diff options
Diffstat (limited to 'turtle2d/src/com/jogamp/graph/math/Quaternion.java')
| -rwxr-xr-x | turtle2d/src/com/jogamp/graph/math/Quaternion.java | 382 |
1 files changed, 382 insertions, 0 deletions
diff --git a/turtle2d/src/com/jogamp/graph/math/Quaternion.java b/turtle2d/src/com/jogamp/graph/math/Quaternion.java new file mode 100755 index 000000000..b77a5fa08 --- /dev/null +++ b/turtle2d/src/com/jogamp/graph/math/Quaternion.java @@ -0,0 +1,382 @@ +/**
+ * Copyright 2010 JogAmp Community. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification, are
+ * permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this list of
+ * conditions and the following disclaimer.
+ *
+ * 2. 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.
+ *
+ * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * The views and conclusions contained in the software and documentation are those of the
+ * authors and should not be interpreted as representing official policies, either expressed
+ * or implied, of JogAmp Community.
+ */
+package com.jogamp.graph.math;
+
+import jogamp.graph.math.MathFloat;
+
+public class Quaternion {
+ protected float x,y,z,w;
+
+ public Quaternion(){
+
+ }
+
+ public Quaternion(float x, float y, float z, float w) {
+ this.x = x;
+ this.y = y;
+ this.z = z;
+ this.w = w;
+ }
+
+ /** Constructor to create a rotation based quaternion from two vectors
+ * @param vector1
+ * @param vector2
+ */
+ public Quaternion(float[] vector1, float[] vector2)
+ {
+ float theta = (float)MathFloat.acos(dot(vector1, vector2));
+ float[] cross = cross(vector1,vector2);
+ cross = normalizeVec(cross);
+
+ this.x = (float)MathFloat.sin(theta/2)*cross[0];
+ this.y = (float)MathFloat.sin(theta/2)*cross[1];
+ this.z = (float)MathFloat.sin(theta/2)*cross[2];
+ this.w = (float)MathFloat.cos(theta/2);
+ this.normalize();
+ }
+
+ /** Transform the rotational quaternion to axis based rotation angles
+ * @return new float[4] with ,theta,Rx,Ry,Rz
+ */
+ public float[] toAxis()
+ {
+ float[] vec = new float[4];
+ float scale = (float)MathFloat.sqrt(x * x + y * y + z * z);
+ vec[0] =(float) MathFloat.acos(w) * 2.0f;
+ vec[1] = x / scale;
+ vec[2] = y / scale;
+ vec[3] = z / scale;
+ return vec;
+ }
+
+ /** Normalize a vector
+ * @param vector input vector
+ * @return normalized vector
+ */
+ private float[] normalizeVec(float[] vector)
+ {
+ float[] newVector = new float[3];
+
+ float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]);
+ if(d> 0.0f)
+ {
+ newVector[0] = vector[0]/d;
+ newVector[1] = vector[1]/d;
+ newVector[2] = vector[2]/d;
+ }
+ return newVector;
+ }
+ /** compute the dot product of two points
+ * @param vec1 vector 1
+ * @param vec2 vector 2
+ * @return the dot product as float
+ */
+ private float dot(float[] vec1, float[] vec2)
+ {
+ return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]);
+ }
+ /** cross product vec1 x vec2
+ * @param vec1 vector 1
+ * @param vec2 vecttor 2
+ * @return the resulting vector
+ */
+ private float[] cross(float[] vec1, float[] vec2)
+ {
+ float[] out = new float[3];
+
+ out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2];
+ out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0];
+ out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1];
+
+ return out;
+ }
+ public float getW() {
+ return w;
+ }
+ public void setW(float w) {
+ this.w = w;
+ }
+ 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;
+ }
+
+ /** Add a quaternion
+ * @param q quaternion
+ */
+ public void add(Quaternion q)
+ {
+ x+=q.x;
+ y+=q.y;
+ z+=q.z;
+ }
+
+ /** Subtract a quaternion
+ * @param q quaternion
+ */
+ public void subtract(Quaternion q)
+ {
+ x-=q.x;
+ y-=q.y;
+ z-=q.z;
+ }
+
+ /** Divide a quaternion by a constant
+ * @param n a float to divide by
+ */
+ public void divide(float n)
+ {
+ x/=n;
+ y/=n;
+ z/=n;
+ }
+
+ /** Multiply this quaternion by
+ * the param quaternion
+ * @param q a quaternion to multiply with
+ */
+ public void mult(Quaternion q)
+ {
+ float w1 = w*q.w - (x*q.x + y*q.y + z*q.z);
+
+ float x1 = w*q.z + q.w*z + y*q.z - z*q.y;
+ float y1 = w*q.x + q.w*x + z*q.x - x*q.z;
+ float z1 = w*q.y + q.w*y + x*q.y - y*q.x;
+
+ w = w1;
+ x = x1;
+ y = y1;
+ z = z1;
+ }
+
+ /** Multiply a quaternion by a constant
+ * @param n a float constant
+ */
+ public void mult(float n)
+ {
+ x*=n;
+ y*=n;
+ z*=n;
+ }
+
+ /** Normalize a quaternion required if
+ * to be used as a rotational quaternion
+ */
+ public void normalize()
+ {
+ float norme = (float)MathFloat.sqrt(w*w + x*x + y*y + z*z);
+ if (norme == 0.0f)
+ {
+ w = 1.0f;
+ x = y = z = 0.0f;
+ }
+ else
+ {
+ float recip = 1.0f/norme;
+
+ w *= recip;
+ x *= recip;
+ y *= recip;
+ z *= recip;
+ }
+ }
+
+ /** Invert the quaternion If rotational,
+ * will produce a the inverse rotation
+ */
+ public void inverse()
+ {
+ float norm = w*w + x*x + y*y + z*z;
+
+ float recip = 1.0f/norm;
+
+ w *= recip;
+ x = -1*x*recip;
+ y = -1*y*recip;
+ z = -1*z*recip;
+ }
+
+ /** Transform this quaternion to a
+ * 4x4 column matrix representing the rotation
+ * @return new float[16] column matrix 4x4
+ */
+ public float[] toMatrix()
+ {
+ float[] matrix = new float[16];
+ matrix[0] = 1.0f - 2*y*y - 2*z*z;
+ matrix[1] = 2*x*y + 2*w*z;
+ matrix[2] = 2*x*z - 2*w*y;
+ matrix[3] = 0;
+
+ matrix[4] = 2*x*y - 2*w*z;
+ matrix[5] = 1.0f - 2*x*x - 2*z*z;
+ matrix[6] = 2*y*z + 2*w*x;
+ matrix[7] = 0;
+
+ matrix[8] = 2*x*z + 2*w*y;
+ matrix[9] = 2*y*z - 2*w*x;
+ matrix[10] = 1.0f - 2*x*x - 2*y*y;
+ matrix[11] = 0;
+
+ matrix[12] = 0;
+ matrix[13] = 0;
+ matrix[14] = 0;
+ matrix[15] = 1;
+ return matrix;
+ }
+
+ /** Set this quaternion from a Sphereical interpolation
+ * of two param quaternion, used mostly for rotational animation
+ * @param a initial quaternion
+ * @param b target quaternion
+ * @param t float between 0 and 1 representing interp.
+ */
+ public void slerp(Quaternion a,Quaternion b, float t)
+ {
+ float omega, cosom, sinom, sclp, sclq;
+ cosom = a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
+ if ((1.0f+cosom) > MathFloat.E) {
+ if ((1.0f-cosom) > MathFloat.E) {
+ omega = (float)MathFloat.acos(cosom);
+ sinom = (float)MathFloat.sin(omega);
+ sclp = (float)MathFloat.sin((1.0f-t)*omega) / sinom;
+ sclq = (float)MathFloat.sin(t*omega) / sinom;
+ }
+ else {
+ sclp = 1.0f - t;
+ sclq = t;
+ }
+ x = sclp*a.x + sclq*b.x;
+ y = sclp*a.y + sclq*b.y;
+ z = sclp*a.z + sclq*b.z;
+ w = sclp*a.w + sclq*b.w;
+ }
+ else {
+ x =-a.y;
+ y = a.x;
+ z =-a.w;
+ w = a.z;
+ sclp = MathFloat.sin((1.0f-t) * MathFloat.PI * 0.5f);
+ sclq = MathFloat.sin(t * MathFloat.PI * 0.5f);
+ x = sclp*a.x + sclq*b.x;
+ y = sclp*a.y + sclq*b.y;
+ z = sclp*a.z + sclq*b.z;
+ }
+ }
+
+ /** Check if this quaternion is empty, ie (0,0,0,1)
+ * @return true if empty, false otherwise
+ */
+ public boolean isEmpty()
+ {
+ if (w==1 && x==0 && y==0 && z==0)
+ return true;
+ return false;
+ }
+
+ /** Check if this quaternion represents an identity
+ * matrix, for rotation.
+ * @return true if it is an identity rep., false otherwise
+ */
+ public boolean isIdentity()
+ {
+ if (w==0 && x==0 && y==0 && z==0)
+ return true;
+ return false;
+ }
+
+ /** compute the quaternion from a 3x3 column matrix
+ * @param m 3x3 column matrix
+ */
+ public void setFromMatrix(float[] m) {
+ float T= m[0] + m[4] + m[8] + 1;
+ if (T>0){
+ float S = 0.5f / (float)MathFloat.sqrt(T);
+ w = 0.25f / S;
+ x = ( m[5] - m[7]) * S;
+ y = ( m[6] - m[2]) * S;
+ z = ( m[1] - m[3] ) * S;
+ }
+ else{
+ if ((m[0] > m[4])&(m[0] > m[8])) {
+ float S = MathFloat.sqrt( 1.0f + m[0] - m[4] - m[8] ) * 2f; // S=4*qx
+ w = (m[7] - m[5]) / S;
+ x = 0.25f * S;
+ y = (m[3] + m[1]) / S;
+ z = (m[6] + m[2]) / S;
+ }
+ else if (m[4] > m[8]) {
+ float S = MathFloat.sqrt( 1.0f + m[4] - m[0] - m[8] ) * 2f; // S=4*qy
+ w = (m[6] - m[2]) / S;
+ x = (m[3] + m[1]) / S;
+ y = 0.25f * S;
+ z = (m[7] + m[5]) / S;
+ }
+ else {
+ float S = MathFloat.sqrt( 1.0f + m[8] - m[0] - m[4] ) * 2f; // S=4*qz
+ w = (m[3] - m[1]) / S;
+ x = (m[6] + m[2]) / S;
+ y = (m[7] + m[5]) / S;
+ z = 0.25f * S;
+ }
+ }
+ }
+
+ /** Check if the the 3x3 matrix (param) is in fact
+ * an affine rotational matrix
+ * @param m 3x3 column matrix
+ * @return true if representing a rotational matrix, false otherwise
+ */
+ public boolean isRotationMatrix(float[] m) {
+ double epsilon = 0.01; // margin to allow for rounding errors
+ if (MathFloat.abs(m[0]*m[3] + m[3]*m[4] + m[6]*m[7]) > epsilon) return false;
+ if (MathFloat.abs(m[0]*m[2] + m[3]*m[5] + m[6]*m[8]) > epsilon) return false;
+ if (MathFloat.abs(m[1]*m[2] + m[4]*m[5] + m[7]*m[8]) > epsilon) return false;
+ if (MathFloat.abs(m[0]*m[0] + m[3]*m[3] + m[6]*m[6] - 1) > epsilon) return false;
+ if (MathFloat.abs(m[1]*m[1] + m[4]*m[4] + m[7]*m[7] - 1) > epsilon) return false;
+ if (MathFloat.abs(m[2]*m[2] + m[5]*m[5] + m[8]*m[8] - 1) > epsilon) return false;
+ return (MathFloat.abs(determinant(m)-1) < epsilon);
+ }
+ private float determinant(float[] m) {
+ return m[0]*m[4]*m[8] + m[3]*m[7]*m[2] + m[6]*m[1]*m[5] - m[0]*m[7]*m[5] - m[3]*m[1]*m[8] - m[6]*m[4]*m[2];
+ }
+}
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