/*
* (C) Copyright 2015-2017 JOML
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/
package org.joml;
/**
* Interface to an immutable quaternion of double-precision floats.
*
* @author Kai Burjack
*/
public interface Quaterniondc {
/**
* @return the first component of the vector part
*/
double x();
/**
* @return the second component of the vector part
*/
double y();
/**
* @return the third component of the vector part
*/
double z();
/**
* @return the real/scalar part of the quaternion
*/
double w();
/**
* Normalize this quaternion and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Quaterniond normalize(Quaterniond dest);
/**
* Add the quaternion <tt>(x, y, z, w)</tt> to this quaternion and store the result in <code>dest</code>.
*
* @param x
* the x component of the vector part
* @param y
* the y component of the vector part
* @param z
* the z component of the vector part
* @param w
* the real/scalar component
* @param dest
* will hold the result
* @return dest
*/
Quaterniond add(double x, double y, double z, double w, Quaterniond dest);
/**
* Add <code>q2</code> to this quaternion and store the result in <code>dest</code>.
*
* @param q2
* the quaternion to add to this
* @param dest
* will hold the result
* @return dest
*/
Quaterniond add(Quaterniondc q2, Quaterniond dest);
/**
* Return the dot product of this {@link Quaterniond} and <code>otherQuat</code>.
*
* @param otherQuat
* the other quaternion
* @return the dot product
*/
double dot(Quaterniondc otherQuat);
/**
* Return the angle in radians represented by this quaternion rotation.
*
* @return the angle in radians
*/
double angle();
/**
* Set the given destination matrix to the rotation represented by <code>this</code>.
*
* @see Matrix3d#set(Quaterniondc)
*
* @param dest
* the matrix to write the rotation into
* @return the passed in destination
*/
Matrix3d get(Matrix3d dest);
/**
* Set the given destination matrix to the rotation represented by <code>this</code>.
*
* @see Matrix3f#set(Quaterniondc)
*
* @param dest
* the matrix to write the rotation into
* @return the passed in destination
*/
Matrix3f get(Matrix3f dest);
/**
* Set the given destination matrix to the rotation represented by <code>this</code>.
*
* @see Matrix4d#set(Quaterniondc)
*
* @param dest
* the matrix to write the rotation into
* @return the passed in destination
*/
Matrix4d get(Matrix4d dest);
/**
* Set the given destination matrix to the rotation represented by <code>this</code>.
*
* @see Matrix4f#set(Quaterniondc)
*
* @param dest
* the matrix to write the rotation into
* @return the passed in destination
*/
Matrix4f get(Matrix4f dest);
/**
* Set the given {@link Quaterniond} to the values of <code>this</code>.
*
* @param dest
* the {@link Quaterniond} to set
* @return the passed in destination
*/
Quaterniond get(Quaterniond dest);
/**
* Multiply this quaternion by <code>q</code> and store the result in <code>dest</code>.
* <p>
* If <tt>T</tt> is <code>this</code> and <tt>Q</tt> is the given
* quaternion, then the resulting quaternion <tt>R</tt> is:
* <p>
* <tt>R = T * Q</tt>
* <p>
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by <tt>Q</tt> first, and then by <tt>T</tt>.
*
* @param q
* the quaternion to multiply <code>this</code> by
* @param dest
* will hold the result
* @return dest
*/
Quaterniond mul(Quaterniondc q, Quaterniond dest);
/**
* Multiply this quaternion by the quaternion represented via <tt>(qx, qy, qz, qw)</tt> and store the result in <code>dest</code>.
* <p>
* If <tt>T</tt> is <code>this</code> and <tt>Q</tt> is the given
* quaternion, then the resulting quaternion <tt>R</tt> is:
* <p>
* <tt>R = T * Q</tt>
* <p>
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by <tt>Q</tt> first, and then by <tt>T</tt>.
*
* @param qx
* the x component of the quaternion to multiply <code>this</code> by
* @param qy
* the y component of the quaternion to multiply <code>this</code> by
* @param qz
* the z component of the quaternion to multiply <code>this</code> by
* @param qw
* the w component of the quaternion to multiply <code>this</code> by
* @param dest
* will hold the result
* @return dest
*/
Quaterniond mul(double qx, double qy, double qz, double qw, Quaterniond dest);
/**
* Pre-multiply this quaternion by <code>q</code> and store the result in <code>dest</code>.
* <p>
* If <tt>T</tt> is <code>this</code> and <tt>Q</tt> is the given quaternion, then the resulting quaternion <tt>R</tt> is:
* <p>
* <tt>R = Q * T</tt>
* <p>
* So, this method uses pre-multiplication, resulting in a vector to be transformed by <tt>T</tt> first, and then by <tt>Q</tt>.
*
* @param q
* the quaternion to pre-multiply <code>this</code> by
* @param dest
* will hold the result
* @return dest
*/
Quaterniond premul(Quaterniondc q, Quaterniond dest);
/**
* Pre-multiply this quaternion by the quaternion represented via <tt>(qx, qy, qz, qw)</tt> and store the result in <code>dest</code>.
* <p>
* If <tt>T</tt> is <code>this</code> and <tt>Q</tt> is the given quaternion, then the resulting quaternion <tt>R</tt> is:
* <p>
* <tt>R = Q * T</tt>
* <p>
* So, this method uses pre-multiplication, resulting in a vector to be transformed by <tt>T</tt> first, and then by <tt>Q</tt>.
*
* @param qx
* the x component of the quaternion to multiply <code>this</code> by
* @param qy
* the y component of the quaternion to multiply <code>this</code> by
* @param qz
* the z component of the quaternion to multiply <code>this</code> by
* @param qw
* the w component of the quaternion to multiply <code>this</code> by
* @param dest
* will hold the result
* @return dest
*/
Quaterniond premul(double qx, double qy, double qz, double qw, Quaterniond dest);
/**
* Transform the given vector by this quaternion.
* This will apply the rotation described by this quaternion to the given vector.
*
* @param vec
* the vector to transform
* @return vec
*/
Vector3d transform(Vector3d vec);
/**
* Transform the given vector by this quaternion.
* This will apply the rotation described by this quaternion to the given vector.
* <p>
* Only the first three components of the given 4D vector are being used and modified.
*
* @param vec
* the vector to transform
* @return vec
*/
Vector4d transform(Vector4d vec);
/**
* Transform the given vector by this quaternion and store the result in <code>dest</code>.
* This will apply the rotation described by this quaternion to the given vector.
*
* @param vec
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3d transform(Vector3dc vec, Vector3d dest);
/**
* Transform the given vector <tt>(x, y, z)</tt> by this quaternion and store the result in <code>dest</code>.
* This will apply the rotation described by this quaternion to the given vector.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3d transform(double x, double y, double z, Vector3d dest);
/**
* Transform the given vector by this quaternion and store the result in <code>dest</code>.
* This will apply the rotation described by this quaternion to the given vector.
* <p>
* Only the first three components of the given 4D vector are being used and set on the destination.
*
* @param vec
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector4d transform(Vector4dc vec, Vector4d dest);
/**
* Transform the given vector <tt>(x, y, z)</tt> by this quaternion and store the result in <code>dest</code>.
* This will apply the rotation described by this quaternion to the given vector.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector4d transform(double x, double y, double z, Vector4d dest);
/**
* Invert this quaternion and store the {@link #normalize(Quaterniond) normalized} result in <code>dest</code>.
* <p>
* If this quaternion is already normalized, then {@link #conjugate(Quaterniond)} should be used instead.
*
* @see #conjugate(Quaterniond)
*
* @param dest
* will hold the result
* @return dest
*/
Quaterniond invert(Quaterniond dest);
/**
* Divide <code>this</code> quaternion by <code>b</code> and store the result in <code>dest</code>.
* <p>
* The division expressed using the inverse is performed in the following way:
* <p>
* <tt>dest = this * b^-1</tt>, where <tt>b^-1</tt> is the inverse of <code>b</code>.
*
* @param b
* the {@link Quaterniondc} to divide this by
* @param dest
* will hold the result
* @return dest
*/
Quaterniond div(Quaterniondc b, Quaterniond dest);
/**
* Conjugate this quaternion and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Quaterniond conjugate(Quaterniond dest);
/**
* Return the square of the length of this quaternion.
*
* @return the length
*/
double lengthSquared();
/**
* Interpolate between <code>this</code> {@link #normalize(Quaterniond) unit} quaternion and the specified
* <code>target</code> {@link #normalize(Quaterniond) unit} quaternion using spherical linear interpolation using the specified interpolation factor <code>alpha</code>,
* and store the result in <code>dest</code>.
* <p>
* This method resorts to non-spherical linear interpolation when the absolute dot product between <code>this</code> and <code>target</code> is
* below <tt>1E-6</tt>.
* <p>
* Reference: <a href="http://fabiensanglard.net/doom3_documentation/37725-293747_293747.pdf">http://fabiensanglard.net</a>
*
* @param target
* the target of the interpolation, which should be reached with <tt>alpha = 1.0</tt>
* @param alpha
* the interpolation factor, within <tt>[0..1]</tt>
* @param dest
* will hold the result
* @return dest
*/
Quaterniond slerp(Quaterniondc target, double alpha, Quaterniond dest);
/**
* Apply scaling to this quaternion, which results in any vector transformed by the quaternion to change
* its length by the given <code>factor</code>, and store the result in <code>dest</code>.
*
* @param factor
* the scaling factor
* @param dest
* will hold the result
* @return dest
*/
Quaterniond scale(double factor, Quaterniond dest);
/**
* Integrate the rotation given by the angular velocity <code>(vx, vy, vz)</code> around the x, y and z axis, respectively,
* with respect to the given elapsed time delta <code>dt</code> and add the differentiate rotation to the rotation represented by this quaternion
* and store the result into <code>dest</code>.
* <p>
* This method pre-multiplies the rotation given by <code>dt</code> and <code>(vx, vy, vz)</code> by <code>this</code>, so
* the angular velocities are always relative to the local coordinate system of the rotation represented by <code>this</code> quaternion.
* <p>
* This method is equivalent to calling: <code>rotateLocal(dt * vx, dt * vy, dt * vz, dest)</code>
* <p>
* Reference: <a href="http://physicsforgames.blogspot.de/2010/02/quaternions.html">http://physicsforgames.blogspot.de/</a>
*
* @see #rotateLocal(double, double, double, Quaterniond)
*
* @param dt
* the delta time
* @param vx
* the angular velocity around the x axis
* @param vy
* the angular velocity around the y axis
* @param vz
* the angular velocity around the z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond integrate(double dt, double vx, double vy, double vz, Quaterniond dest);
/**
* Compute a linear (non-spherical) interpolation of <code>this</code> and the given quaternion <code>q</code>
* and store the result in <code>dest</code>.
* <p>
* Reference: <a href="http://fabiensanglard.net/doom3_documentation/37725-293747_293747.pdf">http://fabiensanglard.net</a>
*
* @param q
* the other quaternion
* @param factor
* the interpolation factor. It is between 0.0 and 1.0
* @param dest
* will hold the result
* @return dest
*/
Quaterniond nlerp(Quaterniondc q, double factor, Quaterniond dest);
/**
* Compute linear (non-spherical) interpolations of <code>this</code> and the given quaternion <code>q</code>
* iteratively and store the result in <code>dest</code>.
* <p>
* This method performs a series of small-step nlerp interpolations to avoid doing a costly spherical linear interpolation, like
* {@link #slerp(Quaterniondc, double, Quaterniond) slerp},
* by subdividing the rotation arc between <code>this</code> and <code>q</code> via non-spherical linear interpolations as long as
* the absolute dot product of <code>this</code> and <code>q</code> is greater than the given <code>dotThreshold</code> parameter.
* <p>
* Thanks to <tt>@theagentd</tt> at <a href="http://www.java-gaming.org/">http://www.java-gaming.org/</a> for providing the code.
*
* @param q
* the other quaternion
* @param alpha
* the interpolation factor, between 0.0 and 1.0
* @param dotThreshold
* the threshold for the dot product of <code>this</code> and <code>q</code> above which this method performs another iteration
* of a small-step linear interpolation
* @param dest
* will hold the result
* @return dest
*/
Quaterniond nlerpIterative(Quaterniondc q, double alpha, double dotThreshold, Quaterniond dest);
/**
* Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in <code>dest</code>.
* <p>
* Because there are multiple possibilities for such a rotation, this method will choose the one that ensures the given up direction to remain
* parallel to the plane spanned by the <code>up</code> and <code>dir</code> vectors.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
* <p>
* Reference: <a href="http://answers.unity3d.com/questions/467614/what-is-the-source-code-of-quaternionlookrotation.html">http://answers.unity3d.com</a>
*
* @see #lookAlong(double, double, double, double, double, double, Quaterniond)
*
* @param dir
* the direction to map to the positive Z axis
* @param up
* the vector which will be mapped to a vector parallel to the plane
* spanned by the given <code>dir</code> and <code>up</code>
* @param dest
* will hold the result
* @return dest
*/
Quaterniond lookAlong(Vector3dc dir, Vector3dc up, Quaterniond dest);
/**
* Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in <code>dest</code>.
* <p>
* Because there are multiple possibilities for such a rotation, this method will choose the one that ensures the given up direction to remain
* parallel to the plane spanned by the <tt>up</tt> and <tt>dir</tt> vectors.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
* <p>
* Reference: <a href="http://answers.unity3d.com/questions/467614/what-is-the-source-code-of-quaternionlookrotation.html">http://answers.unity3d.com</a>
*
* @param dirX
* the x-coordinate of the direction to look along
* @param dirY
* the y-coordinate of the direction to look along
* @param dirZ
* the z-coordinate of the direction to look along
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Quaterniond dest);
/**
* Compute the difference between <code>this</code> and the <code>other</code> quaternion
* and store the result in <code>dest</code>.
* <p>
* The difference is the rotation that has to be applied to get from
* <code>this</code> rotation to <code>other</code>. If <tt>T</tt> is <code>this</code>, <tt>Q</tt>
* is <code>other</code> and <tt>D</tt> is the computed difference, then the following equation holds:
* <p>
* <tt>T * D = Q</tt>
* <p>
* It is defined as: <tt>D = T^-1 * Q</tt>, where <tt>T^-1</tt> denotes the {@link #invert(Quaterniond) inverse} of <tt>T</tt>.
*
* @param other
* the other quaternion
* @param dest
* will hold the result
* @return dest
*/
Quaterniond difference(Quaterniondc other, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> that rotates the <tt>fromDir</tt> vector to point along <tt>toDir</tt> and
* store the result in <code>dest</code>.
* <p>
* Since there can be multiple possible rotations, this method chooses the one with the shortest arc.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
* <p>
* Reference: <a href="http://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another#answer-1171995">stackoverflow.com</a>
*
* @param fromDirX
* the x-coordinate of the direction to rotate into the destination direction
* @param fromDirY
* the y-coordinate of the direction to rotate into the destination direction
* @param fromDirZ
* the z-coordinate of the direction to rotate into the destination direction
* @param toDirX
* the x-coordinate of the direction to rotate to
* @param toDirY
* the y-coordinate of the direction to rotate to
* @param toDirZ
* the z-coordinate of the direction to rotate to
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> that rotates the <code>fromDir</code> vector to point along <code>toDir</code> and
* store the result in <code>dest</code>.
* <p>
* Because there can be multiple possible rotations, this method chooses the one with the shortest arc.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotateTo(double, double, double, double, double, double, Quaterniond)
*
* @param fromDir
* the starting direction
* @param toDir
* the destination direction
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateTo(Vector3dc fromDir, Vector3dc toDir, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the basis unit axes of the
* cartesian space and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotate(double, double, double, Quaterniond)
*
* @param anglesXYZ
* the angles in radians to rotate about the x, y and z axes, respectively
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotate(Vector3dc anglesXYZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the basis unit axes of the
* cartesian space and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @param angleX
* the angle in radians to rotate about the x axis
* @param angleY
* the angle in radians to rotate about the y axis
* @param angleZ
* the angle in radians to rotate about the z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotate(double angleX, double angleY, double angleZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the basis unit axes of the
* local coordinate system represented by this quaternion and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>R * Q</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>R * Q * v</code>, the
* rotation represented by <code>this</code> will be applied first!
*
* @param angleX
* the angle in radians to rotate about the local x axis
* @param angleY
* the angle in radians to rotate about the local y axis
* @param angleZ
* the angle in radians to rotate about the local z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateLocal(double angleX, double angleY, double angleZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the x axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotate(double, double, double, Quaterniond)
*
* @param angle
* the angle in radians to rotate about the x axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateX(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the y axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotate(double, double, double, Quaterniond)
*
* @param angle
* the angle in radians to rotate about the y axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateY(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the z axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotate(double, double, double, Quaterniond)
*
* @param angle
* the angle in radians to rotate about the z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateZ(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local x axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>R * Q</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>R * Q * v</code>, the
* rotation represented by <code>this</code> will be applied first!
*
* @param angle
* the angle in radians to rotate about the local x axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateLocalX(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local y axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>R * Q</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>R * Q * v</code>, the
* rotation represented by <code>this</code> will be applied first!
*
* @param angle
* the angle in radians to rotate about the local y axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateLocalY(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local z axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>R * Q</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>R * Q * v</code>, the
* rotation represented by <code>this</code> will be applied first!
*
* @param angle
* the angle in radians to rotate about the local z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateLocalZ(double angle, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles using rotation sequence <tt>XYZ</tt> and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling: <tt>rotateX(angleX, dest).rotateY(angleY).rotateZ(angleZ)</tt>
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @param angleX
* the angle in radians to rotate about the x axis
* @param angleY
* the angle in radians to rotate about the y axis
* @param angleZ
* the angle in radians to rotate about the z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateXYZ(double angleX, double angleY, double angleZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles, using the rotation sequence <tt>ZYX</tt> and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling: <tt>rotateZ(angleZ, dest).rotateY(angleY).rotateX(angleX)</tt>
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @param angleZ
* the angle in radians to rotate about the z axis
* @param angleY
* the angle in radians to rotate about the y axis
* @param angleX
* the angle in radians to rotate about the x axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateZYX(double angleZ, double angleY, double angleX, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles, using the rotation sequence <tt>YXZ</tt> and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling: <tt>rotateY(angleY, dest).rotateX(angleX).rotateZ(angleZ)</tt>
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @param angleY
* the angle in radians to rotate about the y axis
* @param angleX
* the angle in radians to rotate about the x axis
* @param angleZ
* the angle in radians to rotate about the z axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateYXZ(double angleY, double angleX, double angleZ, Quaterniond dest);
/**
* Get the euler angles in radians in rotation sequence <tt>XYZ</tt> of this quaternion and store them in the
* provided parameter <code>eulerAngles</code>.
*
* @param eulerAngles
* will hold the euler angles in radians
* @return the passed in vector
*/
Vector3d getEulerAnglesXYZ(Vector3d eulerAngles);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the specified axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @param angle
* the angle in radians to rotate about the specified axis
* @param axisX
* the x coordinate of the rotation axis
* @param axisY
* the y coordinate of the rotation axis
* @param axisZ
* the z coordinate of the rotation axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateAxis(double angle, double axisX, double axisY, double axisZ, Quaterniond dest);
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the specified axis
* and store the result in <code>dest</code>.
* <p>
* If <code>Q</code> is <code>this</code> quaternion and <code>R</code> the quaternion representing the
* specified rotation, then the new quaternion will be <code>Q * R</code>. So when transforming a
* vector <code>v</code> with the new quaternion by using <code>Q * R * v</code>, the
* rotation added by this method will be applied first!
*
* @see #rotateAxis(double, double, double, double, Quaterniond)
*
* @param angle
* the angle in radians to rotate about the specified axis
* @param axis
* the rotation axis
* @param dest
* will hold the result
* @return dest
*/
Quaterniond rotateAxis(double angle, Vector3dc axis, Quaterniond dest);
/**
* Obtain the direction of <tt>+X</tt> before the rotation transformation represented by <code>this</code> quaternion is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).invert();
* inv.transform(dir.set(1, 0, 0));
* </pre>
*
* @param dir
* will hold the direction of <tt>+X</tt>
* @return dir
*/
Vector3d positiveX(Vector3d dir);
/**
* Obtain the direction of <tt>+X</tt> before the rotation transformation represented by <code>this</code> <i>normalized</i> quaternion is applied.
* The quaternion <i>must</i> be {@link #normalize(Quaterniond) normalized} for this method to work.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).conjugate();
* inv.transform(dir.set(1, 0, 0));
* </pre>
*
* @param dir
* will hold the direction of <tt>+X</tt>
* @return dir
*/
Vector3d normalizedPositiveX(Vector3d dir);
/**
* Obtain the direction of <tt>+Y</tt> before the rotation transformation represented by <code>this</code> quaternion is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).invert();
* inv.transform(dir.set(0, 1, 0));
* </pre>
*
* @param dir
* will hold the direction of <tt>+Y</tt>
* @return dir
*/
Vector3d positiveY(Vector3d dir);
/**
* Obtain the direction of <tt>+Y</tt> before the rotation transformation represented by <code>this</code> <i>normalized</i> quaternion is applied.
* The quaternion <i>must</i> be {@link #normalize(Quaterniond) normalized} for this method to work.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).conjugate();
* inv.transform(dir.set(0, 1, 0));
* </pre>
*
* @param dir
* will hold the direction of <tt>+Y</tt>
* @return dir
*/
Vector3d normalizedPositiveY(Vector3d dir);
/**
* Obtain the direction of <tt>+Z</tt> before the rotation transformation represented by <code>this</code> quaternion is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).invert();
* inv.transform(dir.set(0, 0, 1));
* </pre>
*
* @param dir
* will hold the direction of <tt>+Z</tt>
* @return dir
*/
Vector3d positiveZ(Vector3d dir);
/**
* Obtain the direction of <tt>+Z</tt> before the rotation transformation represented by <code>this</code> <i>normalized</i> quaternion is applied.
* The quaternion <i>must</i> be {@link #normalize(Quaterniond) normalized} for this method to work.
* <p>
* This method is equivalent to the following code:
* <pre>
* Quaterniond inv = new Quaterniond(this).conjugate();
* inv.transform(dir.set(0, 0, 1));
* </pre>
*
* @param dir
* will hold the direction of <tt>+Z</tt>
* @return dir
*/
Vector3d normalizedPositiveZ(Vector3d dir);
}