Piecewise Smooth Surfaces Reconstruction for Finite Element Mixed Meshes

Piecewise smooth surfaces reconstruction algorithm for finite element mixed meshes is proposed in this paper. Meshes are supposed to have been segmented and T shaped nodes among segments are permitted, i.e. a boundary in one segment can be split into at least two boundaries of other segments. A frame of B-spline curves is constructed first, which interpolates boundary nodes of all segments. All the B-spline curves should satisfy the condition that opposite curves in quad segments, i.e. segments with rectangle topology, have the same knots vector. Two situations need to be considered for all the segments. For a quad segment, the initial B-spline surface is constructed by skinning its four boundary curves. For a segment with non-rectangle topology or a segment with holes inside, a trimmed B-spline surface is developed. There are also two cases when an initial trimmed base surface is to be constructed. If two appropriate neighbor curves in the outer boundaries loop of the segment are found, the base surface can be obtained by sweeping and extending. Otherwise, the initial base surface is built by skinning the boundary curves of the bounding box for projected points of all nodes on a least squares fitting plane. Nodes in each segment are parameterized by projection on the corresponding base surface. All base surfaces are recalculated with geometry and additional shape preservation constraints. Examples indicate efficiency of our algorithm.