<title>Volumetric measurements from an isosurface algorithm</title>

Abstract

Scientific visualization methods have become the new standards for analyzing scientific datasets. However, while these visualization routines provide an excellent qualitative means for data analysis, many researchers still require quantitative information about their data. This paper describes how the marching cubes iso-surface algorithm can be modified to produce not only the qualitative information about the shape of a surface but also some quantitative information regarding the volume of space contained within or beneath that surface. The original marching cubes algorithm decomposes a dataset into cubes based on the grid structure provided. It then searches each cube, determining whether or not the surface intersects that particular cube. During this search, volume calculations can be performed for each cube or partial cube that is contained within or beneath the surface. The results of these calculations can then be summed to obtain a measurement for the volume of space that is within or beneath the surface. These additional tasks can easily be incorporated into the marching cubes algorithm, providing the researcher with a volumetric measurement to support the more qualitative visual information generally produced by an iso-surface algorithm.

3D Volume Calculation For the Marching Cubes Algorithm in Cartesian Coordinates

“…Most of the publications are concerning on how to deal with interface reconstructions, while only few papers exists to show how to calculate the partial volumes enclosed by the interface. Current volume calculation methods [5,4] often first tetrahedralize the partial volumes and then calculate the volume using the tetrahedra. This approach is difficult to write computer code to deal with all possible cases.…”