SolidOfRevolutionTable

class SolidOfRevolutionTable : public feasst::VisitModelInner
Model solids of revolution using a tabular potential that is precomputed and read from a file. An additional assumption is that the solids of revolution are not only rotationally symmetric about the axis of revolution, but also symmetric about the plane perpendicular to the axis of revolution that passes through the center of the particle. This class is implemented in a similar fashion as VisitModelInnerAniso, except that directors are used for orientations and not euler angles.
The relative position and orientation of two solids of revolution is given by given by three orientational degrees of freedom and one radial distance, r, between the centers of the two bodies.
The three orientational degrees of freedom (i.e., three angles) are defined by two unit vectors which represent the orientation of the axis of symmetry of each shape (e.g., i2 and j2), and the vector connecting the centers of the two shapes, (rij = ri  rj).
i <— rij — j >>>>> ij psi thetaj / on rij \ j2 j2i2 obtain dihedral i2 / thetai project 
This implementation computes cos(psi), where normally you would expect it to be psi. The tabular potential uses the cos(psi) convention(cos(pia)=cos(a)), and the nj=j2cross(uij) leads to cos(psi). Use the right hand rule to see that psi was computed with the negative. See: http://math.stackexchange.com/questions/47059/howdoicalculateadihedralanglegivencartesiancoordinates
r = rij uij = rij/r cos thetai = i2 .dot. (uij) cos thetaj = j2 .dot. ( uij) ni = i2 .cross. uij nj = j2 .cross. (uij) cos psi = ni .dot. nj
Bounds: theta(i,j) [0, pi/2] > symmetry, if theta > pi/2, theta=pitheta psi [0, pi] > symmetry, if psi > pi, psi = 2pipsi costheta(i,j) ~ [0, 1] cospsi ~ [1, 1]
The radial distance, r, is transformed into z which varies from z=0 at the hard contact distance, r_h, to z=1 at the cutoff, r_c. A stretching parameter, \(\gamma\), increases the resolution at shorter distances when negative.
\(z=[(r^\gamma  r_h^\gamma)/(r_c^\gamma  r_h^\gamma)]\).
The format of the tabular potential stored in a file is as follows.
The first line should be ‘site_types’ followed by the number of site types and then the identity of each of those site types in order of the tables given below. (e.g., “site_types n i” where n is the number of site types and each following number is the type of each anisotropic site.)
There is a table for each unique pair of site types. For example, if the first line is as follows: “site_types 2 1 7” then the first table will be for interactions of site type 1 with site type 1 (i.e., 11), the second table will be for 17 interactions, and the third table will be for 77 interactions.
For each pair of site types, i <= j, a table is given by the following lines.
“num_orientations_per_half_pi [value]” is used to determine the resolution of all 5 orientational degrees of freedom.
”gamma [value]” is the expononent for the definition of z. But, if gamma==0, then use a square well potential.
”delta [value]” is the distance between the hard particle inner cutoff and the outer cutoff when the potential goes to zero (e.g., delta = r_c  r_h).
”num_z [value]” is the number of energy values along the z parameter.
”smoothing_distance [value]” is the distance to linearly interpolate the energy to zero. Specifically, r_c  smoothing_distance is the z=1 value. If smoothing_distance is <= 0, then it is not used at all.
The remaining lines are for each unique set of the three angles separated by spaces. The outer loop is cos(theta1), with range [0, pi/2]. The next loop is cos(theta2) in [0, 1], then cos(psi) in [1, 0]. The number of lines should be (2k+1)(k+1)^2, where k=num_orientations_per_half_pi. Each line then reports the contact distance, r_h, followed by num_z values of the potential energy uniformly in the z range of [0, 1].
Coordinate axes and references:
z  __ x the reference is for the axis of rotation to point along the zaxis / which is how one defines the rotation matrices for the theta_i/j and psi y
In order to obtain the orientation given thetai, thetaj, psi and d: place two particles on the origin with axes of rotation along the zaxis rotate the first particle by an angle phi = pi/2  thetai about the y axis (toward the xaxis) rotate the second particle by an angle phi = pi/2 thetaj about the y axis (toward the negative xaxis) rotate the second particle by an angle psi about the xaxis translate the second particle by a distance, d along the xaxis
If using superballs, only the zexponent, a3 can be different from a1=a2. In this case, the reference position has the axis of revolution along the zaxis. Therefore, when thetai = PI/2, the particle is in the ‘reference’ orientation.
Public Functions
Arguments
table_file: table file with format described above.
ignore_energy: do not read the energy table (default: false).