In fields ranging from science to engineering, reconstructing 3D solids from cross-sections is key—but how can we do it *optimally*? This paper offers a solution for constructing a surface over a set of cross-sectional contours by separately determining an optimal surface between each pair of consecutive contours. This surface, to be composed of triangular tiles, is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph. A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression, in terms of the number of contour points, for an upper bound on the number of operations required to execute the algorithm. An illustrated example which involves the construction of a minimum area surface describing a human head is included. The algorithm provides a general solution for surface reconstruction and a fast algorithm for finding minimum cost cycles.
Appearing in Communications of the ACM, this paper addresses a problem relevant to computer science, graphics, and scientific visualization. By presenting a general solution and a fast algorithm for surface reconstruction, the research aligns with the journal's focus on publishing innovative contributions in computer science.