org.joml.Quaterniond Maven / Gradle / Ivy
/*
* The MIT License
*
* Copyright (c) 2015-2019 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;
import org.joml.internal.Options;
import org.joml.internal.Runtime;
/**
* 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 (x=0, y=0, z=0, w=1),
* where (x, y, z) is the vector part of the quaternion and w 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 Quaterniond}.
*
* @param source
* the {@link Quaterniond} 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 = 1.0 / Math.sqrt(x * x + y * y + z * z + w * w);
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
return this;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#normalize(org.joml.Quaterniond)
*/
public Quaterniond normalize(Quaterniond dest) {
double invNorm = 1.0 / Math.sqrt(x * x + y * y + z * z + w * w);
dest.x = x * invNorm;
dest.y = y * invNorm;
dest.z = z * invNorm;
dest.w = w * invNorm;
return dest;
}
/**
* Add the quaternion (x, y, z, w) 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#add(double, double, double, double, org.joml.Quaterniond)
*/
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 q2 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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#add(org.joml.Quaterniondc, org.joml.Quaterniond)
*/
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#dot(org.joml.Quaterniondc)
*/
public double dot(Quaterniondc otherQuat) {
return this.x * otherQuat.x() + this.y * otherQuat.y() + this.z * otherQuat.z() + this.w * otherQuat.w();
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#angle()
*/
public double angle() {
double angle = 2.0 * Math.acos(w);
return angle <= Math.PI ? angle : Math.PI + Math.PI - angle;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#get(org.joml.Matrix3d)
*/
public Matrix3d get(Matrix3d dest) {
return dest.set(this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#get(org.joml.Matrix3f)
*/
public Matrix3f get(Matrix3f dest) {
return dest.set(this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#get(org.joml.Matrix4d)
*/
public Matrix4d get(Matrix4d dest) {
return dest.set(this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#get(org.joml.Matrix4f)
*/
public Matrix4f get(Matrix4f dest) {
return dest.set(this);
}
/**
* Set the given {@link Quaterniond} to the values of this.
*
* @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 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).
*
* This method assumes that the given rotation axis (x, y, z) 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 = 1.0 / Math.sqrt(m00 * m00 + m01 * m01 + m02 * m02);
double lenY = 1.0 / Math.sqrt(m10 * m10 + m11 * m11 + m12 * m12);
double lenZ = 1.0 / Math.sqrt(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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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 q.
*
* If T is this and Q is the given
* quaternion, then the resulting quaternion R is:
*
* R = T * Q
*
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by Q first, and then by T.
*
* @param q
* the quaternion to multiply this by
* @return this
*/
public Quaterniond mul(Quaterniondc q) {
return mul(q, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#mul(org.joml.Quaterniondc, org.joml.Quaterniond)
*/
public Quaterniond mul(Quaterniondc q, Quaterniond dest) {
dest.set(w * q.x() + x * q.w() + y * q.z() - z * q.y(),
w * q.y() - x * q.z() + y * q.w() + z * q.x(),
w * q.z() + x * q.y() - y * q.x() + z * q.w(),
w * q.w() - x * q.x() - y * q.y() - z * q.z());
return dest;
}
/**
* Multiply this quaternion by the quaternion represented via (qx, qy, qz, qw).
*
* If T is this and Q is the given
* quaternion, then the resulting quaternion R is:
*
* R = T * Q
*
* So, this method uses post-multiplication like the matrix classes, resulting in a
* vector to be transformed by Q first, and then by T.
*
* @param qx
* the x component of the quaternion to multiply this by
* @param qy
* the y component of the quaternion to multiply this by
* @param qz
* the z component of the quaternion to multiply this by
* @param qw
* the w component of the quaternion to multiply this by
* @return this
*/
public Quaterniond mul(double qx, double qy, double qz, double qw) {
set(w * qx + x * qw + y * qz - z * qy,
w * qy - x * qz + y * qw + z * qx,
w * qz + x * qy - y * qx + z * qw,
w * qw - x * qx - y * qy - z * qz);
return this;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#mul(double, double, double, double, org.joml.Quaterniond)
*/
public Quaterniond mul(double qx, double qy, double qz, double qw, Quaterniond dest) {
dest.set(w * qx + x * qw + y * qz - z * qy,
w * qy - x * qz + y * qw + z * qx,
w * qz + x * qy - y * qx + z * qw,
w * qw - x * qx - y * qy - z * qz);
return dest;
}
/**
* Pre-multiply this quaternion by q.
*
* If T is this and Q is the given quaternion, then the resulting quaternion R is:
*
* R = Q * T
*
* So, this method uses pre-multiplication, resulting in a vector to be transformed by T first, and then by Q.
*
* @param q
* the quaternion to pre-multiply this by
* @return this
*/
public Quaterniond premul(Quaterniondc q) {
return premul(q, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#premul(org.joml.Quaterniondc, org.joml.Quaterniond)
*/
public Quaterniond premul(Quaterniondc q, Quaterniond dest) {
dest.set(q.w() * x + q.x() * w + q.y() * z - q.z() * y,
q.w() * y - q.x() * z + q.y() * w + q.z() * x,
q.w() * z + q.x() * y - q.y() * x + q.z() * w,
q.w() * w - q.x() * x - q.y() * y - q.z() * z);
return dest;
}
/**
* Pre-multiply this quaternion by the quaternion represented via (qx, qy, qz, qw).
*
* If T is this and Q is the given quaternion, then the resulting quaternion R is:
*
* R = Q * T
*
* So, this method uses pre-multiplication, resulting in a vector to be transformed by T first, and then by Q.
*
* @param qx
* the x component of the quaternion to multiply this by
* @param qy
* the y component of the quaternion to multiply this by
* @param qz
* the z component of the quaternion to multiply this by
* @param qw
* the w component of the quaternion to multiply this by
* @return this
*/
public Quaterniond premul(double qx, double qy, double qz, double qw) {
return premul(qx, qy, qz, qw, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#premul(double, double, double, double, org.joml.Quaterniond)
*/
public Quaterniond premul(double qx, double qy, double qz, double qw, Quaterniond dest) {
dest.set(qw * x + qx * w + qy * z - qz * y,
qw * y - qx * z + qy * w + qz * x,
qw * z + qx * y - qy * x + qz * w,
qw * w - qx * x - qy * y - qz * z);
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(org.joml.Vector3d)
*/
public Vector3d transform(Vector3d vec){
return transform(vec.x, vec.y, vec.z, vec);
}
public Vector3d transformPositiveX(Vector3d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = w2 + x2 - z2 - y2;
dest.y = xy + zw + zw + xy;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector4d transformPositiveX(Vector4d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = z * z;
double zw = z * w;
double xy = x * y;
double xz = x * z;
double yw = y * w;
dest.x = w2 + x2 - z2 - y2;
dest.y = xy + zw + zw + xy;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector3d transformUnitPositiveX(Vector3d dest) {
double y2 = y * y;
double z2 = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = 1.0 - y2 - y2 - z2 - z2;
dest.y = xy + zw + xy + zw;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector4d transformUnitPositiveX(Vector4d dest) {
double y2 = y * y;
double z2 = z * z;
double xy = x * y;
double xz = x * z;
double yw = y * w;
double zw = z * w;
dest.x = 1.0 - y2 - y2 - z2 - z2;
dest.y = xy + zw + xy + zw;
dest.z = xz - yw + xz - yw;
return dest;
}
public Vector3d transformPositiveY(Vector3d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = 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 = y2 - z2 + w2 - x2;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector4d transformPositiveY(Vector4d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = 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 = y2 - z2 + w2 - x2;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector4d transformUnitPositiveY(Vector4d dest) {
double x2 = x * x;
double z2 = 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 - x2 - x2 - z2 - z2;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector3d transformUnitPositiveY(Vector3d dest) {
double x2 = x * x;
double z2 = 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 - x2 - x2 - z2 - z2;
dest.z = yz + yz + xw + xw;
return dest;
}
public Vector3d transformPositiveZ(Vector3d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = 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 = z2 - y2 - x2 + w2;
return dest;
}
public Vector4d transformPositiveZ(Vector4d dest) {
double w2 = w * w;
double x2 = x * x;
double y2 = y * y;
double z2 = 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 = z2 - y2 - x2 + w2;
return dest;
}
public Vector4d transformUnitPositiveZ(Vector4d dest) {
double x2 = x * x;
double y2 = 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 - x2 - x2 - y2 - y2;
return dest;
}
public Vector3d transformUnitPositiveZ(Vector3d dest) {
double x2 = x * x;
double y2 = 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 - x2 - x2 - y2 - y2;
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(org.joml.Vector4d)
*/
public Vector4d transform(Vector4d vec){
return transform(vec, vec);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(org.joml.Vector3dc, org.joml.Vector3d)
*/
public Vector3d transform(Vector3dc vec, Vector3d dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(double, double, double, org.joml.Vector3d)
*/
public Vector3d transform(double x, double y, double z, Vector3d dest) {
double w2 = this.w * this.w;
double x2 = this.x * this.x;
double y2 = this.y * this.y;
double z2 = this.z * this.z;
double zw = this.z * this.w, zwd = zw + zw;
double xy = this.x * this.y, xyd = xy + xy;
double xz = this.x * this.z, xzd = xz + xz;
double yw = this.y * this.w, ywd = yw + yw;
double yz = this.y * this.z, yzd = yz + yz;
double xw = this.x * this.w, xwd = xw + xw;
double m00 = w2 + x2 - z2 - y2;
double m01 = xyd + zwd;
double m02 = xzd - ywd;
double m10 = xyd - zwd;
double m11 = y2 - z2 + w2 - x2;
double m12 = yzd + xwd;
double m20 = ywd + xzd;
double m21 = yzd - xwd;
double m22 = z2 - y2 - x2 + w2;
dest.x = m00 * x + m10 * y + m20 * z;
dest.y = m01 * x + m11 * y + m21 * z;
dest.z = m02 * x + m12 * y + m22 * z;
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(org.joml.Vector4dc, org.joml.Vector4d)
*/
public Vector4d transform(Vector4dc vec, Vector4d dest) {
return transform(vec.x(), vec.y(), vec.z(), dest);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#transform(double, double, double, org.joml.Vector4d)
*/
public Vector4d transform(double x, double y, double z, Vector4d dest) {
double w2 = this.w * this.w;
double x2 = this.x * this.x;
double y2 = this.y * this.y;
double z2 = this.z * this.z;
double zw = this.z * this.w, zwd = zw + zw;
double xy = this.x * this.y, xyd = xy + xy;
double xz = this.x * this.z, xzd = xz + xz;
double yw = this.y * this.w, ywd = yw + yw;
double yz = this.y * this.z, yzd = yz + yz;
double xw = this.x * this.w, xwd = xw + xw;
double m00 = w2 + x2 - z2 - y2;
double m01 = xyd + zwd;
double m02 = xzd - ywd;
double m10 = xyd - zwd;
double m11 = y2 - z2 + w2 - x2;
double m12 = yzd + xwd;
double m20 = ywd + xzd;
double m21 = yzd - xwd;
double m22 = z2 - y2 - x2 + w2;
dest.x = m00 * x + m10 * y + m20 * z;
dest.y = m01 * x + m11 * y + m21 * z;
dest.z = m02 * x + m12 * y + m22 * z;
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#invert(org.joml.Quaterniond)
*/
public Quaterniond invert(Quaterniond dest) {
double invNorm = 1.0 / (x * x + y * y + z * z + w * w);
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.
*
* If this quaternion is already normalized, then {@link #conjugate()} should be used instead.
*
* @see #conjugate()
*
* @return this
*/
public Quaterniond invert() {
return invert(this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#div(org.joml.Quaterniondc, org.joml.Quaterniond)
*/
public Quaterniond div(Quaterniondc b, Quaterniond dest) {
double invNorm = 1.0 / (b.x() * b.x() + b.y() * b.y() + 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;
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/**
* Divide this quaternion by b.
*
* The division expressed using the inverse is performed in the following way:
*
* this = this * b^-1, where b^-1 is the inverse of b.
*
* @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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#conjugate(org.joml.Quaterniond)
*/
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#lengthSquared()
*/
public double lengthSquared() {
return x * x + y * y + z * z + w * w;
}
/**
* Set this quaternion from the supplied euler angles (in radians) with rotation order XYZ.
*
* This method is equivalent to calling: rotationX(angleX).rotateY(angleY).rotateZ(angleZ)
*
* Reference: this stackexchange answer
*
* @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.
*
* This method is equivalent to calling: rotationZ(angleZ).rotateY(angleY).rotateX(angleX)
*
* Reference: this stackexchange answer
*
* @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.
*
* This method is equivalent to calling: rotationY(angleY).rotateX(angleX).rotateZ(angleZ)
*
* Reference: https://en.wikipedia.org
*
* @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 this {@link #normalize() unit} quaternion and the specified
* target {@link #normalize() unit} quaternion using spherical linear interpolation using the specified interpolation factor alpha.
*
* This method resorts to non-spherical linear interpolation when the absolute dot product between this and target is
* below 1E-6.
*
* @param target
* the target of the interpolation, which should be reached with alpha = 1.0
* @param alpha
* the interpolation factor, within [0..1]
* @return this
*/
public Quaterniond slerp(Quaterniondc target, double alpha) {
return slerp(target, alpha, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#slerp(org.joml.Quaterniondc, double, org.joml.Quaterniond)
*/
public Quaterniond slerp(Quaterniondc target, double alpha, Quaterniond dest) {
double cosom = x * target.x() + y * target.y() + 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 = 1.0 / Math.sqrt(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 = scale0 * x + scale1 * target.x();
dest.y = scale0 * y + scale1 * target.y();
dest.z = scale0 * z + scale1 * target.z();
dest.w = scale0 * w + scale1 * target.w();
return dest;
}
/**
* Interpolate between all of the quaternions given in qs via spherical linear interpolation using the specified interpolation factors weights,
* and store the result in dest.
*
* This method will interpolate between each two successive quaternions via {@link #slerp(Quaterniondc, double)} using their relative interpolation weights.
*
* This method resorts to non-spherical linear interpolation when the absolute dot product of any two interpolated quaternions is below 1E-6f.
*
* Reference: http://gamedev.stackexchange.com/
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in qs
* @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 factor.
*
* @param factor
* the scaling factor
* @return this
*/
public Quaterniond scale(double factor) {
return scale(factor, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#scale(double, org.joml.Quaterniond)
*/
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 factor.
*
* @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 (vx, vy, vz) around the x, y and z axis, respectively,
* with respect to the given elapsed time delta dt and add the differentiate rotation to the rotation represented by this quaternion.
*
* This method pre-multiplies the rotation given by dt and (vx, vy, vz) by this, so
* the angular velocities are always relative to the local coordinate system of the rotation represented by this quaternion.
*
* This method is equivalent to calling: rotateLocal(dt * vx, dt * vy, dt * vz)
*
* Reference: http://physicsforgames.blogspot.de/
*
* @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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#integrate(double, double, double, double, org.joml.Quaterniond)
*/
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 */
dest.set(dqW * x + dqX * w + dqY * z - dqZ * y,
dqW * y - dqX * z + dqY * w + dqZ * x,
dqW * z + dqX * y - dqY * x + dqZ * w,
dqW * w - dqX * x - dqY * y - dqZ * z);
return dest;
}
/**
* Compute a linear (non-spherical) interpolation of this and the given quaternion q
* and store the result in this.
*
* @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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#nlerp(org.joml.Quaterniondc, double, org.joml.Quaterniond)
*/
public Quaterniond nlerp(Quaterniondc q, double factor, Quaterniond dest) {
double cosom = x * q.x() + y * q.y() + z * q.z() + w * q.w();
double scale0 = 1.0 - factor;
double scale1 = (cosom >= 0.0) ? factor : -factor;
dest.x = scale0 * x + scale1 * q.x();
dest.y = scale0 * y + scale1 * q.y();
dest.z = scale0 * z + scale1 * q.z();
dest.w = scale0 * w + scale1 * q.w();
double s = 1.0 / Math.sqrt(dest.x * dest.x + dest.y * dest.y + 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 qs via non-spherical linear interpolation using the
* specified interpolation factors weights, and store the result in dest.
*
* This method will interpolate between each two successive quaternions via {@link #nlerp(Quaterniondc, double)}
* using their relative interpolation weights.
*
* Reference: http://gamedev.stackexchange.com/
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in qs
* @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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#nlerpIterative(org.joml.Quaterniondc, double, double, org.joml.Quaterniond)
*/
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 = q1x * q2x + q1y * q2y + 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 = scale0 * q2x + scale1 * q1x;
q2y = scale0 * q2y + scale1 * q1y;
q2z = scale0 * q2z + scale1 * q1z;
q2w = scale0 * q2w + scale1 * q1w;
double s = 1.0 / Math.sqrt(q2x * q2x + q2y * q2y + q2z * q2z + q2w * q2w);
q2x *= s;
q2y *= s;
q2z *= s;
q2w *= s;
alphaN = alphaN + alphaN;
} else {
q1x = scale0 * q1x + scale1 * q2x;
q1y = scale0 * q1y + scale1 * q2y;
q1z = scale0 * q1z + scale1 * q2z;
q1w = scale0 * q1w + scale1 * q2w;
double s = 1.0 / Math.sqrt(q1x * q1x + q1y * q1y + q1z * q1z + q1w * q1w);
q1x *= s;
q1y *= s;
q1z *= s;
q1w *= s;
alphaN = alphaN + alphaN - 1.0;
}
dot = q1x * q2x + q1y * q2y + q1z * q2z + q1w * q2w;
absDot = Math.abs(dot);
}
double scale0 = 1.0 - alphaN;
double scale1 = dot >= 0.0 ? alphaN : -alphaN;
double destX = scale0 * q1x + scale1 * q2x;
double destY = scale0 * q1y + scale1 * q2y;
double destZ = scale0 * q1z + scale1 * q2z;
double destW = scale0 * q1w + scale1 * q2w;
double s = 1.0 / Math.sqrt(destX * destX + destY * destY + destZ * destZ + destW * destW);
dest.x *= s;
dest.y *= s;
dest.z *= s;
dest.w *= s;
return dest;
}
/**
* Compute linear (non-spherical) interpolations of this and the given quaternion q
* iteratively and store the result in this.
*
* 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 this and q via non-spherical linear interpolations as long as
* the absolute dot product of this and q is greater than the given dotThreshold parameter.
*
* Thanks to @theagentd at http://www.java-gaming.org/ 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 this and q 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 qs via iterative non-spherical linear interpolation using the
* specified interpolation factors weights, and store the result in dest.
*
* This method will interpolate between each two successive quaternions via {@link #nlerpIterative(Quaterniondc, double, double)}
* using their relative interpolation weights.
*
* Reference: http://gamedev.stackexchange.com/
*
* @param qs
* the quaternions to interpolate over
* @param weights
* the weights of each individual quaternion in qs
* @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.
*
* 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 up and dir vectors.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, the
* rotation added by this method will be applied first!
*
* Reference: http://answers.unity3d.com
*
* @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 dir and up
* @return this
*/
public Quaterniond lookAlong(Vector3dc dir, Vector3dc up) {
return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#lookAlong(org.joml.Vector3dc, org.joml.Vector3dc, org.joml.Quaterniond)
*/
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.
*
* 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 up and dir vectors.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, the
* rotation added by this method will be applied first!
*
* Reference: http://answers.unity3d.com
*
* @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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#lookAlong(double, double, double, double, double, double, org.joml.Quaterniond)
*/
public Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Quaterniond dest) {
// Normalize direction
double invDirLength = 1.0 / Math.sqrt(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 = 1.0 / Math.sqrt(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 */
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/**
* Return a string representation of this quaternion.
*
* This method creates a new {@link DecimalFormat} on every invocation with the format string "0.000E0;-".
*
* @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 "(" + formatter.format(x) + " " + formatter.format(y) + " " + formatter.format(z) + " " + formatter.format(w) + ")";
}
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 this and the other quaternion
* and store the result in this.
*
* The difference is the rotation that has to be applied to get from
* this rotation to other. If T is this, Q
* is other and D is the computed difference, then the following equation holds:
*
* T * D = Q
*
* It is defined as: D = T^-1 * Q, where T^-1 denotes the {@link #invert() inverse} of T.
*
* @param other
* the other quaternion
* @return this
*/
public Quaterniond difference(Quaterniondc other) {
return difference(other, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#difference(org.joml.Quaterniondc, org.joml.Quaterniond)
*/
public Quaterniond difference(Quaterniondc other, Quaterniond dest) {
double invNorm = 1.0 / (x * x + y * y + z * z + w * w);
double x = -this.x * invNorm;
double y = -this.y * invNorm;
double z = -this.z * invNorm;
double w = this.w * invNorm;
dest.set(w * other.x() + x * other.w() + y * other.z() - z * other.y(),
w * other.y() - x * other.z() + y * other.w() + z * other.x(),
w * other.z() + x * other.y() - y * other.x() + z * other.w(),
w * other.w() - x * other.x() - y * other.y() - z * other.z());
return dest;
}
/**
* Set this quaternion to a rotation that rotates the fromDir vector to point along toDir.
*
* Since there can be multiple possible rotations, this method chooses the one with the shortest arc.
*
* Reference: stackoverflow.com
*
* @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) {
x = fromDirY * toDirZ - fromDirZ * toDirY;
y = fromDirZ * toDirX - fromDirX * toDirZ;
z = fromDirX * toDirY - fromDirY * toDirX;
w = Math.sqrt((fromDirX * fromDirX + fromDirY * fromDirY + fromDirZ * fromDirZ) *
(toDirX * toDirX + toDirY * toDirY + toDirZ * toDirZ)) +
(fromDirX * toDirX + fromDirY * toDirY + fromDirZ * toDirZ);
double invNorm = 1.0 / Math.sqrt(x * x + y * y + z * z + w * w);
if (Double.isInfinite(invNorm)) {
// Rotation is ambiguous: Find appropriate rotation axis (1. try toDir x +Z)
x = toDirY; y = -toDirX; z = 0.0; w = 0.0;
invNorm = (float) (1.0 / Math.sqrt(x * x + y * y));
if (Double.isInfinite(invNorm)) {
// 2. try toDir x +X
x = 0.0; y = toDirZ; z = -toDirY; w = 0.0;
invNorm = (float) (1.0 / Math.sqrt(y * y + z * z));
}
}
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
return this;
}
/**
* Set this quaternion to a rotation that rotates the fromDir vector to point along toDir.
*
* 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());
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateTo(double, double, double, double, double, double, org.joml.Quaterniond)
*/
public Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ,
double toDirX, double toDirY, double toDirZ, Quaterniond dest) {
double x = fromDirY * toDirZ - fromDirZ * toDirY;
double y = fromDirZ * toDirX - fromDirX * toDirZ;
double z = fromDirX * toDirY - fromDirY * toDirX;
double w = Math.sqrt((fromDirX * fromDirX + fromDirY * fromDirY + fromDirZ * fromDirZ) *
(toDirX * toDirX + toDirY * toDirY + toDirZ * toDirZ)) +
(fromDirX * toDirX + fromDirY * toDirY + fromDirZ * toDirZ);
double invNorm = 1.0 / Math.sqrt(x * x + y * y + z * z + w * w);
if (Double.isInfinite(invNorm)) {
// Rotation is ambiguous: Find appropriate rotation axis (1. try toDir x +Z)
x = toDirY; y = -toDirX; z = 0.0; w = 0.0;
invNorm = (float) (1.0 / Math.sqrt(x * x + y * y));
if (Double.isInfinite(invNorm)) {
// 2. try toDir x +X
x = 0.0; y = toDirZ; z = -toDirY; w = 0.0;
invNorm = (float) (1.0 / Math.sqrt(y * y + z * z));
}
}
x *= invNorm;
y *= invNorm;
z *= invNorm;
w *= invNorm;
/* Multiply */
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/**
* 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 = 1.0 / Math.sqrt(axisX * axisX + axisY * axisY + axisZ * axisZ);
x = axisX * invVLength * sinAngle;
y = axisY * invVLength * sinAngle;
z = axisZ * invVLength * sinAngle;
w = (float) Math.cosFromSin(sinAngle, hangle);
return this;
}
/**
* 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);
w = cos;
x = sin;
y = 0.0;
z = 0.0;
return this;
}
/**
* 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);
w = cos;
x = 0.0;
y = sin;
z = 0.0;
return this;
}
/**
* 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);
w = cos;
x = 0.0;
y = 0.0;
z = sin;
return this;
}
/**
* Apply a rotation to this that rotates the fromDir vector to point along toDir.
*
* Since there can be multiple possible rotations, this method chooses the one with the shortest arc.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateTo(org.joml.Vector3dc, org.joml.Vector3dc, org.joml.Quaterniond)
*/
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 this that rotates the fromDir vector to point along toDir.
*
* Because there can be multiple possible rotations, this method chooses the one with the shortest arc.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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 this quaternion rotating the given radians about the x axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateX(double, org.joml.Quaterniond)
*/
public Quaterniond rotateX(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
dest.set(w * sin + x * cos,
y * cos + z * sin,
z * cos - y * sin,
w * cos - x * sin);
return dest;
}
/**
* Apply a rotation to this quaternion rotating the given radians about the y axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateY(double, org.joml.Quaterniond)
*/
public Quaterniond rotateY(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
dest.set(x * cos - z * sin,
w * sin + y * cos,
x * sin + z * cos,
w * cos - y * sin);
return dest;
}
/**
* Apply a rotation to this quaternion rotating the given radians about the z axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateZ(double, org.joml.Quaterniond)
*/
public Quaterniond rotateZ(double angle, Quaterniond dest) {
double sin = Math.sin(angle * 0.5);
double cos = Math.cosFromSin(sin, angle * 0.5);
dest.set(x * cos + y * sin,
y * cos - x * sin,
w * sin + z * cos,
w * cos - z * sin);
return dest;
}
/**
* Apply a rotation to this quaternion rotating the given radians about the local x axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be R * Q. So when transforming a
* vector v with the new quaternion by using R * Q * v, the
* rotation represented by this 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateLocalX(double, org.joml.Quaterniond)
*/
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 this quaternion rotating the given radians about the local y axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be R * Q. So when transforming a
* vector v with the new quaternion by using R * Q * v, the
* rotation represented by this 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateLocalY(double, org.joml.Quaterniond)
*/
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 this quaternion rotating the given radians about the local z axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be R * Q. So when transforming a
* vector v with the new quaternion by using R * Q * v, the
* rotation represented by this 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateLocalZ(double, org.joml.Quaterniond)
*/
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 this quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles using rotation sequence XYZ.
*
* This method is equivalent to calling: rotateX(angleX).rotateY(angleY).rotateZ(angleZ)
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateXYZ(double, double, double, org.joml.Quaterniond)
*/
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
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/**
* Apply a rotation to this quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles, using the rotation sequence ZYX.
*
* This method is equivalent to calling: rotateZ(angleZ).rotateY(angleY).rotateX(angleX)
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateZYX(double, double, double, org.joml.Quaterniond)
*/
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
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/**
* Apply a rotation to this quaternion rotating the given radians about the cartesian base unit axes,
* called the euler angles, using the rotation sequence YXZ.
*
* This method is equivalent to calling: rotateY(angleY).rotateX(angleX).rotateZ(angleZ)
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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 angleZ, double angleY, double angleX) {
return rotateYXZ(angleZ, angleY, angleX, this);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateYXZ(double, double, double, org.joml.Quaterniond)
*/
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
dest.set(this.w * x + this.x * w + this.y * z - this.z * y,
this.w * y - this.x * z + this.y * w + this.z * x,
this.w * z + this.x * y - this.y * x + this.z * w,
this.w * w - this.x * x - this.y * y - this.z * z);
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#getEulerAnglesXYZ(org.joml.Vector3d)
*/
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.asin(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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateAxis(double, double, double, double, org.joml.Quaterniond)
*/
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 = 1.0 / Math.sqrt(axisX * axisX + 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);
dest.set(w * rx + x * rw + y * rz - z * ry,
w * ry - x * rz + y * rw + z * rx,
w * rz + x * ry - y * rx + z * rw,
w * rw - x * rx - y * ry - z * rz);
return dest;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#rotateAxis(double, org.joml.Vector3dc, org.joml.Quaterniond)
*/
public Quaterniond rotateAxis(double angle, Vector3dc axis, Quaterniond dest) {
return rotateAxis(angle, axis.x(), axis.y(), axis.z(), dest);
}
/**
* Apply a rotation to this quaternion rotating the given radians about the specified axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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 this quaternion rotating the given radians about the specified axis.
*
* If Q is this quaternion and R the quaternion representing the
* specified rotation, then the new quaternion will be Q * R. So when transforming a
* vector v with the new quaternion by using Q * R * v, 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);
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#positiveX(org.joml.Vector3d)
*/
public Vector3d positiveX(Vector3d dir) {
double invNorm = 1.0 / (x * x + y * y + z * z + w * w);
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#normalizedPositiveX(org.joml.Vector3d)
*/
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#positiveY(org.joml.Vector3d)
*/
public Vector3d positiveY(Vector3d dir) {
double invNorm = 1.0 / (x * x + y * y + z * z + w * w);
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#normalizedPositiveY(org.joml.Vector3d)
*/
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#positiveZ(org.joml.Vector3d)
*/
public Vector3d positiveZ(Vector3d dir) {
double invNorm = 1.0 / (x * x + y * y + z * z + w * w);
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;
}
/* (non-Javadoc)
* @see org.joml.Quaterniondc#normalizedPositiveZ(org.joml.Vector3d)
*/
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;
}
}