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. Kinematic analyses of polygonal models are not feasible because the computation time is proportional to the product of the large number of polygons in the bone models (the patella, femur, and tibia in the knee). 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 have developed two different
techniques [2, 3] to reconstruct the
shape of 3D objects from a dense, unorganized cloud of points. 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. We have then enhanced the algorithm
to make it capable of automatically detecting sharp features and
recostructing them accurately.