Author's: FENGFU PENG and JIPENG NIU
Pages: [105] - [129]
Received Date: August 29, 2012
Submitted by:
A method to construct the free spline curve and surface is presented
in this paper, in which proposes four rational basis functions, each
of them includes a common control handle and two variables. One of the
variables is determined by a function in a set with a single
parameter, and the other is defined by a multi-integral upper limit
functions about the previous variable. For a spatial control polygon
of four points, a spline curve can be produced by the basis functions,
which can approximate the control edges at will via changing the
control handle. Additionally, the authors consider the properties of
shape-preserving and the spline curves at the endpoints. By
constraining the control handle for the spline, the endpoint
curvatures are less than some threshold at both endpoints. For a range
of points, consequently, one approximately curve can be connected by this spline
curves without other conditions required.
basis functions, rational spline, curve approximation, integral spline.