Geometric shape recognition of freeform curves and surfaces

Recognizing the construction methods of(piecewise) polynomial or rational curves and surfaces is of great importance, e.g., for geometrical data exchange between two different modeling systems. We formulate intrinsic conditions that are parameterization independent whenever possible, These conditions can detect: (i) whether a curve segment is a line, a circle, or a planar curve; (ii) whether a surface patch is a plane, a sphere, a cylinder, or a cone; and (iii) whether a surface is constructed as a surface of revolution/extrusion, a ruled/developable surface, or a generalized cylinder. (C) 1997 Academic Press.