Polar isodistance curves on parametric surfaces

Abstract

In this paper, a new method for interrogation of parametric surfaces is introduced. The basic idea is to consider the distance measured on certain curves on a surface as an interrogation tool. To this aim, two different sets of characteristic curves are considered: The normal section curves and the geodesic curves. The differential equations of these sets of curves starting radially from a given point of the surface are stated. Then, they are solved numerically, introducing the arc-length on the surface as the integration variable. Associated with those curves we construct the polar isodistance curves which are obtained by joining the points at the same distance from a given point of the surface along the section or geodesic curves. Finally, some illustrative examples for NURBS surfaces, by far the most common surfaces in industry, are also described. © Springer-Verlag Berlin Heidelberg 2002.