Modifications of Classical Surface Reconstruction Algorithms for Visualization of a Function Defined on a Rectangular Grid

In the paper, modifications of visualization algorithms for real-valued functions of two and three arguments given on a rectangular or parallelepipedal grid are considered. In the case of two arguments, the graph of the function is a surface embedded into the three-dimensional space. The majority of scientific visualization systems offer visualization procedures for such surfaces, but they construct them under the assumption that the functions are continuous. In the paper, for the case of a discontinuous function, a modification of this algorithm is proposed. In addition, the algorithm removes “plateaus” that occur after cutting the function at some level (in order to remove too large values). Visualization of a function of three arguments implies showing its level sets, that is, regions of the space of arguments where the magnitudes of the function do not exceed a certain value. In the case of a grid function, such sets are “voxel” sets, that is, they are composed of grid cells. With that, some smoothing of the surface of such sets is required, which is carried out by the Marching Cubes algorithm and algorithms of the Laplacian family. A modification of the Marching Cubes algorithm is proposed, which preserves the symmetry of the set surface with respect to the coordinate planes, axes, or some point, if the rendered set has such a symmetry.