US 5,636,338 A · Method for designing curved shapes for use by a computer

Abstract

Methods for forming computer models of curves, networks, or surfaces from user defined specifications of the shape to be modeled. Each specification includes a set of geometric constraints, such as positions, tangents curvatures, and torsions, and may also include discontinuity specifications. In the preferred embodiment, curves are computed so as to locally minimize a scale invariant functional of the geometry of the curve, such as a magnitude of variation in curvature of the curve (MVC) or a magnitude of curvature of the curve (MEC), while satisfying a user defined specification. An improvement on the MVC functional is to add a magnitude of variation in torsion of the curve. An improvement on the MEC functional is to add a magnitude of torsion of the curve. Networks of curves are produced using similar techniques of computing a local minimum of a functional of the geometry of the curves comprising the network, such as a magnitude of variation in curvature of the curves (MVN) or a magnitude of curvature of the curves (MEN), while satisfying a user defined specification. An improvement on these methods is to make the MVN and MEN functionals scale invariant. Another improvement is to make the MVN and MEN functionals torsion dependent. Surfaces are produced using a technique of computing a locally minimized functional of a magnitude of variation in curvature of the surface (MVS), while satisfying a set of surface constraints. An improvement on this method is to make the MVS functional scale invariant.

Claims101

Dependent claims

A method for producing a representation of a curve for display by a computer system, comprising:

specifying a desired shaped of the curve utilizing a set of geometric constraints;
specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape;
producing a representation of the curve based on the functional and the set of geometric constraints;
and
displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.

2 more elements

Dependencies are inferred from the claim text.

Method for designing curved shapes for use by a computer

Life of this patent

Method for designing curved shapes for use by a computer

Life of this patent

Abstract

Claims101