The Combinatorics of Real Algebraic Splines over a Simplicial Complex
نویسنده
چکیده
We bound the dimension of xed degree real algebraic interpolatory spline spaces. For a given planar triangulation T real algebraic splines interpolate speciied zi values at the vertices vi = (xi; yi) of T. For a three dimensional simplicial complex ST , real algebraic splines interpolate the boundary vertices vj = (xj; yj; zj) of ST. The main results of this paper are lower bounds on the dimension of degree m real algebraic C 0 and C 1 interpolatory splines over T and implicit real algebraic C 1 interpolatory splines over ST .
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