Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
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X-ray crystallography produces molecular models (spheres for every atom of the molecule) from electron density maps (distribution of electrons over 3d space). These maps seldom have enough resolution to identify hydrogens, which are added later using simple geometric rules. For example, the structure refinement toolbox PHENIX places hydrogen at a distance of 0.82 AA from the bonded oxygen nucleus, while the structure validation toolbox Molprobity places this hydrogen at a distance of 1 AA from the bonded oxygen. To harmonize these numbers we wanted to use bond lengths that were consistent with the electron density maps based on quantum calculations and hence at a higher resolution than experimentally determined maps. In this video we describe geometric tools based on curvature and contour trees for identifying spherical patches on the iso-surfaces of electron density. These tools allow us to determine lengths of hydrogen covalent bonds from high resolution electron density maps.