Seidel, Hans-Peter2015-10-052015-10-0519881017-4656https://doi.org/10.2312/egtp.19881008This paper presents an algorithm for the automatic detection of closed piecewise parametric surfaces without any inside or outside, e.g. a Klein bottle. The algorithm is able to decide whether a given closed surface is orientable or not. If non-orientable, the surface will not divide Euclidean 3-space into two halves. Therefore a non-orientable surface can never serve as the boundary of a solid object. The algorithm is based on results from algebraic topology and thus avoids the computation of derivatives and normal vectors. Several applications of the algorithm to rational tensor product B-spline surfaces are given.10.2312/egtp.19881008