G2 blending of corners with piecewise algebraic surfaces

In this paper, we present a construction approach to blend the corner of three coordinate planes with G² continuous piecewise algebraic surfaces. For each pair of two coordinate planes, an algebraic surface patch (which is defined in a tetrahedron or a prism) is used to blend the two coordinate planes, and then a center patch is constructed to blend the three algebraic surface patches. The defining region and the shape of the blending surface can be easily adjusted with a few free parameters. Examples are provided to illustrate the blending method. The result can be combined with a potential method to blend three arbitrary algebraic surfaces intersecting transversally at a common point.