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.
