Surface Generation

Spicoli can generate surfaces from the following other types of objects:

Molecules: Accessible vs Molecular

OESpicoli provides two functions for generating surfaces directly from molecules: OEMakeAccessibleSurface and OEMakeMolecularSurface. Both functions require the definition of a solvent molecule’s probe radius. The default solvent is water with a probe radius of 1.4 Ångströms.

The accessible surface is created by representing each atom as a hard sphere [Lee-Richards-1971]. The radius of each sphere is the radius of the atom plus the probe radius. Figures 1 and 2 demonstrate how the spheres are packed together to form the surface. In the figures, portions of the surface are colored based upon each atom’s contribution to the final accessible surface.

../_images/AccessibleSpheres.png ../_images/AccessibleSurfaces.png
Figure 1 Figure 2
Accessible Spheres Accessible Surface

The molecular surface is composed of atom centered spheres plus reentrants [Connolly-1983]. Each sphere’s radius is the atomic radii of the atom it is associated with. The defining characteristic of the molecular surface is the reentrant as shown in Figures 3 and 4. The reentrant models the portion of the molecule inaccessible to solvent. For this reason the volume enclosed by the molecular surface is sometimes referred to as the “solvent-excluded” volume.

../_images/MolecularSpheres.png ../_images/MolecularSurfaces.png
Figure 3 Figure 4
Molecular Spheres Molecular Surface

Note

The atoms associated with every surface vertex can be obtained by using the OESurface::GetAtoms and OESurface::GetAtomsElement methods. For an accessible surface this is simple to define, it is the atom closest to the vertex. However, for the molecular surface it is not so clear because of the re-entrants. Typically, it is the closest atom to the vertex, but that is not guaranteed. If this guarantee is required you should call the OESurfaceToMoleculeDistance function on the molecule and surface.

Grids

In Spicoli the construction of surfaces from a molecule proceeds through a grid intermediate. The space between grid points determines the resolution of the surface, i.e., how many triangles there are and the size of each triangle. Grids usually consist of equidistant points aligned along orthogonal axes, but this need not always be the case (for instance, electron density grids from crystallography).

Scalar values are placed at every grid point. Surfaces are constructed by tracing out a contour through the grid points. A contour is a separator of points based on whether they are greater than or less than a given value. The separator is a line in two dimensions and a surface in three dimensions. This is similar to how topographic maps use lines to convey elevation.

When dealing with surfaces the points on the grid with a value less than the chosen contour value are inside the surface and vice versa. OEMakeSurfaceFromGrid will generate a surface from a grid using a variation of the marching cubes algorithm.

Figure 5 is an example of a two dimensional molecular Gaussian grid for a simple molecule arbitrarily oriented in the grid. Figure 6 shows a contour at 1.0 of that same molecular Gaussian grid.

../_images/MolecularGaussianGrid.png ../_images/MolecularGaussianGridContour.png
Figure 5 Figure 6
Molecular Gaussian Grid Molecular Gaussian Grid Contour

Hint

Grids and surfaces are fairly interchangeable. A grid can be constructed from a surface using the OEMakeGridFromSurface function. Then that grid can be used to recreate the original surface by using the OEMakeSurfaceFromGrid function.

Surface Subsets

Surface subsetting is done through the use of Cliques. The triangle, not the vertex, is the most physically relevant intrinsic property of the surface. To maintain a constant surface area for the sum of all partitions Spicoli will not duplicate triangles across surface partitions. However, this does not restrict the duplication of vertices across partitions.

Therefore, the sum of the surface area of every partition will equal the surface area of the whole surface. The sum of OESurface::GetNumTriangles over every partition will equal the total number of triangles in the whole surface. However, the sum of OESurface::GetNumVertices over every partition will not equal the total number of vertices in the whole surface.

Geometric Primitives

Spicoli provides the following free functions to construct surfaces from primitive geometric shapes:

Boxes:OEMakeBoxSurface
Spheres:OEMakeSphericalSurface
Ellipsoids:OEMakeEllipsoidSurface