Numerical Methods in Approximation Theory, Vol. 9 pp 207-220 | Cite as
C1 Interpolation on Higher-Dimensional Analogues of the 4-Direction Mesh
Chapter
Abstract
The well-known square mesh with both diagonals drawn in is generalized to the m-dimensional mesh Δ m generated by {(v 1, ..., v m ): v i ∈ {−1, 0, 1}, i = 1,...,m}. Sharp necessary and sufficient conditions on data at the vertices of Δ m are given that allow interpolation of the data by m-variate, C 1 piecewise polynomials of degree m + 1. For degree m + 2 and higher, values and normals at the vertices can be stably interpolated and a unit-norm C 2 Lagrange function for each vertex is exhibited.
Keywords
Piecewise Polynomial Spline Space Continuity Constraint Yorktown Height Arbitrary Data
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