US 5,701,404 A · Method and system for efficiently trimming a nurbs surface with a projected curve

Abstract

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.

Claims21

Dependent claims

A method for defining a trim region on a three-dimensional representation of a surface, as a function of a curve, comprising the steps of:

(a) defining a plurality of spaced-apart sample points along the curve;
(b) projecting rays from the plurality of points generally in a direction toward the surface, so that at least some of the rays intersect the surface at points of intersection;
(c) mapping each of the points of intersection of the rays with the surface into a U,V parametric domain;
(d) determining a number of the points of intersection of each ray with the surface;
(e) if the number of the points of intersection of two adjacent rays with the surface are equal, connecting corresponding points of intersection of said adjacent rays on the surface, to define at least a portion of a trim region;
(f) if the number of the points of intersection of two adjacent rays with the surface are different, detecting a transition of the surface that is disposed between said adjacent rays, where said transition indicates a location where one of the adjacent rays enters or leaves the surface, thereby defining a remaining portion of the trim region;
and
(g) displaying the surface and trim regions on a display.

5 more elements

A system for defining a trim region on a three-dimensional representation of a surface, as a function of a curve, comprising the steps of:

(a) a memory for storing a plurality of machine instructions that define a software program;
(b) a processor for executing the plurality of machine instructions, causing functions to be carried out by the system, said functions including:
(i) defining a plurality of spaced-apart sample points along the curve;
(ii) projecting rays from the plurality of points generally in a direction toward the surface, so that at least some of the rays intersect the surface at points of intersection;
(iii) mapping each intersection of the surface by the rays into a U,V parametric domain;
(iv) determining a number of the points of intersection of each ray with the surface;
(v) if the number of the points of intersection of two adjacent rays with the surface are equal, connecting corresponding points of intersection of said adjacent rays on the surface, to define at least a portion of a trim region;
(vi) if the number of the points of intersection of two adjacent rays with the surface are different, detecting a transition of the surface that is disposed between said adjacent rays, where said transition indicates a location where one of the adjacent rays enters or leaves the surface, thereby defining a remaining portion of the trim region;
and
(c) a display, said processor executing the plurality of machine instruction to cause the surface and the trim region to be visually represented on the display.

7 more elements

Dependencies are inferred from the claim text.

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

Life of this patent

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

Life of this patent

Abstract

Claims21