Abstract: A method for creating a parameterization of an input surface in a 3-D computer graphics system comprises specifying a plurality of boundary curves on the surface that define a patch of the surface. The boundary curves are typically specified using a user-interactive curve editing procedure, but may also be specified automatically. Similarly, a feature curve is specified on the surface. The method then automatically generates a parameterization of the patch such that a discretized higher order energy functional defined on the surface is minimized subject to the constraint that iso-curves of the parameterization are attracted to follow the feature curve. The method is useful for converting dense irregular polygon meshes into surface models suitable for interactive modification and animation.

Abstract: A method for creating a smooth parameterization and fitting it to an input surface in a 3-D computer graphics system comprises specifying a plurality of boundary curves on the surface that define a patch of the surface. The boundary curves are typically specified using a user-interactive curve editing procedure, but may also be specified automatically. The method then automatically generates a parameterization of the patch such that a discretized higher order energy functional defined on the surface is minimized. The method further comprises the step of fitting a smooth surface to the input surface, where the smooth surface has a parameterization as generated in the previous step. The fitting and parameterization steps are independently controlled to give the user a high degree of flexibility and control over both steps. The method is useful for converting dense irregular polygon meshes into surface models suitable for interactive modification and animation.

Abstract: A computer-implemented method for drawing and manipulating curves on polygon mesh surfaces possesses a built in surface constraint that provides a better intuition for the shape and position of a curve than conventional unconstrained three dimensional space curves. The method includes storing the following graphical data structures in a memory: a 2-D polygon mesh embedded in a 3-D ambient space, a 1-D face point curve v embedded in the 2-D polygon mesh, a first-order curve weighting function &agr;, and a second-order curve weighting function &bgr;. The method also comprises computing a displacement dv of the face point curve v to produce a displaced face point curve v′=v+dv, wherein v′ is embedded in the 2-D polygon mesh, and wherein the displacement dv is computed in dependence upon &agr; and &bgr;. A rendered representation of the polygon mesh and the displaced face point curve are then displayed.