Tight linear envelopes for splines
D Lutterkort, J Peters - Numerische Mathematik, 2001 - Springer
Numerische Mathematik, 2001•Springer
A sharp bound on the distance between a spline and its B-spline control polygon is derived.
The bound yields a piecewise linear envelope enclosing spline and polygon. This envelope
is particularly simple for uniform splines and splines in Bernstein-Bézier form and shrinks by
a factor of 4 for each uniform subdivision step. The envelope can be easily and efficiently
implemented due to its explicit and constructive nature.
The bound yields a piecewise linear envelope enclosing spline and polygon. This envelope
is particularly simple for uniform splines and splines in Bernstein-Bézier form and shrinks by
a factor of 4 for each uniform subdivision step. The envelope can be easily and efficiently
implemented due to its explicit and constructive nature.
Summary
A sharp bound on the distance between a spline and its B-spline control polygon is derived. The bound yields a piecewise linear envelope enclosing spline and polygon. This envelope is particularly simple for uniform splines and splines in Bernstein-Bézier form and shrinks by a factor of 4 for each uniform subdivision step. The envelope can be easily and efficiently implemented due to its explicit and constructive nature.
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