crystallography and NMR. For example, advanced X-ray crystallography technology is able to offer decisive structural information at Armstrong and sub-Armstrong resolutions, while an important advantage of NMR experiments is that they are able to provide biomolecular structural information under physiological conditions. The continuously effort in the past few decades has made X-ray crystallography and NMR technologically relatively well developed, except for their use in special circumstances, such as the study of membrane proteins. However, theses approaches are not directly suitable for proteasomes, subcellular structures, organelles, cells and tissues, whose study has become increasingly popular in structural biology. Currently, a unique experimental tool for imaging subcellular structures, organelles, multiprotein complexes and even cells and tissues is cryo-EM [@Volkmann:2010].

The rapid advances of experimental technology in the past few decades have led to the accumulation of vast amount of three-dimensional (3D) biomolecular structural data. The [Protein Data Bank (PDB)](http://www.rcsb.org/pdb/home/home.do) has collected more than one hundred twenty thousands of 3D biomolecular structures. Biomolecular geometric information holds the key to our understanding of biomolecular structure, function, and dynamics. It has wide spread applications in virtual screening, computer-aid drug design, binding pocket descriptor, quantitative structure activity relationship, protein design, RNA design, molecular machine design, etc. 