The NURBS Book

ion. For example, when dealing with curves for interactive design, he works with them without regard to the number of control points and knots. Or, for example, when dealing with curve/curve intersection, he might descend his thinking to the level of the control polygon if the overlapping of bounding boxes is what needs to be examined. For these and many other similar reasons, Nlib V2.0 considers every geometric entity as an object built from simpler components. In the design of a huge structure, simple building blocks are created first from basic data types. One of the basic elements of a curve object is the control point. It can be rational or nonrational, two-dimensional or three-dimensional, that is, it needs to hold two, three, or four coordinates. In addition, it plays a dual role as a control point for B-spline computations and as a Euclidean point used for simple geometric manipulations, such as computing distances, bounding boxes, and so on. A third requirement is to be able to refer to this entity as P [i] , just as its mathematical abstraction is referred to in the book. To simplify matters and to satisfy object based concepts, we separated control points from "regular" Euclidean points just as we did in the book, by writing P for a Euclidean point and pw for a control point that can be weighted. Hence the definitions of points are (see Figure 13.1): typedef struct point { REAL x, y, Z; } POINT; typedef struct cpoint { REAL x, y, Z, W· , } CPOINT;