Localized Editing of Catmull-Rom Splines

M. Eyiyurekli and D. Breen, ``Localized Editing of Catmull-Rom Splines,'' Computer-Aided Design and Applications, Vol. 6, No. 3, 2009, pp. 307-316.

Abstract:
Catmull-Rom (C-R) splines offer many useful modeling properties, such as affine invariance, global smoothness, and local control. They are therefore of great interest to Computer Aided Design (CAD) users. C-R splines are easily evaluated and are a good choice for interactive applications because they interpolate their control points and therefore provide an intuitive way to represent and edit curves in these applications. We have developed an interactive free-form surface-editing framework that uses Catmull-Rom splines for sketch-based editing. Mouse strokes are translated into splines that are used to define free-form surface deformations. Direct control point manipulation is provided for the modification of the splines. Unfortunately, the definition of C-R splines dictates that moving one control point only affects a small, fixed portion of the curve. In order to provide greater flexibility, control and expressiveness, we have developed techniques that expand and generalize the result of modifying one C-R control point. The techniques allow the user to define the range and type of influence that manipulation of a single control point may produce on a C-R curve, providing a versatile and powerful localized curve editing capability.



Last modified on June 10, 2009.