Titlebook: Bézier and B-Spline Techniques; Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny Textbook 2002 Springer-Verlag Berlin Heidelberg 2002 B-spl

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核心

Smooth curvesenerally, a curve is said to be .. if it has an r times continuously differentiate parametrization. An even more general smoothness concept is based on the continuity of higher order geometric invariants. Piecewise polynomial curves with this general smoothness can be nicely studied using a geometri

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Tensor product surfacescontrol curves control the surface. The surface representation by these control points has properties analogous to those of a univariate curve (e.g., Bézier or B-spline) representation. This is due to the fact that one can deal with these surfaces by applying just curve algorithms. Similarly, one ca

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Bézier representation of triangular patchesrty, basically all properties of the Bézier representation of curves have a surface equivalent. The Bézier representation over triangles can be generalized further to Bézier representations over multi-dimensional simplices, see Chapter 19.

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Stationary subdivision for arbitrary netsk presented a similar generalization for bicubic splines. Their algorithms can be applied to arbitrary quadrilateral control nets and yield sequences of control nets that converge to piecewise biquadratic or bicubic surfaces with finitely many so-called extraordinary points.