A triangular G1 patch from boundary curves

Abstract

For some applications it is necessary to fit an irregular surface to given data, e.g. to develop a geometric model of a human skeletal bone from computerized tomography scans. Such a surface does not always have easily distinguishable isoparametric lines. It is thus not convenient to use standard global curve fitting techniques such as those based on B-splines. A global method may also smooth away essential features. A reasonable approach is to use a composite surface where individual surface patches are locally determined. To obtain some visual smoothness it is desirable that these patches join their neighbours in a manner that preserves positional as well as tangent plane continuity. Several methods have been presented for constructing surfaces in such a manner. A common initial stage in developing the patches is to determine a network of boundary curves. This article reports on some results using boundary curves based on a recent technique for point normal interpolation.