Geometric modeling involves the creation, inspection and analysis of geometric models. One of the four types used is curve modeling. At the point where two curves join, there are three possibilities: point continuity, tangent continuity or curvature continuity. Point continuity is when two curves are joined, each has no limit to the distance away from the point of junction. Tangent continuity means that when joined end to end, the curves have the same slope at their meeting point, and this has the effect of looking like an undulating line. Curvature continuity means that the curves have the same curvature as well as the same slope.
The methods for calculating geometric curves enable, via the use of formulas, the exact parameters of any curve to be rationalized. What this means is that by setting the curve within the parameters of an x and y axis, distances of any point from 0 can be obtained. The x and y axes are simply two lines that intersect, one horizontal one vertical. The point of intersection is zero.
NURBS are non-uniform rational B-splines. Implicit equations and parametric functions described in the previous section are examples of NURBS. Fundamentally, it uses mathematical formulas to describe any shape from a simple line to the most complex three dimensional representation of curves. These abilities make NURBS ideal for computer-aided design and can be used widely, from animation to manufacturing.
There are many fine examples of geometric curves as art. One is at the Pratt Institute School of Art in Brooklyn, NY. The drawing is three dimensional in appearance, and there are five wings coming out from the center, each constructed by approximately 40 curves.