/// Determines the Hermann-Mauguin symbol of the rotation-, rotoinversion- or
/// screw-axis.
std::string SymmetryElementRotationGenerator::determineSymbol(
const SymmetryOperation &operation) const {
const Kernel::IntMatrix &matrix = operation.matrix();
int trace = matrix.Trace();
int determinant = matrix.determinant();
if (trace == 0 && determinant == -1) {
return "-3";
}
std::string symbol;
if (determinant < 0) {
symbol += "-";
}
symbol += boost::lexical_cast<std::string>(operation.order());
int translation =
static_cast<int>(static_cast<double>(operation.order()) *
Kernel::V3D(determineTranslation(operation)).norm());
if (translation != 0) {
symbol += boost::lexical_cast<std::string>(translation);
}
return symbol;
}
/// Checks the trace and determinat of the matrix to determine if the matrix
/// belongs to a rotation.
bool SymmetryElementRotationGenerator::canProcess(
const SymmetryOperation &operation) const {
const Kernel::IntMatrix &matrix = operation.matrix();
int determinant = matrix.determinant();
int trace = matrix.Trace();
return (abs(trace) != 3) && !(trace == 1 && determinant == -1);
}
/// Generates an instance of SymmetryElementMirror with the corresponding
/// symbol, axis and translation vector.
SymmetryElement_sptr SymmetryElementMirrorGenerator::generateElement(
const SymmetryOperation &operation) const {
const Kernel::IntMatrix &matrix = operation.matrix();
V3R axis = determineAxis(matrix);
V3R translation = determineTranslation(operation);
std::string symbol = determineSymbol(operation);
return boost::make_shared<SymmetryElementMirror>(symbol, axis, translation);
}
/**
* Transforms the operation using the internally stored SymmetryOperation.
*
* This method returns the transformed symmetry operation, using the
* following relation:
*
* S' = O^-1 * S * O
*
* Where O is the internally stored operation.
*
* @param operation :: SymmetryOperation to transform.
* @return Transformed symmetry operation.
*/
SymmetryOperation GroupTransformation::transformOperation(
const SymmetryOperation &operation) const {
MatrixVectorPair<double, V3R> op =
m_inversePair *
MatrixVectorPair<double, V3R>(convertMatrix<double>(operation.matrix()),
operation.vector()) *
m_matrixVectorPair;
return SymmetryOperation(op.getMatrix(), op.getVector());
}
/// Determines the rotation sense according to the description in ITA 11.2.
SymmetryElementRotation::RotationSense
SymmetryElementRotationGenerator::determineRotationSense(
const SymmetryOperation &operation, const V3R &rotationAxis) const {
Kernel::V3D pointOnAxis1 = rotationAxis;
Kernel::V3D pointOnAxis2 = rotationAxis * 2;
Kernel::V3D pointOffAxis = rotationAxis + Kernel::V3D(2.1, 5.05, -1.1);
Kernel::V3D generatedPoint = operation * pointOffAxis;
Kernel::DblMatrix matrix(3, 3, false);
matrix.setColumn(0, pointOnAxis2 - pointOnAxis1);
matrix.setColumn(1, pointOffAxis - pointOnAxis1);
matrix.setColumn(2, generatedPoint - pointOnAxis1);
double determinant = matrix.determinant() * operation.matrix().determinant();
if (determinant < 0) {
return SymmetryElementRotation::Negative;
} else {
return SymmetryElementRotation::Positive;
}
}
/// Checks that the trace of the matrix is 1 and the determinant is -1.
bool SymmetryElementMirrorGenerator::canProcess(
const SymmetryOperation &operation) const {
const Kernel::IntMatrix &matrix = operation.matrix();
return matrix.Trace() == 1 && matrix.determinant() == -1;
}