Title: A new simultaneous extension method for B-spline curves blending with G²-continuity

Authors: Hongying Yu; Xuegeng Lyu

Addresses: School of Mechatronic Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China ' School of Mechatronic Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China

Abstract: Curve blending is an extremely common problem in CAD systems. The current blending methods were looking for a third curve to join curves and some of the methods needed to distinguish the transition curve were C-or S-shaped. In this paper, we study a simultaneous extension method to blend curves with G²-continuity. The method simultaneously extends the two curves at one of their endpoints and makes them intersect at a common joint under geometric constraints. The basic concept of B-spline curves and its extension theory is presented firstly. Then we propose the blending algorithm of simultaneous extension. This method does not need to prejudge the shape of transition curves, which is, without considering the placement of two original curves and reduces the number of blending joints from two to one. Four curve blending examples are presented to verify the validity of the new method.

Keywords: curves blending; simultaneous extension method; B-spline curve; G²-continuity.

DOI: 10.1504/IJCSM.2020.107598

International Journal of Computing Science and Mathematics, 2020 Vol.11 No.4, pp.385 - 396

Received: 17 Oct 2017
Accepted: 20 Nov 2017
Published online: 02 Jun 2020 *

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