  In applications that involve interactive curve and surface modeling, the
intuitive manipulation of shapes is crucial. For instance, user interaction is
facilitated if a geometrical object can be manipulated through control points
that interpolate the shape itself. Additionally, models for shape
representation often need to provide local shape control and they need to be
able to reproduce common shape primitives such as ellipsoids, spheres,
cylinders, or tori. We present a general framework to construct families of
compactly-supported interpolators that are piecewise-exponential polynomial.
They can be designed to satisfy regularity constraints of any order and they
enable one to build parametric deformable shape models by suitable linear
combinations of interpolators. They allow to change the resolution of shapes
based on the refinability of B-splines. We illustrate their use on examples to
construct shape models that involve curves and surfaces with applications to
interactive modeling and character design.
