Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

TL;DR

This paper introduces a new framework for creating compactly-supported, smooth interpolators that enable flexible, local shape control and resolution adjustment in interactive shape modeling applications.

Contribution

The authors develop a general method for constructing piecewise-exponential polynomial interpolators with customizable regularity, facilitating advanced shape modeling and manipulation.

Findings

Interpolators support arbitrary regularity constraints

Enable local shape control and shape primitive reproduction

Allow resolution changes via refinability of B-splines

Abstract

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.