/// <summary> Takes the given Z Matrix coordinates and converts them to cartesian coordinates.
/// The first Atom end up in the origin, the second on on the x axis, and the third
/// one in the XY plane. The rest is added by applying the Zmatrix distances, angles
/// and dihedrals.
///
/// </summary>
/// <param name="distances"> Array of distance variables of the Z matrix
/// </param>
/// <param name="angles"> Array of angle variables of the Z matrix
/// </param>
/// <param name="dihedrals"> Array of distance variables of the Z matrix
/// </param>
/// <param name="first_atoms"> Array of atom ids of the first involed atom in distance, angle and dihedral
/// </param>
/// <param name="second_atoms"> Array of atom ids of the second involed atom in angle and dihedral
/// </param>
/// <param name="third_atoms"> Array of atom ids of the third involed atom in dihedral
///
/// </param>
/// <cdk.dictref> blue-obelisk:zmatrixCoordinatesIntoCartesianCoordinates </cdk.dictref>
public static Point3d[] zmatrixToCartesian(double[] distances, int[] first_atoms, double[] angles, int[] second_atoms, double[] dihedrals, int[] third_atoms)
{
Point3d[] cartesianCoords = new Point3d[distances.Length];
for (int index = 0; index < distances.Length; index++)
{
if (index == 0)
{
cartesianCoords[index] = new Point3d(0d, 0d, 0d);
}
else if (index == 1)
{
cartesianCoords[index] = new Point3d(distances[1], 0d, 0d);
}
else if (index == 2)
{
cartesianCoords[index] = new Point3d((-System.Math.Cos((angles[2] / 180) * System.Math.PI)) * distances[2] + distances[1], System.Math.Sin((angles[2] / 180) * System.Math.PI) * distances[2], 0d);
}
else
{
Vector3d cd = new Vector3d();
cd.sub(cartesianCoords[third_atoms[index]], cartesianCoords[second_atoms[index]]);
Vector3d bc = new Vector3d();
bc.sub(cartesianCoords[second_atoms[index]], cartesianCoords[first_atoms[index]]);
Vector3d n1 = new Vector3d();
n1.cross(cd, bc);
n1.normalize();
Vector3d n2 = rotate(n1, bc, dihedrals[index]);
n2.normalize();
Vector3d ba = rotate(bc, n2, -angles[index]);
ba.normalize();
Vector3d ban = new Vector3d(ba);
ban.scale(distances[index]);
Point3d result = new Point3d();
result.add(cartesianCoords[first_atoms[index]], ba);
cartesianCoords[index] = result;
}
}
return cartesianCoords;
}
private static double getAngle(IAtom atom1, IAtom atom2, IAtom atom3)
{
Vector3d centerAtom = new Vector3d();
centerAtom.x = atom1.X3d;
centerAtom.y = atom1.Y3d;
centerAtom.z = atom1.Z3d;
Vector3d firstAtom = new Vector3d();
Vector3d secondAtom = new Vector3d();
firstAtom.x = atom2.X3d;
firstAtom.y = atom2.Y3d;
firstAtom.z = atom2.Z3d;
secondAtom.x = atom3.X3d;
secondAtom.y = atom3.Y3d;
secondAtom.z = atom3.Z3d;
firstAtom.sub(centerAtom);
secondAtom.sub(centerAtom);
return firstAtom.angle(secondAtom);
}