Choosing nodes in parametric curve interpolation
Computer-Aided Design
A variational approach to subdivision
Computer Aided Geometric Design
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
On the problems of smoothing and near-interpolation
Mathematics of Computation
An abstract formulation of variational refinement
Journal of Approximation Theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
| Hi-index | 7.29 |
A non-uniform, variational refinement scheme is presented for computing piecewise linear curves that minimize a certain discrete energy functional subject to convex constraints on the error from interpolation. Optimality conditions are derived for both the fixed and free-knot problems. These conditions are expressed in terms of jumps in certain (discrete) derivatives. A computational algorithm is given that applies to constraints whose boundaries are either piecewise linear or spherical. The results are applied to closed periodic curves, open curves with various boundary conditions, and (approximate) Hermite interpolation.