Uniform Interval Implicitization of Rational Surfaces

Parametric curves/surfaces and algebraic curves/surfaces are two common types of representations of geometric objects in computer aided design and geometric modeling. Both of these representations have their own advantages and disadvantages. Thus it is important to have both representations at the same time. In this paper, a new concept called uniform interval implicitization of rational curves is proposed, which is finding an uniform interval curve with lower degree bounding a given rational curve and minimizing some objective function. An algorithm and some examples are provided to demonstrate the theory.