Creating Smooth Implicit Surfaces from Polygonal Meshes
Implicit surfaces have long been used for a myriad of tasks in computer graphics, including modeling soft or organic objects, morphing, and constructive solid geometry. Although operating on implicit surfaces is usually straight-forward, creating them is not --- interactive techniques are impractical for complex models, and automatic techniques have been largely unexplored. We introduce a practical method for creating implicit surfaces from polygonal models that produces high-quality results for complex models. Whereas much previous work has been done with primitives such as ``blobbies,'' we use surfaces based on a variational interpolation technique (the 3D generalization of thin-plate interpolation). Given a polygonal mesh, we convert the data to a volumetric representation and use this as a guide to create the implicit surface iteratively. Carefully chosen metrics evaluate each intermediate surface and control further refinement. We have applied this method successfully to a variety of polygonal meshes.