Managing the shape of planar splines by their control polygons

E. Kantorowitz and Y. Schechner

Computer Science Department, 
Technion-Israel Institute of Technology, 
32000, Haifa, Israel

Received 8 November 1990;  revised 31 July 1992.  
Available online 27 February 2003.


Abstract

A practical formulation of the shape-preservation theorem is presented. 
It states how the control points should be positioned to obtain a prescribed
curve shape and avoid shape anomalies. The concept of hyperconvex polygons 
is introduced. These polygons can be intersected by straight lines at three 
points, and are therefore not covered by previous versions of the theorem. 
The extended theorem addresses all the possible control-point configurations, 
and is proved for important classes of planar B-splines and beta2-splines.

Author Keywords: planar splines; B-splines; beta-splines; rational splines; 
shapes; hyperconvex polygons; inflection; anomalies; interactive design 


The DOI identity code of the paper is

doi:10.1016/0010-4485(93)90030-R

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