Mesh Generation and Flexible Shape Comparisons for Bio-Molecules

Abstract Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace- Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating different surface shapes but rely only on a small set of signature values. The shape descriptor is applied to shape comparison between molecules with deformed structures. The proposed methods are implemented into a program that can be used as a stand-alone software tool or as a plug-in to other existing molecular modeling tools. Particularly, the code is encapsulated into a software toolkit with a user-friendly graphical interface developed by the authors.