Surface patch techniques for computational geometry

Abstract

A method and system for computer aided design (CAD) is disclosed for designing geometric objects, wherein interpolation and/or blending between such objects is performed while deformation data is being input. Thus, a designer obtains immediate feedback to input modifications without separately entering a command(s) for performing such deformations. A novel N-sided surface generation technique is also disclosed herein to efficiently and accurately convert surfaces of high polynomial degree into a collection of lower degree surfaces. E.g., the N-sided surface generation technique disclosed herein subdivides parameter space objects (e.g., polygons) of seven or more sides into a collection of subpolygons, wherein each subpolygon has a reduced number of sides. More particularly, each subpolygon has 3 or 4 sides. The present disclosure is particularly useful for designing the shape of surfaces. Thus, the present disclosure is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft. Additionally, the present disclosure provides for efficient animation via repeatedly modifying surfaces of an animated object such as a representation of a face.

What is claimed is: 
     
         1 . A method for decomposing a geometric surface into a plurality of surfaces, comprising:
 obtaining a plurality of object space boundary curves defining the geometric surface patch, wherein each of the boundary curves is represented as a weighted sum, such that:   (a) a first plurality of terms of the weighted sum, wherein each term includes a product of: (i) a point L i  on a first tangent to the boundary curve at a first end point of the boundary curve, and (ii) a corresponding weighting for L i , wherein the point L i  and its corresponding weighting is determined according to a function that is of degree one in its domain space and monotonically varies between a predetermined first value and a predetermined second value, the first value less than the second value;   (b) a second plurality of terms of the weighted sum, wherein each term of the second plurality includes a product of: (i) a point R i  on a tangent to the boundary curve at a second end point of the boundary curve, and (ii) a corresponding weighting for R i , wherein the point R i  and its corresponding weighting is determined according to the function that is of degree one in its domain space;   (c) for each point L i  of the first tangent, there is a corresponding point R i  of the second tangent, wherein the corresponding weightings therefor sum to one and each varies between zero and one;   subdividing a parametric domain for the geometric surface into polygons, each having less than five sides, wherein for each side of each polygon, there is a corresponding curve having the side as its domain, and the curve represented as a weighted sum satisfying (a) through (c) above, wherein the points on the curve are within a predetermined tolerance of the surface;   generating, for each of the polygons P j , a corresponding object space surface S j  having the polygon P j  as the domain for the corresponding object space surface S j , wherein each point on the boundary of S j  is an image of a point on the boundary of P j , and each interior point of S j  is a weighted sum of boundary points of S j  wherein each weight (WT) of the weighted sum of boundary points of S j  is a product of weight terms wherein each weight term is dependent upon a distance from corresponding side of the polygon.