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#ifndef MATH_QUATERNION_HPP |
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#define MATH_QUATERNION_HPP |
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#include "math/Vector.hpp" |
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|
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namespace oopse{ |
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/** |
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* @class Quaternion Quaternion.hpp "math/Quaternion.hpp" |
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* @brief |
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* Quaternion is a sort of a higher-level complex number. |
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* It is defined as Q = w + x*i + y*j + z*k, |
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* where w, x, y, and z are numbers of type T (e.g. double), and |
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* i*i = -1; j*j = -1; k*k = -1; |
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* i*j = k; j*k = i; k*i = j; |
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*/ |
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template<typename Real> |
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class Quaternion : public Vector<Real, 4> { |
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public: |
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Quaternion(); |
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}; |
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/** Constructs and initializes a Quaternion from w, x, y, z values */ |
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Quaternion(Real w, Real x, Real y, Real z) { |
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data_[0] = w; |
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data_[1] = x; |
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data_[2] = y; |
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data_[3] = z; |
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} |
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|
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/** |
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* |
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*/ |
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Quaternion(const Vector<Real,4>& v) |
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: Vector<Real, 4>(v){ |
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} |
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|
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/** */ |
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Quaternion& operator =(const Vector<Real, 4>& v){ |
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if (this == & v) |
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return *this; |
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|
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Vector<Real, 4>::operator=(v); |
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return *this; |
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} |
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|
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real w() const { |
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return data_[0]; |
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} |
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|
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/** |
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* Returns the reference of the first element of this quaternion. |
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* @return the reference of the first element of this quaternion |
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*/ |
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Real& w() { |
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return data_[0]; |
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} |
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|
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/** |
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* Returns the value of the first element of this quaternion. |
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* @return the value of the first element of this quaternion |
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*/ |
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Real x() const { |
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return data_[1]; |
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} |
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|
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/** |
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* Returns the reference of the second element of this quaternion. |
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* @return the reference of the second element of this quaternion |
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*/ |
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Real& x() { |
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return data_[1]; |
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} |
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|
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/** |
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* Returns the value of the thirf element of this quaternion. |
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* @return the value of the third element of this quaternion |
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*/ |
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Real y() const { |
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return data_[2]; |
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} |
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|
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/** |
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* Returns the reference of the third element of this quaternion. |
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* @return the reference of the third element of this quaternion |
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*/ |
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Real& y() { |
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return data_[2]; |
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} |
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|
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/** |
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* Returns the value of the fourth element of this quaternion. |
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* @return the value of the fourth element of this quaternion |
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*/ |
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Real z() const { |
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return data_[3]; |
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} |
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/** |
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* Returns the reference of the fourth element of this quaternion. |
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* @return the reference of the fourth element of this quaternion |
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*/ |
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Real& z() { |
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return data_[3]; |
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} |
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|
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/** |
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* Returns the inverse of this quaternion |
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* @return inverse |
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* @note since quaternion is a complex number, the inverse of quaternion |
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* q = w + xi + yj+ zk is inv_q = (w -xi - yj - zk)/(|q|^2) |
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*/ |
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Quaternion<Real> inverse(){ |
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Quaternion<Real> q; |
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Real d = this->lengthSquared(); |
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|
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q.w() = w() / d; |
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q.x() = -x() / d; |
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q.y() = -y() / d; |
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q.z() = -z() / d; |
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|
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return q; |
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} |
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|
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/** |
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* Sets the value to the multiplication of itself and another quaternion |
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* @param q the other quaternion |
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*/ |
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void mul(const Quaternion<Real>& q) { |
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|
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Real a0( (z() - y()) * (q.y() - q.z()) ); |
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Real a1( (w() + x()) * (q.w() + q.x()) ); |
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Real a2( (w() - x()) * (q.y() + q.z()) ); |
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Real a3( (y() + z()) * (q.w() - q.x()) ); |
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Real b0( -(x() - z()) * (q.x() - q.y()) ); |
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Real b1( -(x() + z()) * (q.x() + q.y()) ); |
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Real b2( (w() + y()) * (q.w() - q.z()) ); |
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Real b3( (w() - y()) * (q.w() + q.z()) ); |
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|
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data_[0] = a0 + 0.5*(b0 + b1 + b2 + b3),; |
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data_[1] = a1 + 0.5*(b0 + b1 - b2 - b3); |
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data_[2] = a2 + 0.5*(b0 - b1 + b2 - b3), |
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data_[3] = a3 + 0.5*(b0 - b1 - b2 + b3) ); |
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} |
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|
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|
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/** Set the value of this quaternion to the division of itself by another quaternion */ |
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void div(const Quaternion<Real>& q) { |
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mul(q.inverse()); |
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} |
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|
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Quaternion<Real>& operator *=(const Quaternion<Real>& q) { |
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mul(q); |
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return *this; |
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} |
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|
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Quaternion<Real>& operator /=(const Quaternion<Real>& q) { |
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mul(q.inverse()); |
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return *this; |
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} |
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|
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/** |
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* Returns the conjugate quaternion of this quaternion |
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* @return the conjugate quaternion of this quaternion |
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*/ |
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Quaternion<Real> conjugate() { |
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return Quaternion<Real>(w(), -x(), -y(), -z()); |
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} |
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|
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/** |
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* Returns the corresponding rotation matrix (3x3) |
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* @return a 3x3 rotation matrix |
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*/ |
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SquareMatrix<Real, 3, 3> toRotationMatrix3() { |
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SquareMatrix<Real, 3, 3> rotMat3; |
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|
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Real w2; |
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Real x2; |
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Real y2; |
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Real z2; |
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|
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if (!isNormalized()) |
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normalize(); |
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|
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w2 = w() * w(); |
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x2 = x() * x(); |
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y2 = y() * y(); |
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z2 = z() * z(); |
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|
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rotMat3(0, 0) = w2 + x2 - y2 - z2; |
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rotMat3(0, 1) = 2.0 * ( x() * y() + w() * z() ); |
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rotMat3(0, 2) = 2.0 * ( x() * z() - w() * y() ); |
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|
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rotMat3(1, 0) = 2.0 * ( x() * y() - w() * z() ); |
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rotMat3(1, 1) = w2 - x2 + y2 - z2; |
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rotMat3(1, 2) = 2.0 * ( y() * z() + w() * x() ); |
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|
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rotMat3(2, 0) = 2.0 * ( x() * z() + w() * y() ); |
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rotMat3(2, 1) = 2.0 * ( y() * z() - w() * x() ); |
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rotMat3(2, 2) = w2 - x2 -y2 +z2; |
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} |
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|
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};//end Quaternion |
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|
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/** |
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* Returns the multiplication of two quaternion |
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* @return the multiplication of two quaternion |
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* @param q1 the first quaternion |
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* @param q2 the second quaternion |
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*/ |
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template<typename Real> |
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inline Quaternion<Real> operator *(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
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Quaternion<Real> result(q1); |
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result *= q2; |
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return result; |
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} |
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|
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/** |
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* Returns the division of two quaternion |
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* @param q1 divisor |
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* @param q2 dividen |
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*/ |
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|
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template<typename Real> |
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inline Quaternion<Real> operator /(const Quaternion<Real>& q1, const Quaternion<Real>& q2) { |
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return q1 * q2.inverse(); |
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} |
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|
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/** |
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* Returns the value of the division of a scalar by a quaternion |
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* @return the value of the division of a scalar by a quaternion |
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* @param s scalar |
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* @param q quaternion |
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* @note for a quaternion q, 1/q = q.inverse() |
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*/ |
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template<typename Real> |
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Quaternion<Real> operator /(const Quaternion<Real>& s, const Quaternion<Real>& q) { |
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|
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Quaternion<Real> x = q.inv(); |
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return x * s; |
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} |
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|
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typedef Quaternion<double> Quat4d; |
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} |
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#endif //MATH_QUATERNION_HPP |