TITLE:
Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization
AUTHORS:
Xuli Han, Jing Yang
KEYWORDS:
Bézier Curve, Degree Reduction, Endpoint Constraint, Differential Constraint, L2-Norm
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.1,
January
11,
2016
ABSTRACT: In this paper, we propose a
new approach to the problem of degree reduction of Bézier curves based on the
given endpoint constraints. A differential term is added for the purpose of controlling
the smoothness to a certain extent. Considering the adjustment of second
derivative in curve design, a modified objective function including two parts
is constructed here. One part is a kind of measure of the distance between
original high order Bézier curve and degree-reduced curve. The other part
represents the second derivative of degree-reduced curve. We tackle two kinds
of conditions which are position vector constraint and tangent vector
constraint respectively. The explicit representations of unknown points are
presented. Some examples are illustrated to show the influence of the
differential terms to approximation and smoothness effect.