/*
* Copyright (c) 2009-2012 jMonkeyEngine
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name of 'jMonkeyEngine' nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package com.jme3.scene.plugins.blender.math;
import java.io.IOException;
import com.jme3.export.InputCapsule;
import com.jme3.export.JmeExporter;
import com.jme3.export.JmeImporter;
import com.jme3.export.OutputCapsule;
import com.jme3.export.Savable;
import com.jme3.math.Quaternion;
/**
* <code>DQuaternion</code> defines a single example of a more general class of
* hypercomplex numbers. DQuaternions extends a rotation in three dimensions to a
* rotation in four dimensions. This avoids "gimbal lock" and allows for smooth
* continuous rotation.
*
* <code>DQuaternion</code> is defined by four double point numbers: {x y z w}.
*
* This class's only purpose is to give better accuracy in floating point operations during computations.
* This is made by copying the original Quaternion class from jme3 core and leaving only required methods and basic computation methods, so that
* the class is smaller and easier to maintain.
* Should any other methods be needed, they will be added.
*
* @author Mark Powell
* @author Joshua Slack
* @author Marcin Roguski (Kaelthas)
*/
public final class DQuaternion implements Savable, Cloneable, java.io.Serializable {
private static final long serialVersionUID = 5009180713885017539L;
/**
* Represents the identity quaternion rotation (0, 0, 0, 1).
*/
public static final DQuaternion IDENTITY = new DQuaternion();
public static final DQuaternion DIRECTION_Z = new DQuaternion();
public static final DQuaternion ZERO = new DQuaternion(0, 0, 0, 0);
protected double x, y, z, w = 1;
/**
* Constructor instantiates a new <code>DQuaternion</code> object
* initializing all values to zero, except w which is initialized to 1.
*
*/
public DQuaternion() {
}
/**
* Constructor instantiates a new <code>DQuaternion</code> object from the
* given list of parameters.
*
* @param x
* the x value of the quaternion.
* @param y
* the y value of the quaternion.
* @param z
* the z value of the quaternion.
* @param w
* the w value of the quaternion.
*/
public DQuaternion(double x, double y, double z, double w) {
this.set(x, y, z, w);
}
public DQuaternion(Quaternion q) {
this(q.getX(), q.getY(), q.getZ(), q.getW());
}
public Quaternion toQuaternion() {
return new Quaternion((float) x, (float) y, (float) z, (float) w);
}
public double getX() {
return x;
}
public double getY() {
return y;
}
public double getZ() {
return z;
}
public double getW() {
return w;
}
/**
* sets the data in a <code>DQuaternion</code> object from the given list
* of parameters.
*
* @param x
* the x value of the quaternion.
* @param y
* the y value of the quaternion.
* @param z
* the z value of the quaternion.
* @param w
* the w value of the quaternion.
* @return this
*/
public DQuaternion set(double x, double y, double z, double w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
return this;
}
/**
* Sets the data in this <code>DQuaternion</code> object to be equal to the
* passed <code>DQuaternion</code> object. The values are copied producing
* a new object.
*
* @param q
* The DQuaternion to copy values from.
* @return this
*/
public DQuaternion set(DQuaternion q) {
x = q.x;
y = q.y;
z = q.z;
w = q.w;
return this;
}
/**
* Sets this DQuaternion to {0, 0, 0, 1}. Same as calling set(0,0,0,1).
*/
public void loadIdentity() {
x = y = z = 0;
w = 1;
}
/**
* <code>norm</code> returns the norm of this quaternion. This is the dot
* product of this quaternion with itself.
*
* @return the norm of the quaternion.
*/
public double norm() {
return w * w + x * x + y * y + z * z;
}
public DQuaternion fromRotationMatrix(double m00, double m01, double m02,
double m10, double m11, double m12, double m20, double m21, double m22) {
// first normalize the forward (F), up (U) and side (S) vectors of the rotation matrix
// so that the scale does not affect the rotation
double lengthSquared = m00 * m00 + m10 * m10 + m20 * m20;
if (lengthSquared != 1f && lengthSquared != 0f) {
lengthSquared = 1.0 / Math.sqrt(lengthSquared);
m00 *= lengthSquared;
m10 *= lengthSquared;
m20 *= lengthSquared;
}
lengthSquared = m01 * m01 + m11 * m11 + m21 * m21;
if (lengthSquared != 1 && lengthSquared != 0f) {
lengthSquared = 1.0 / Math.sqrt(lengthSquared);
m01 *= lengthSquared;
m11 *= lengthSquared;
m21 *= lengthSquared;
}
lengthSquared = m02 * m02 + m12 * m12 + m22 * m22;
if (lengthSquared != 1f && lengthSquared != 0f) {
lengthSquared = 1.0 / Math.sqrt(lengthSquared);
m02 *= lengthSquared;
m12 *= lengthSquared;
m22 *= lengthSquared;
}
// Use the Graphics Gems code, from
// ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z
// *NOT* the "Matrix and Quaternions FAQ", which has errors!
// the trace is the sum of the diagonal elements; see
// http://mathworld.wolfram.com/MatrixTrace.html
double t = m00 + m11 + m22;
// we protect the division by s by ensuring that s>=1
if (t >= 0) { // |w| >= .5
double s = Math.sqrt(t + 1); // |s|>=1 ...
w = 0.5f * s;
s = 0.5f / s; // so this division isn't bad
x = (m21 - m12) * s;
y = (m02 - m20) * s;
z = (m10 - m01) * s;
} else if (m00 > m11 && m00 > m22) {
double s = Math.sqrt(1.0 + m00 - m11 - m22); // |s|>=1
x = s * 0.5f; // |x| >= .5
s = 0.5f / s;
y = (m10 + m01) * s;
z = (m02 + m20) * s;
w = (m21 - m12) * s;
} else if (m11 > m22) {
double s = Math.sqrt(1.0 + m11 - m00 - m22); // |s|>=1
y = s * 0.5f; // |y| >= .5
s = 0.5f / s;
x = (m10 + m01) * s;
z = (m21 + m12) * s;
w = (m02 - m20) * s;
} else {
double s = Math.sqrt(1.0 + m22 - m00 - m11); // |s|>=1
z = s * 0.5f; // |z| >= .5
s = 0.5f / s;
x = (m02 + m20) * s;
y = (m21 + m12) * s;
w = (m10 - m01) * s;
}
return this;
}
/**
* <code>toRotationMatrix</code> converts this quaternion to a rotational
* matrix. The result is stored in result. 4th row and 4th column values are
* untouched. Note: the result is created from a normalized version of this quat.
*
* @param result
* The Matrix4f to store the result in.
* @return the rotation matrix representation of this quaternion.
*/
public Matrix toRotationMatrix(Matrix result) {
Vector3d originalScale = new Vector3d();
result.toScaleVector(originalScale);
result.setScale(1, 1, 1);
double norm = this.norm();
// we explicitly test norm against one here, saving a division
// at the cost of a test and branch. Is it worth it?
double s = norm == 1f ? 2f : norm > 0f ? 2f / norm : 0;
// compute xs/ys/zs first to save 6 multiplications, since xs/ys/zs
// will be used 2-4 times each.
double xs = x * s;
double ys = y * s;
double zs = z * s;
double xx = x * xs;
double xy = x * ys;
double xz = x * zs;
double xw = w * xs;
double yy = y * ys;
double yz = y * zs;
double yw = w * ys;
double zz = z * zs;
double zw = w * zs;
// using s=2/norm (instead of 1/norm) saves 9 multiplications by 2 here
result.set(0, 0, 1 - (yy + zz));
result.set(0, 1, xy - zw);
result.set(0, 2, xz + yw);
result.set(1, 0, xy + zw);
result.set(1, 1, 1 - (xx + zz));
result.set(1, 2, yz - xw);
result.set(2, 0, xz - yw);
result.set(2, 1, yz + xw);
result.set(2, 2, 1 - (xx + yy));
result.setScale(originalScale);
return result;
}
/**
* <code>fromAngleAxis</code> sets this quaternion to the values specified
* by an angle and an axis of rotation. This method creates an object, so
* use fromAngleNormalAxis if your axis is already normalized.
*
* @param angle
* the angle to rotate (in radians).
* @param axis
* the axis of rotation.
* @return this quaternion
*/
public DQuaternion fromAngleAxis(double angle, Vector3d axis) {
Vector3d normAxis = axis.normalize();
this.fromAngleNormalAxis(angle, normAxis);
return this;
}
/**
* <code>fromAngleNormalAxis</code> sets this quaternion to the values
* specified by an angle and a normalized axis of rotation.
*
* @param angle
* the angle to rotate (in radians).
* @param axis
* the axis of rotation (already normalized).
*/
public DQuaternion fromAngleNormalAxis(double angle, Vector3d axis) {
if (axis.x == 0 && axis.y == 0 && axis.z == 0) {
this.loadIdentity();
} else {
double halfAngle = 0.5f * angle;
double sin = Math.sin(halfAngle);
w = Math.cos(halfAngle);
x = sin * axis.x;
y = sin * axis.y;
z = sin * axis.z;
}
return this;
}
/**
* <code>add</code> adds the values of this quaternion to those of the
* parameter quaternion. The result is returned as a new quaternion.
*
* @param q
* the quaternion to add to this.
* @return the new quaternion.
*/
public DQuaternion add(DQuaternion q) {
return new DQuaternion(x + q.x, y + q.y, z + q.z, w + q.w);
}
/**
* <code>add</code> adds the values of this quaternion to those of the
* parameter quaternion. The result is stored in this DQuaternion.
*
* @param q
* the quaternion to add to this.
* @return This DQuaternion after addition.
*/
public DQuaternion addLocal(DQuaternion q) {
x += q.x;
y += q.y;
z += q.z;
w += q.w;
return this;
}
/**
* <code>subtract</code> subtracts the values of the parameter quaternion
* from those of this quaternion. The result is returned as a new
* quaternion.
*
* @param q
* the quaternion to subtract from this.
* @return the new quaternion.
*/
public DQuaternion subtract(DQuaternion q) {
return new DQuaternion(x - q.x, y - q.y, z - q.z, w - q.w);
}
/**
* <code>subtract</code> subtracts the values of the parameter quaternion
* from those of this quaternion. The result is stored in this DQuaternion.
*
* @param q
* the quaternion to subtract from this.
* @return This DQuaternion after subtraction.
*/
public DQuaternion subtractLocal(DQuaternion q) {
x -= q.x;
y -= q.y;
z -= q.z;
w -= q.w;
return this;
}
/**
* <code>mult</code> multiplies this quaternion by a parameter quaternion.
* The result is returned as a new quaternion. It should be noted that
* quaternion multiplication is not commutative so q * p != p * q.
*
* @param q
* the quaternion to multiply this quaternion by.
* @return the new quaternion.
*/
public DQuaternion mult(DQuaternion q) {
return this.mult(q, null);
}
/**
* <code>mult</code> multiplies this quaternion by a parameter quaternion.
* The result is returned as a new quaternion. It should be noted that
* quaternion multiplication is not commutative so q * p != p * q.
*
* It IS safe for q and res to be the same object.
* It IS NOT safe for this and res to be the same object.
*
* @param q
* the quaternion to multiply this quaternion by.
* @param res
* the quaternion to store the result in.
* @return the new quaternion.
*/
public DQuaternion mult(DQuaternion q, DQuaternion res) {
if (res == null) {
res = new DQuaternion();
}
double qw = q.w, qx = q.x, qy = q.y, qz = q.z;
res.x = x * qw + y * qz - z * qy + w * qx;
res.y = -x * qz + y * qw + z * qx + w * qy;
res.z = x * qy - y * qx + z * qw + w * qz;
res.w = -x * qx - y * qy - z * qz + w * qw;
return res;
}
/**
* <code>mult</code> multiplies this quaternion by a parameter vector. The
* result is returned as a new vector.
*
* @param v
* the vector to multiply this quaternion by.
* @return the new vector.
*/
public Vector3d mult(Vector3d v) {
return this.mult(v, null);
}
/**
* Multiplies this DQuaternion by the supplied quaternion. The result is
* stored in this DQuaternion, which is also returned for chaining. Similar
* to this *= q.
*
* @param q
* The DQuaternion to multiply this one by.
* @return This DQuaternion, after multiplication.
*/
public DQuaternion multLocal(DQuaternion q) {
double x1 = x * q.w + y * q.z - z * q.y + w * q.x;
double y1 = -x * q.z + y * q.w + z * q.x + w * q.y;
double z1 = x * q.y - y * q.x + z * q.w + w * q.z;
w = -x * q.x - y * q.y - z * q.z + w * q.w;
x = x1;
y = y1;
z = z1;
return this;
}
/**
* <code>mult</code> multiplies this quaternion by a parameter vector. The
* result is returned as a new vector.
*
* @param v
* the vector to multiply this quaternion by.
* @param store
* the vector to store the result in. It IS safe for v and store
* to be the same object.
* @return the result vector.
*/
public Vector3d mult(Vector3d v, Vector3d store) {
if (store == null) {
store = new Vector3d();
}
if (v.x == 0 && v.y == 0 && v.z == 0) {
store.set(0, 0, 0);
} else {
double vx = v.x, vy = v.y, vz = v.z;
store.x = w * w * vx + 2 * y * w * vz - 2 * z * w * vy + x * x * vx + 2 * y * x * vy + 2 * z * x * vz - z * z * vx - y * y * vx;
store.y = 2 * x * y * vx + y * y * vy + 2 * z * y * vz + 2 * w * z * vx - z * z * vy + w * w * vy - 2 * x * w * vz - x * x * vy;
store.z = 2 * x * z * vx + 2 * y * z * vy + z * z * vz - 2 * w * y * vx - y * y * vz + 2 * w * x * vy - x * x * vz + w * w * vz;
}
return store;
}
/**
*
* <code>toString</code> creates the string representation of this <code>DQuaternion</code>. The values of the quaternion are displaced (x,
* y, z, w), in the following manner: <br>
* (x, y, z, w)
*
* @return the string representation of this object.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
return "(" + x + ", " + y + ", " + z + ", " + w + ")";
}
/**
* <code>equals</code> determines if two quaternions are logically equal,
* that is, if the values of (x, y, z, w) are the same for both quaternions.
*
* @param o
* the object to compare for equality
* @return true if they are equal, false otherwise.
*/
@Override
public boolean equals(Object o) {
if (!(o instanceof DQuaternion)) {
return false;
}
if (this == o) {
return true;
}
DQuaternion comp = (DQuaternion) o;
if (Double.compare(x, comp.x) != 0) {
return false;
}
if (Double.compare(y, comp.y) != 0) {
return false;
}
if (Double.compare(z, comp.z) != 0) {
return false;
}
if (Double.compare(w, comp.w) != 0) {
return false;
}
return true;
}
/**
*
* <code>hashCode</code> returns the hash code value as an integer and is
* supported for the benefit of hashing based collection classes such as
* Hashtable, HashMap, HashSet etc.
*
* @return the hashcode for this instance of DQuaternion.
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
long hash = 37;
hash = 37 * hash + Double.doubleToLongBits(x);
hash = 37 * hash + Double.doubleToLongBits(y);
hash = 37 * hash + Double.doubleToLongBits(z);
hash = 37 * hash + Double.doubleToLongBits(w);
return (int) hash;
}
public void write(JmeExporter e) throws IOException {
OutputCapsule cap = e.getCapsule(this);
cap.write(x, "x", 0);
cap.write(y, "y", 0);
cap.write(z, "z", 0);
cap.write(w, "w", 1);
}
public void read(JmeImporter e) throws IOException {
InputCapsule cap = e.getCapsule(this);
x = cap.readFloat("x", 0);
y = cap.readFloat("y", 0);
z = cap.readFloat("z", 0);
w = cap.readFloat("w", 1);
}
@Override
public DQuaternion clone() {
try {
return (DQuaternion) super.clone();
} catch (CloneNotSupportedException e) {
throw new AssertionError(); // can not happen
}
}
}