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shape_constants.hpp
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shape_constants.hpp
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/* $Id: shape_constants.hpp 685605 2024-07-26 12:29:33Z thiessen $
* ===========================================================================
*
* PUBLIC DOMAIN NOTICE
* National Center for Biotechnology Information
*
* This software/database is a "United States Government Work" under the
* terms of the United States Copyright Act. It was written as part of
* the author's official duties as a United States Government employee and
* thus cannot be copyrighted. This software/database is freely available
* to the public for use. The National Library of Medicine and the U.S.
* Government have not placed any restriction on its use or reproduction.
*
* Although all reasonable efforts have been taken to ensure the accuracy
* and reliability of the software and data, the NLM and the U.S.
* Government do not and cannot warrant the performance or results that
* may be obtained by using this software or data. The NLM and the U.S.
* Government disclaim all warranties, express or implied, including
* warranties of performance, merchantability or fitness for any particular
* purpose.
*
* Please cite the author in any work or product based on this material.
*
* ===========================================================================
*
* Authors: Evan Bolton, Leonid Zaslavsky, Paul Thiessen
*
* ===========================================================================
*/
#ifndef ALIGN3D_SHAPE_CONSTANTS__HPP
#define ALIGN3D_SHAPE_CONSTANTS__HPP
namespace Align3D {
// Grant-Pickup Parameters
// Based on Sunghwan Kim's research, a cut-off of 3.6A gives 0.0087,
// @ 3.8A gives 0.00095, @ 4.0A gives 0.00051, @ 4.4A gives 0.00013
// ST AB overlap contribution between two carbon atoms...
// this suggests that a cutoff of 4.5A may be overkill and may be reduced
// to a smaller value
const double default_dCutOff = 4.5;
extern double dCutOff;
extern double d2CutOff;
// Shape method parameters from Grant, Gallardo and Pickup paper
// A Fast Method of Molecular Shape Comparison:
// A Simple Application of A Gaussian Description of Molecular Shape
// const double p = 2.0 * sqrt( 2.0 ); // p = 2.828427..
const double pi = 3.14159265358979323846;
const double _p_ = 2.7;
const double _p2_ = _p_ * _p_;
const double lambda = ( 4.0 * pi ) / ( 3.0 * _p_ ); //const double lambda = 1.5514037795505151794877251275454; // 4*PI/(3*p);
const double kappa = pi / pow( lambda, ( 2.0 / 3.0 ) ); //const double kappa = 2.344228685405120246556971866528f; // PI / ( (lambda)^(2/3) );
// Grid matrix rotation extent titrated to maximize neighbor count using validation suite
// const float rot1 = 0.980198f, rot2 = 0.19802f; const double qrot = 0.100; // 0.10 3163642
// const float rot1 = 0.976089f, rot2 = 0.21737f; // 0.11 3171031
// const float rot1 = 0.95599f, rot2 = 0.293399f; // 0.15 3193121
// const float rot1 = 0.94057f, rot2 = 0.3396f; // 0.175 3200725
// const float rot1 = 0.923077f, rot2 = 0.384615f; // 0.200 3205001
// const float rot1 = 0.915525f, rot2 = 0.402260f; // 0.210
const float rot1 = 0.911634686611f, rot2 = 0.411001457621f; // 0.215
const double drot1 = 0.911634686611, drot2 = 0.411001457621; // 0.215
// const float rot1 = 0.907669f, rot2 = 0.419687f; // 0.220
// const float rot1 = 0.903629f, rot2 = 0.428316f; // 0.225 3205614
// const float rot1 = 0.899516f, rot2 = 0.436889f; // 0.230
// const float rot1 = 0.895330f, rot2 = 0.445403f; // 0.235
const float fqrot1 = 0.977659114061f, fqrot = 0.210196709523f; // 0.215 (un-normalized)
const float pqmatrix_type[4][7][12] = {
// Rot/Trans matrices for 1st four starting points with +/- rotation permutations
// correspond to the three zeroed quaternions with +/-0.215 change (later normalized)
{
{ 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 0 X, Y, Z
{ fqrot1, fqrot, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ fqrot1, -fqrot, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ fqrot1, 0.0, fqrot, 0.0, 0.0, 0.0, 0.0 },
{ fqrot1, 0.0, -fqrot, 0.0, 0.0, 0.0, 0.0 },
{ fqrot1, 0.0, 0.0, fqrot, 0.0, 0.0, 0.0 },
{ fqrot1, 0.0, 0.0, -fqrot, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 1 X, -Y, -Z
{ fqrot, fqrot1, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ fqrot, -fqrot1, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, fqrot1, fqrot, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, fqrot1, -fqrot, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, fqrot1, 0.0, fqrot, 0.0, 0.0, 0.0 },
{ 0.0, fqrot1, 0.0, -fqrot, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 2 -X, -Y, Z
{ fqrot, 0.0, 0.0, fqrot1, 0.0, 0.0, 0.0 },
{ fqrot, 0.0, 0.0, -fqrot1, 0.0, 0.0, 0.0 },
{ 0.0, fqrot, 0.0, fqrot1, 0.0, 0.0, 0.0 },
{ 0.0, -fqrot, 0.0, fqrot1, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, fqrot, fqrot1, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, -fqrot, fqrot1, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, // 3 -X, Y, -Z
{ fqrot, 0.0, fqrot1, 0.0, 0.0, 0.0, 0.0 },
{ fqrot, 0.0, -fqrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, fqrot, fqrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, -fqrot, fqrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, fqrot1, fqrot, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, fqrot1, -fqrot, 0.0, 0.0, 0.0 }
}
};
// Quaternion form of the "matrix_type" matrices
const float qmvalf = 0.707106781187f;
const float qmatrix_type[16][7] = {
{ 1.0, 0.0, 0.0, 0.0, 0, 0, 0 }, // 0 X, Y, Z
{ 0.0, 1.0, 0.0, 0.0, 0, 0, 0 }, // 1 X, -Y, -Z
{ 0.0, 0.0, 0.0, 1.0, 0, 0, 0 }, // 2 -X, -Y, Z
{ 0.0, 0.0, 1.0, 0.0, 0, 0, 0 }, // 3 -X, Y, -Z
{ qmvalf, -qmvalf, 0.0, 0.0, 0, 0, 0 }, // 4 X, Z, -Y
{ qmvalf, qmvalf, 0.0, 0.0, 0, 0, 0 }, // 5 X, -Z, Y
{ 0.0, 0.0, -qmvalf, qmvalf, 0, 0, 0 }, // 6 -X, -Z, -Y
{ 0.0, 0.0, qmvalf, qmvalf, 0, 0, 0 }, // 7 -X, Z, Y
{ qmvalf, 0.0, 0.0, -qmvalf, 0, 0, 0 }, // 8 Y, -X, Z
{ 0.0, qmvalf, qmvalf, 0.0, 0, 0, 0 }, // 9 Y, X, -Z
{ qmvalf, 0.0, 0.0, qmvalf, 0, 0, 0 }, // 10 -Y, X, Z
{ 0.0, -qmvalf, qmvalf, 0.0, 0, 0, 0 }, // 11 -Y, -X, -Z
{ qmvalf, 0.0, qmvalf, 0.0, 0, 0, 0 }, // 12 Z, Y, -X
{ 0.0, qmvalf, 0.0, qmvalf, 0, 0, 0 }, // 13 Z, -Y, X
{ 0.0, -qmvalf, 0.0, qmvalf, 0, 0, 0 }, // 14 -Z, -Y, -X
{ qmvalf, 0.0, -qmvalf, 0.0, 0, 0, 0 } // 15 -Z, Y, X
};
const double qmval = 0.707106781187;
const double qmatrix_typed[16][7] = {
{ 1.0, 0.0, 0.0, 0.0, 0, 0, 0 }, // 0 X, Y, Z
{ 0.0, 1.0, 0.0, 0.0, 0, 0, 0 }, // 1 X, -Y, -Z
{ 0.0, 0.0, 0.0, 1.0, 0, 0, 0 }, // 2 -X, -Y, Z
{ 0.0, 0.0, 1.0, 0.0, 0, 0, 0 }, // 3 -X, Y, -Z
{ qmval, -qmval, 0.0, 0.0, 0, 0, 0 }, // 4 X, Z, -Y
{ qmval, qmval, 0.0, 0.0, 0, 0, 0 }, // 5 X, -Z, Y
{ 0.0, 0.0, -qmval, qmval, 0, 0, 0 }, // 6 -X, -Z, -Y
{ 0.0, 0.0, qmval, qmval, 0, 0, 0 }, // 7 -X, Z, Y
{ qmval, 0.0, 0.0, -qmval, 0, 0, 0 }, // 8 Y, -X, Z
{ 0.0, qmval, qmval, 0.0, 0, 0, 0 }, // 9 Y, X, -Z
{ qmval, 0.0, 0.0, qmval, 0, 0, 0 }, // 10 -Y, X, Z
{ 0.0, -qmval, qmval, 0.0, 0, 0, 0 }, // 11 -Y, -X, -Z
{ qmval, 0.0, qmval, 0.0, 0, 0, 0 }, // 12 Z, Y, -X
{ 0.0, qmval, 0.0, qmval, 0, 0, 0 }, // 13 Z, -Y, X
{ 0.0, -qmval, 0.0, qmval, 0, 0, 0 }, // 14 -Z, -Y, -X
{ qmval, 0.0, -qmval, 0.0, 0, 0, 0 } // 15 -Z, Y, X
};
// Grid symmetry transformations for starting points
const float matrix_type[16][12] = {
// Rxx Rxy Rxz Ryx Ryy Ryz Rzx Rzy Rzz Tx Ty Tz
{ 1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f }, // 0 X, Y, Z
{ 1.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f }, // 1 X, -Y, -Z
{-1.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f }, // 2 -X, -Y, Z
{-1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f }, // 3 -X, Y, -Z
{ 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 4 X, Z, -Y
{ 1.0f, 0.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 5 X, -Z, Y
{-1.0f, 0.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 6 -X, -Z, -Y
{-1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 7 -X, Z, Y
{ 0.0f, 1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f }, // 8 Y, -X, Z
{ 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f }, // 9 Y, X, -Z
{ 0.0f,-1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f }, // 10 -Y, X, Z
{ 0.0f,-1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f }, // 11 -Y, -X, -Z
{ 0.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 12 Z, Y, -X
{ 0.0f, 0.0f, 1.0f, 0.0f,-1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 13 Z, -Y, X
{ 0.0f, 0.0f,-1.0f, 0.0f,-1.0f, 0.0f,-1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f }, // 14 -Z, -Y, -X
{ 0.0f, 0.0f,-1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } // 15 -Z, Y, X
};
const double matrix_typed[16][12] = {
// Rxx Rxy Rxz Ryx Ryy Ryz Rzx Rzy Rzz Tx Ty Tz
{ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 0 X, Y, Z
{ 1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0 }, // 1 X, -Y, -Z
{-1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 2 -X, -Y, Z
{-1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0 }, // 3 -X, Y, -Z
{ 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0 }, // 4 X, Z, -Y
{ 1.0, 0.0, 0.0, 0.0, 0.0,-1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, // 5 X, -Z, Y
{-1.0, 0.0, 0.0, 0.0, 0.0,-1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0 }, // 6 -X, -Z, -Y
{-1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, // 7 -X, Z, Y
{ 0.0, 1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 8 Y, -X, Z
{ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0 }, // 9 Y, X, -Z
{ 0.0,-1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 10 -Y, X, Z
{ 0.0,-1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0 }, // 11 -Y, -X, -Z
{ 0.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 12 Z, Y, -X
{ 0.0, 0.0, 1.0, 0.0,-1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 13 Z, -Y, X
{ 0.0, 0.0,-1.0, 0.0,-1.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 14 -Z, -Y, -X
{ 0.0, 0.0,-1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 } // 15 -Z, Y, X
};
const double qrot1 = 0.977659114061, qrot = 0.210196709523; // 0.215 (un-normalized)
const double pqmatrix_typed[4][7][12] = {
// Rot/Trans matrices for 1st four starting points with +/- rotation permutations
// correspond to the three zeroed quaternions with +/-0.215 change (later normalized)
{
{ 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 0 X, Y, Z
{ qrot1, qrot, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ qrot1, -qrot, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ qrot1, 0.0, qrot, 0.0, 0.0, 0.0, 0.0 },
{ qrot1, 0.0, -qrot, 0.0, 0.0, 0.0, 0.0 },
{ qrot1, 0.0, 0.0, qrot, 0.0, 0.0, 0.0 },
{ qrot1, 0.0, 0.0, -qrot, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, // 1 X, -Y, -Z
{ qrot, qrot1, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ qrot, -qrot1, 0.0, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, qrot1, qrot, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, qrot1, -qrot, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, qrot1, 0.0, qrot, 0.0, 0.0, 0.0 },
{ 0.0, qrot1, 0.0, -qrot, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }, // 2 -X, -Y, Z
{ qrot, 0.0, 0.0, qrot1, 0.0, 0.0, 0.0 },
{ qrot, 0.0, 0.0, -qrot1, 0.0, 0.0, 0.0 },
{ 0.0, qrot, 0.0, qrot1, 0.0, 0.0, 0.0 },
{ 0.0, -qrot, 0.0, qrot1, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, qrot, qrot1, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, -qrot, qrot1, 0.0, 0.0, 0.0 }
}, {
{ 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 }, // 3 -X, Y, -Z
{ qrot, 0.0, qrot1, 0.0, 0.0, 0.0, 0.0 },
{ qrot, 0.0, -qrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, qrot, qrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, -qrot, qrot1, 0.0, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, qrot1, qrot, 0.0, 0.0, 0.0 },
{ 0.0, 0.0, qrot1, -qrot, 0.0, 0.0, 0.0 }
}
};
const double pmatrix_typed[4][7][12] = {
// Rot/Trans matrices for 1st four starting points with +/- rotation permutations
// correspond to the three zeroed quaternions with +/-0.225 change (later normalized)
{
{ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 }, // 0 X, Y, Z
{ 1.0, 0.0, 0.0, 0.0, drot1,-drot2, 0.0, drot2, drot1, 0.0,0.0,0.0 }, // 1, -.225, 0, 0 {Y-Z Z+Y}
{ 1.0, 0.0, 0.0, 0.0, drot1, drot2, 0.0,-drot2, drot1, 0.0,0.0,0.0 }, // 1, +.225, 0, 0 {Y+Z Z-Y}
{ drot1, 0.0, drot2, 0.0, 1.0, 0.0,-drot2, 0.0, drot1, 0.0,0.0,0.0 }, // 1, 0, -.225, 0 {X+Z Z-X}
{ drot1, 0.0,-drot2, 0.0, 1.0, 0.0, drot2, 0.0, drot1, 0.0,0.0,0.0 }, // 1, 0, +.225, 0 {X-Z Z+X}
{ drot1,-drot2, 0.0, drot2, drot1, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 }, // 1, 0, 0, -.225 {X-Y Y+X}
{ drot1, drot2, 0.0,-drot2, drot1, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 } // 1, 0, 0, +.225 {X+Y Y-X}
}, {
{ 1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 }, // 1 X, -Y, -Z
{ 1.0, 0.0, 0.0, 0.0,-drot1,-drot2, 0.0, drot2,-drot1, 0.0,0.0,0.0 },
{ 1.0, 0.0, 0.0, 0.0,-drot1, drot2, 0.0,-drot2,-drot1, 0.0,0.0,0.0 },
{ drot1, drot2, 0.0, drot2,-drot1, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 },
{ drot1,-drot2, 0.0,-drot2,-drot1, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 },
{ drot1, 0.0, drot2, 0.0,-1.0, 0.0, drot2, 0.0,-drot1, 0.0,0.0,0.0 },
{ drot1, 0.0,-drot2, 0.0,-1.0, 0.0,-drot2, 0.0,-drot1, 0.0,0.0,0.0 }
}, {
{-1.0, 0.0, 0.0, 0.0,-1.0, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 }, // 2 -X, -Y, Z
{-drot1,-drot2, 0.0, drot2,-drot1, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 },
{-drot1, drot2, 0.0,-drot2,-drot1, 0.0, 0.0, 0.0, 1.0, 0.0,0.0,0.0 },
{-drot1, 0.0, drot2, 0.0,-1.0, 0.0, drot2, 0.0, drot1, 0.0,0.0,0.0 },
{-drot1, 0.0,-drot2, 0.0,-1.0, 0.0,-drot2, 0.0, drot1, 0.0,0.0,0.0 },
{-1.0, 0.0, 0.0, 0.0,-drot1, drot2, 0.0, drot2, drot1, 0.0,0.0,0.0 },
{-1.0, 0.0, 0.0, 0.0,-drot1,-drot2, 0.0,-drot2, drot1, 0.0,0.0,0.0 }
}, {
{-1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 }, // 3 -X, Y, -Z
{-drot1, 0.0, drot2, 0.0, 1.0, 0.0,-drot2, 0.0,-drot1, 0.0,0.0,0.0 },
{-drot1, 0.0,-drot2, 0.0, 1.0, 0.0, drot2, 0.0,-drot1, 0.0,0.0,0.0 },
{-drot1, drot2, 0.0, drot2, drot1, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 },
{-drot1,-drot2, 0.0,-drot2, drot1, 0.0, 0.0, 0.0,-1.0, 0.0,0.0,0.0 },
{-1.0, 0.0, 0.0, 0.0, drot1, drot2, 0.0, drot2,-drot1, 0.0,0.0,0.0 },
{-1.0, 0.0, 0.0, 0.0, drot1,-drot2, 0.0,-drot2,-drot1, 0.0,0.0,0.0 }
}
};
}
#endif // ALIGN3D_SHAPE_CONSTANTS__HPP