Generating smooth surfaces with bicubic splines over triangular meshes: toward automatic model building from unorganized 3D points

The paper presents an algorithm for constructing tangent plane continuous (G¹) surfaces with piecewise polynomials over triangular meshes. The input mesh can be of arbitrary topological type, that is, any number of faces can meet at a mesh vertex. The mesh is first refined to one solely with quadrilateral cells. Rectangular Bezier patches are then assigned to each of the cells and control points are determined so that G¹ continuity across the patch boundaries is maintained. Since all the patches are rectangular, the resulting surface can be rendered efficiently by current commercial graphic hardware/software. In addition, by exploiting the fact that all the faces of the original mesh are triangular, the degree of each patch is optimized to three while a more general method dealing with arbitrary irregular meshes requires biquartic patches. Several surface examples generated from real 3D data are shown