/*
* The MIT License
*
* Copyright (c) 2015-2020 Richard Greenlees
*
* 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;
import java.io.Externalizable;
import java.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectOutput;
import java.text.DecimalFormat;
import java.text.NumberFormat;
/**
* Quaternion of 4 double-precision floats which can represent rotation and uniform scaling.
*
* @author Richard Greenlees
* @author Kai Burjack
*/
public class Quaterniond implements Externalizable, Quaterniondc {
private static final long serialVersionUID = 1L;
/**
* The first component of the vector part.
*/
public double x;
/**
* The second component of the vector part.
*/
public double y;
/**
* The third component of the vector part.
*/
public double z;
/**
* The real/scalar part of the quaternion.
*/
public double w;
/**
* Create a new {@link Quaterniond} and initialize it with <code>(x=0, y=0, z=0, w=1)</code>,
* where <code>(x, y, z)</code> is the vector part of the quaternion and <code>w</code> is the real/scalar part.
*/
public Quaterniond() {
this.w = 1.0;
}
/**
* Create a new {@link Quaterniond} and initialize its components to the given values.
*
* @param x
* the first component of the imaginary part
* @param y
* the second component of the imaginary part
* @param z
* the third component of the imaginary part
* @param w
* the real part
*/
public Quaterniond(double x, double y, double z, double w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
/**
* Create a new {@link Quaterniond} and initialize its components to the same values as the given {@link Quaterniondc}.
*
* @param source
* the {@link Quaterniondc} to take the component values from
*/
public Quaterniond(Quaterniondc source) {
x = source.x();
y = source.y();
z = source.z();
w = source.w();
}
/**
* Create a new {@link Quaterniond} and initialize its components to the same values as the given {@link Quaternionfc}.
*
* @param source
* the {@link Quaternionfc} to take the component values from
*/
public Quaterniond(Quaternionfc source) {
x = source.x();
y = source.y();
z = source.z();
w = source.w();
}
/**
* Create a new {@link Quaterniond} and initialize it to represent the same rotation as the given {@link AxisAngle4f}.
*
* @param axisAngle
* the axis-angle to initialize this quaternion with
*/
public Quaterniond(AxisAngle4f axisAngle) {
double s = Math.sin(axisAngle.angle * 0.5);
x = axisAngle.x * s;
y = axisAngle.y * s;
z = axisAngle.z * s;
w = Math.cosFromSin(s, axisAngle.angle * 0.5);
}
/**
* Create a new {@link Quaterniond} and initialize it to represent the same rotation as the given {@link AxisAngle4d}.
*
* @param axisAngle
* the axis-angle to initialize this quaternion with
*/
public Quaterniond(AxisAngle4d axisAngle) {
double s = Math.sin(axisAngle.angle * 0.5);
x = axisAngle.x * s;
y = axisAngle.y * s;
z = axisAngle.z * s;
w = Math.cosFromSin(s, axisAngle.angle * 0.5);
}
/**
* @return the first component of the vector part
*/
public double x() {
return this.x;
}
/**
* @return the second component of the vector part
*/
public double y() {
return this.y;
}
/**
* @return the third component of the vector part
*/
public double z() {
return this.z;
}
/**
* @return the real/scalar part of the quaternion
*/
public double w() {
return this.w;
}
/**
* Normalize this quaternion.
*
* @return this
*/
public Quaterniond normalize() {
double invNorm = Math.invsqrt(lengthSquared());
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
return this;
}
public Quaterniond normalize(Quaterniond dest) {
double invNorm = Math.invsqrt(lengthSquared());
dest.x = x * invNorm;
dest.y = y * invNorm;
dest.z = z * invNorm;
dest.w = w * invNorm;
return dest;
}
/**
* Add the quaternion <code>(x, y, z, w)</code> to this quaternion.
*
* @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
* @return this
*/
public Quaterniond add(double x, double y, double z, double w) {
return add(x, y, z, w, this);
}
public Quaterniond add(double x, double y, double z, double w, Quaterniond dest) {
dest.x = this.x + x;
dest.y = this.y + y;
dest.z = this.z + z;
dest.w = this.w + w;
return dest;
}
/**
* Add <code>q2</code> to this quaternion.
*
* @param q2
* the quaternion to add to this
* @return this
*/
public Quaterniond add(Quaterniondc q2) {
x += q2.x();
y += q2.y();
z += q2.z();
w += q2.w();
return this;
}
public Quaterniond add(Quaterniondc q2, Quaterniond dest) {
dest.x = x + q2.x();
dest.y = y + q2.y();
dest.z = z + q2.z();
dest.w = w + q2.w();
return dest;
}
public double dot(Quaterniondc otherQuat) {
return this.x * otherQuat.x() + this.y * otherQuat.y() + this.z * otherQuat.z() + this.w * otherQuat.w();
}
public double angle() {
return 2.0 * Math.safeAcos(w);
}
public Matrix3d get(Matrix3d dest) {
return dest.set(this);
}
public Matrix3f get(Matrix3f dest) {
return dest.set(this);
}
public Matrix4d get(Matrix4d dest) {
return dest.set(this);
}
public Matrix4f get(Matrix4f dest) {
return dest.set(this);
}
public AxisAngle4f get(AxisAngle4f dest) {
double x = this.x;
double y = this.y;
double z = this.z;
double w = this.w;
if (w > 1.0) {
double invNorm = Math.invsqrt(lengthSquared());
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
}
dest.angle = (float) (2.0 * Math.acos(w));
double s = Math.sqrt(1.0 - w * w);
if (s < 0.001) {
dest.x = (float) x;
dest.y = (float) y;
dest.z = (float) z;
} else {
s = 1.0 / s;
dest.x = (float) (x * s);
dest.y = (float) (y * s);
dest.z = (float) (z * s);
}
return dest;
}
public AxisAngle4d get(AxisAngle4d dest) {
double x = this.x;
double y = this.y;
double z = this.z;
double w = this.w;
if (w > 1.0) {
double invNorm = Math.invsqrt(lengthSquared());
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
}
dest.angle = 2.0 * Math.acos(w);
double s = Math.sqrt(1.0 - w * w);
if (s < 0.001) {
dest.x = x;
dest.y = y;
dest.z = z;
} else {
s = 1.0 / s;
dest.x = x * s;
dest.y = y * s;
dest.z = z * s;
}
return dest;
}
/**
* Set the given {@link Quaterniond} to the values of <code>this</code>.
*
* @see #set(Quaterniondc)
*
* @param dest
* the {@link Quaterniond} to set
* @return the passed in destination
*/
public Quaterniond get(Quaterniond dest) {
return dest.set(this);
}
/**
* Set the given {@link Quaternionf} to the values of <code>this</code>.
*
* @see #set(Quaterniondc)
*
* @param dest
* the {@link Quaternionf} to set
* @return the passed in destination
*/
public Quaternionf get(Quaternionf dest) {
return dest.set(this);
}
/**
* Set this quaternion to the new values.
*
* @param x
* the new value of x
* @param y
* the new value of y
* @param z
* the new value of z
* @param w
* the new value of w
* @return this
*/
public Quaterniond set(double x, double y, double z, double w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
return this;
}
/**
* Set this quaternion to be a copy of q.
*
* @param q
* the {@link Quaterniondc} to copy
* @return this
*/
public Quaterniond set(Quaterniondc q) {
x = q.x();
y = q.y();
z = q.z();
w = q.w();
return this;
}
/**
* Set this quaternion to be a copy of q.
*
* @param q
* the {@link Quaternionfc} to copy
* @return this
*/
public Quaterniond set(Quaternionfc q) {
x = q.x();
y = q.y();
z = q.z();
w = q.w();
return this;
}
/**
* Set this {@link Quaterniond} to be equivalent to the given
* {@link AxisAngle4f}.
*
* @param axisAngle
* the {@link AxisAngle4f}
* @return this
*/
public Quaterniond set(AxisAngle4f axisAngle) {
return setAngleAxis(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* Set this {@link Quaterniond} to be equivalent to the given
* {@link AxisAngle4d}.
*
* @param axisAngle
* the {@link AxisAngle4d}
* @return this
*/
public Quaterniond set(AxisAngle4d axisAngle) {
return setAngleAxis(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* Set this quaternion to a rotation equivalent to the supplied axis and
* angle (in radians).
* <p>
* This method assumes that the given rotation axis <code>(x, y, z)</code> is already normalized
*
* @param angle
* the angle in radians
* @param x
* the x-component of the normalized rotation axis
* @param y
* the y-component of the normalized rotation axis
* @param z
* the z-component of the normalized rotation axis
* @return this
*/
public Quaterniond setAngleAxis(double angle, double x, double y, double z) {
double s = Math.sin(angle * 0.5);
this.x = x * s;
this.y = y * s;
this.z = z * s;
this.w = Math.cosFromSin(s, angle * 0.5);
return this;
}
/**
* Set this quaternion to be a representation of the supplied axis and
* angle (in radians).
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis
* @return this
*/
public Quaterniond setAngleAxis(double angle, Vector3dc axis) {
return setAngleAxis(angle, axis.x(), axis.y(), axis.z());
}
private void setFromUnnormalized(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22) {
double nm00 = m00, nm01 = m01, nm02 = m02;
double nm10 = m10, nm11 = m11, nm12 = m12;
double nm20 = m20, nm21 = m21, nm22 = m22;
double lenX = Math.invsqrt(m00 * m00 + m01 * m01 + m02 * m02);
double lenY = Math.invsqrt(m10 * m10 + m11 * m11 + m12 * m12);
double lenZ = Math.invsqrt(m20 * m20 + m21 * m21 + m22 * m22);
nm00 *= lenX; nm01 *= lenX; nm02 *= lenX;
nm10 *= lenY; nm11 *= lenY; nm12 *= lenY;
nm20 *= lenZ; nm21 *= lenZ; nm22 *= lenZ;
setFromNormalized(nm00, nm01, nm02, nm10, nm11, nm12, nm20, nm21, nm22);
}
private void setFromNormalized(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22) {
double t;
double tr = m00 + m11 + m22;
if (tr >= 0.0) {
t = Math.sqrt(tr + 1.0);
w = t * 0.5;
t = 0.5 / t;
x = (m12 - m21) * t;
y = (m20 - m02) * t;
z = (m01 - m10) * t;
} else {
if (m00 >= m11 && m00 >= m22) {
t = Math.sqrt(m00 - (m11 + m22) + 1.0);
x = t * 0.5;
t = 0.5 / t;
y = (m10 + m01) * t;
z = (m02 + m20) * t;
w = (m12 - m21) * t;
} else if (m11 > m22) {
t = Math.sqrt(m11 - (m22 + m00) + 1.0);
y = t * 0.5;
t = 0.5 / t;
z = (m21 + m12) * t;
x = (m10 + m01) * t;
w = (m20 - m02) * t;
} else {
t = Math.sqrt(m22 - (m00 + m11) + 1.0);
z = t * 0.5;
t = 0.5 / t;
x = (m02 + m20) * t;
y = (m21 + m12) * t;
w = (m01 - m10) * t;
}
}
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix4fc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix4x3fc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix4x3dc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix4fc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix4x3fc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix4x3dc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix4dc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix4dc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix3fc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix3fc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
* <p>
* This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromUnnormalized(Matrix3dc mat) {
setFromUnnormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the rotational component of the given matrix.
*
* @param mat
* the matrix whose rotational component is used to set this quaternion
* @return this
*/
public Quaterniond setFromNormalized(Matrix3dc mat) {
setFromNormalized(mat.m00(), mat.m01(), mat.m02(), mat.m10(), mat.m11(), mat.m12(), mat.m20(), mat.m21(), mat.m22());
return this;
}
/**
* Set this quaternion to be a representation of the supplied axis and
* angle (in radians).
*
* @param axis
* the rotation axis
* @param angle
* the angle in radians
* @return this
*/
public Quaterniond fromAxisAngleRad(Vector3dc axis, double angle) {
return fromAxisAngleRad(axis.x(), axis.y(), axis.z(), angle);
}
/**
* Set this quaternion to be a representation of the supplied axis and
* angle (in radians).
*
* @param axisX
* the x component of the rotation axis
* @param axisY
* the y component of the rotation axis
* @param axisZ
* the z component of the rotation axis
* @param angle
* the angle in radians
* @return this
*/
public Quaterniond fromAxisAngleRad(double axisX, double axisY, double axisZ, double angle) {
double hangle = angle / 2.0;
double sinAngle = Math.sin(hangle);
double vLength = Math.sqrt(axisX * axisX + axisY * axisY + axisZ * axisZ);
x = axisX / vLength * sinAngle;
y = axisY / vLength * sinAngle;
z = axisZ / vLength * sinAngle;
w = Math.cosFromSin(sinAngle, hangle);
return this;
}
/**
* Set this quaternion to be a representation of the supplied axis and
* angle (in degrees).
*
* @param axis
* the rotation axis
* @param angle
* the angle in degrees
* @return this
*/
public Quaterniond fromAxisAngleDeg(Vector3dc axis, double angle) {
return fromAxisAngleRad(axis.x(), axis.y(), axis.z(), Math.toRadians(angle));
}
/**
* Set this quaternion to be a representation of the supplied axis and
* angle (in degrees).
*
* @param axisX
* the x component of the rotation axis
* @param axisY
* the y component of the rotation axis
* @param axisZ
* the z component of the rotation axis
* @param angle
* the angle in radians
* @return this
*/
public Quaterniond fromAxisAngleDeg(double axisX, double axisY, double axisZ, double angle) {
return fromAxisAngleRad(axisX, axisY, axisZ, Math.toRadians(angle));
}
/**
* Multiply this quaternion by <code>q</code>.
* <p>
* If <code>T</code> is <code>this</code> and <code>Q</code> is the given
* quaternion, then the resulting quaternion <code>R</code> is:
* <p>
* <code>R = T * Q</code>
* <p>
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by <code>Q</code> first, and then by <code>T</code>.
*
* @param q
* the quaternion to multiply <code>this</code> by
* @return this
*/
public Quaterniond mul(Quaterniondc q) {
return mul(q, this);
}
public Quaterniond mul(Quaterniondc q, Quaterniond dest) {
return mul(q.x(), q.y(), q.z(), q.w(), dest);
}
/**
* Multiply this quaternion by the quaternion represented via <code>(qx, qy, qz, qw)</code>.
* <p>
* If <code>T</code> is <code>this</code> and <code>Q</code> is the given
* quaternion, then the resulting quaternion <code>R</code> is:
* <p>
* <code>R = T * Q</code>
* <p>
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by <code>Q</code> first, and then by <code>T</code>.
*
* @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
* @return this
*/
public Quaterniond mul(double qx, double qy, double qz, double qw) {
return mul(qx, qy, qz, qw, this);
}
public Quaterniond mul(double qx, double qy, double qz, double qw, Quaterniond dest) {
return dest.set(Math.fma(w, qx, Math.fma(x, qw, Math.fma(y, qz, -z * qy))),
Math.fma(w, qy, Math.fma(-x, qz, Math.fma(y, qw, z * qx))),
Math.fma(w, qz, Math.fma(x, qy, Math.fma(-y, qx, z * qw))),
Math.fma(w, qw, Math.fma(-x, qx, Math.fma(-y, qy, -z * qz))));
}
/**
* Pre-multiply this quaternion by <code>q</code>.
* <p>
* If <code>T</code> is <code>this</code> and <code>Q</code> is the given quaternion, then the resulting quaternion <code>R</code> is:
* <p>
* <code>R = Q * T</code>
* <p>
* So, this method uses pre-multiplication, resulting in a vector to be transformed by <code>T</code> first, and then by <code>Q</code>.
*
* @param q
* the quaternion to pre-multiply <code>this</code> by
* @return this
*/
public Quaterniond premul(Quaterniondc q) {
return premul(q, this);
}
public Quaterniond premul(Quaterniondc q, Quaterniond dest) {
return premul(q.x(), q.y(), q.z(), q.w(), dest);
}
/**
* Pre-multiply this quaternion by the quaternion represented via <code>(qx, qy, qz, qw)</code>.
* <p>
* If <code>T</code> is <code>this</code> and <code>Q</code> is the given quaternion, then the resulting quaternion <code>R</code> is:
* <p>
* <code>R = Q * T</code>
* <p>
* So, this method uses pre-multiplication, resulting in a vector to be transformed by <code>T</code> first, and then by <code>Q</code>.
*
* @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
* @return this
*/
public Quaterniond premul(double qx, double qy, double qz, double qw) {
return premul(qx, qy, qz, qw, this);
}
public Quaterniond premul(double qx, double qy, double qz, double qw, Quaterniond dest) {
return dest.set(Math.fma(qw, x, Math.fma(qx, w, Math.fma(qy, z, -qz * y))),
Math.fma(qw, y, Math.fma(-qx, z, Math.fma(qy, w, qz * x))),
Math.fma(qw, z, Math.fma(qx, y, Math.fma(-qy, x, qz * w))),
Math.fma(qw, w, Math.fma(-qx, x, Math.fma(-qy, y, -qz * z))));
}
public Vector3d transform(Vector3d vec){
return transform(vec.x, vec.y, vec.z, vec);
}
public Vector3d transformInverse(Vector3d vec){
return transformInverse(vec.x, vec.y, vec.z, vec);
}
public Vector3d transformUnit(Vector3d vec){
return transformUnit(vec.x, vec.y, vec.z, vec);
}
public Vector3d transformInverseUnit(Vector3d vec){
return transformInverseUnit(vec.x, vec.y, vec.z, vec);
}
public Vector3d transformPositiveX(Vector3d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = ww + xx - zz - yy;
dest.y = xy + zw + zw + xy;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector4d transformPositiveX(Vector4d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = ww + xx - zz - yy;
dest.y = xy + zw + zw + xy;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector3d transformUnitPositiveX(Vector3d dest) {
double yy = y * y;
double zz = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = 1.0 - yy - yy - zz - zz;
dest.y = xy + zw + xy + zw;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector4d transformUnitPositiveX(Vector4d dest) {
double yy = y * y;
double zz = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = 1.0 - yy - yy - zz - zz;
dest.y = xy + zw + xy + zw;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector3d transformPositiveY(Vector3d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double yz = y * z;
double xw = x * w;
dest.x = -zw + xy - zw + xy;
dest.y = yy - zz + ww - xx;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector4d transformPositiveY(Vector4d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double yz = y * z;
double xw = x * w;
dest.x = -zw + xy - zw + xy;
dest.y = yy - zz + ww - xx;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector4d transformUnitPositiveY(Vector4d dest) {
double xx = x * x;
double zz = z * z;
double xy = x * y;
double yz = y * z;
double xw = x * w;
double zw = z * w;
dest.x = xy - zw + xy - zw;
dest.y = 1.0 - xx - xx - zz - zz;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector3d transformUnitPositiveY(Vector3d dest) {
double xx = x * x;
double zz = z * z;
double xy = x * y;
double yz = y * z;
double xw = x * w;
double zw = z * w;
dest.x = xy - zw + xy - zw;
dest.y = 1.0 - xx - xx - zz - zz;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector3d transformPositiveZ(Vector3d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double xz = x * z;
double yw = y * w;
double yz = y * z;
double xw = x * w;
dest.x = yw + xz + xz + yw;
dest.y = yz + yz - xw - xw;
dest.z = zz - yy - xx + ww;
return dest;
}
public Vector4d transformPositiveZ(Vector4d dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double xz = x * z;
double yw = y * w;
double yz = y * z;
double xw = x * w;
dest.x = yw + xz + xz + yw;
dest.y = yz + yz - xw - xw;
dest.z = zz - yy - xx + ww;
return dest;
}
public Vector4d transformUnitPositiveZ(Vector4d dest) {
double xx = x * x;
double yy = y * y;
double xz = x * z;
double yz = y * z;
double xw = x * w;
double yw = y * w;
dest.x = xz + yw + xz + yw;
dest.y = yz + yz - xw - xw;
dest.z = 1.0 - xx - xx - yy - yy;
return dest;
}
public Vector3d transformUnitPositiveZ(Vector3d dest) {
double xx = x * x;
double yy = y * y;
double xz = x * z;
double yz = y * z;
double xw = x * w;
double yw = y * w;
dest.x = xz + yw + xz + yw;
dest.y = yz + yz - xw - xw;
dest.z = 1.0 - xx - xx - yy - yy;
return dest;
}
public Vector4d transform(Vector4d vec){
return transform(vec, vec);
}
public Vector4d transformInverse(Vector4d vec){
return transformInverse(vec, vec);
}
public Vector3d transform(Vector3dc vec, Vector3d dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3d transformInverse(Vector3dc vec, Vector3d dest) {
return transformInverse(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3d transform(double x, double y, double z, Vector3d dest) {
double xx = this.x * this.x, yy = this.y * this.y, zz = this.z * this.z, ww = this.w * this.w;
double xy = this.x * this.y, xz = this.x * this.z, yz = this.y * this.z, xw = this.x * this.w;
double zw = this.z * this.w, yw = this.y * this.w, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy - zw) * k, y, (2 * (xz + yw) * k) * z)),
Math.fma(2 * (xy + zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz - xw) * k) * z)),
Math.fma(2 * (xz - yw) * k, x, Math.fma(2 * (yz + xw) * k, y, ((zz - xx - yy + ww) * k) * z)));
}
public Vector3d transformInverse(double x, double y, double z, Vector3d dest) {
double n = 1.0 / Math.fma(this.x, this.x, Math.fma(this.y, this.y, Math.fma(this.z, this.z, this.w * this.w)));
double qx = this.x * n, qy = this.y * n, qz = this.z * n, qw = this.w * n;
double xx = qx * qx, yy = qy * qy, zz = qz * qz, ww = qw * qw;
double xy = qx * qy, xz = qx * qz, yz = qy * qz, xw = qx * qw;
double zw = qz * qw, yw = qy * qw, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy + zw) * k, y, (2 * (xz - yw) * k) * z)),
Math.fma(2 * (xy - zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz + xw) * k) * z)),
Math.fma(2 * (xz + yw) * k, x, Math.fma(2 * (yz - xw) * k, y, ((zz - xx - yy + ww) * k) * z)));
}
public Vector4d transform(Vector4dc vec, Vector4d dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4d transformInverse(Vector4dc vec, Vector4d dest) {
return transformInverse(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4d transform(double x, double y, double z, Vector4d dest) {
double xx = this.x * this.x, yy = this.y * this.y, zz = this.z * this.z, ww = this.w * this.w;
double xy = this.x * this.y, xz = this.x * this.z, yz = this.y * this.z, xw = this.x * this.w;
double zw = this.z * this.w, yw = this.y * this.w, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy - zw) * k, y, (2 * (xz + yw) * k) * z)),
Math.fma(2 * (xy + zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz - xw) * k) * z)),
Math.fma(2 * (xz - yw) * k, x, Math.fma(2 * (yz + xw) * k, y, ((zz - xx - yy + ww) * k) * z)), dest.w);
}
public Vector4d transformInverse(double x, double y, double z, Vector4d dest) {
double n = 1.0 / Math.fma(this.x, this.x, Math.fma(this.y, this.y, Math.fma(this.z, this.z, this.w * this.w)));
double qx = this.x * n, qy = this.y * n, qz = this.z * n, qw = this.w * n;
double xx = qx * qx, yy = qy * qy, zz = qz * qz, ww = qw * qw;
double xy = qx * qy, xz = qx * qz, yz = qy * qz, xw = qx * qw;
double zw = qz * qw, yw = qy * qw, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy + zw) * k, y, (2 * (xz - yw) * k) * z)),
Math.fma(2 * (xy - zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz + xw) * k) * z)),
Math.fma(2 * (xz + yw) * k, x, Math.fma(2 * (yz - xw) * k, y, ((zz - xx - yy + ww) * k) * z)));
}
public Vector3f transform(Vector3f vec){
return transform(vec.x, vec.y, vec.z, vec);
}
public Vector3f transformInverse(Vector3f vec){
return transformInverse(vec.x, vec.y, vec.z, vec);
}
public Vector4d transformUnit(Vector4d vec){
return transformUnit(vec, vec);
}
public Vector4d transformInverseUnit(Vector4d vec){
return transformInverseUnit(vec, vec);
}
public Vector3d transformUnit(Vector3dc vec, Vector3d dest) {
return transformUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3d transformInverseUnit(Vector3dc vec, Vector3d dest) {
return transformInverseUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3d transformUnit(double x, double y, double z, Vector3d dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set(Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy - zw), y, (2 * (xz + yw)) * z)),
Math.fma(2 * (xy + zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz - xw)) * z)),
Math.fma(2 * (xz - yw), x, Math.fma(2 * (yz + xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Vector3d transformInverseUnit(double x, double y, double z, Vector3d dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set(Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy + zw), y, (2 * (xz - yw)) * z)),
Math.fma(2 * (xy - zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz + xw)) * z)),
Math.fma(2 * (xz + yw), x, Math.fma(2 * (yz - xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Vector4d transformUnit(Vector4dc vec, Vector4d dest) {
return transformUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4d transformInverseUnit(Vector4dc vec, Vector4d dest) {
return transformInverseUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4d transformUnit(double x, double y, double z, Vector4d dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set(Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy - zw), y, (2 * (xz + yw)) * z)),
Math.fma(2 * (xy + zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz - xw)) * z)),
Math.fma(2 * (xz - yw), x, Math.fma(2 * (yz + xw), y, Math.fma(-2, xx + yy, 1) * z)),
dest.w);
}
public Vector4d transformInverseUnit(double x, double y, double z, Vector4d dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set(Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy + zw), y, (2 * (xz - yw)) * z)),
Math.fma(2 * (xy - zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz + xw)) * z)),
Math.fma(2 * (xz + yw), x, Math.fma(2 * (yz - xw), y, Math.fma(-2, xx + yy, 1) * z)),
dest.w);
}
public Vector3f transformUnit(Vector3f vec){
return transformUnit(vec.x, vec.y, vec.z, vec);
}
public Vector3f transformInverseUnit(Vector3f vec){
return transformInverseUnit(vec.x, vec.y, vec.z, vec);
}
public Vector3f transformPositiveX(Vector3f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = (float) (ww + xx - zz - yy);
dest.y = (float) (xy + zw + zw + xy);
dest.z = (float) (xz - yw + xz - yw);
return dest;
}
public Vector4f transformPositiveX(Vector4f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = (float) (ww + xx - zz - yy);
dest.y = (float) (xy + zw + zw + xy);
dest.z = (float) (xz - yw + xz - yw);
return dest;
}
public Vector3f transformUnitPositiveX(Vector3f dest) {
double yy = y * y;
double zz = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = (float) (1.0 - yy - yy - zz - zz);
dest.y = (float) (xy + zw + xy + zw);
dest.z = (float) (xz - yw + xz - yw);
return dest;
}
public Vector4f transformUnitPositiveX(Vector4f dest) {
double yy = y * y;
double zz = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = (float) (1.0 - yy - yy - zz - zz);
dest.y = (float) (xy + zw + xy + zw);
dest.z = (float) (xz - yw + xz - yw);
return dest;
}
public Vector3f transformPositiveY(Vector3f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double yz = y * z;
double xw = x * w;
dest.x = (float) (-zw + xy - zw + xy);
dest.y = (float) (yy - zz + ww - xx);
dest.z = (float) (yz + yz + xw + xw);
return dest;
}
public Vector4f transformPositiveY(Vector4f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double zw = z * w;
double xy = x * y;
double yz = y * z;
double xw = x * w;
dest.x = (float) (-zw + xy - zw + xy);
dest.y = (float) (yy - zz + ww - xx);
dest.z = (float) (yz + yz + xw + xw);
return dest;
}
public Vector4f transformUnitPositiveY(Vector4f dest) {
double xx = x * x;
double zz = z * z;
double xy = x * y;
double yz = y * z;
double xw = x * w;
double zw = z * w;
dest.x = (float) (xy - zw + xy - zw);
dest.y = (float) (1.0 - xx - xx - zz - zz);
dest.z = (float) (yz + yz + xw + xw);
return dest;
}
public Vector3f transformUnitPositiveY(Vector3f dest) {
double xx = x * x;
double zz = z * z;
double xy = x * y;
double yz = y * z;
double xw = x * w;
double zw = z * w;
dest.x = (float) (xy - zw + xy - zw);
dest.y = (float) (1.0 - xx - xx - zz - zz);
dest.z = (float) (yz + yz + xw + xw);
return dest;
}
public Vector3f transformPositiveZ(Vector3f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double xz = x * z;
double yw = y * w;
double yz = y * z;
double xw = x * w;
dest.x = (float) (yw + xz + xz + yw);
dest.y = (float) (yz + yz - xw - xw);
dest.z = (float) (zz - yy - xx + ww);
return dest;
}
public Vector4f transformPositiveZ(Vector4f dest) {
double ww = w * w;
double xx = x * x;
double yy = y * y;
double zz = z * z;
double xz = x * z;
double yw = y * w;
double yz = y * z;
double xw = x * w;
dest.x = (float) (yw + xz + xz + yw);
dest.y = (float) (yz + yz - xw - xw);
dest.z = (float) (zz - yy - xx + ww);
return dest;
}
public Vector4f transformUnitPositiveZ(Vector4f dest) {
double xx = x * x;
double yy = y * y;
double xz = x * z;
double yz = y * z;
double xw = x * w;
double yw = y * w;
dest.x = (float) (xz + yw + xz + yw);
dest.y = (float) (yz + yz - xw - xw);
dest.z = (float) (1.0 - xx - xx - yy - yy);
return dest;
}
public Vector3f transformUnitPositiveZ(Vector3f dest) {
double xx = x * x;
double yy = y * y;
double xz = x * z;
double yz = y * z;
double xw = x * w;
double yw = y * w;
dest.x = (float) (xz + yw + xz + yw);
dest.y = (float) (yz + yz - xw - xw);
dest.z = (float) (1.0 - xx - xx - yy - yy);
return dest;
}
public Vector4f transform(Vector4f vec){
return transform(vec, vec);
}
public Vector4f transformInverse(Vector4f vec){
return transformInverse(vec, vec);
}
public Vector3f transform(Vector3fc vec, Vector3f dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3f transformInverse(Vector3fc vec, Vector3f dest) {
return transformInverse(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3f transform(double x, double y, double z, Vector3f dest) {
double xx = this.x * this.x, yy = this.y * this.y, zz = this.z * this.z, ww = this.w * this.w;
double xy = this.x * this.y, xz = this.x * this.z, yz = this.y * this.z, xw = this.x * this.w;
double zw = this.z * this.w, yw = this.y * this.w, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy - zw) * k, y, (2 * (xz + yw) * k) * z)),
Math.fma(2 * (xy + zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz - xw) * k) * z)),
Math.fma(2 * (xz - yw) * k, x, Math.fma(2 * (yz + xw) * k, y, ((zz - xx - yy + ww) * k) * z)));
}
public Vector3f transformInverse(double x, double y, double z, Vector3f dest) {
double n = 1.0 / Math.fma(this.x, this.x, Math.fma(this.y, this.y, Math.fma(this.z, this.z, this.w * this.w)));
double qx = this.x * n, qy = this.y * n, qz = this.z * n, qw = this.w * n;
double xx = qx * qx, yy = qy * qy, zz = qz * qz, ww = qw * qw;
double xy = qx * qy, xz = qx * qz, yz = qy * qz, xw = qx * qw;
double zw = qz * qw, yw = qy * qw, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy + zw) * k, y, (2 * (xz - yw) * k) * z)),
Math.fma(2 * (xy - zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz + xw) * k) * z)),
Math.fma(2 * (xz + yw) * k, x, Math.fma(2 * (yz - xw) * k, y, ((zz - xx - yy + ww) * k) * z)));
}
public Vector4f transform(Vector4fc vec, Vector4f dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4f transformInverse(Vector4fc vec, Vector4f dest) {
return transformInverse(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4f transform(double x, double y, double z, Vector4f dest) {
double xx = this.x * this.x, yy = this.y * this.y, zz = this.z * this.z, ww = this.w * this.w;
double xy = this.x * this.y, xz = this.x * this.z, yz = this.y * this.z, xw = this.x * this.w;
double zw = this.z * this.w, yw = this.y * this.w, k = 1 / (xx + yy + zz + ww);
return dest.set((float) Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy - zw) * k, y, (2 * (xz + yw) * k) * z)),
(float) Math.fma(2 * (xy + zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz - xw) * k) * z)),
(float) Math.fma(2 * (xz - yw) * k, x, Math.fma(2 * (yz + xw) * k, y, ((zz - xx - yy + ww) * k) * z)), dest.w);
}
public Vector4f transformInverse(double x, double y, double z, Vector4f dest) {
double n = 1.0 / Math.fma(this.x, this.x, Math.fma(this.y, this.y, Math.fma(this.z, this.z, this.w * this.w)));
double qx = this.x * n, qy = this.y * n, qz = this.z * n, qw = this.w * n;
double xx = qx * qx, yy = qy * qy, zz = qz * qz, ww = qw * qw;
double xy = qx * qy, xz = qx * qz, yz = qy * qz, xw = qx * qw;
double zw = qz * qw, yw = qy * qw, k = 1 / (xx + yy + zz + ww);
return dest.set(Math.fma((xx - yy - zz + ww) * k, x, Math.fma(2 * (xy + zw) * k, y, (2 * (xz - yw) * k) * z)),
Math.fma(2 * (xy - zw) * k, x, Math.fma((yy - xx - zz + ww) * k, y, (2 * (yz + xw) * k) * z)),
Math.fma(2 * (xz + yw) * k, x, Math.fma(2 * (yz - xw) * k, y, ((zz - xx - yy + ww) * k) * z)), dest.w);
}
public Vector4f transformUnit(Vector4f vec){
return transformUnit(vec, vec);
}
public Vector4f transformInverseUnit(Vector4f vec){
return transformInverseUnit(vec, vec);
}
public Vector3f transformUnit(Vector3fc vec, Vector3f dest) {
return transformUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3f transformInverseUnit(Vector3fc vec, Vector3f dest) {
return transformInverseUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector3f transformUnit(double x, double y, double z, Vector3f dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set((float) Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy - zw), y, (2 * (xz + yw)) * z)),
(float) Math.fma(2 * (xy + zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz - xw)) * z)),
(float) Math.fma(2 * (xz - yw), x, Math.fma(2 * (yz + xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Vector3f transformInverseUnit(double x, double y, double z, Vector3f dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set((float) Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy + zw), y, (2 * (xz - yw)) * z)),
(float) Math.fma(2 * (xy - zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz + xw)) * z)),
(float) Math.fma(2 * (xz + yw), x, Math.fma(2 * (yz - xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Vector4f transformUnit(Vector4fc vec, Vector4f dest) {
return transformUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4f transformInverseUnit(Vector4fc vec, Vector4f dest) {
return transformInverseUnit(vec.x(), vec.y(), vec.z(), dest);
}
public Vector4f transformUnit(double x, double y, double z, Vector4f dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set((float) Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy - zw), y, (2 * (xz + yw)) * z)),
(float) Math.fma(2 * (xy + zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz - xw)) * z)),
(float) Math.fma(2 * (xz - yw), x, Math.fma(2 * (yz + xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Vector4f transformInverseUnit(double x, double y, double z, Vector4f dest) {
double xx = this.x * this.x, xy = this.x * this.y, xz = this.x * this.z;
double xw = this.x * this.w, yy = this.y * this.y, yz = this.y * this.z;
double yw = this.y * this.w, zz = this.z * this.z, zw = this.z * this.w;
return dest.set((float) Math.fma(Math.fma(-2, yy + zz, 1), x, Math.fma(2 * (xy + zw), y, (2 * (xz - yw)) * z)),
(float) Math.fma(2 * (xy - zw), x, Math.fma(Math.fma(-2, xx + zz, 1), y, (2 * (yz + xw)) * z)),
(float) Math.fma(2 * (xz + yw), x, Math.fma(2 * (yz - xw), y, Math.fma(-2, xx + yy, 1) * z)));
}
public Quaterniond invert(Quaterniond dest) {
double invNorm = 1.0 / lengthSquared();
dest.x = -x * invNorm;
dest.y = -y * invNorm;
dest.z = -z * invNorm;
dest.w = w * invNorm;
return dest;
}
/**
* Invert this quaternion and {@link #normalize() normalize} it.
* <p>
* If this quaternion is already normalized, then {@link #conjugate()} should be used instead.
*
* @see #conjugate()
*
* @return this
*/
public Quaterniond invert() {
return invert(this);
}
public Quaterniond div(Quaterniondc b, Quaterniond dest) {
double invNorm = 1.0 / Math.fma(b.x(), b.x(), Math.fma(b.y(), b.y(), Math.fma(b.z(), b.z(), b.w() * b.w())));
double x = -b.x() * invNorm;
double y = -b.y() * invNorm;
double z = -b.z() * invNorm;
double w = b.w() * invNorm;
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
/**
* Divide <code>this</code> quaternion by <code>b</code>.
* <p>
* The division expressed using the inverse is performed in the following way:
* <p>
* <code>this = this * b^-1</code>, where <code>b^-1</code> is the inverse of <code>b</code>.
*
* @param b
* the {@link Quaterniondc} to divide this by
* @return this
*/
public Quaterniond div(Quaterniondc b) {
return div(b, this);
}
/**
* Conjugate this quaternion.
*
* @return this
*/
public Quaterniond conjugate() {
x = -x;
y = -y;
z = -z;
return this;
}
public Quaterniond conjugate(Quaterniond dest) {
dest.x = -x;
dest.y = -y;
dest.z = -z;
dest.w = w;
return dest;
}
/**
* Set this quaternion to the identity.
*
* @return this
*/
public Quaterniond identity() {
x = 0.0;
y = 0.0;
z = 0.0;
w = 1.0;
return this;
}
public double lengthSquared() {
return Math.fma(x, x, Math.fma(y, y, Math.fma(z, z, w * w)));
}
/**
* Set this quaternion from the supplied euler angles (in radians) with rotation order XYZ.
* <p>
* This method is equivalent to calling: <code>rotationX(angleX).rotateY(angleY).rotateZ(angleZ)</code>
* <p>
* Reference: <a href="http://gamedev.stackexchange.com/questions/13436/glm-euler-angles-to-quaternion#answer-13446">this stackexchange answer</a>
*
* @param angleX
* the angle in radians to rotate about x
* @param angleY
* the angle in radians to rotate about y
* @param angleZ
* the angle in radians to rotate about z
* @return this
*/
public Quaterniond rotationXYZ(double angleX, double angleY, double angleZ) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double cycz = cy * cz;
double sysz = sy * sz;
double sycz = sy * cz;
double cysz = cy * sz;
w = cx*cycz - sx*sysz;
x = sx*cycz + cx*sysz;
y = cx*sycz - sx*cysz;
z = cx*cysz + sx*sycz;
return this;
}
/**
* Set this quaternion from the supplied euler angles (in radians) with rotation order ZYX.
* <p>
* This method is equivalent to calling: <code>rotationZ(angleZ).rotateY(angleY).rotateX(angleX)</code>
* <p>
* Reference: <a href="http://gamedev.stackexchange.com/questions/13436/glm-euler-angles-to-quaternion#answer-13446">this stackexchange answer</a>
*
* @param angleX
* the angle in radians to rotate about x
* @param angleY
* the angle in radians to rotate about y
* @param angleZ
* the angle in radians to rotate about z
* @return this
*/
public Quaterniond rotationZYX(double angleZ, double angleY, double angleX) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double cycz = cy * cz;
double sysz = sy * sz;
double sycz = sy * cz;
double cysz = cy * sz;
w = cx*cycz + sx*sysz;
x = sx*cycz - cx*sysz;
y = cx*sycz + sx*cysz;
z = cx*cysz - sx*sycz;
return this;
}
/**
* Set this quaternion from the supplied euler angles (in radians) with rotation order YXZ.
* <p>
* This method is equivalent to calling: <code>rotationY(angleY).rotateX(angleX).rotateZ(angleZ)</code>
* <p>
* Reference: <a href="https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles">https://en.wikipedia.org</a>
*
* @param angleY
* the angle in radians to rotate about y
* @param angleX
* the angle in radians to rotate about x
* @param angleZ
* the angle in radians to rotate about z
* @return this
*/
public Quaterniond rotationYXZ(double angleY, double angleX, double angleZ) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double x = cy * sx;
double y = sy * cx;
double z = sy * sx;
double w = cy * cx;
this.x = x * cz + y * sz;
this.y = y * cz - x * sz;
this.z = w * sz - z * cz;
this.w = w * cz + z * sz;
return this;
}
/**
* Interpolate between <code>this</code> {@link #normalize() unit} quaternion and the specified
* <code>target</code> {@link #normalize() unit} quaternion using spherical linear interpolation using the specified interpolation factor <code>alpha</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 <code>1E-6</code>.
*
* @param target
* the target of the interpolation, which should be reached with <code>alpha = 1.0</code>
* @param alpha
* the interpolation factor, within <code>[0..1]</code>
* @return this
*/
public Quaterniond slerp(Quaterniondc target, double alpha) {
return slerp(target, alpha, this);
}
public Quaterniond slerp(Quaterniondc target, double alpha, Quaterniond dest) {
double cosom = Math.fma(x, target.x(), Math.fma(y, target.y(), Math.fma(z, target.z(), w * target.w())));
double absCosom = Math.abs(cosom);
double scale0, scale1;
if (1.0 - absCosom > 1E-6) {
double sinSqr = 1.0 - absCosom * absCosom;
double sinom = Math.invsqrt(sinSqr);
double omega = Math.atan2(sinSqr * sinom, absCosom);
scale0 = Math.sin((1.0 - alpha) * omega) * sinom;
scale1 = Math.sin(alpha * omega) * sinom;
} else {
scale0 = 1.0 - alpha;
scale1 = alpha;
}
scale1 = cosom >= 0.0 ? scale1 : -scale1;
dest.x = Math.fma(scale0, x, scale1 * target.x());
dest.y = Math.fma(scale0, y, scale1 * target.y());
dest.z = Math.fma(scale0, z, scale1 * target.z());
dest.w = Math.fma(scale0, w, scale1 * target.w());
return dest;
}
/**
* Interpolate between all of the quaternions given in <code>qs</code> via spherical linear interpolation using the specified interpolation factors <code>weights</code>,
* and store the result in <code>dest</code>.
* <p>
* This method will interpolate between each two successive quaternions via {@link #slerp(Quaterniondc, double)} using their relative interpolation weights.
* <p>
* This method resorts to non-spherical linear interpolation when the absolute dot product of any two interpolated quaternions is below <code>1E-6f</code>.
* <p>
* Reference: <a href="http://gamedev.stackexchange.com/questions/62354/method-for-interpolation-between-3-quaternions#answer-62356">http://gamedev.stackexchange.com/</a>
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in <code>qs</code>
* @param dest
* will hold the result
* @return dest
*/
public static Quaterniondc slerp(Quaterniond[] qs, double[] weights, Quaterniond dest) {
dest.set(qs[0]);
double w = weights[0];
for (int i = 1; i < qs.length; i++) {
double w0 = w;
double w1 = weights[i];
double rw1 = w1 / (w0 + w1);
w += w1;
dest.slerp(qs[i], rw1);
}
return dest;
}
/**
* Apply scaling to this quaternion, which results in any vector transformed by this quaternion to change
* its length by the given <code>factor</code>.
*
* @param factor
* the scaling factor
* @return this
*/
public Quaterniond scale(double factor) {
return scale(factor, this);
}
public Quaterniond scale(double factor, Quaterniond dest) {
double sqrt = Math.sqrt(factor);
dest.x = sqrt * x;
dest.y = sqrt * y;
dest.z = sqrt * z;
dest.w = sqrt * w;
return dest;
}
/**
* Set this quaternion to represent scaling, which results in a transformed vector to change
* its length by the given <code>factor</code>.
*
* @param factor
* the scaling factor
* @return this
*/
public Quaterniond scaling(double factor) {
double sqrt = Math.sqrt(factor);
this.x = 0.0;
this.y = 0.0;
this.z = 0.0;
this.w = sqrt;
return this;
}
/**
* 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.
* <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)</code>
* <p>
* Reference: <a href="http://physicsforgames.blogspot.de/2010/02/quaternions.html">http://physicsforgames.blogspot.de/</a>
*
* @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
* @return this
*/
public Quaterniond integrate(double dt, double vx, double vy, double vz) {
return integrate(dt, vx, vy, vz, this);
}
public Quaterniond integrate(double dt, double vx, double vy, double vz, Quaterniond dest) {
double thetaX = dt * vx * 0.5;
double thetaY = dt * vy * 0.5;
double thetaZ = dt * vz * 0.5;
double thetaMagSq = thetaX * thetaX + thetaY * thetaY + thetaZ * thetaZ;
double s;
double dqX, dqY, dqZ, dqW;
if (thetaMagSq * thetaMagSq / 24.0 < 1E-8) {
dqW = 1.0 - thetaMagSq * 0.5;
s = 1.0 - thetaMagSq / 6.0;
} else {
double thetaMag = Math.sqrt(thetaMagSq);
double sin = Math.sin(thetaMag);
s = sin / thetaMag;
dqW = Math.cosFromSin(sin, thetaMag);
}
dqX = thetaX * s;
dqY = thetaY * s;
dqZ = thetaZ * s;
/* Pre-multiplication */
return dest.set(Math.fma(dqW, x, Math.fma(dqX, w, Math.fma(dqY, z, -dqZ * y))),
Math.fma(dqW, y, Math.fma(-dqX, z, Math.fma(dqY, w, dqZ * x))),
Math.fma(dqW, z, Math.fma(dqX, y, Math.fma(-dqY, x, dqZ * w))),
Math.fma(dqW, w, Math.fma(-dqX, x, Math.fma(-dqY, y, -dqZ * z))));
}
/**
* Compute a linear (non-spherical) interpolation of <code>this</code> and the given quaternion <code>q</code>
* and store the result in <code>this</code>.
*
* @param q
* the other quaternion
* @param factor
* the interpolation factor. It is between 0.0 and 1.0
* @return this
*/
public Quaterniond nlerp(Quaterniondc q, double factor) {
return nlerp(q, factor, this);
}
public Quaterniond nlerp(Quaterniondc q, double factor, Quaterniond dest) {
double cosom = Math.fma(x, q.x(), Math.fma(y, q.y(), Math.fma(z, q.z(), w * q.w())));
double scale0 = 1.0 - factor;
double scale1 = (cosom >= 0.0) ? factor : -factor;
dest.x = Math.fma(scale0, x, scale1 * q.x());
dest.y = Math.fma(scale0, y, scale1 * q.y());
dest.z = Math.fma(scale0, z, scale1 * q.z());
dest.w = Math.fma(scale0, w, scale1 * q.w());
double s = Math.invsqrt(Math.fma(dest.x, dest.x, Math.fma(dest.y, dest.y, Math.fma(dest.z, dest.z, dest.w * dest.w))));
dest.x *= s;
dest.y *= s;
dest.z *= s;
dest.w *= s;
return dest;
}
/**
* Interpolate between all of the quaternions given in <code>qs</code> via non-spherical linear interpolation using the
* specified interpolation factors <code>weights</code>, and store the result in <code>dest</code>.
* <p>
* This method will interpolate between each two successive quaternions via {@link #nlerp(Quaterniondc, double)}
* using their relative interpolation weights.
* <p>
* Reference: <a href="http://gamedev.stackexchange.com/questions/62354/method-for-interpolation-between-3-quaternions#answer-62356">http://gamedev.stackexchange.com/</a>
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in <code>qs</code>
* @param dest
* will hold the result
* @return dest
*/
public static Quaterniondc nlerp(Quaterniond[] qs, double[] weights, Quaterniond dest) {
dest.set(qs[0]);
double w = weights[0];
for (int i = 1; i < qs.length; i++) {
double w0 = w;
double w1 = weights[i];
double rw1 = w1 / (w0 + w1);
w += w1;
dest.nlerp(qs[i], rw1);
}
return dest;
}
public Quaterniond nlerpIterative(Quaterniondc q, double alpha, double dotThreshold, Quaterniond dest) {
double q1x = x, q1y = y, q1z = z, q1w = w;
double q2x = q.x(), q2y = q.y(), q2z = q.z(), q2w = q.w();
double dot = Math.fma(q1x, q2x, Math.fma(q1y, q2y, Math.fma(q1z, q2z, q1w * q2w)));
double absDot = Math.abs(dot);
if (1.0 - 1E-6 < absDot) {
return dest.set(this);
}
double alphaN = alpha;
while (absDot < dotThreshold) {
double scale0 = 0.5;
double scale1 = dot >= 0.0 ? 0.5 : -0.5;
if (alphaN < 0.5) {
q2x = Math.fma(scale0, q2x, scale1 * q1x);
q2y = Math.fma(scale0, q2y, scale1 * q1y);
q2z = Math.fma(scale0, q2z, scale1 * q1z);
q2w = Math.fma(scale0, q2w, scale1 * q1w);
float s = (float) Math.invsqrt(Math.fma(q2x, q2x, Math.fma(q2y, q2y, Math.fma(q2z, q2z, q2w * q2w))));
q2x *= s;
q2y *= s;
q2z *= s;
q2w *= s;
alphaN = alphaN + alphaN;
} else {
q1x = Math.fma(scale0, q1x, scale1 * q2x);
q1y = Math.fma(scale0, q1y, scale1 * q2y);
q1z = Math.fma(scale0, q1z, scale1 * q2z);
q1w = Math.fma(scale0, q1w, scale1 * q2w);
float s = (float) Math.invsqrt(Math.fma(q1x, q1x, Math.fma(q1y, q1y, Math.fma(q1z, q1z, q1w * q1w))));
q1x *= s;
q1y *= s;
q1z *= s;
q1w *= s;
alphaN = alphaN + alphaN - 1.0;
}
dot = Math.fma(q1x, q2x, Math.fma(q1y, q2y, Math.fma(q1z, q2z, q1w * q2w)));
absDot = Math.abs(dot);
}
double scale0 = 1.0 - alphaN;
double scale1 = dot >= 0.0 ? alphaN : -alphaN;
double resX = Math.fma(scale0, q1x, scale1 * q2x);
double resY = Math.fma(scale0, q1y, scale1 * q2y);
double resZ = Math.fma(scale0, q1z, scale1 * q2z);
double resW = Math.fma(scale0, q1w, scale1 * q2w);
double s = Math.invsqrt(Math.fma(resX, resX, Math.fma(resY, resY, Math.fma(resZ, resZ, resW * resW))));
dest.x = resX * s;
dest.y = resY * s;
dest.z = resZ * s;
dest.w = resW * s;
return dest;
}
/**
* Compute linear (non-spherical) interpolations of <code>this</code> and the given quaternion <code>q</code>
* iteratively and store the result in <code>this</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 <code>@theagentd</code> 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
* @return this
*/
public Quaterniond nlerpIterative(Quaterniondc q, double alpha, double dotThreshold) {
return nlerpIterative(q, alpha, dotThreshold, this);
}
/**
* Interpolate between all of the quaternions given in <code>qs</code> via iterative non-spherical linear interpolation using the
* specified interpolation factors <code>weights</code>, and store the result in <code>dest</code>.
* <p>
* This method will interpolate between each two successive quaternions via {@link #nlerpIterative(Quaterniondc, double, double)}
* using their relative interpolation weights.
* <p>
* Reference: <a href="http://gamedev.stackexchange.com/questions/62354/method-for-interpolation-between-3-quaternions#answer-62356">http://gamedev.stackexchange.com/</a>
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in <code>qs</code>
* @param dotThreshold
* the threshold for the dot product of each two interpolated quaternions above which {@link #nlerpIterative(Quaterniondc, double, double)} performs another iteration
* of a small-step linear interpolation
* @param dest
* will hold the result
* @return dest
*/
public static Quaterniond nlerpIterative(Quaterniondc[] qs, double[] weights, double dotThreshold, Quaterniond dest) {
dest.set(qs[0]);
double w = weights[0];
for (int i = 1; i < qs.length; i++) {
double w0 = w;
double w1 = weights[i];
double rw1 = w1 / (w0 + w1);
w += w1;
dest.nlerpIterative(qs[i], rw1, dotThreshold);
}
return dest;
}
/**
* Apply a rotation to this quaternion that maps the given direction to the positive Z axis.
* <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>
* @return this
*/
public Quaterniond lookAlong(Vector3dc dir, Vector3dc up) {
return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), this);
}
public Quaterniond lookAlong(Vector3dc dir, Vector3dc up, Quaterniond dest) {
return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), dest);
}
/**
* Apply a rotation to this quaternion that maps the given direction to the positive Z axis.
* <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 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
* @return this
*/
public Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ) {
return lookAlong(dirX, dirY, dirZ, upX, upY, upZ, this);
}
public Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Quaterniond dest) {
// Normalize direction
double invDirLength = Math.invsqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
double dirnX = -dirX * invDirLength;
double dirnY = -dirY * invDirLength;
double dirnZ = -dirZ * invDirLength;
// left = up x dir
double leftX, leftY, leftZ;
leftX = upY * dirnZ - upZ * dirnY;
leftY = upZ * dirnX - upX * dirnZ;
leftZ = upX * dirnY - upY * dirnX;
// normalize left
double invLeftLength = Math.invsqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
leftX *= invLeftLength;
leftY *= invLeftLength;
leftZ *= invLeftLength;
// up = direction x left
double upnX = dirnY * leftZ - dirnZ * leftY;
double upnY = dirnZ * leftX - dirnX * leftZ;
double upnZ = dirnX * leftY - dirnY * leftX;
/* Convert orthonormal basis vectors to quaternion */
double x, y, z, w;
double t;
double tr = leftX + upnY + dirnZ;
if (tr >= 0.0) {
t = Math.sqrt(tr + 1.0);
w = t * 0.5;
t = 0.5 / t;
x = (dirnY - upnZ) * t;
y = (leftZ - dirnX) * t;
z = (upnX - leftY) * t;
} else {
if (leftX > upnY && leftX > dirnZ) {
t = Math.sqrt(1.0 + leftX - upnY - dirnZ);
x = t * 0.5;
t = 0.5 / t;
y = (leftY + upnX) * t;
z = (dirnX + leftZ) * t;
w = (dirnY - upnZ) * t;
} else if (upnY > dirnZ) {
t = Math.sqrt(1.0 + upnY - leftX - dirnZ);
y = t * 0.5;
t = 0.5 / t;
x = (leftY + upnX) * t;
z = (upnZ + dirnY) * t;
w = (leftZ - dirnX) * t;
} else {
t = Math.sqrt(1.0 + dirnZ - leftX - upnY);
z = t * 0.5;
t = 0.5 / t;
x = (dirnX + leftZ) * t;
y = (upnZ + dirnY) * t;
w = (upnX - leftY) * t;
}
}
/* Multiply */
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
/**
* Return a string representation of this quaternion.
* <p>
* This method creates a new {@link DecimalFormat} on every invocation with the format string "<code>0.000E0;-</code>".
*
* @return the string representation
*/
public String toString() {
return Runtime.formatNumbers(toString(Options.NUMBER_FORMAT));
}
/**
* Return a string representation of this quaternion by formatting the components with the given {@link NumberFormat}.
*
* @param formatter
* the {@link NumberFormat} used to format the quaternion components with
* @return the string representation
*/
public String toString(NumberFormat formatter) {
return "(" + Runtime.format(x, formatter) + " " + Runtime.format(y, formatter) + " " + Runtime.format(z, formatter) + " " + Runtime.format(w, formatter) + ")";
}
public void writeExternal(ObjectOutput out) throws IOException {
out.writeDouble(x);
out.writeDouble(y);
out.writeDouble(z);
out.writeDouble(w);
}
public void readExternal(ObjectInput in) throws IOException,
ClassNotFoundException {
x = in.readDouble();
y = in.readDouble();
z = in.readDouble();
w = in.readDouble();
}
public int hashCode() {
final int prime = 31;
int result = 1;
long temp;
temp = Double.doubleToLongBits(w);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(x);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(y);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(z);
result = prime * result + (int) (temp ^ (temp >>> 32));
return result;
}
public boolean equals(Object obj) {
if (this == obj)
return true;
if (obj == null)
return false;
if (getClass() != obj.getClass())
return false;
Quaterniond other = (Quaterniond) obj;
if (Double.doubleToLongBits(w) != Double.doubleToLongBits(other.w))
return false;
if (Double.doubleToLongBits(x) != Double.doubleToLongBits(other.x))
return false;
if (Double.doubleToLongBits(y) != Double.doubleToLongBits(other.y))
return false;
if (Double.doubleToLongBits(z) != Double.doubleToLongBits(other.z))
return false;
return true;
}
/**
* Compute the difference between <code>this</code> and the <code>other</code> quaternion
* and store the result in <code>this</code>.
* <p>
* The difference is the rotation that has to be applied to get from
* <code>this</code> rotation to <code>other</code>. If <code>T</code> is <code>this</code>, <code>Q</code>
* is <code>other</code> and <code>D</code> is the computed difference, then the following equation holds:
* <p>
* <code>T * D = Q</code>
* <p>
* It is defined as: <code>D = T^-1 * Q</code>, where <code>T^-1</code> denotes the {@link #invert() inverse} of <code>T</code>.
*
* @param other
* the other quaternion
* @return this
*/
public Quaterniond difference(Quaterniondc other) {
return difference(other, this);
}
public Quaterniond difference(Quaterniondc other, Quaterniond dest) {
double invNorm = 1.0 / lengthSquared();
double x = -this.x * invNorm;
double y = -this.y * invNorm;
double z = -this.z * invNorm;
double w = this.w * invNorm;
dest.set(Math.fma(w, other.x(), Math.fma(x, other.w(), Math.fma(y, other.z(), -z * other.y()))),
Math.fma(w, other.y(), Math.fma(-x, other.z(), Math.fma(y, other.w(), z * other.x()))),
Math.fma(w, other.z(), Math.fma(x, other.y(), Math.fma(-y, other.x(), z * other.w()))),
Math.fma(w, other.w(), Math.fma(-x, other.x(), Math.fma(-y, other.y(), -z * other.z()))));
return dest;
}
/**
* Set <code>this</code> quaternion to a rotation that rotates the <code>fromDir</code> vector to point along <code>toDir</code>.
* <p>
* Since there can be multiple possible rotations, this method chooses the one with the shortest arc.
* <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
* @return this
*/
public Quaterniond rotationTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ) {
double fn = Math.invsqrt(Math.fma(fromDirX, fromDirX, Math.fma(fromDirY, fromDirY, fromDirZ * fromDirZ)));
double tn = Math.invsqrt(Math.fma(toDirX, toDirX, Math.fma(toDirY, toDirY, toDirZ * toDirZ)));
double fx = fromDirX * fn, fy = fromDirY * fn, fz = fromDirZ * fn;
double tx = toDirX * tn, ty = toDirY * tn, tz = toDirZ * tn;
double dot = fx * tx + fy * ty + fz * tz;
double x, y, z, w;
if (dot < -1.0 + 1E-6) {
x = fy;
y = -fx;
z = 0.0;
w = 0.0;
if (x * x + y * y == 0.0) {
x = 0.0;
y = fz;
z = -fy;
w = 0.0;
}
this.x = x;
this.y = y;
this.z = z;
this.w = 0;
} else {
double sd2 = Math.sqrt((1.0 + dot) * 2.0);
double isd2 = 1.0 / sd2;
double cx = fy * tz - fz * ty;
double cy = fz * tx - fx * tz;
double cz = fx * ty - fy * tx;
x = cx * isd2;
y = cy * isd2;
z = cz * isd2;
w = sd2 * 0.5;
double n2 = Math.invsqrt(Math.fma(x, x, Math.fma(y, y, Math.fma(z, z, w * w))));
this.x = x * n2;
this.y = y * n2;
this.z = z * n2;
this.w = w * n2;
}
return this;
}
/**
* Set <code>this</code> quaternion to a rotation that rotates the <code>fromDir</code> vector to point along <code>toDir</code>.
* <p>
* Because there can be multiple possible rotations, this method chooses the one with the shortest arc.
*
* @see #rotationTo(double, double, double, double, double, double)
*
* @param fromDir
* the starting direction
* @param toDir
* the destination direction
* @return this
*/
public Quaterniond rotationTo(Vector3dc fromDir, Vector3dc toDir) {
return rotationTo(fromDir.x(), fromDir.y(), fromDir.z(), toDir.x(), toDir.y(), toDir.z());
}
public Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ,
double toDirX, double toDirY, double toDirZ, Quaterniond dest) {
double fn = Math.invsqrt(Math.fma(fromDirX, fromDirX, Math.fma(fromDirY, fromDirY, fromDirZ * fromDirZ)));
double tn = Math.invsqrt(Math.fma(toDirX, toDirX, Math.fma(toDirY, toDirY, toDirZ * toDirZ)));
double fx = fromDirX * fn, fy = fromDirY * fn, fz = fromDirZ * fn;
double tx = toDirX * tn, ty = toDirY * tn, tz = toDirZ * tn;
double dot = fx * tx + fy * ty + fz * tz;
double x, y, z, w;
if (dot < -1.0 + 1E-6) {
x = fy;
y = -fx;
z = 0.0;
w = 0.0;
if (x * x + y * y == 0.0) {
x = 0.0;
y = fz;
z = -fy;
w = 0.0;
}
} else {
double sd2 = Math.sqrt((1.0 + dot) * 2.0);
double isd2 = 1.0 / sd2;
double cx = fy * tz - fz * ty;
double cy = fz * tx - fx * tz;
double cz = fx * ty - fy * tx;
x = cx * isd2;
y = cy * isd2;
z = cz * isd2;
w = sd2 * 0.5;
double n2 = Math.invsqrt(Math.fma(x, x, Math.fma(y, y, Math.fma(z, z, w * w))));
x *= n2;
y *= n2;
z *= n2;
w *= n2;
}
/* Multiply */
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
/**
* Set this {@link Quaterniond} to a rotation of the given angle in radians about the supplied
* axis, all of which are specified via the {@link AxisAngle4f}.
*
* @see #rotationAxis(double, double, double, double)
*
* @param axisAngle
* the {@link AxisAngle4f} giving the rotation angle in radians and the axis to rotate about
* @return this
*/
public Quaterniond rotationAxis(AxisAngle4f axisAngle) {
return rotationAxis(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* Set this quaternion to a rotation of the given angle in radians about the supplied axis.
*
* @param angle
* the rotation angle in radians
* @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
* @return this
*/
public Quaterniond rotationAxis(double angle, double axisX, double axisY, double axisZ) {
double hangle = angle / 2.0;
double sinAngle = Math.sin(hangle);
double invVLength = Math.invsqrt(axisX * axisX + axisY * axisY + axisZ * axisZ);
return set(axisX * invVLength * sinAngle,
axisY * invVLength * sinAngle,
axisZ * invVLength * sinAngle,
Math.cosFromSin(sinAngle, hangle));
}
/**
* Set this quaternion to represent a rotation of the given radians about the x axis.
*
* @param angle
* the angle in radians to rotate about the x axis
* @return this
*/
public Quaterniond rotationX(double angle) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return set(sin, 0, cos, 0);
}
/**
* Set this quaternion to represent a rotation of the given radians about the y axis.
*
* @param angle
* the angle in radians to rotate about the y axis
* @return this
*/
public Quaterniond rotationY(double angle) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return set(0, sin, 0, cos);
}
/**
* Set this quaternion to represent a rotation of the given radians about the z axis.
*
* @param angle
* the angle in radians to rotate about the z axis
* @return this
*/
public Quaterniond rotationZ(double angle) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return set(0, 0, sin, cos);
}
/**
* Apply a rotation to <code>this</code> that rotates the <code>fromDir</code> vector to point along <code>toDir</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!
*
* @see #rotateTo(double, double, double, double, double, double, Quaterniond)
*
* @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
* @return this
*/
public Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ) {
return rotateTo(fromDirX, fromDirY, fromDirZ, toDirX, toDirY, toDirZ, this);
}
public Quaterniond rotateTo(Vector3dc fromDir, Vector3dc toDir, Quaterniond dest) {
return rotateTo(fromDir.x(), fromDir.y(), fromDir.z(), toDir.x(), toDir.y(), toDir.z(), dest);
}
/**
* Apply a rotation to <code>this</code> that rotates the <code>fromDir</code> vector to point along <code>toDir</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
* @return this
*/
public Quaterniond rotateTo(Vector3dc fromDir, Vector3dc toDir) {
return rotateTo(fromDir.x(), fromDir.y(), fromDir.z(), toDir.x(), toDir.y(), toDir.z(), this);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the x axis.
* <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 x axis
* @return this
*/
public Quaterniond rotateX(double angle) {
return rotateX(angle, this);
}
public Quaterniond rotateX(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return dest.set(w * sin + x * cos,
y * cos + z * sin,
z * cos - y * sin,
w * cos - x * sin);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the y axis.
* <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 y axis
* @return this
*/
public Quaterniond rotateY(double angle) {
return rotateY(angle, this);
}
public Quaterniond rotateY(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return dest.set(x * cos - z * sin,
w * sin + y * cos,
x * sin + z * cos,
w * cos - y * sin);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the z axis.
* <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 z axis
* @return this
*/
public Quaterniond rotateZ(double angle) {
return rotateZ(angle, this);
}
public Quaterniond rotateZ(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
return dest.set(x * cos + y * sin,
y * cos - x * sin,
w * sin + z * cos,
w * cos - z * sin);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local x axis.
* <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
* @return this
*/
public Quaterniond rotateLocalX(double angle) {
return rotateLocalX(angle, this);
}
public Quaterniond rotateLocalX(double angle, Quaterniond dest) {
double hangle = angle * 0.5;
double s = Math.sin(hangle);
double c = Math.cosFromSin(s, hangle);
dest.set(c * x + s * w,
c * y - s * z,
c * z + s * y,
c * w - s * x);
return dest;
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local y axis.
* <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
* @return this
*/
public Quaterniond rotateLocalY(double angle) {
return rotateLocalY(angle, this);
}
public Quaterniond rotateLocalY(double angle, Quaterniond dest) {
double hangle = angle * 0.5;
double s = Math.sin(hangle);
double c = Math.cosFromSin(s, hangle);
dest.set(c * x + s * z,
c * y + s * w,
c * z - s * x,
c * w - s * y);
return dest;
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the local z axis.
* <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
* @return this
*/
public Quaterniond rotateLocalZ(double angle) {
return rotateLocalZ(angle, this);
}
public Quaterniond rotateLocalZ(double angle, Quaterniond dest) {
double hangle = angle * 0.5;
double s = Math.sin(hangle);
double c = Math.cosFromSin(s, hangle);
dest.set(c * x - s * y,
c * y + s * x,
c * z + s * w,
c * w - s * z);
return 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 <code>XYZ</code>.
* <p>
* This method is equivalent to calling: <code>rotateX(angleX).rotateY(angleY).rotateZ(angleZ)</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
* @return this
*/
public Quaterniond rotateXYZ(double angleX, double angleY, double angleZ) {
return rotateXYZ(angleX, angleY, angleZ, this);
}
public Quaterniond rotateXYZ(double angleX, double angleY, double angleZ, Quaterniond dest) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double cycz = cy * cz;
double sysz = sy * sz;
double sycz = sy * cz;
double cysz = cy * sz;
double w = cx*cycz - sx*sysz;
double x = sx*cycz + cx*sysz;
double y = cx*sycz - sx*cysz;
double z = cx*cysz + sx*sycz;
// right-multiply
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
/**
* 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 <code>ZYX</code>.
* <p>
* This method is equivalent to calling: <code>rotateZ(angleZ).rotateY(angleY).rotateX(angleX)</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 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
* @return this
*/
public Quaterniond rotateZYX(double angleZ, double angleY, double angleX) {
return rotateZYX(angleZ, angleY, angleX, this);
}
public Quaterniond rotateZYX(double angleZ, double angleY, double angleX, Quaterniond dest) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double cycz = cy * cz;
double sysz = sy * sz;
double sycz = sy * cz;
double cysz = cy * sz;
double w = cx*cycz + sx*sysz;
double x = sx*cycz - cx*sysz;
double y = cx*sycz + sx*cysz;
double z = cx*cysz - sx*sycz;
// right-multiply
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
/**
* 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 <code>YXZ</code>.
* <p>
* This method is equivalent to calling: <code>rotateY(angleY).rotateX(angleX).rotateZ(angleZ)</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 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
* @return this
*/
public Quaterniond rotateYXZ(double angleY, double angleX, double angleZ) {
return rotateYXZ(angleY, angleX, angleZ, this);
}
public Quaterniond rotateYXZ(double angleY, double angleX, double angleZ, Quaterniond dest) {
double sx = Math.sin(angleX * 0.5);
double cx = Math.cosFromSin(sx, angleX * 0.5);
double sy = Math.sin(angleY * 0.5);
double cy = Math.cosFromSin(sy, angleY * 0.5);
double sz = Math.sin(angleZ * 0.5);
double cz = Math.cosFromSin(sz, angleZ * 0.5);
double yx = cy * sx;
double yy = sy * cx;
double yz = sy * sx;
double yw = cy * cx;
double x = yx * cz + yy * sz;
double y = yy * cz - yx * sz;
double z = yw * sz - yz * cz;
double w = yw * cz + yz * sz;
// right-multiply
return dest.set(Math.fma(this.w, x, Math.fma(this.x, w, Math.fma(this.y, z, -this.z * y))),
Math.fma(this.w, y, Math.fma(-this.x, z, Math.fma(this.y, w, this.z * x))),
Math.fma(this.w, z, Math.fma(this.x, y, Math.fma(-this.y, x, this.z * w))),
Math.fma(this.w, w, Math.fma(-this.x, x, Math.fma(-this.y, y, -this.z * z))));
}
public Vector3d getEulerAnglesXYZ(Vector3d eulerAngles) {
eulerAngles.x = Math.atan2(2.0 * (x*w - y*z), 1.0 - 2.0 * (x*x + y*y));
eulerAngles.y = Math.safeAsin(2.0 * (x*z + y*w));
eulerAngles.z = Math.atan2(2.0 * (z*w - x*y), 1.0 - 2.0 * (y*y + z*z));
return eulerAngles;
}
public Quaterniond rotateAxis(double angle, double axisX, double axisY, double axisZ, Quaterniond dest) {
double hangle = angle / 2.0;
double sinAngle = Math.sin(hangle);
double invVLength = Math.invsqrt(Math.fma(axisX, axisX, Math.fma(axisY, axisY, axisZ * axisZ)));
double rx = axisX * invVLength * sinAngle;
double ry = axisY * invVLength * sinAngle;
double rz = axisZ * invVLength * sinAngle;
double rw = Math.cosFromSin(sinAngle, hangle);
return dest.set(Math.fma(this.w, rx, Math.fma(this.x, rw, Math.fma(this.y, rz, -this.z * ry))),
Math.fma(this.w, ry, Math.fma(-this.x, rz, Math.fma(this.y, rw, this.z * rx))),
Math.fma(this.w, rz, Math.fma(this.x, ry, Math.fma(-this.y, rx, this.z * rw))),
Math.fma(this.w, rw, Math.fma(-this.x, rx, Math.fma(-this.y, ry, -this.z * rz))));
}
public Quaterniond rotateAxis(double angle, Vector3dc axis, Quaterniond dest) {
return rotateAxis(angle, axis.x(), axis.y(), axis.z(), dest);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the specified axis.
* <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
* @return this
*/
public Quaterniond rotateAxis(double angle, Vector3dc axis) {
return rotateAxis(angle, axis.x(), axis.y(), axis.z(), this);
}
/**
* Apply a rotation to <code>this</code> quaternion rotating the given radians about the specified axis.
* <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 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
* @return this
*/
public Quaterniond rotateAxis(double angle, double axisX, double axisY, double axisZ) {
return rotateAxis(angle, axisX, axisY, axisZ, this);
}
public Vector3d positiveX(Vector3d dir) {
double invNorm = 1.0 / lengthSquared();
double nx = -x * invNorm;
double ny = -y * invNorm;
double nz = -z * invNorm;
double nw = w * invNorm;
double dy = ny + ny;
double dz = nz + nz;
dir.x = -ny * dy - nz * dz + 1.0;
dir.y = nx * dy + nw * dz;
dir.z = nx * dz - nw * dy;
return dir;
}
public Vector3d normalizedPositiveX(Vector3d dir) {
double dy = y + y;
double dz = z + z;
dir.x = -y * dy - z * dz + 1.0;
dir.y = x * dy - w * dz;
dir.z = x * dz + w * dy;
return dir;
}
public Vector3d positiveY(Vector3d dir) {
double invNorm = 1.0 / lengthSquared();
double nx = -x * invNorm;
double ny = -y * invNorm;
double nz = -z * invNorm;
double nw = w * invNorm;
double dx = nx + nx;
double dy = ny + ny;
double dz = nz + nz;
dir.x = nx * dy - nw * dz;
dir.y = -nx * dx - nz * dz + 1.0;
dir.z = ny * dz + nw * dx;
return dir;
}
public Vector3d normalizedPositiveY(Vector3d dir) {
double dx = x + x;
double dy = y + y;
double dz = z + z;
dir.x = x * dy + w * dz;
dir.y = -x * dx - z * dz + 1.0;
dir.z = y * dz - w * dx;
return dir;
}
public Vector3d positiveZ(Vector3d dir) {
double invNorm = 1.0 / lengthSquared();
double nx = -x * invNorm;
double ny = -y * invNorm;
double nz = -z * invNorm;
double nw = w * invNorm;
double dx = nx + nx;
double dy = ny + ny;
double dz = nz + nz;
dir.x = nx * dz + nw * dy;
dir.y = ny * dz - nw * dx;
dir.z = -nx * dx - ny * dy + 1.0;
return dir;
}
public Vector3d normalizedPositiveZ(Vector3d dir) {
double dx = x + x;
double dy = y + y;
double dz = z + z;
dir.x = x * dz - w * dy;
dir.y = y * dz + w * dx;
dir.z = -x * dx - y * dy + 1.0;
return dir;
}
/**
* Conjugate <code>this</code> by the given quaternion <code>q</code> by computing <code>q * this * q^-1</code>.
*
* @param q
* the {@link Quaterniondc} to conjugate <code>this</code> by
* @return this
*/
public Quaterniond conjugateBy(Quaterniondc q) {
return conjugateBy(q, this);
}
/**
* Conjugate <code>this</code> by the given quaternion <code>q</code> by computing <code>q * this * q^-1</code>
* and store the result into <code>dest</code>.
*
* @param q
* the {@link Quaterniondc} to conjugate <code>this</code> by
* @param dest
* will hold the result
* @return dest
*/
public Quaterniond conjugateBy(Quaterniondc q, Quaterniond dest) {
double invNorm = 1.0 / q.lengthSquared();
double qix = -q.x() * invNorm, qiy = -q.y() * invNorm, qiz = -q.z() * invNorm, qiw = q.w() * invNorm;
double qpx = Math.fma(q.w(), x, Math.fma(q.x(), w, Math.fma(q.y(), z, -q.z() * y)));
double qpy = Math.fma(q.w(), y, Math.fma(-q.x(), z, Math.fma(q.y(), w, q.z() * x)));
double qpz = Math.fma(q.w(), z, Math.fma(q.x(), y, Math.fma(-q.y(), x, q.z() * w)));
double qpw = Math.fma(q.w(), w, Math.fma(-q.x(), x, Math.fma(-q.y(), y, -q.z() * z)));
return dest.set(Math.fma(qpw, qix, Math.fma(qpx, qiw, Math.fma(qpy, qiz, -qpz * qiy))),
Math.fma(qpw, qiy, Math.fma(-qpx, qiz, Math.fma(qpy, qiw, qpz * qix))),
Math.fma(qpw, qiz, Math.fma(qpx, qiy, Math.fma(-qpy, qix, qpz * qiw))),
Math.fma(qpw, qiw, Math.fma(-qpx, qix, Math.fma(-qpy, qiy, -qpz * qiz))));
}
public boolean isFinite() {
return Math.isFinite(x) && Math.isFinite(y) && Math.isFinite(z) && Math.isFinite(w);
}
}
