VMDBase<TYPE>
VMDBase<TYPE>::getNormalVector(const std::vector<VMDBase<TYPE>> &vectors) {
if (vectors.empty())
throw std::invalid_argument(
"VMDBase::getNormalVector: Must give at least 1 vector");
size_t nd = vectors[0].getNumDims();
if (nd < 2)
throw std::invalid_argument(
"VMDBase::getNormalVector: Must have at least 2 dimensions!");
if (vectors.size() != nd - 1)
throw std::invalid_argument("VMDBase::getNormalVector: Must have as many "
"N-1 vectors if there are N dimensions.");
for (size_t i = 0; i < vectors.size(); i++)
if (vectors[i].getNumDims() != nd)
throw std::invalid_argument("VMDBase::getNormalVector: Inconsistent "
"number of dimensions in the vectors given!");
// Start the normal vector
VMDBase normal = VMDBase(nd);
TYPE sign = +1.0;
for (size_t d = 0; d < nd; d++) {
// Make the sub-determinant with the columns of every other dimension.
Matrix<TYPE> mat(nd - 1, nd - 1);
for (size_t row = 0; row < vectors.size(); row++) {
VMDBase vec = vectors[row];
size_t col = 0;
for (size_t i = 0; i < nd; i++) {
if (i != d) // Skip the column of this dimension
{
mat[row][col] = vec[i];
col++;
}
}
} // Building the matrix rows
TYPE det = mat.determinant();
// The determinant of the sub-matrix = the normal at that dimension
normal[d] = sign * det;
// Sign flips each time
sign *= TYPE(-1.0);
} // each dimension of the normal vector
// Unity normal is better.
double length = normal.normalize();
if (length == 0)
throw std::runtime_error("VMDBase::getNormalVector: 0-length normal found. "
"Are your vectors collinear?");
return normal;
}
std::vector<VMDBase<TYPE>>
VMDBase<TYPE>::makeVectorsOrthogonal(std::vector<VMDBase> &vectors) {
if (vectors.size() != 2)
throw std::runtime_error(
"VMDBase::makeVectorsOrthogonal(): Need 2 input vectors.");
if (vectors[0].getNumDims() != 3 || vectors[1].getNumDims() != 3)
throw std::runtime_error(
"VMDBase::makeVectorsOrthogonal(): Need 3D input vectors.");
std::vector<V3D> in, out;
for (size_t i = 0; i < vectors.size(); i++)
in.push_back(V3D(vectors[i][0], vectors[i][1], vectors[i][2]));
out = V3D::makeVectorsOrthogonal(in);
std::vector<VMDBase> retVal;
for (size_t i = 0; i < out.size(); i++)
retVal.push_back(VMDBase(out[i]));
return retVal;
}