Abstract
This paper describes a method which generates Straight Homogeneous Generalized Cylinder (SHGC) representation of an object from its range image. When a plane curve sweeps along a straight axis changing its size, it generates a 3D surface. The SHGC represents the shape of an object surface as such the swept surface. In order to generate SHGC representation of an object, the axis, the cross section curve to sweep, and the sweeping rule must be extracted from the given object surface. Here, to extract them, we utilize the fact that the parabolic curves of the SHGC surface lie on the cross section curves or on the meridian curves.
We, first, calculate the Gaussian curvature at every point of the surface, and extract its parabolic curves. A parabolic curve of the SHGC surface lie on a plane. Secondly, we obtain the cross sections of the object by shifting the cross section plane. If at two points on different two cross section curves, their tangent lines are parallel, and a straight line connecting these two points crosses with the axis of the object. So, referring every pair of the cross section curves, we obtain the axis. Then, the sweeping rule curve is obtained as a cross section of the object with a plane including the axis. Some experimental results show that the proposed method can also generate the SHGC representation from a part of the range image of an object.
