NURBS geometry has five important qualities that make it an ideal choice for computer-aided modeling. NURBS curves and surfaces behave in similar ways and share terminology. Since curves are the easiest to describe, we will cover them in detail. This number is usually 1, 2, 3, or 5, but can be any positive whole number.
Sometimes the terms linear, quadratic, cubic, and quintic are used. Linear means degree 1, quadratic means degree 2, cubic means degree 3, and quintic means degree 5. The control points have an associated number called a weight. With a few exceptions, weights are positive numbers. Otherwise, the curve is called rational. Sometimes this list of numbers is called the knot vector. In this term, the word vector does not mean 3D direction. This list of knot numbers must satisfy several technical conditions.
The standard way to ensure that the technical conditions are satisfied is to require the numbers to stay the same or get larger as you go down the list and to limit the number of duplicate values to no more than the degree. For example, for a degree 3 NURBS curve with 11 control points, the list of numbers 0,0,0,1,2,2,2,3,7,7,9,9,9 is a satisfactory list of knots. Necessary cookies are absolutely essential for the website to function properly. These cookies ensure basic functionalities and security features of the website, anonymously.
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