A new efficient algorithm for fitting rectangular boxes and cubes in 3D

In this paper, we introduce a new approach for fitting rectangular boxes and cubes given as a set of voxels in a three-dimensional voxel space. This extends our work on fitting rectangles and squares described in H. Suesse et al, (2001) to three dimensions. It is also based on our normalization method published in K. Voss et al (1997) and (1999). Here we also encounter the problem of normalizing the rotation as it is necessary for rectangles and squares, but here we have two degenerate cases to handle. The first one are cubes, the second one are rectangular boxes with two edges of equal length and the length of the third edge different from them. Our method delivers good fitting results, even if the boxes are heavily distorted for example by cutting-off vertices.