Continuity Adjustments to Triangular Bézier Patches That Retain Polynomial Precision

In this paper, I discuss a method for increasing the continuity between two polynomial patches by adjusting their control points. The method described in this paper leaves the control points unchanged if the patches already meet with the desired level of continuity. Next I give two C degree n polynomial interpolation schemes that reproduce degree n polynomials, and show how to apply my continuity increasing scheme to these interpolants without decreasing their polynomial precision. The second of these interpolants is interesting in its own right, as it requires less data than other methods. Finally, I apply my continuity method to Clough-Tocher methods, and create split domain schemes with top-level polynomial precision.