The Design of Bézier Surface Through Quintic Bézier Asymptotic Quadrilateral (Journal of Computational Mathematics, 2019)
The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents thenecessary and sufficient conditions for quadrilateral with non-inflection being asymptoticboundary curves of a surface. And then, with given corner data, we model quintic Bézierasymptotic quadrilateral interpolated by a smooth Bézier surface of bi-eleven degree. Wehandle the available degrees of freedom during the construction to get an optimized result.Some representative surfaces bounded by asymptotic curves with lines or inflections arealso discussed by examples. The presented interpolation scheme for the construction oftensor-product Bézier surfaces is compatible with the CAD systems.