Ray Quaternion::applyRotation(const Ray& ray) const
{
Quaternion origin = (*this) * Quaternion(ray.m_Origin) * (conjugate());
Quaternion dir = (*this) * Quaternion(ray.m_Dir) * (conjugate());
return Ray(Vector(origin[1], origin[2], origin[3], ray.m_Origin[3]),
Vector(dir[1], dir[2], dir[3], ray.m_Dir[3]));
}
Vector Vector::operator-(const Vector vec) const
{
return Vector(
p[0]-vec[0],
p[1]-vec[1],
p[2]-vec[2],
p[3]-vec[3]);
}
Vector Vector::operator+(const Vector vec) const
{
return Vector(
p[0]+vec[0],
p[1]+vec[1],
p[2]+vec[2],
p[3]+vec[3]);
}
Vector Vector::cross(const Vector& vec) const
{
return Vector(
p[1]*vec[2] - p[2]*vec[1],
p[2]*vec[0] - p[0]*vec[2],
p[0]*vec[1] - p[1]*vec[0],
0.0f
);
}
Vector Vector::badVector()
{
return Vector(0.0f, 0.0f, 0.0f, 0.0f);
}
Vector Vector::operator-() const
{
return Vector(-p[0], -p[1], -p[2], p[3]);
}
Vector Vector::operator*(float scalar) const
{
return Vector(p[0]*scalar, p[1]*scalar, p[2]*scalar, p[3]);
}
Vector Quaternion::applyRotation(const Vector& vec) const
{
Quaternion result = (*this) * Quaternion(vec) * (conjugate());
return Vector(result[1], result[2], result[3], vec[3]);
}
bool LinearAlgebra::getCylinderFit( int n, double* x, double* y, double* z, Vector* p1, Vector* p2, double* radius )
{
// 1: Get the best fit Lxy on xy projection of points
// 2: Get the best fit Lxz on xz projection of points
// 3: Combine Lxy, Lxz to get the axis of cylinder
// 4. Define the centroid to be a point on the axis
// 5. Let radius of cyinder be average of radii of above two fits
// 6. Some how get the extent of the axis
double m1, m2, c1, c2, radius1, radius2;
// step 1:
if( !leastSquares( n, x, y, &m1, &c1, &radius1 ) ) return false;
// step 2:
if( !leastSquares( n, x, z, &m2, &c2, &radius2 ) ) return false;
// step 3:
// sin t = sqrt( m^2 / ( 1 + m^2 ) )
// cos t = sqrt( 1 / ( 1 + m^2 ) )
// The dcs of line 1 are norm( cos t1, sin t1, 0, 0 )
// The dcs of line 2 are norm( cos t2, 0, sin t2, 0 )
// The DCs are norm( cost1+cos t2, sint1, sin t2, 0 )
double sin_t1 = sqrt( m1*m1 / ( 1.0 + m1*m1) );
double cos_t1 = sqrt( 1 / ( 1.0 + m1*m1 ) );
if( m1 < 0 ) sin_t1 = -1* sin_t1;
double sin_t2 = sqrt( m2*m2 / ( 1.0 + m2*m2) );
double cos_t2 = sqrt( 1 / ( 1.0 + m2*m2 ) );
if( m2 < 0 ) sin_t2 = -1*sin_t2;
Vector DCs = Vector( (float)(cos_t1+cos_t2), (float)sin_t1, (float)sin_t2, 0 );
DCs.normalize();
// step 4:
double x0, y0, z0; // point on axis ( say centroid )
if( !mean( x, n, &x0 ) ) return false;
if( !mean( y, n, &y0 ) ) return false;
if( !mean( z, n, &z0 ) ) return false;
// step 5:
*radius = ( radius1 + radius2 ) * 0.5;
// step 6:
// minLen = maxLen = 0
// for each point P
// get norm ( p-p0 )
// compute cos t = dot prod ( axis dcs with prev result )
// len = len( ( p-p0 ) * cos t )
// update minLen, maxLen with len and sign of cos t
// end
// Endpoints are center + max Len, center - minLen
double minLen = 0, maxLen = 0;
int i;
for( i=0; i<n; i++ )
{
Vector diff( (float)(x[i] - x0), (float)(y[i] - y0), (float)(z[i] - z0), 0);
Vector normdiff = diff;
normdiff.normalize();
double cos_t = DCs.dot(normdiff);
Vector proj( diff*(float)cos_t );
double len = proj.norm();
if( cos_t < 0 ) len *= -1;
if( len < minLen ) minLen = len;
if( len > maxLen ) maxLen = len;
}
// Endpoints are center + max Len, center - minLen
p1->set((float)(x0+minLen*DCs[0]), (float)(y0+minLen*DCs[1]), (float)(z0+minLen*DCs[2]), 1);
p2->set((float)(x0+maxLen*DCs[0]), (float)(y0+maxLen*DCs[1]), (float)(z0+maxLen*DCs[2]), 1);
return true;
}
