Parameterization and applications of Catmull-Rom curves Conference Paper

abstract

• The behavior of CatmullRom 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 CatmullRom 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 intersection-free CatmullRom curves can be generated using these properties. Finally, we discuss two example applications of CatmullRom curves and show how the choice of parameterization makes a significant difference in each of these applications. 2010 Elsevier Ltd. All rights reserved.

authors

• Keyser, John
• Schaefer, Scott

published proceedings

• COMPUTER-AIDED DESIGN

altmetric score

• 6

author list (cited authors)

• Yuksel, C., Schaefer, S., & Keyser, J.

citation count

• 59

complete list of authors

• Yuksel, Cem||Schaefer, Scott||Keyser, John

publication date

• July 2011

publisher

• Elsevier  Publisher

published in

• Computer Aided Design  Journal

keywords

• Animation Curves
• Catmull-rom Splines
• Centripetal Parameterization
• Chordal Parameterization
• Parameterization
• Path Curves
• Uniform Parameterization

Digital Object Identifier (DOI)

• 10.1016/j.cad.2010.08.008

start page

• 747

end page

• 755

volume

• 43

issue

• 7

URL

• http://dx.doi.org/10.1016/j.cad.2010.08.008