Paper Info
Title
Rational Pythagorean-hodograph space curves
Abstract
A method for constructing rational Pythagorean-hodograph (PH) curves in R^3 is proposed, based on prescribing a field of rational unit tangent vectors. This tangent field, together with its first derivative, defines the orientation of the curve osculating planes. Augmenting this orientation information with a rational support function, that specifies the distance of each osculating plane from the origin, then completely defines a one-parameter family of osculating planes, whose envelope is a developable ruled surface. The rational PH space curve is identified as the edge of regression (or cuspidal edge) of this developable surface. Such curves have rational parametric speed, and also rational adapted frames that satisfy the same conditions as polynomial PH curves in order to be rotation-minimizing with respect to the tangent. The key properties of such rational PH space curves are derived and illustrated by examples, and simple algorithms for their practical construction by geometric Hermite interpolation are also proposed.
Year
DOI
Venue
2011
10.1016/j.cagd.2011.01.002
Computer Aided Geometric Design
Keywords
Field
DocType
polynomial ph curve,rational pythagorean-hodograph space curve,rational parametric speed,rational ph space curve,pythagorean-hodograph curves,rational frames,tangent developable,rational space curves,rational pythagorean-hodograph,edge of regression,tangent field,hermite interpolation,rational support function,osculating plane,cuspidal edge,rational unit tangent vector,developable surface,support function,ruled surface,satisfiability
Osculating plane,Tangent developable,Rational motion,Topology,Osculating curve,Mathematical analysis,Tangent vector,Rational point,Tangential developable,Osculating circle,Mathematics
Journal
Volume
Issue
ISSN
28
2
Computer Aided Geometric Design
Citations 
PageRank 
References 
9
0.55
28
Authors
2
Name
Order
Citations
PageRank
Rida T. Farouki11396137.40
Zbynk Šír2543.25