Quadric and cubic bitetrahedral patches

Abstract

Algebraic surface patches bounded by tetrahedra are promising building blocks for low-degree implicit spline surfaces. General algebraic surface patches may have topological anomalies such as singular points and multiple sheets. The A-patch technique avoids many of these anomalies but does not ensure that the surface patches are connected and have no holes. Requiring these qualities often places overly restrictive conditions on the patch. We present a technique for building a bitetrahedral patch that is single sheeted, smooth, and singly connected in a pair of face-adjacent tetrahedra. The bitetrahedral patch technique is applicable to most low-degree algebraic surface patches, and it establishes single sheetedness, smoothness, and single connectness when existing techniques fail. © 1995 Springer-Verlag.