Smooth Surfaces Over Arbitrary Meshes

Monday, April 23, 2001 - 2:00pm - 3:00pm
Keller 3-180
Stefanie Hahmann (Grenoble Institute of Technology)
Triangular Bezier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bezier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this talk, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. The tangent directions of the boundary curves at the mesh vertices are now completely free and the degree of the patch boundary curves is elevated to degree five. The importance of these two features is twice. First, irregular triangulations can be handled better in the sense that unwanted undulations due to flat triangles in the mesh are significantly reduced. Second, the interpolation scheme is locally refinable. We explain why the original 4-split method doesn't possess this important property.