Fused Sphere Guided Homotopy Method

Figure 7.1 Illustration of the principle of the Fused Spheres Guided Homotopy Method (FSGH), applied for the generation of dot representations of density scalable MIDCO surfaces for the water molecule. Three families of atomic spheres (thin lines) and their envelope surfaces (heavy lines) are shown in the upper part of the figure. In the lower part of the figure, the selected point sets on the innermost family of spheres are connected by interpolating lines to the exposed points (black dots) on the envelope surfaces of two enlarged families of spheres. Linear interpolation along the lines for two selected density values leads to two families of white dots, generating approximations of two MIDCO s (heavy lines in the lower figure).

The FSGH method (Fused Sphere Guided Homotopy method) [43]. This method has been designed for the construction of approximate, density scalable ("inflatable") isodensity contour surfaces and their dot representations (i.e., for continuous transformations between different isodensity surfaces of a given molecule). 

Density Scalable Atomic Sphere (DSAS) surfaces [255]. This technique generates radii for atomic spheres for any desired electron density at the surface. The method is used for inexpensive representations of MIDCO s of large molecules, in combination with the Fused Sphere Guided Homotopy method (FSGH) [43]. 

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