Theisel, Holger2015-02-162015-02-1620021467-8659https://doi.org/10.1111/1467-8659.00563In this paper we study the exact contours of a piecewise trilinear scalar field. We show how to represent these contours exactly as trimmed surfaces of triangular rational cubic Bezier patches. As part of this, we introduce an extension of the marching cubes algorithm which gives a topologically exact triangular approximation of the contours for any case. Finally, we modify the exact contours to be globally G1 continuous without changing their topologies. We test the algorithm on both theoretical and practical data sets.10.1111/1467-8659.0056319-32