Edge-Orthogonal Patches through a Given Rational Bézier Curve

Applications in computational fluid dynamics (CFD) have led to the problem of finding a rational Bézier patch with a given edge parameter line k the way that the parameter lines of the other type intersect k orthogonally. This is what we call an ‘orthogonal continuation of k’. The variety of solutions to the problem is being investigated and a very geometric way for the construction of the solutions is being offered. Using some fundamental features of polynomials we can establish a link between the properties of the weight polynomial and the elevation of degree which is necessary to find non-trivial orthogonal continuations. For some cases which turn out to be unsolvable, and for cases where the solution existing has a very high degree, we can describe a Monte Carlo method providing surprisingly good approximations. This method is even capable of coping with tasks where the right angle is replaced by some arbitrary angle function.