Parametric surfaces

References

Books

J. Foley and A. Van Dam. Computer Graphics: Principles and Practice. Addison-Wesley, 1990.

Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design. Academic Press, 1990.

Web sites

The excellent Crash course in Computer Graphics, by Michael Capps, section Splines : covers splines and Bezier in 2D and contains very nice Java applets.
3D surfaces in Java (I deny any responsibility for applets)

Approximating vs Interpolating

Approximating vs Interpolating

Interpolation (2D)

The curve goes through its control points. Click here for equations.

natural cubic splines
Lagrange polynomials (usually bad for graphics)

Approximation (2D)

The curve approximates its control points. Click here for equations.

Bezier
B-splines / NURBS (Non-Uniform Rational B-Splines, see de Boor algorithm to construct them)

Extension to 3D

Demo: Seth's NURBS (?)

Eric Amram, Feb 1998, MIT 6.838 Advanced Topics in Computer Graphics - Prof. Seth Teller.