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Useful surfaces for design.
Polynomials In R2 and in R3, polynomials are useful surfaces.
Spline Curves Splines are useful for approximating smooth shapes.
Rational Curves Curves defined as ratios of polynomials.


Polynomials are surfaces of the form

The paraboloid is an excellent example.

Spline Curves

Spline curves are often used in design because they make it easy to approximate any smooth shape with a polynomial curve (or a blend of several polynomial curves). A spline curve is based on a collection of control points that determine the shape of the curve, and allow its shape to be adjusted easily.

Rational Surfaces

A surface is said to be rational if it is a ratio of two polynomials. The serpentine curve is a rational curve.