set with a spherical rational curve. The results are extended to rational B-spline curves and tensor product B-spline surfaces." @default.
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- W2089358519 date "1993-08-01" @default.
- W2089358519 modified "2023-09-28" @default.
- W2089358519 title "An algebraic approach to curves and surfaces on the sphere and on other quadrics" @default.
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- W2089358519 doi "https://doi.org/10.1016/0167-8396(93)90037-4" @default.
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