On the parameterization of Catmull-Rom curves

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On the parameterization of Catmull-Rom curves
The behavior of Catmull-Rom curves heavily depends on the choice of parameter values at the control points. We analyze a class of parameterizations ranging from uniform to chordal parameterization and show that, within this class, curves with centripetal parameterization contain properties that no other curves in this family possess. Researchers have previously indicated that centripetal parameterization produces visually favorable curves compared to uniform and chordal parameterizations. However, the mathematical reasons behind this behavior have been ambiguous. In this paper we prove that, for cubic Catmull-Rom curves, centripetal parameterization is the only parameterization in this family that guarantees that the curves do not form cusps or self-intersections within curve segments. Furthermore, we provide a formulation that bounds the distance of the curve to the control polygon and explain how globally intersectionfree Catmull-Rom curves can be generated using these properties. C...
Cem Yuksel, Scott Schaefer, John Keyser
Added 28 May 2010
Updated 28 May 2010
Type Conference
Year 2009
Where SMA
Authors Cem Yuksel, Scott Schaefer, John Keyser
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