/// Returns a rotation matrix whose third column is equal to the given vector.
Matrix3D Matrix3D::rotationMatrixFromZAxisForDXF(const Real3D& dir)
{
// Normalize the target direction
// If it is degenerate, returns the identity matrix
Real3D target = dir;
REAL len = target.mod();
if (len == 0) return Matrix3D(1);
target /= len;
if (!target.isfinite()) return Matrix3D(1);
// Choice of xAxis: see AutoCAD documentation.
Real3D v;
if( fabs(target[0])*64 < 1 && fabs(target[1])*64 < 1 )
v = Real3D(0,1,0) ^ target;
else
v = Real3D(0,0,1) ^ target;
v = v.vers();
Real3D w = (target^v).vers();
Matrix3D rot;
rot.setCols(v, w, target);
// Debug Check
assert(fabs(rot.det()-1) < Math::TOLERANCE);
return rot;
}
// Reflects a point w.r.t. a plane through "origin",
// whose normal vector is "normal".
Real3D Real3D::reflect(const Real3D& origin, const Real3D& normal) const
{
Real3D v(*this);
REAL sqrmod = normal.sqrmod();
REAL scal_prod;
// If the normal vector is null returns this with no reflection at all.
if(sqrmod >= 1E-20) {
v -= origin;
if(fabs(1. - sqrmod) < Math::TOLERANCE) {
scal_prod = normal*v;
v -= 2*scal_prod*normal;
} else {
// If the normal vector is not normalized computes the normalized vector.
Real3D actualNormal(normal.vers());
scal_prod = actualNormal*v;
v -= 2*scal_prod*actualNormal;
}
}
return v;
}
