The Combinatorics of Algebraic Splines
نویسنده
چکیده
We characterize the dimension of fixed degree functional and implicit algebraic splines in three dimensional (x,y,z) space. For a a given planar triangulation T both functional and implicit algebraic splines interpolate specified Zi values at the vertices Vi = (XitY;) of T. For a three dimensional triangulation 57 the implicit algebraic splines interpolate the boundary vertices Vj = (Xj, Yj I Zj) of ST. The main results are "1. lower bounds on the dimension of degree m rational function and implicit algebraic, Co and C 1 interpolatory splines over T and implicit algebraic C 1 interpolatory splines over ST. 2. explicit CO interpolatory basis for degree 3 implicit algebraic splines over T and C 1 interpolatory bases for degree 5 and degree 7, implicit algebraic splines over convex S7 and arbitrary S7, respectively.
منابع مشابه
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