The shapes of many products that surround us are designed on CAD systems using
geometric modeling techniques. The curves and surfaces most widely used for
this purpose are parametric piecewise polynomials (or rationals, when needed)
with a particular basis known as B-splines. I will define these
representations for curves and surfaces, and discuss some of their properties
and techniques for their use. A few geometric modeling problems encountered
in the CAD software industry will be presented, and their solutions using
these curves and surfaces outlined.
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