forked from MagicBane/Server
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1265 lines
36 KiB
1265 lines
36 KiB
3 years ago
|
// • ▌ ▄ ·. ▄▄▄· ▄▄ • ▪ ▄▄· ▄▄▄▄· ▄▄▄· ▐▄▄▄ ▄▄▄ .
|
||
|
|
// ·██ ▐███▪▐█ ▀█ ▐█ ▀ ▪██ ▐█ ▌▪▐█ ▀█▪▐█ ▀█ •█▌ ▐█▐▌·
|
||
|
|
// ▐█ ▌▐▌▐█·▄█▀▀█ ▄█ ▀█▄▐█·██ ▄▄▐█▀▀█▄▄█▀▀█ ▐█▐ ▐▌▐▀▀▀
|
||
|
|
// ██ ██▌▐█▌▐█ ▪▐▌▐█▄▪▐█▐█▌▐███▌██▄▪▐█▐█ ▪▐▌██▐ █▌▐█▄▄▌
|
||
|
|
// ▀▀ █▪▀▀▀ ▀ ▀ ·▀▀▀▀ ▀▀▀·▀▀▀ ·▀▀▀▀ ▀ ▀ ▀▀ █▪ ▀▀▀
|
||
|
|
// Magicbane Emulator Project © 2013 - 2022
|
||
|
|
// www.magicbane.com
|
||
|
|
|
||
|
|
package engine.math;
|
||
|
|
|
||
|
|
import org.pmw.tinylog.Logger;
|
||
|
|
|
||
|
|
import java.io.IOException;
|
||
|
|
import java.io.ObjectInput;
|
||
|
|
import java.io.ObjectOutput;
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>Quaternion</code> defines a single example of a more general class of
|
||
|
|
* hypercomplex numbers. Quaternions extends a rotation in three dimensions to a
|
||
|
|
* rotation in four dimensions. This avoids "gimbal lock" and allows for smooth
|
||
|
|
* continuous rotation.
|
||
|
|
*
|
||
|
|
* <code>Quaternion</code> is defined by four floating point numbers: {x y z w}.
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
|
||
|
|
public class Quaternion {
|
||
|
|
|
||
|
|
public float x, y, z, w;
|
||
|
|
public float angleX, angleY,angleZ;
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructor instantiates a new <code>Quaternion</code> object
|
||
|
|
* initializing all values to zero, except w which is initialized to 1.
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
public Quaternion() {
|
||
|
|
x = 0;
|
||
|
|
y = 0;
|
||
|
|
z = 0;
|
||
|
|
w = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructor instantiates a new <code>Quaternion</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 Quaternion(float x, float y, float z, float w) {
|
||
|
|
this.x = x;
|
||
|
|
this.y = y;
|
||
|
|
this.z = z;
|
||
|
|
this.w = w;
|
||
|
|
float[] angles = new float[3];
|
||
|
|
angles = this.toAngles(angles);
|
||
|
|
angleX = angles[0];
|
||
|
|
angleY = angles[1];
|
||
|
|
angleZ = angles[2];
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* sets the data in a <code>Quaternion</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 void set(float x, float y, float z, float w) {
|
||
|
|
this.x = x;
|
||
|
|
this.y = y;
|
||
|
|
this.z = z;
|
||
|
|
this.w = w;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Sets the data in this <code>Quaternion</code> object to be equal to the
|
||
|
|
* passed <code>Quaternion</code> object. The values are copied producing a
|
||
|
|
* new object.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* The Quaternion to copy values from.
|
||
|
|
* @return this for chaining
|
||
|
|
*/
|
||
|
|
public Quaternion set(Quaternion q) {
|
||
|
|
this.x = q.x;
|
||
|
|
this.y = q.y;
|
||
|
|
this.z = q.z;
|
||
|
|
this.w = q.w;
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructor instantiates a new <code>Quaternion</code> object from a
|
||
|
|
* collection of rotation angles.
|
||
|
|
*
|
||
|
|
* @param angles
|
||
|
|
* the angles of rotation (x, y, z) that will define the
|
||
|
|
* <code>Quaternion</code>.
|
||
|
|
*/
|
||
|
|
public Quaternion(float[] angles) {
|
||
|
|
fromAngles(angles);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructor instantiates a new <code>Quaternion</code> object from an
|
||
|
|
* interpolation between two other quaternions.
|
||
|
|
*
|
||
|
|
* @param q1
|
||
|
|
* the first quaternion.
|
||
|
|
* @param q2
|
||
|
|
* the second quaternion.
|
||
|
|
* @param interp
|
||
|
|
* the amount to interpolate between the two quaternions.
|
||
|
|
*/
|
||
|
|
public Quaternion(Quaternion q1, Quaternion q2, float interp) {
|
||
|
|
slerp(q1, q2, interp);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructor instantiates a new <code>Quaternion</code> object from an
|
||
|
|
* existing quaternion, creating a copy.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* the quaternion to copy.
|
||
|
|
*/
|
||
|
|
public Quaternion(Quaternion q) {
|
||
|
|
this.x = q.x;
|
||
|
|
this.y = q.y;
|
||
|
|
this.z = q.z;
|
||
|
|
this.w = q.w;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Sets this Quaternion to {0, 0, 0, 1}. Same as calling set(0,0,0,1).
|
||
|
|
*/
|
||
|
|
public void loadIdentity() {
|
||
|
|
x = y = z = 0;
|
||
|
|
w = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @return true if this Quaternion is {0,0,0,1}
|
||
|
|
*/
|
||
|
|
public boolean isIdentity() {
|
||
|
|
return x == 0 && y == 0 && z == 0 && w == 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>fromAngles</code> builds a quaternion from the Euler rotation
|
||
|
|
* angles (y,r,p).
|
||
|
|
*
|
||
|
|
* @param angles
|
||
|
|
* the Euler angles of rotation (in radians).
|
||
|
|
*/
|
||
|
|
public void fromAngles(float[] angles) {
|
||
|
|
if (angles.length != 3)
|
||
|
|
throw new IllegalArgumentException(
|
||
|
|
"Angles array must have three elements");
|
||
|
|
|
||
|
|
fromAngles(angles[0], angles[1], angles[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>fromAngles</code> builds a Quaternion from the Euler rotation
|
||
|
|
* angles (y,r,p). Note that we are applying in order: roll, pitch, yaw but
|
||
|
|
* we've ordered them in x, y, and z for convenience. See:
|
||
|
|
* http://www.euclideanspace
|
||
|
|
* .com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
|
||
|
|
*
|
||
|
|
* @param yaw
|
||
|
|
* the Euler yaw of rotation (in radians). (aka Bank, often rot
|
||
|
|
* around x)
|
||
|
|
* @param roll
|
||
|
|
* the Euler roll of rotation (in radians). (aka Heading, often
|
||
|
|
* rot around y)
|
||
|
|
* @param pitch
|
||
|
|
* the Euler pitch of rotation (in radians). (aka Attitude, often
|
||
|
|
* rot around z)
|
||
|
|
*/
|
||
|
|
public Quaternion fromAngles(float yaw, float roll, float pitch) {
|
||
|
|
float angle;
|
||
|
|
float sinRoll, sinPitch, sinYaw, cosRoll, cosPitch, cosYaw;
|
||
|
|
angle = pitch * 0.5f;
|
||
|
|
sinPitch = FastMath.sin(angle);
|
||
|
|
cosPitch = FastMath.cos(angle);
|
||
|
|
angle = roll * 0.5f;
|
||
|
|
sinRoll = FastMath.sin(angle);
|
||
|
|
cosRoll = FastMath.cos(angle);
|
||
|
|
angle = yaw * 0.5f;
|
||
|
|
sinYaw = FastMath.sin(angle);
|
||
|
|
cosYaw = FastMath.cos(angle);
|
||
|
|
|
||
|
|
// variables used to reduce multiplication calls.
|
||
|
|
float cosRollXcosPitch = cosRoll * cosPitch;
|
||
|
|
float sinRollXsinPitch = sinRoll * sinPitch;
|
||
|
|
float cosRollXsinPitch = cosRoll * sinPitch;
|
||
|
|
float sinRollXcosPitch = sinRoll * cosPitch;
|
||
|
|
|
||
|
|
w = (cosRollXcosPitch * cosYaw - sinRollXsinPitch * sinYaw);
|
||
|
|
x = (cosRollXcosPitch * sinYaw + sinRollXsinPitch * cosYaw);
|
||
|
|
y = (sinRollXcosPitch * cosYaw + cosRollXsinPitch * sinYaw);
|
||
|
|
z = (cosRollXsinPitch * cosYaw - sinRollXcosPitch * sinYaw);
|
||
|
|
|
||
|
|
normalize();
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>toAngles</code> returns this quaternion converted to Euler rotation
|
||
|
|
* angles (yaw,roll,pitch).<br/>
|
||
|
|
* See http://www.euclideanspace.com/maths/geometry/rotations/conversions/
|
||
|
|
* quaternionToEuler/index.htm
|
||
|
|
*
|
||
|
|
* @param angles
|
||
|
|
* the float[] in which the angles should be stored, or null if
|
||
|
|
* you want a new float[] to be created
|
||
|
|
* @return the float[] in which the angles are stored.
|
||
|
|
*/
|
||
|
|
public float[] toAngles(float[] angles) {
|
||
|
|
if (angles == null)
|
||
|
|
angles = new float[3];
|
||
|
|
else if (angles.length != 3)
|
||
|
|
throw new IllegalArgumentException(
|
||
|
|
"Angles array must have three elements");
|
||
|
|
|
||
|
|
float sqw = w * w;
|
||
|
|
float sqx = x * x;
|
||
|
|
float sqy = y * y;
|
||
|
|
float sqz = z * z;
|
||
|
|
float unit = sqx + sqy + sqz + sqw; // if normalized is one, otherwise
|
||
|
|
// is correction factor
|
||
|
|
float test = x * y + z * w;
|
||
|
|
if (test > 0.499 * unit) { // singularity at north pole
|
||
|
|
angles[1] = 2 * FastMath.atan2(x, w);
|
||
|
|
angles[2] = FastMath.HALF_PI;
|
||
|
|
angles[0] = 0;
|
||
|
|
} else if (test < -0.499 * unit) { // singularity at south pole
|
||
|
|
angles[1] = -2 * FastMath.atan2(x, w);
|
||
|
|
angles[2] = -FastMath.HALF_PI;
|
||
|
|
angles[0] = 0;
|
||
|
|
} else {
|
||
|
|
angles[1] = FastMath.atan2(2 * y * w - 2 * x * z, sqx - sqy - sqz
|
||
|
|
+ sqw); // roll or heading
|
||
|
|
angles[2] = FastMath.asin(2 * test / unit); // pitch or attitude
|
||
|
|
angles[0] = FastMath.atan2(2 * x * w - 2 * y * z, -sqx + sqy - sqz
|
||
|
|
+ sqw); // yaw or bank
|
||
|
|
}
|
||
|
|
return angles;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
*
|
||
|
|
* <code>fromRotationMatrix</code> generates a quaternion from a supplied
|
||
|
|
* matrix. This matrix is assumed to be a rotational matrix.
|
||
|
|
*
|
||
|
|
* @param matrix
|
||
|
|
* the matrix that defines the rotation.
|
||
|
|
*/
|
||
|
|
public Quaternion fromRotationMatrix(Matrix3f matrix) {
|
||
|
|
return fromRotationMatrix(matrix.m00, matrix.m01, matrix.m02,
|
||
|
|
matrix.m10, matrix.m11, matrix.m12, matrix.m20, matrix.m21,
|
||
|
|
matrix.m22);
|
||
|
|
}
|
||
|
|
|
||
|
|
public Quaternion fromRotationMatrix(float m00, float m01, float m02,
|
||
|
|
float m10, float m11, float m12, float m20, float m21, float m22) {
|
||
|
|
// 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
|
||
|
|
float t = m00 + m11 + m22;
|
||
|
|
|
||
|
|
// we protect the division by s by ensuring that s>=1
|
||
|
|
if (t >= 0) { // |w| >= .5
|
||
|
|
float s = FastMath.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)) {
|
||
|
|
float s = FastMath.sqrt(1.0f + 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) {
|
||
|
|
float s = FastMath.sqrt(1.0f + 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 {
|
||
|
|
float s = FastMath.sqrt(1.0f + 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. Note: the result is created from a normalized version of this
|
||
|
|
* quat.
|
||
|
|
*
|
||
|
|
* @return the rotation matrix representation of this quaternion.
|
||
|
|
*/
|
||
|
|
public Matrix3f toRotationMatrix() {
|
||
|
|
Matrix3f matrix = new Matrix3f();
|
||
|
|
return toRotationMatrix(matrix);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>toRotationMatrix</code> converts this quaternion to a rotational
|
||
|
|
* matrix. The result is stored in result.
|
||
|
|
*
|
||
|
|
* @param result
|
||
|
|
* The Matrix3f to store the result in.
|
||
|
|
* @return the rotation matrix representation of this quaternion.
|
||
|
|
*/
|
||
|
|
public Matrix3f toRotationMatrix(Matrix3f result) {
|
||
|
|
|
||
|
|
float norm = norm();
|
||
|
|
// we explicitly test norm against one here, saving a division
|
||
|
|
// at the cost of a test and branch. Is it worth it?
|
||
|
|
float 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.
|
||
|
|
float xs = x * s;
|
||
|
|
float ys = y * s;
|
||
|
|
float zs = z * s;
|
||
|
|
float xx = x * xs;
|
||
|
|
float xy = x * ys;
|
||
|
|
float xz = x * zs;
|
||
|
|
float xw = w * xs;
|
||
|
|
float yy = y * ys;
|
||
|
|
float yz = y * zs;
|
||
|
|
float yw = w * ys;
|
||
|
|
float zz = z * zs;
|
||
|
|
float zw = w * zs;
|
||
|
|
|
||
|
|
// using s=2/norm (instead of 1/norm) saves 9 multiplications by 2 here
|
||
|
|
result.m00 = 1 - (yy + zz);
|
||
|
|
result.m01 = (xy - zw);
|
||
|
|
result.m02 = (xz + yw);
|
||
|
|
result.m10 = (xy + zw);
|
||
|
|
result.m11 = 1 - (xx + zz);
|
||
|
|
result.m12 = (yz - xw);
|
||
|
|
result.m20 = (xz - yw);
|
||
|
|
result.m21 = (yz + xw);
|
||
|
|
result.m22 = 1 - (xx + yy);
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <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 Matrix4f toRotationMatrix(Matrix4f result) {
|
||
|
|
|
||
|
|
float norm = norm();
|
||
|
|
// we explicitly test norm against one here, saving a division
|
||
|
|
// at the cost of a test and branch. Is it worth it?
|
||
|
|
float 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.
|
||
|
|
float xs = x * s;
|
||
|
|
float ys = y * s;
|
||
|
|
float zs = z * s;
|
||
|
|
float xx = x * xs;
|
||
|
|
float xy = x * ys;
|
||
|
|
float xz = x * zs;
|
||
|
|
float xw = w * xs;
|
||
|
|
float yy = y * ys;
|
||
|
|
float yz = y * zs;
|
||
|
|
float yw = w * ys;
|
||
|
|
float zz = z * zs;
|
||
|
|
float zw = w * zs;
|
||
|
|
|
||
|
|
// using s=2/norm (instead of 1/norm) saves 9 multiplications by 2 here
|
||
|
|
result.m00 = 1 - (yy + zz);
|
||
|
|
result.m01 = (xy - zw);
|
||
|
|
result.m02 = (xz + yw);
|
||
|
|
result.m10 = (xy + zw);
|
||
|
|
result.m11 = 1 - (xx + zz);
|
||
|
|
result.m12 = (yz - xw);
|
||
|
|
result.m20 = (xz - yw);
|
||
|
|
result.m21 = (yz + xw);
|
||
|
|
result.m22 = 1 - (xx + yy);
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>getRotationColumn</code> returns one of three columns specified by
|
||
|
|
* the parameter. This column is returned as a <code>Vector3f</code> object.
|
||
|
|
*
|
||
|
|
* @param i
|
||
|
|
* the column to retrieve. Must be between 0 and 2.
|
||
|
|
* @return the column specified by the index.
|
||
|
|
* @throws Exception
|
||
|
|
*/
|
||
|
|
public Vector3f getRotationColumn(int i) throws Exception {
|
||
|
|
return getRotationColumn(i, null);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>getRotationColumn</code> returns one of three columns specified by
|
||
|
|
* the parameter. This column is returned as a <code>Vector3f</code> object.
|
||
|
|
* The value is retrieved as if this quaternion was first normalized.
|
||
|
|
*
|
||
|
|
* @param i
|
||
|
|
* the column to retrieve. Must be between 0 and 2.
|
||
|
|
* @param store
|
||
|
|
* the vector object to store the result in. if null, a new one
|
||
|
|
* is created.
|
||
|
|
* @return the column specified by the index.
|
||
|
|
* @throws Exception
|
||
|
|
*/
|
||
|
|
public Vector3f getRotationColumn(int i, Vector3f store) throws Exception {
|
||
|
|
if (store == null)
|
||
|
|
store = new Vector3f();
|
||
|
|
|
||
|
|
float norm = norm();
|
||
|
|
if (norm != 1.0f) {
|
||
|
|
norm = FastMath.invSqrt(norm);
|
||
|
|
}
|
||
|
|
|
||
|
|
float xx = x * x * norm;
|
||
|
|
float xy = x * y * norm;
|
||
|
|
float xz = x * z * norm;
|
||
|
|
float xw = x * w * norm;
|
||
|
|
float yy = y * y * norm;
|
||
|
|
float yz = y * z * norm;
|
||
|
|
float yw = y * w * norm;
|
||
|
|
float zz = z * z * norm;
|
||
|
|
float zw = z * w * norm;
|
||
|
|
|
||
|
|
switch (i) {
|
||
|
|
case 0:
|
||
|
|
store.x = 1 - 2 * (yy + zz);
|
||
|
|
store.y = 2 * (xy + zw);
|
||
|
|
store.z = 2 * (xz - yw);
|
||
|
|
break;
|
||
|
|
case 1:
|
||
|
|
store.x = 2 * (xy - zw);
|
||
|
|
store.y = 1 - 2 * (xx + zz);
|
||
|
|
store.z = 2 * (yz + xw);
|
||
|
|
break;
|
||
|
|
case 2:
|
||
|
|
store.x = 2 * (xz + yw);
|
||
|
|
store.y = 2 * (yz - xw);
|
||
|
|
store.z = 1 - 2 * (xx + yy);
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new Exception("Invalid column index. " + i);
|
||
|
|
}
|
||
|
|
|
||
|
|
return store;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <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 Quaternion fromAngleAxis(float angle, Vector3f axis) {
|
||
|
|
Vector3f normAxis = axis.normalize();
|
||
|
|
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 Quaternion fromAngleNormalAxis(float angle, Vector3f axis) {
|
||
|
|
if (axis.x == 0 && axis.y == 0 && axis.z == 0) {
|
||
|
|
loadIdentity();
|
||
|
|
} else {
|
||
|
|
float halfAngle = 0.5f * angle;
|
||
|
|
float sin = FastMath.sin(halfAngle);
|
||
|
|
w = FastMath.cos(halfAngle);
|
||
|
|
x = sin * axis.x;
|
||
|
|
y = sin * axis.y;
|
||
|
|
z = sin * axis.z;
|
||
|
|
}
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>toAngleAxis</code> sets a given angle and axis to that represented
|
||
|
|
* by the current quaternion. The values are stored as following: The axis
|
||
|
|
* is provided as a parameter and built by the method, the angle is returned
|
||
|
|
* as a float.
|
||
|
|
*
|
||
|
|
* @param axisStore
|
||
|
|
* the object we'll store the computed axis in.
|
||
|
|
* @return the angle of rotation in radians.
|
||
|
|
*/
|
||
|
|
public float toAngleAxis(Vector3f axisStore) {
|
||
|
|
float sqrLength = x * x + y * y + z * z;
|
||
|
|
float angle;
|
||
|
|
if (sqrLength == 0.0f) {
|
||
|
|
angle = 0.0f;
|
||
|
|
if (axisStore != null) {
|
||
|
|
axisStore.x = 1.0f;
|
||
|
|
axisStore.y = 0.0f;
|
||
|
|
axisStore.z = 0.0f;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
angle = (2.0f * FastMath.acos(w));
|
||
|
|
if (axisStore != null) {
|
||
|
|
float invLength = (1.0f / FastMath.sqrt(sqrLength));
|
||
|
|
axisStore.x = x * invLength;
|
||
|
|
axisStore.y = y * invLength;
|
||
|
|
axisStore.z = z * invLength;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return angle;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>slerp</code> sets this quaternion's value as an interpolation
|
||
|
|
* between two other quaternions.
|
||
|
|
*
|
||
|
|
* @param q1
|
||
|
|
* the first quaternion.
|
||
|
|
* @param q2
|
||
|
|
* the second quaternion.
|
||
|
|
* @param t
|
||
|
|
* the amount to interpolate between the two quaternions.
|
||
|
|
*/
|
||
|
|
public Quaternion slerp(Quaternion q1, Quaternion q2, float t) {
|
||
|
|
// Create a local quaternion to store the interpolated quaternion
|
||
|
|
if (q1.x == q2.x && q1.y == q2.y && q1.z == q2.z && q1.w == q2.w) {
|
||
|
|
this.set(q1);
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
float result = (q1.x * q2.x) + (q1.y * q2.y) + (q1.z * q2.z)
|
||
|
|
+ (q1.w * q2.w);
|
||
|
|
|
||
|
|
if (result < 0.0f) {
|
||
|
|
// Negate the second quaternion and the result of the dot product
|
||
|
|
q2.x = -q2.x;
|
||
|
|
q2.y = -q2.y;
|
||
|
|
q2.z = -q2.z;
|
||
|
|
q2.w = -q2.w;
|
||
|
|
result = -result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Set the first and second scale for the interpolation
|
||
|
|
float scale0 = 1 - t;
|
||
|
|
float scale1 = t;
|
||
|
|
|
||
|
|
// Check if the angle between the 2 quaternions was big enough to
|
||
|
|
// warrant such calculations
|
||
|
|
if ((1 - result) > 0.1f) {// Get the angle between the 2 quaternions,
|
||
|
|
// and then store the sin() of that angle
|
||
|
|
float theta = FastMath.acos(result);
|
||
|
|
float invSinTheta = 1f / FastMath.sin(theta);
|
||
|
|
|
||
|
|
// Calculate the scale for q1 and q2, according to the angle and
|
||
|
|
// it's sine value
|
||
|
|
scale0 = FastMath.sin((1 - t) * theta) * invSinTheta;
|
||
|
|
scale1 = FastMath.sin((t * theta)) * invSinTheta;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Calculate the x, y, z and w values for the quaternion by using a
|
||
|
|
// special
|
||
|
|
// form of linear interpolation for quaternions.
|
||
|
|
this.x = (scale0 * q1.x) + (scale1 * q2.x);
|
||
|
|
this.y = (scale0 * q1.y) + (scale1 * q2.y);
|
||
|
|
this.z = (scale0 * q1.z) + (scale1 * q2.z);
|
||
|
|
this.w = (scale0 * q1.w) + (scale1 * q2.w);
|
||
|
|
|
||
|
|
// Return the interpolated quaternion
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Sets the values of this quaternion to the slerp from itself to q2 by
|
||
|
|
* changeAmnt
|
||
|
|
*
|
||
|
|
* @param q2
|
||
|
|
* Final interpolation value
|
||
|
|
* @param changeAmnt
|
||
|
|
* The amount difference
|
||
|
|
*/
|
||
|
|
public void slerp(Quaternion q2, float changeAmnt) {
|
||
|
|
if (this.x == q2.x && this.y == q2.y && this.z == q2.z
|
||
|
|
&& this.w == q2.w) {
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
float result = (this.x * q2.x) + (this.y * q2.y) + (this.z * q2.z)
|
||
|
|
+ (this.w * q2.w);
|
||
|
|
|
||
|
|
if (result < 0.0f) {
|
||
|
|
// Negate the second quaternion and the result of the dot product
|
||
|
|
q2.x = -q2.x;
|
||
|
|
q2.y = -q2.y;
|
||
|
|
q2.z = -q2.z;
|
||
|
|
q2.w = -q2.w;
|
||
|
|
result = -result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Set the first and second scale for the interpolation
|
||
|
|
float scale0 = 1 - changeAmnt;
|
||
|
|
float scale1 = changeAmnt;
|
||
|
|
|
||
|
|
// Check if the angle between the 2 quaternions was big enough to
|
||
|
|
// warrant such calculations
|
||
|
|
if ((1 - result) > 0.1f) {
|
||
|
|
// Get the angle between the 2 quaternions, and then store the sin()
|
||
|
|
// of that angle
|
||
|
|
float theta = FastMath.acos(result);
|
||
|
|
float invSinTheta = 1f / FastMath.sin(theta);
|
||
|
|
|
||
|
|
// Calculate the scale for q1 and q2, according to the angle and
|
||
|
|
// it's sine value
|
||
|
|
scale0 = FastMath.sin((1 - changeAmnt) * theta) * invSinTheta;
|
||
|
|
scale1 = FastMath.sin((changeAmnt * theta)) * invSinTheta;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Calculate the x, y, z and w values for the quaternion by using a
|
||
|
|
// special
|
||
|
|
// form of linear interpolation for quaternions.
|
||
|
|
this.x = (scale0 * this.x) + (scale1 * q2.x);
|
||
|
|
this.y = (scale0 * this.y) + (scale1 * q2.y);
|
||
|
|
this.z = (scale0 * this.z) + (scale1 * q2.z);
|
||
|
|
this.w = (scale0 * this.w) + (scale1 * q2.w);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <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 Quaternion add(Quaternion q) {
|
||
|
|
return new Quaternion(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 Quaternion.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* the quaternion to add to this.
|
||
|
|
* @return This Quaternion after addition.
|
||
|
|
*/
|
||
|
|
public Quaternion addLocal(Quaternion q) {
|
||
|
|
this.x += q.x;
|
||
|
|
this.y += q.y;
|
||
|
|
this.z += q.z;
|
||
|
|
this.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 Quaternion subtract(Quaternion q) {
|
||
|
|
return new Quaternion(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 Quaternion.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* the quaternion to subtract from this.
|
||
|
|
* @return This Quaternion after subtraction.
|
||
|
|
*/
|
||
|
|
public Quaternion subtractLocal(Quaternion q) {
|
||
|
|
this.x -= q.x;
|
||
|
|
this.y -= q.y;
|
||
|
|
this.z -= q.z;
|
||
|
|
this.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 cummulative so q * p != p * q.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* the quaternion to multiply this quaternion by.
|
||
|
|
* @return the new quaternion.
|
||
|
|
*/
|
||
|
|
public Quaternion mult(Quaternion q) {
|
||
|
|
return mult(q, null);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>mult</code> multiplies this quaternion by a parameter quaternion
|
||
|
|
* (q). 'this' is not modified. It should be noted that quaternion
|
||
|
|
* multiplication is not cummulative so q * p != p * q.
|
||
|
|
*
|
||
|
|
* It IS safe for q 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 (may be null). If
|
||
|
|
* non-null, the input values of 'res' will be ignored and
|
||
|
|
* replaced.
|
||
|
|
* @return If specified res is null, then a new Quaternion; otherwise
|
||
|
|
* returns the populated 'res'.
|
||
|
|
*/
|
||
|
|
public Quaternion mult(Quaternion q, Quaternion res) {
|
||
|
|
if (res == null)
|
||
|
|
res = new Quaternion();
|
||
|
|
float 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;
|
||
|
|
|
||
|
|
float[] angles = new float[3];
|
||
|
|
angles = res.toAngles(angles);
|
||
|
|
res.angleX = angles[0];
|
||
|
|
res.angleY = angles[1];
|
||
|
|
res.angleZ = angles[2];
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>apply</code> multiplies this quaternion by a parameter matrix
|
||
|
|
* internally.
|
||
|
|
*
|
||
|
|
* @param matrix
|
||
|
|
* the matrix to apply to this quaternion.
|
||
|
|
*/
|
||
|
|
public void apply(Matrix3f matrix) {
|
||
|
|
float oldX = x, oldY = y, oldZ = z, oldW = w;
|
||
|
|
fromRotationMatrix(matrix);
|
||
|
|
float tempX = x, tempY = y, tempZ = z, tempW = w;
|
||
|
|
|
||
|
|
x = oldX * tempW + oldY * tempZ - oldZ * tempY + oldW * tempX;
|
||
|
|
y = -oldX * tempZ + oldY * tempW + oldZ * tempX + oldW * tempY;
|
||
|
|
z = oldX * tempY - oldY * tempX + oldZ * tempW + oldW * tempZ;
|
||
|
|
w = -oldX * tempX - oldY * tempY - oldZ * tempZ + oldW * tempW;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
*
|
||
|
|
* <code>fromAxes</code> creates a <code>Quaternion</code> that represents
|
||
|
|
* the coordinate system defined by three axes. These axes are assumed to be
|
||
|
|
* orthogonal and no error checking is applied. Thus, the user must insure
|
||
|
|
* that the three axes being provided indeed represents a proper right
|
||
|
|
* handed coordinate system.
|
||
|
|
*
|
||
|
|
* @param axis
|
||
|
|
* the array containing the three vectors representing the
|
||
|
|
* coordinate system.
|
||
|
|
*/
|
||
|
|
public Quaternion fromAxes(Vector3f[] axis) {
|
||
|
|
if (axis.length != 3)
|
||
|
|
throw new IllegalArgumentException(
|
||
|
|
"Axis array must have three elements");
|
||
|
|
return fromAxes(axis[0], axis[1], axis[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
*
|
||
|
|
* <code>fromAxes</code> creates a <code>Quaternion</code> that represents
|
||
|
|
* the coordinate system defined by three axes. These axes are assumed to be
|
||
|
|
* orthogonal and no error checking is applied. Thus, the user must insure
|
||
|
|
* that the three axes being provided indeed represents a proper right
|
||
|
|
* handed coordinate system.
|
||
|
|
*
|
||
|
|
* @param xAxis
|
||
|
|
* vector representing the x-axis of the coordinate system.
|
||
|
|
* @param yAxis
|
||
|
|
* vector representing the y-axis of the coordinate system.
|
||
|
|
* @param zAxis
|
||
|
|
* vector representing the z-axis of the coordinate system.
|
||
|
|
*/
|
||
|
|
public Quaternion fromAxes(Vector3f xAxis, Vector3f yAxis, Vector3f zAxis) {
|
||
|
|
return fromRotationMatrix(xAxis.x, yAxis.x, zAxis.x, xAxis.y, yAxis.y,
|
||
|
|
zAxis.y, xAxis.z, yAxis.z, zAxis.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
*
|
||
|
|
* <code>toAxes</code> takes in an array of three vectors. Each vector
|
||
|
|
* corresponds to an axis of the coordinate system defined by the quaternion
|
||
|
|
* rotation.
|
||
|
|
*
|
||
|
|
* @param axis
|
||
|
|
* the array of vectors to be filled.
|
||
|
|
* @throws Exception
|
||
|
|
*/
|
||
|
|
public void toAxes(Vector3f axis[]) throws Exception {
|
||
|
|
Matrix3f tempMat = toRotationMatrix();
|
||
|
|
axis[0] = tempMat.getColumn(0, axis[0]);
|
||
|
|
axis[1] = tempMat.getColumn(1, axis[1]);
|
||
|
|
axis[2] = tempMat.getColumn(2, axis[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>mult</code> multiplies this quaternion by a parameter vector. The
|
||
|
|
* result is returned as a new vector. 'this' is not modified.
|
||
|
|
*
|
||
|
|
* @param v
|
||
|
|
* the vector to multiply this quaternion by.
|
||
|
|
* @return the new vector.
|
||
|
|
*/
|
||
|
|
public Vector3f mult(Vector3f v) {
|
||
|
|
return mult(v, null);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>mult</code> multiplies this quaternion by a parameter vector. The
|
||
|
|
* result is stored in the supplied vector This method is very poorly named,
|
||
|
|
* since the specified vector is modified and, contrary to the other *Local
|
||
|
|
* methods in this and other jME classes, <b>'this' remains unchanged</b>.
|
||
|
|
*
|
||
|
|
* @param v
|
||
|
|
* the vector which this Quaternion multiplies.
|
||
|
|
* @return v
|
||
|
|
*/
|
||
|
|
public Vector3f multLocal(Vector3f v) {
|
||
|
|
float tempX, tempY;
|
||
|
|
tempX = w * w * v.x + 2 * y * w * v.z - 2 * z * w * v.y + x * x * v.x
|
||
|
|
+ 2 * y * x * v.y + 2 * z * x * v.z - z * z * v.x - y * y * v.x;
|
||
|
|
tempY = 2 * x * y * v.x + y * y * v.y + 2 * z * y * v.z + 2 * w * z
|
||
|
|
* v.x - z * z * v.y + w * w * v.y - 2 * x * w * v.z - x * x
|
||
|
|
* v.y;
|
||
|
|
v.z = 2 * x * z * v.x + 2 * y * z * v.y + z * z * v.z - 2 * w * y * v.x
|
||
|
|
- y * y * v.z + 2 * w * x * v.y - x * x * v.z + w * w * v.z;
|
||
|
|
v.x = tempX;
|
||
|
|
v.y = tempY;
|
||
|
|
return v;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Multiplies this Quaternion by the supplied quaternion. The result is
|
||
|
|
* stored in this Quaternion, which is also returned for chaining. Similar
|
||
|
|
* to this *= q.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* The Quaternion to multiply this one by.
|
||
|
|
* @return This Quaternion, after multiplication.
|
||
|
|
*/
|
||
|
|
public Quaternion multLocal(Quaternion q) {
|
||
|
|
float x1 = x * q.w + y * q.z - z * q.y + w * q.x;
|
||
|
|
float y1 = -x * q.z + y * q.w + z * q.x + w * q.y;
|
||
|
|
float 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Multiplies this Quaternion by the supplied quaternion. The result is
|
||
|
|
* stored in this Quaternion, which is also returned for chaining. Similar
|
||
|
|
* to this *= q.
|
||
|
|
*
|
||
|
|
* @param qx
|
||
|
|
* - quat x value
|
||
|
|
* @param qy
|
||
|
|
* - quat y value
|
||
|
|
* @param qz
|
||
|
|
* - quat z value
|
||
|
|
* @param qw
|
||
|
|
* - quat w value
|
||
|
|
*
|
||
|
|
* @return This Quaternion, after multiplication.
|
||
|
|
*/
|
||
|
|
public Quaternion multLocal(float qx, float qy, float qz, float qw) {
|
||
|
|
float x1 = x * qw + y * qz - z * qy + w * qx;
|
||
|
|
float y1 = -x * qz + y * qw + z * qx + w * qy;
|
||
|
|
float z1 = x * qy - y * qx + z * qw + w * qz;
|
||
|
|
w = -x * qx - y * qy - z * qz + w * qw;
|
||
|
|
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. 'this' is not modified.
|
||
|
|
*
|
||
|
|
* @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 Vector3f mult(Vector3f v, Vector3f store) {
|
||
|
|
if (store == null)
|
||
|
|
store = new Vector3f();
|
||
|
|
if (v.x == 0 && v.y == 0 && v.z == 0) {
|
||
|
|
store.set(0, 0, 0);
|
||
|
|
} else {
|
||
|
|
float 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>mult</code> multiplies this quaternion by a parameter scalar. The
|
||
|
|
* result is returned as a new quaternion.
|
||
|
|
*
|
||
|
|
* @param scalar
|
||
|
|
* the quaternion to multiply this quaternion by.
|
||
|
|
* @return the new quaternion.
|
||
|
|
*/
|
||
|
|
public Quaternion mult(float scalar) {
|
||
|
|
return new Quaternion(scalar * x, scalar * y, scalar * z, scalar * w);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>mult</code> multiplies this quaternion by a parameter scalar. The
|
||
|
|
* result is stored locally.
|
||
|
|
*
|
||
|
|
* @param scalar
|
||
|
|
* the quaternion to multiply this quaternion by.
|
||
|
|
* @return this.
|
||
|
|
*/
|
||
|
|
public Quaternion multLocal(float scalar) {
|
||
|
|
w *= scalar;
|
||
|
|
x *= scalar;
|
||
|
|
y *= scalar;
|
||
|
|
z *= scalar;
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>dot</code> calculates and returns the dot product of this
|
||
|
|
* quaternion with that of the parameter quaternion.
|
||
|
|
*
|
||
|
|
* @param q
|
||
|
|
* the quaternion to calculate the dot product of.
|
||
|
|
* @return the dot product of this and the parameter quaternion.
|
||
|
|
*/
|
||
|
|
public float dot(Quaternion q) {
|
||
|
|
return w * q.w + x * q.x + y * q.y + z * q.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <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 float norm() {
|
||
|
|
return w * w + x * x + y * y + z * z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>normalize</code> normalizes the current <code>Quaternion</code>
|
||
|
|
*/
|
||
|
|
public void normalize() {
|
||
|
|
float n = FastMath.invSqrt(norm());
|
||
|
|
x *= n;
|
||
|
|
y *= n;
|
||
|
|
z *= n;
|
||
|
|
w *= n;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>inverse</code> returns the inverse of this quaternion as a new
|
||
|
|
* quaternion. If this quaternion does not have an inverse (if its normal is
|
||
|
|
* 0 or less), then null is returned.
|
||
|
|
*
|
||
|
|
* @return the inverse of this quaternion or null if the inverse does not
|
||
|
|
* exist.
|
||
|
|
*/
|
||
|
|
public Quaternion inverse() {
|
||
|
|
float norm = norm();
|
||
|
|
if (norm > 0.0) {
|
||
|
|
float invNorm = 1.0f / norm;
|
||
|
|
return new Quaternion(-x * invNorm, -y * invNorm, -z * invNorm, w
|
||
|
|
* invNorm);
|
||
|
|
}
|
||
|
|
// return an invalid result to flag the error
|
||
|
|
return null;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>inverse</code> calculates the inverse of this quaternion and
|
||
|
|
* returns this quaternion after it is calculated. If this quaternion does
|
||
|
|
* not have an inverse (if it's norma is 0 or less), nothing happens
|
||
|
|
*
|
||
|
|
* @return the inverse of this quaternion
|
||
|
|
*/
|
||
|
|
public Quaternion inverseLocal() {
|
||
|
|
float norm = norm();
|
||
|
|
if (norm > 0.0) {
|
||
|
|
float invNorm = 1.0f / norm;
|
||
|
|
x *= -invNorm;
|
||
|
|
y *= -invNorm;
|
||
|
|
z *= -invNorm;
|
||
|
|
w *= invNorm;
|
||
|
|
}
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>negate</code> inverts the values of the quaternion.
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
public void negate() {
|
||
|
|
x *= -1;
|
||
|
|
y *= -1;
|
||
|
|
z *= -1;
|
||
|
|
w *= -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <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 Quaternion)) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (this == o) {
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
Quaternion comp = (Quaternion) o;
|
||
|
|
if (Float.compare(x, comp.x) != 0)
|
||
|
|
return false;
|
||
|
|
if (Float.compare(y, comp.y) != 0)
|
||
|
|
return false;
|
||
|
|
if (Float.compare(z, comp.z) != 0)
|
||
|
|
return false;
|
||
|
|
return Float.compare(w, comp.w) == 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
*
|
||
|
|
* <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 Quaternion.
|
||
|
|
* @see java.lang.Object#hashCode()
|
||
|
|
*/
|
||
|
|
@Override
|
||
|
|
public int hashCode() {
|
||
|
|
int hash = 37;
|
||
|
|
hash = 37 * hash + Float.floatToIntBits(x);
|
||
|
|
hash = 37 * hash + Float.floatToIntBits(y);
|
||
|
|
hash = 37 * hash + Float.floatToIntBits(z);
|
||
|
|
hash = 37 * hash + Float.floatToIntBits(w);
|
||
|
|
return hash;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>readExternal</code> builds a quaternion from an
|
||
|
|
* <code>ObjectInput</code> object. <br>
|
||
|
|
* NOTE: Used with serialization. Not to be called manually.
|
||
|
|
*
|
||
|
|
* @param in
|
||
|
|
* the ObjectInput value to read from.
|
||
|
|
* @throws IOException
|
||
|
|
* if the ObjectInput value has problems reading a float.
|
||
|
|
* @see java.io.Externalizable
|
||
|
|
*/
|
||
|
|
public void readExternal(ObjectInput in) throws IOException {
|
||
|
|
x = in.readFloat();
|
||
|
|
y = in.readFloat();
|
||
|
|
z = in.readFloat();
|
||
|
|
w = in.readFloat();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>writeExternal</code> writes this quaternion out to a
|
||
|
|
* <code>ObjectOutput</code> object. NOTE: Used with serialization. Not to
|
||
|
|
* be called manually.
|
||
|
|
*
|
||
|
|
* @param out
|
||
|
|
* the object to write to.
|
||
|
|
* @throws IOException
|
||
|
|
* if writing to the ObjectOutput fails.
|
||
|
|
* @see java.io.Externalizable
|
||
|
|
*/
|
||
|
|
public void writeExternal(ObjectOutput out) throws IOException {
|
||
|
|
out.writeFloat(x);
|
||
|
|
out.writeFloat(y);
|
||
|
|
out.writeFloat(z);
|
||
|
|
out.writeFloat(w);
|
||
|
|
}
|
||
|
|
|
||
|
|
private static final Vector3f tmpYaxis = new Vector3f();
|
||
|
|
private static final Vector3f tmpZaxis = new Vector3f();
|
||
|
|
private static final Vector3f tmpXaxis = new Vector3f();
|
||
|
|
|
||
|
|
/**
|
||
|
|
* <code>lookAt</code> is a convienence method for auto-setting the
|
||
|
|
* quaternion based on a direction and an up vector. It computes the
|
||
|
|
* rotation to transform the z-axis to point into 'direction' and the y-axis
|
||
|
|
* to 'up'.
|
||
|
|
*
|
||
|
|
* @param direction
|
||
|
|
* where to look at in terms of local coordinates
|
||
|
|
* @param up
|
||
|
|
* a vector indicating the local up direction. (typically {0, 1,
|
||
|
|
* 0} in jME.)
|
||
|
|
*/
|
||
|
|
public void lookAt(Vector3f direction, Vector3f up) {
|
||
|
|
tmpZaxis.set(direction).normalizeLocal();
|
||
|
|
tmpXaxis.set(up).crossLocal(direction).normalizeLocal();
|
||
|
|
tmpYaxis.set(direction).crossLocal(tmpXaxis).normalizeLocal();
|
||
|
|
fromAxes(tmpXaxis, tmpYaxis, tmpZaxis);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @return A new quaternion that describes a rotation that would point you
|
||
|
|
* in the exact opposite direction of this Quaternion.
|
||
|
|
*/
|
||
|
|
public Quaternion opposite() {
|
||
|
|
return opposite(null);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @param store
|
||
|
|
* A Quaternion to store our result in. If null, a new one is
|
||
|
|
* created.
|
||
|
|
* @return The store quaternion (or a new Quaterion, if store is null) that
|
||
|
|
* describes a rotation that would point you in the exact opposite
|
||
|
|
* direction of this Quaternion.
|
||
|
|
*/
|
||
|
|
public Quaternion opposite(Quaternion store) {
|
||
|
|
if (store == null)
|
||
|
|
store = new Quaternion();
|
||
|
|
|
||
|
|
Vector3f axis = new Vector3f();
|
||
|
|
float angle = toAngleAxis(axis);
|
||
|
|
|
||
|
|
store.fromAngleAxis(FastMath.PI + angle, axis);
|
||
|
|
return store;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @return This Quaternion, altered to describe a rotation that would point
|
||
|
|
* you in the exact opposite direction of where it is pointing
|
||
|
|
* currently.
|
||
|
|
*/
|
||
|
|
public Quaternion oppositeLocal() {
|
||
|
|
return opposite(this);
|
||
|
|
}
|
||
|
|
|
||
|
|
@Override
|
||
|
|
public Quaternion clone() {
|
||
|
|
try {
|
||
|
|
return (Quaternion) super.clone();
|
||
|
|
} catch (CloneNotSupportedException e) {
|
||
|
|
Logger.error( e);
|
||
|
|
throw new AssertionError(); // can not happen
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
public float getX() {
|
||
|
|
return x;
|
||
|
|
}
|
||
|
|
|
||
|
|
public void setX(float x) {
|
||
|
|
this.x = x;
|
||
|
|
}
|
||
|
|
|
||
|
|
public float getY() {
|
||
|
|
return y;
|
||
|
|
}
|
||
|
|
|
||
|
|
public void setY(float y) {
|
||
|
|
this.y = y;
|
||
|
|
}
|
||
|
|
|
||
|
|
public float getZ() {
|
||
|
|
return z;
|
||
|
|
}
|
||
|
|
|
||
|
|
public void setZ(float z) {
|
||
|
|
this.z = z;
|
||
|
|
}
|
||
|
|
|
||
|
|
public float getW() {
|
||
|
|
return w;
|
||
|
|
}
|
||
|
|
|
||
|
|
public void setW(float w) {
|
||
|
|
this.w = w;
|
||
|
|
}
|
||
|
|
}
|