A Generalized Blending Scheme for Arbitrary Order of Continuity

In this thesis, new templates and formulas of blending functions, schemes, and algorithms are derived for solving the scattered data interpolation problem. The resulting data fitting scheme interpolates the positions and derivatives of a triangular mesh, and for each triangle of the mesh blends three triangular sub-surfaces, and creates a triangular patch. Similar to some existing schemes, the resulting surface inherits the derivatives of the sub-surfaces on the boundaries. In contrast with existing schemes, the new scheme has additional properties: The order of interpolated derivatives is extended to arbitrary values, and the restrictions of the sub-surfaces are relaxed. Then based on the properties of the new blending functions, an algorithm for constructing smooth triangular surfaces with global geometric continuity is described. The new blending functions and the scheme are then extended to multi-sided faces. The algorithm using these new blending functions accepts data sites formed by multi-sided polygons