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])); }
Quaternion Quaternion::rotation(float angle, float x, float y, float z) { float len = (float)sqrt(x*x+y*y+z*z); if(len!=0.0) { len = (float)(sin(angle/2.0f)/len); return Quaternion((float) cos(angle/2.0f), x*len, y*len, z*len); } else { return Quaternion(); } }
Quaternion Quaternion::rotation(float angle, const Vector& axis) { float len = (float)sqrt(axis[0]*axis[0]+axis[1]*axis[1]+axis[2]*axis[2]); if(len!=0.0) { len = (float)(sin(angle/2.0f)/len); return Quaternion((float) cos(angle/2.0f), axis[0]*len, axis[1]*len, axis[2]*len); } else { return Quaternion(); } }
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 ); }
Quaternion Quaternion::operator*(const Quaternion& quat) const { return Quaternion( p[0]*quat[0] - p[1]*quat[1] - p[2]*quat[2] - p[3]*quat[3], p[0]*quat[1] + p[1]*quat[0] + p[2]*quat[3] - p[3]*quat[2], p[0]*quat[2] - p[1]*quat[3] + p[2]*quat[0] + p[3]*quat[1], p[0]*quat[3] + p[1]*quat[2] - p[2]*quat[1] + p[3]*quat[0] ); }
Matrix Quaternion::buildMatrix() const { float w = p[0]; float x = p[1]; float y = p[2]; float z = p[3]; return Matrix( 1.0f-2.0f*y*y-2.0f*z*z, 2.0f*x*y-2.0f*w*z, 2.0f*x*z + 2.0f*w*y, 0.0f, 2.0f*x*y + 2.0f*w*z, 1.0f - 2.0f*x*x - 2.0f*z*z, 2.0f*y*z - 2.0f*w*x, 0.0f, 2.0f*x*z - 2.0f*w*y, 2.0f*y*z + 2.0f*w*x, 1.0f - 2.0f*x*x - 2.0f*y*y, 0.0f, 0.0f,0.0f,0.0f,1.0f ); }
Quaternion Quaternion::power(double scalar) { float Dest[4]; double theta; if(p[0]>=0.9999f) { theta = 0; } else if(p[0]<=-0.9999f) { theta = 2.0*3.1415926535897932384626433832795; } else { theta = acos(p[0]); } double u[3]; double scale = p[1]*p[1]+p[2]*p[2]+p[3]*p[3]; scale = sqrt(scale); if(p[1]==0.0f && p[2]==0.0f && p[3]==0.0f) { u[0] = 0.0; u[1] = 0.0; u[2] = 0.0; } else { u[0] = p[1]/scale; u[1] = p[2]/scale; u[2] = p[3]/scale; } Dest[0] = (float)cos(scalar*theta); Dest[1] = (float)(u[0] * sin(scalar*theta)); Dest[2] = (float)(u[1] * sin(scalar*theta)); Dest[3] = (float)(u[2] * sin(scalar*theta)); return Quaternion(Dest[0], Dest[1], Dest[2], Dest[3]); }
Vector Vector::operator*(float scalar) const { return Vector(p[0]*scalar, p[1]*scalar, p[2]*scalar, p[3]); }
Quaternion Quaternion::operator*(float scalar) const { return Quaternion(p[0]*scalar, p[1]*scalar, p[2]*scalar, p[3]*scalar); }
Vector Quaternion::applyRotation(const Vector& vec) const { Quaternion result = (*this) * Quaternion(vec) * (conjugate()); return Vector(result[1], result[2], result[3], vec[3]); }
Quaternion Quaternion::conjugate() const { return Quaternion(p[0], -p[1], -p[2], -p[3]); }
Quaternion Quaternion::operator/(float scalar) const { return Quaternion(p[0]/scalar, p[1]/scalar, p[2]/scalar, p[3]/scalar); }
Vector Vector::operator-() const { return Vector(-p[0], -p[1], -p[2], p[3]); }
Vector Vector::badVector() { return Vector(0.0f, 0.0f, 0.0f, 0.0f); }
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; }