The accumulation of data on structural variation in cancer genomes provides an opportunity to better understand the mechanisms of genomic alterations and the forces of selection that act upon these alterations in cancer. Here we test evidence supporting the influence of two major forces, spatial chromosome structure and purifying (or negative) selection, on the landscape of somatic copy-number alterations (SCNAs) in cancer. Using a maximum likelihood approach, we compare SCNA maps and three-dimensional genome architecture as determined by genome-wide chromosome conformation capture (HiC) and described by the proposed fractal-globule model. This analysis suggests that the distribution of chromosomal alterations in cancer is spatially related to three-dimensional genomic architecture and that purifying selection, as well as positive selection, influences SCNAs during somatic evolution of cancer cells.