کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
440830 691285 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Parameterization and applications of Catmull–Rom curves
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
Parameterization and applications of Catmull–Rom curves
چکیده انگلیسی

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 intersection-free Catmull–Rom curves can be generated using these properties. Finally, we discuss two example applications of Catmull–Rom curves and show how the choice of parameterization makes a significant difference in each of these applications.

Research highlights
► A class of parameterization options for Catmull–Rom curves is analyzed in detail.
► The centripetal parameterization has unique abilities that do not exist in any other parameterization.
► Intersection free Catmull–Rom curves can be generated using centripetal parameterization.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer-Aided Design - Volume 43, Issue 7, July 2011, Pages 747–755
نویسندگان
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