1. A method for decomposing a predetermined geometric surface into a plurality of geometric surface patches, comprising performing the following steps by computer equipment: wherein a parametric domain for the predetermined geometric surface is divided into polygons, each of the polygons having less than five sides, wherein for a side of each polygon, there is a corresponding object space boundary curve provided to approximate a corresponding portion of the predetermined geometric surface, the object space boundary curve being for one of the plurality of geometric surface patches for approximating the predetermined geometric surface, the object space boundary curve having the side as a domain therefor, and each point, P, of the object space boundary curve represented as a corresponding weighted sum, having weights therefor, such that (a) through (c) below are satisfied: (a) there is a first term of the corresponding weighted sum, wherein the first term includes a product of: (i) a point L on a first tangent to the object space boundary curve at a first end point of the object space boundary curve, and (ii) a first of the weights of the corresponding weighted sum for P, wherein the point L and the first weight is determined according to a function having a domain space whose values also identify points of the side for the object space boundary curve, and the function monotonically varies between a predetermined first value and a predetermined second value, the predetermined first value less than the predetermined second value; wherein the first tangent is a line or vector that is tangent to the object space boundary curve along a length thereof at the first end point; (b) there is a second term of the corresponding weighted sum, wherein second term includes a product of: (i) a point R i on a second tangent to the object space boundary curve at a second end point of the object space boundary curve, and (ii) a second of the weights of the corresponding weighted sum for P, wherein the point R i and the second weight is determined according to the function; wherein the second tangent is a line or vector that is tangent to the object space boundary curve along a length thereof at the second end point; wherein for the point P of the object space boundary curve, the weights of the corresponding weighted sum, include the first and second weights, and the first and second weights sum to one and each of the first and second weights is in a range of zero and one; (c) each point on the object space boundary curve is within a predetermined tolerance of the predetermined geometric surface; generating, for each of the polygons P j , a corresponding one of the geometric surface patches S j having the polygon P j as the domain for the corresponding one geometric surface patch S j , wherein the object space boundary curve for the polygon P j is included in the boundary of S j , and each interior point of S j : (1) has is a corresponding interior point of the polygon P j , and (2) 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 value of the of the corresponding point from a side of the polygon P j ; wherein the predetermined geometric surface is represented by a parametric polynomial of at least a particular degree, and each of the plurality of geometric surface patches is represented by a corresponding polynomial of lower degree than the particular degree; wherein each geometric surface patch S j conforms to a corresponding portion of the predetermined geometric surface so that there is no more than a desired amount of error between the predetermined geometric surface and the plurality of geometric surface patches; and for the polygons, individually identified as P j , a step of using their corresponding geometric surface patches S j , in place of the predetermined geometric surface, for obtaining a design or shape of an article of manufacture or for modeling of a process or physical feature.