Volume no :8, Issue no: 2, November (2012)

HYPERBOLIC PARABOLOID SPLINE FOR SPATIAL DATA FITTING AND APPROXIMATION

Author's: FENGFU PENG and JIPENG NIU
Pages: [105] - [129]
Received Date: August 29, 2012
Submitted by:

Abstract

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.

Keywords

basis functions, rational spline, curve approximation, integral spline.