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Standard operations

The maxon::Quaternion class delivers a set of standard mathematical operators to perform calculation with quaternion. The operators deliver are:

• maxon::Quaternion::operator+=() : right-assigns the sum of the current value and of the maxon::Quaternion used in the expression;
• maxon::Quaternion::operator-=() : right-assigns the difference of the current value and of the maxon::Quaternion used in the expression;
• maxon::Quaternion::operator*=() : right-assigns the product of the current value and of the maxon::Quaternion used in the expression;
• maxon::Quaternion::operator+() : returns the sum of two maxon::Quaternion instances;
• maxon::Quaternion::operator-() : returns the difference of two maxon::Quaternion instances;
• maxon::Quaternion::operator*() : returns the product of two maxon::Quaternion instances;
• maxon::Quaternion::operator*(const ValueType s) const : returns a maxon::Quaternion instance scaled by "s";
• maxon::Quaternion::operator*(const ValueType s, const QuaternionType& q) : scales the passed maxon::Quaternion instance "q" by the passed parameter's value "s".

// just allocate a constant quaternion using the four components const maxon::Quaternion<maxon::Float> quaternionA(1, 0, 0, 12); DiagnosticOutput (diagIDString + "quaternionA: @" , quaternionA);

// just allocate a quaternion equal to the previous one maxon::Quaternion<maxon::Float> quaternionB = quaternionA; DiagnosticOutput (diagIDString + "quaternionB: @" , quaternionB);

// sum A to B quaternionB += quaternionA; DiagnosticOutput (diagIDString + "quaternionB += quaternionA: @" , quaternionB);

// subtract A to B quaternionB -= quaternionA; DiagnosticOutput (diagIDString + "quaternionB -= quaternionA: @" , quaternionB);

// sum A and B const maxon::Quaternion<maxon::Float> quaternionAsumB = quaternionA + quaternionB; DiagnosticOutput (diagIDString + "quaternionAsumB : @" , quaternionAsumB);

// subtract A and B const maxon::Quaternion<maxon::Float> quaternionAdifB = quaternionA - quaternionB; DiagnosticOutput (diagIDString + "quaternionAdifB: @" , quaternionAdifB);

// multiply A and B const maxon::Quaternion<maxon::Float> quaternionAprdB = quaternionA * quaternionB; DiagnosticOutput (diagIDString + "quaternionAprdB: @" , quaternionAprdB);

// multiply B and A const maxon::Quaternion<maxon::Float> quaternionBprdA = quaternionB * quaternionA; DiagnosticOutput (diagIDString + "quaternionBprdA: @" , quaternionBprdA);

// scale A by scalar s const maxon::Float scalar = 2; const maxon::Quaternion<maxon::Float> quaternionAscaled = quaternionA * scalar; DiagnosticOutput (diagIDString + "quaternionAscaled: @" , quaternionAscaled);

Get and Set operations

The maxon::Quaternion class is provided with a number of get methods to retrieve useful data from a maxon::Quaternion instance:

• maxon::Quaternion::GetMatrix() : returns the rotation matrix computed from the quaternion instance;
• maxon::Quaternion::GetAxisRotation() : calculate axis and rotation angle from quaternion and returns an error if the quaternion is not normalized or the direction of the axis is undefined;
• maxon::Quaternion::GetSquaredLength() : gets the squared length of the quaternion;
• maxon::Quaternion::GetLength() : gets the length of the quaternion;
• maxon::Quaternion::GetNormalized() : gets the quaternion with normalized length and returns an error if the quaternion length is zero;
• maxon::Quaternion::GetInverse() : gets the inverse of a quaternion and returns an error if the quaternion's length is zero;
• maxon::Quaternion::GetConjugate() : gets the conjugated quaternion;
• maxon::Quaternion::GetLog() : gets the natural logarithm of a quaternion and returns an error if the quaternion's length is zero;
• maxon::Quaternion::GetExp() : gets the exponential of a quaternion and returns an error if the quaternion's length is zero;
• maxon::Quaternion::GetPow() : gets the power of quaternion by the passed value and returns an error if the quaternion's length is zero;
• maxon::Quaternion::GetDot() : gets the "dot" product of two quaternions;
• maxon::Quaternion::GetLerp() : gets the linear interpolation of two quaternions using the passed blend parameter;
• maxon::Quaternion::GetSlerp() : gets the spherical linear interpolation of two quaternions using the passed blend parameter;
• maxon::Quaternion::GetSquad() : gets the spherical quadrangle interpolation of a sequence of quaternions qi and qi+1 using the passed blend parameter;
• maxon::Quaternion::GetInnerQuaternion() : gets the inner quaternion from the series of quaternions qi-1 and qi+1;
• maxon::Quaternion::GetSpline() : gets the spherical spline interpolation of two quaternions qi and qi+1 using the passed blend parameter.

// just allocate a constant quaternion using the four components // representing a rotation of 90 deg around Y-axis in left-handed c.sys const maxon::Quaternion<maxon::Float> quatY90 (0, sin( PI05 /2), 0, cos( PI05 /2));

// get the rotation matrix associated with the quaternion const maxon::Matrix rotMat = quatY90.GetMatrix();

// get the axis and rotation angle associated with the quaternion maxon::Vector rotAxis; maxon::Float rotAngle; quatY90.GetAxisRotation(rotAxis, rotAngle) iferr_return ;

// get the squared length of the quaternion const maxon::Float valSqLength = quatY90.GetSquaredLength();

// get the length of the quaternion const maxon::Float valLength = quatY90.GetLength();

// get the normalized quaternion const maxon::Quaternion<maxon::Float> quatNormalized = quatY90. GetNormalized () iferr_return ;

// get the inverse quaternion const maxon::Quaternion<maxon::Float> quatInverted = quatY90. GetInverse () iferr_return ;

// get the conjugate quaternion const maxon::Quaternion<maxon::Float> quatConjugated = quatY90. GetConjugate ();

// get the natural log quaternion const maxon::Quaternion<maxon::Float> quatLog = quatY90. GetLog () iferr_return ;

// get the exponential equaternion const maxon::Quaternion<maxon::Float> quatExp = quatY90. GetExp () iferr_return ;

// get the quaternion elevated to the given power const maxon::Quaternion<maxon::Float> quatPow = quatY90. GetPow (3.0) iferr_return ;

// get the dot product of two quaternion const maxon::Float valDotProduct = maxon::Quaternion<maxon::Float>::GetDot (quatY90, quatConjugated);

// get the linear interpolation of the given quaternion and the given blend ratio const maxon::Quaternion<maxon::Float> quatX90 (sin( PI05 /2), 0, 0, cos( PI05 /2)); const maxon::Quaternion<maxon::Float> quatLERP = maxon::Quaternion<maxon::Float>::GetLerp (quatY90, quatX90, 0.5) iferr_return ;

// get the spherical linear interpolation of the given quaternion and the given blend ratio const maxon :: Quaternion < maxon :: Float > quatSLERP = maxon :: Quaternion < maxon :: Float >::GetSlerp(quatY90, quatX90, 0.5) iferr_return ;

// get the spherical quadrangle interpolation of a sequence of quaternions qi and qi+1 using the passed blend parameter const maxon :: Quaternion < maxon :: Float > quatA (1, 0, 0, 1); const maxon :: Quaternion < maxon :: Float > quatAp1 (1, 1, 0, 1); const maxon :: Quaternion < maxon :: Float > quatB (0, 0, 1, 1); const maxon :: Quaternion < maxon :: Float > quatBp1 (0, 1, 1, 1); const maxon :: Quaternion < maxon :: Float > quatSQUAD = maxon :: Quaternion < maxon :: Float >::GetSquad(quatA, quatAp1, quatB, quatBp1, 0.4) iferr_return ;

// get the inner quaternion from a sequance of quaternions qi-1, qi and qi+1 const maxon :: Quaternion < maxon :: Float > quatCm1 (-1, 1, 0, 1); const maxon :: Quaternion < maxon :: Float > quatC (1, 1, 0, 1); const maxon :: Quaternion < maxon :: Float > quatCp1 (2, 1, 0, 1); const maxon :: Quaternion < maxon :: Float > quatInner = maxon :: Quaternion < maxon :: Float >::GetInnerQuaternion(quatCm1, quatC, quatCp1) iferr_return ;

// get the spline quaternion from a sequence of quaternions const maxon :: Quaternion < maxon :: Float > quatDm1 (0, 0, 0, 1); const maxon :: Quaternion < maxon :: Float > quatD (1, 0, 0, 1); const maxon :: Quaternion < maxon :: Float > quatDp1 (2, 0, 0, 2); const maxon :: Quaternion < maxon :: Float > quatDp2 (3, 0, 0, 2); const maxon :: Quaternion < maxon :: Float > quatSpline = maxon :: Quaternion < maxon :: Float >::GetSpline(quatDm1, quatD, quatDp1, quatDp2, 0.75) iferr_return ;

The maxon::Quaternion class is provided with a number of "set" methods to define a maxon::Quaternion instance:

• maxon::Quaternion::SetMatrix() : sets the quaternion based on the passed rotation matrix;
• maxon::Quaternion::SetRotation() : sets the quaternion based on the rotation of order X -> Y -> Z;
• maxon::Quaternion::SetAxisRotation() : sets the quaternion based on the given rotation axis and rotation value.

// allocate a constant transformation matrix representing // a rotation of 90 deg around Y-axis in left-handed c.sys const maxon::SqrMat3<maxon::Vector> mat3x3( maxon::Vector (0, 0, 1), maxon::Vector (0, 1, 0), maxon::Vector (-1.0, 0.0, 0.0));

// allocate a quaternion and set the values accordingly to the matrix defined maxon::Quaternion<maxon::Float> quatA; quatA. SetMatrix (mat3x3);

// allocate a Eulerian rotation vector (each component of the vector // represents a rotation around an axis) represeting a rotation of 90 deg // around Y-axis in left-handed c.sys const maxon::Vector rotVet (0.0, PI05 , 0.0);

// allocate a quaternion and set the values accordingly to the vector defined maxon::Quaternion<maxon::Float> quatB; quatB. SetRotation (rotVet);

// allocate a vector representing a rotation axis and value representing the rotation amount const maxon::Vector rotAxis (0.0, 1.0, 0.0); const maxon::Float rotAngle( PI05 );

// allocate a quaternion and set the values accordingly to the axis and angle defined maxon::Quaternion<maxon::Float> quatC; quatC. SetAxisRotation (rotAxis, rotAngle);

The maxon::Quaternion class can be used to easily perform a rotation on a geometrical entity.

// define the rotation around the Y-axis const maxon::Vector axis_Y (0.0, 1.0, 0.0);

// define the rotation amount in radians const maxon::Float rot_angle ( PI05 );

// allocate and define the quaternion used to rotate the point maxon::Quaternion<maxon::Float> rotate_on_Y; rotate_on_Y. SetAxisRotation (axis_Y, rot_angle);

// the new point should now be on the Z-axis const maxon::Vector point_on_Z = rotate_on_Y. GetMatrix () * point_on_X;

Conversion

A maxon::Quaternion instance can be converted to maxon::String using:

• maxon::Quaternion::ToString() : returns a maxon::String representation of the maxon::Quaternion 对象。

// just allocate a complex object const maxon::Quaternion<maxon::Float> quatA(1, 1, 0, 1); const maxon::String stringQuaternion = quatA. ToString ( nullptr ); DiagnosticOutput (diagIDString + "quatA: @" , quatA); DiagnosticOutput (diagIDString + "quatA.ToString(): @" , stringQuaternion);

Utilities

A maxon::Quaternion instance can be read from and written to disk by serializing the data contained using the conventional functions.

// file URL const maxon::Url url = (targetFolder + "quaternion.txt" _s) iferr_return ; const maxon::Id fileID( "net.maxonexample.quaternion" );

// save to file maxon::WriteDocument (url, maxon::OPENSTREAMFLAGS::NONE , fileID, savedQuat, maxon::IOFORMAT::JSON ) iferr_return ;

// read from file maxon::Quaternion<maxon::Float> loadedQuat; maxon::ReadDocument (url, fileID, loadedQuat) iferr_return ;

延伸阅读

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