GEOMETRIC SHAPE-RECOGNITION OF FREEFORM CURVES AND SURFACES

Recognizing the construction methods of(piecewise) polynomial or ratio nal curves and surfaces is of great importance, e.g., for geometrical data exchange between two different modeling systems. We formulate int rinsic conditions that are parameterization independent whenever possi ble, These conditions can detect: (i) whether a curve segment is a lin e, a circle, or a planar curve; (ii) whether a surface patch is a plan e, a sphere, a cylinder, or a cone; and (iii) whether a surface is con structed as a surface of revolution/extrusion, a ruled/developable sur face, or a generalized cylinder. (C) 1997 Academic Press.