We reconstruct smooth boundary models of bones from CT data. Although previous research demonstrates the feasibility of polyhedral shape reconstruction, these models are inappropriate for joint modeling. They require far more elements than do smooth models to achieve a given accuracy. Modern graphics hardware can display the smooth models faster and better than the polygonal models.
Incremental modification is difficult because changes in one vertex can effect the entire model.
The derivative discontinuities increase model error, degrade dynamical simulation, stress analysis, and shading. Smooth models solve these problems, but complicate reconstruction. The best current algorithms can fail on seemingly straightforward problems. We build a boundary representation of the object, based on implicit polynomial surface patches of low degree, that has the desired geometric continuity and approximates the data within a user-specified parameter . Our first algorithm can reconstruct surfaces that are -smooth everywhere.