Linear Envelopes for Uniform B-spline Curves
Abstract
We derive an efficiently computable, tight bound on the distance between a uniform spline and its B-Spline control polygon in terms of the second differences of the control points. The bound yields a piecewise linear envelope enclosing the spline and its control polygon. For quadratic and cubic splines the envelope has minimal possible width at the break points, and for all degrees the maximal width shrinks by a factor of 4 under uniform refinement. We extend the construction to tight envelopes for parametric curves.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP012034
Entities
People
- David Lutterkort
- Jörg Peters
Organizations
- Purdue University