(untitled) (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 the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bézier asymptotic quadrilateral interpolated by a smooth Bézier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bézier surfaces is compatible with the CAD systems.