B-spline Patches Fitting on Surfaces and Triangular Meshes

In this paper a technique for the construction of quartic polynomial B-spline patches fitting on analytical surfaces and triangle meshes is presented. The input data are curvature values and principal directions at a given surface point which can be computed directly, if the surface is represented by a vector function. In the case of discrete surface representation, i.e. on a triangle mesh the required input data are computed from a circular neighborhood of a specified triangle facet. Such a surface patch may replace a well defined region of the mesh, and can be used e.g. in re-triangulation, meshsimplification and rendering algorithms.