Method and system for efficiently trimming a nurbs surface with a projected curve

摘要

A curve projected onto a NURBS surface defines trim regions on the NURBS surface. A plurality of spaced-apart points are defined on the curve and rays are project through the points toward a NURBS surface. Any intersections of the rays with the NURBS surface is mapped into the U,V domain. Corresponding points of adjacent rays are connected to define at least a portion of each trim region on the NURBS surface. Transitions on the NURBS surface between adjacent rays are detected based upon differences in the number of intersections of adjacent rays. The location of each transition is determined to within a selected tolerance by using a binary subdivision of the interval between adjacent rays. The location of such transitions is used to determine how intersections of the rays with the surface at the boundaries of the NURBS surface should be connected. Parity assigned to the rays at each intersection determines the direction in which intersections along the rays are connected. The technique enables real-time trimming of the NURBS surface to be carried out in response to any change to the curve and/or NURBS surface topology.