"CONTOUR" Algorithm for Finding and Visualizing Flat Sections of 3D-Objects

One of the visualization problems implies finding boundaries and insides of flat sections of 3D objects specified analytically. This problem is to be solved to analyze the results and to control the geometry specification. On the one hand, the analytic definition of profiles for “not simple” 3D-objects in general case is actually unsolvable problem; on the other hand, it is necessary to apply virtual designing of 3D-objects in the field of numerical simulation. The paper presents the classical approach to finding and visualizing the flat sections – the algorithm of scanning beams in a proper plane. The limitations for this approach application are considered and its shortfalls are demonstrated with some examples. The numerical algorithm “CONTOUR” is proposed for finding the connected section contour of 3D-objects, which are specified analytically in the form of second-order planes and rotation connected by multiple-theoretic operations. “CONTOUR” algorithm suggests using topologically parallel scanning for generating the empirical values, and then, considering them in the process of isoline generation, the polygonal section contour is constructed. Essentially, CONTOUR algorithm is an algorithm of second order of accuracy and corresponds to the discretization error specified in advance.