Abstract: In this paper, 2-D problem of shape-preserving splines
is formulated as the Differential Multipoint Boundary Value Problem (DMBVP) for
thin plate tension splines. For a numerical treatment of this problem, we
replace the differential operator by its difference approximation. This gives us
a system of linear equations with the matrix of a special structure. We found
that this matrix is positive definite. Therefore, we can solve efficiently this
system of linear equations by direct or iterative methods. For the required
memory of this algorithm is about n and the computational time especially the operation count is about
for each iteration, where n
is the number of unknowns in the interpolation problem.
Keywords and phrases: shape-preserving spline, DMBVP, CAGD, finite-difference, SOR.
