Piecewise algebraic surface computation and smoothing from a discrete model

This paper describes a constrained smoothing method for implicit surfaces defined on a voxelization. This method is suitable for computing a closed smooth surface that approximates an initial set of face connected voxels. The implicit surface is defined as the zero-set of a tensor-product uniform cubic Bspline. The smoothing process is based on increasing the Bspline continuity from C2 to C3 on the boundary faces of the voxels. The final surface is guaranteed to pierce a predefined subset of voxels.