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

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution