Bivariate Hermite Interpolation and Numerical Curves

Error bounds for bivariate piecewise hermite interpolation

Unique Solvability in Bivariate Hermite Interpolation

We consider the question of unique solvability in the context of bivariate Hermite interpolation. Starting from arbitrary nodes, we prescribe arbitrary conditions of Hermite type, and find an appropriate interpolation space in which the problem has a unique solution. We show that the coefficient matrix of the associated linear system is a nonsingular submatrix of a generalized Kronecker product...

Case study in bivariate Hermite interpolation

In this article we investigate the minimal dimension of a subspace of C1(R2) needed to interpolate an arbitrary function and some of its prescribed partial derivatives at two arbitrary points. The subspace in question may depend on the derivatives, but not on the location of the points. Several results of this type are known for Lagrange interpolation. As far as I know, this is the first such s...

Optimal Geometric Hermite Interpolation of Curves

Bernstein{B ezier two{point Hermite G 2 interpolants to plane and space curves can be of degree up to 5, depending on the situation. We give a complete characterization for the cases of degree 3 to 5 and prove that rational representations are only required for degree 3. x1. Introduction and Overview We consider recovery of curves from irregularly sampled data. If the curves are to be represent...

An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...