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Edge-orthogonal patches through a given rational Bézier curve. (English) Zbl 0920.68139
Summary: 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.
MSC:
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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