/// <summary>
/// Checks these 6 atoms to see if they form a trigonal-bipyramidal shape.
/// </summary>
/// <param name="atomA">one of the axial atoms</param>
/// <param name="atomB">the central atom</param>
/// <param name="atomC">one of the equatorial atoms</param>
/// <param name="atomD">one of the equatorial atoms</param>
/// <param name="atomE">one of the equatorial atoms</param>
/// <param name="atomF">the other axial atom</param>
/// <returns>true if the geometry is trigonal-bipyramidal</returns>
public static bool IsTrigonalBipyramidal(IAtom atomA, IAtom atomB, IAtom atomC, IAtom atomD, IAtom atomE, IAtom atomF)
{
Vector3 pointA = atomA.Point3D.Value;
Vector3 pointB = atomB.Point3D.Value;
Vector3 pointC = atomC.Point3D.Value;
Vector3 pointD = atomD.Point3D.Value;
Vector3 pointE = atomE.Point3D.Value;
Vector3 pointF = atomF.Point3D.Value;
bool isColinearABF = StereoTool.IsColinear(pointA, pointB, pointF);
if (isColinearABF)
{
// the normal to the equatorial plane
Vector3 normal = StereoTool.GetNormal(pointC, pointD, pointE);
// get the side of the plane that axis point A is
TetrahedralSign handednessCDEA = StereoTool.GetHandedness(normal, pointC, pointF);
// get the side of the plane that axis point F is
TetrahedralSign handednessCDEF = StereoTool.GetHandedness(normal, pointC, pointA);
// in other words, the two axial points (A,F) are on opposite sides
// of the equatorial plane CDE
return(handednessCDEA != handednessCDEF);
}
else
{
return(false);
}
}
private static TetrahedralSign GetHandedness(Vector3 pointA, Vector3 pointB, Vector3 pointC, Vector3 pointD)
{
// assumes anti-clockwise for a right-handed system
Vector3 normal = StereoTool.GetNormal(pointA, pointB, pointC);
// it doesn't matter which of points {A,B,C} is used
return(StereoTool.GetHandedness(normal, pointA, pointD));
}
/// <summary>
/// Gets the tetrahedral handedness of four atoms - three of which form the
/// 'base' of the tetrahedron, and the other the apex. Note that it assumes
/// a right-handed coordinate system, and that the points {A,B,C} are in
/// a counter-clockwise order in the plane they share.
/// </summary>
/// <param name="baseAtomA">the first atom in the base of the tetrahedron</param>
/// <param name="baseAtomB">the second atom in the base of the tetrahedron</param>
/// <param name="baseAtomC">the third atom in the base of the tetrahedron</param>
/// <param name="apexAtom">the atom in the point of the tetrahedron</param>
/// <returns>the sign of the tetrahedron</returns>
public static TetrahedralSign GetHandedness(IAtom baseAtomA, IAtom baseAtomB, IAtom baseAtomC, IAtom apexAtom)
{
Vector3 pointA = baseAtomA.Point3D.Value;
Vector3 pointB = baseAtomB.Point3D.Value;
Vector3 pointC = baseAtomC.Point3D.Value;
Vector3 pointD = apexAtom.Point3D.Value;
return(StereoTool.GetHandedness(pointA, pointB, pointC, pointD));
}
public void TetrahedralPlusAtomsAboveXYClockwiseTest()
{
// above the XY plane
IAtom baseA = new Atom("C", new Vector3(0, 0, 1));
IAtom baseB = new Atom("C", new Vector3(1, 0, 1));
IAtom baseC = new Atom("C", new Vector3(1, 1, 1));
IAtom positiveApex = new Atom("C", new Vector3(0.5, 0.5, 2));
TetrahedralSign tetSign = StereoTool.GetHandedness(baseC, baseB, baseA, positiveApex);
Assert.AreEqual(TetrahedralSign.Minus, tetSign);
}
public void TetrahedralMinusAtomsBelowXYTest()
{
// below the XY plane
IAtom baseA = new Atom("C", new Vector3(0, 0, -1));
IAtom baseB = new Atom("C", new Vector3(1, 0, -1));
IAtom baseC = new Atom("C", new Vector3(1, 1, -1));
IAtom negativeApex = new Atom("C", new Vector3(0.5, 0.5, -2));
TetrahedralSign tetSign = StereoTool.GetHandedness(baseA, baseB, baseC, negativeApex);
Assert.AreEqual(TetrahedralSign.Minus, tetSign);
}
/// <summary>
/// Take four atoms, and return <see cref="TetrahedralStereo.Clockwise"/> or <see cref="TetrahedralStereo.AntiClockwise"/>.
/// The first atom is the one pointing towards the observer.
/// </summary>
/// <param name="atom1">the atom pointing towards the observer</param>
/// <param name="atom2">the second atom (points away)</param>
/// <param name="atom3">the third atom (points away)</param>
/// <param name="atom4">the fourth atom (points away)</param>
/// <returns>clockwise or anticlockwise</returns>
public static TetrahedralStereo GetStereo(IAtom atom1, IAtom atom2, IAtom atom3, IAtom atom4)
{
// a normal is calculated for the base atoms (2, 3, 4) and compared to
// the first atom. PLUS indicates ACW.
TetrahedralSign sign = StereoTool.GetHandedness(atom2, atom3, atom4, atom1);
if (sign == TetrahedralSign.Plus)
{
return(TetrahedralStereo.AntiClockwise);
}
else
{
return(TetrahedralStereo.Clockwise);
}
}