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5.7.3 Rational polynomial parametric/procedural parametric and procedural parametric/procedural parametric curve/surface intersections (Cases E2/E6)

The intersection problem between a rational polynomial parametric curve or a procedural parametric curve and a procedural parametric surface is defined as:
    (5.72)

Similar to Case E1, this problem reduces to three nonlinear equations in three unknowns involving non-polynomial functions, for which bounds are not generally available.

A possible approach is to use the minimization technique

    (5.73)

in a cube . Comments under the point/PP curve intersection case (see Sect. 5.4.3) also apply to this problem.



December 2009