X-Git-Url: http://source.jalview.org/gitweb/?p=jalviewjs.git;a=blobdiff_plain;f=src%2Fjavajs%2Futil%2FQuat.java;fp=src%2Fjavajs%2Futil%2FQuat.java;h=6b93578eadb9e0596b8ca166aec5b4ddfa62c9a1;hp=56a7d1f0a4abfc4a2cf58880df13c38c81f1fd09;hb=b9b7a352eee79b7764c3b09c9d19663075061d8c;hpb=7301a2415adab88038b291fc54caeeb3a5a47a44
diff --git a/src/javajs/util/Quat.java b/src/javajs/util/Quat.java
index 56a7d1f..6b93578 100644
--- a/src/javajs/util/Quat.java
+++ b/src/javajs/util/Quat.java
@@ -1,815 +1,815 @@
-/* $RCSfile$
- * $Author: hansonr $
- * $Date: 2007-04-05 09:07:28 -0500 (Thu, 05 Apr 2007) $
- * $Revision: 7326 $
- *
- * Copyright (C) 2003-2005 The Jmol Development Team
- *
- * Contact: jmol-developers@lists.sf.net
- *
- * This library is free software; you can redistribute it and/or
- * modify it under the terms of the GNU Lesser General Public
- * License as published by the Free Software Foundation; either
- * version 2.1 of the License, or (at your option) any later version.
- *
- * This library is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public
- * License along with this library; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
- */
-package javajs.util;
-
-/*
- * Standard UNIT quaternion math -- for rotation.
- *
- * All rotations can be represented as two identical quaternions.
- * This is because any rotation can be considered from either end of the
- * rotational axis -- either as a + rotation or a - rotation. This code
- * is designed to always maintain the quaternion with a rotation in the
- * [0, PI) range.
- *
- * This ensures that the reported theta is always positive, and the normal
- * reported is always associated with a positive theta.
- *
- * @author Bob Hanson, hansonr@stolaf.edu 6/2008
- *
- */
-
-public class Quat {
- public float q0, q1, q2, q3;
- private M3 mat;
-
- private final static P4 qZero = new P4();
- private static final double RAD_PER_DEG = Math.PI / 180;
-
- public Quat() {
- q0 = 1;
- }
-
- public static Quat newQ(Quat q) {
- Quat q1 = new Quat();
- q1.set(q);
- return q1;
- }
-
- public static Quat newVA(T3 v, float theta) {
- Quat q = new Quat();
- q.setTA(v, theta);
- return q;
- }
-
- public static Quat newM(M3 mat) {
- Quat q = new Quat();
- q.setM(M3.newM3(mat));
- return q;
- }
-
- public static Quat newAA(A4 a) {
- Quat q = new Quat();
- q.setAA(a);
- return q;
- }
-
- public static Quat newP4(P4 pt) {
- Quat q = new Quat();
- q.setP4(pt);
- return q;
- }
-
- /**
- * Note that q0 is the last parameter here
- *
- * @param q1
- * @param q2
- * @param q3
- * @param q0
- * @return {q1 q2 q3 q0}
- */
- public static Quat new4(float q1, float q2, float q3, float q0) {
- Quat q = new Quat();
- if (q0 < -1) {
- q.q0 = -1;
- return q;
- }
- if (q0 > 1) {
- q.q0 = 1;
- return q;
- }
- q.q0 = q0;
- q.q1 = q1;
- q.q2 = q2;
- q.q3 = q3;
- return q;
- }
-
- public void set(Quat q) {
- q0 = q.q0;
- q1 = q.q1;
- q2 = q.q2;
- q3 = q.q3;
- }
-
- /**
- * {x y z w} --> {q1 q2 q3 q0} and factored
- *
- * @param pt
- */
- private void setP4(P4 pt) {
- float factor = (pt == null ? 0 : pt.distance4(qZero));
- if (factor == 0) {
- q0 = 1;
- return;
- }
- q0 = pt.w / factor;
- q1 = pt.x / factor;
- q2 = pt.y / factor;
- q3 = pt.z / factor;
- }
-
- /**
- * q = (cos(theta/2), sin(theta/2) * n)
- *
- * @param pt
- * @param theta
- */
- public void setTA(T3 pt, float theta) {
- if (pt.x == 0 && pt.y == 0 && pt.z == 0) {
- q0 = 1;
- return;
- }
- double fact = (Math.sin(theta / 2 * RAD_PER_DEG) / Math.sqrt(pt.x
- * pt.x + pt.y * pt.y + pt.z * pt.z));
- q0 = (float) (Math.cos(theta / 2 * RAD_PER_DEG));
- q1 = (float) (pt.x * fact);
- q2 = (float) (pt.y * fact);
- q3 = (float) (pt.z * fact);
- }
-
- public void setAA(A4 a) {
- A4 aa = A4.newAA(a);
- if (aa.angle == 0)
- aa.y = 1;
- setM(new M3().setAA(aa));
- }
-
- private void setM(M3 mat) {
-
- /*
- * Changed 7/16/2008 to double precision for 11.5.48.
- *
- *
- *
- * RayTrace Software Package, release 3.0. May 3, 2006.
- *
- * Mathematics Subpackage (VrMath)
- *
- * Author: Samuel R. Buss
- *
- * Software is "as-is" and carries no warranty. It may be used without
- * restriction, but if you modify it, please change the filenames to
- * prevent confusion between different versions. Please acknowledge
- * all use of the software in any publications or products based on it.
- *
- * Bug reports: Sam Buss, sbuss@ucsd.edu.
- * Web page: http://math.ucsd.edu/~sbuss/MathCG
-
- // Use Shepperd's algorithm, which is stable, does not lose
- // significant precision and uses only one sqrt.
- // J. Guidance and Control, 1 (1978) 223-224.
-
- *
- *
- * Except, that code has errors.
- *
- * CORRECTIONS (as noted below) of Quaternion.cpp. I have reported the bug.
- *
- * -- Bob Hanson
- *
- * theory:
- * cos(theta/2)^2 = (cos(theta) + 1)/2
- * and
- * trace = (1-x^2)ct + (1-y^2)ct + (1-z^2)ct + 1 = 2cos(theta) + 1
- * or
- * cos(theta) = (trace - 1)/2
- *
- * so in general,
- *
- * w = cos(theta/2)
- * = sqrt((cos(theta)+1)/2)
- * = sqrt((trace-1)/4+1/2)
- * = sqrt((trace+1)/4)
- * = sqrt(trace+1)/2
- *
- * but there are precision issues, so we allow for other situations.
- * note -- trace >= 0.5 when cos(theta) >= -0.25 (-104.48 <= theta <= 104.48).
- * this code cleverly matches the precision in all four options.
- *
- */
-
- this.mat = mat;
-
- double trace = mat.m00 + mat.m11 + mat.m22;
- double temp;
- double w, x, y, z;
- if (trace >= 0.5) {
- w = Math.sqrt(1.0 + trace);
- x = (mat.m21 - mat.m12) / w;
- y = (mat.m02 - mat.m20) / w;
- z = (mat.m10 - mat.m01) / w;
- } else if ((temp = mat.m00 + mat.m00 - trace) >= 0.5) {
- x = Math.sqrt(1.0 + temp);
- w = (mat.m21 - mat.m12) / x;
- y = (mat.m10 + mat.m01) / x;
- z = (mat.m20 + mat.m02) / x;
- } else if ((temp = mat.m11 + mat.m11 - trace) >= 0.5
- || mat.m11 > mat.m22) {
- y = Math.sqrt(1.0 + temp);
- w = (mat.m02 - mat.m20) / y;
- x = (mat.m10 + mat.m01) / y;
- z = (mat.m21 + mat.m12) / y;
- } else {
- z = Math.sqrt(1.0 + mat.m22 + mat.m22 - trace);
- w = (mat.m10 - mat.m01) / z;
- x = (mat.m20 + mat.m02) / z; // was -
- y = (mat.m21 + mat.m12) / z; // was -
- }
-
- q0 = (float) (w * 0.5);
- q1 = (float) (x * 0.5);
- q2 = (float) (y * 0.5);
- q3 = (float) (z * 0.5);
-
- /*
- * Originally from http://www.gamedev.net/community/forums/topic.asp?topic_id=448380
- * later algorithm was adapted from Visualizing Quaternions, by Andrew J. Hanson
- * (Morgan Kaufmann, 2006), page 446
- *
- * HOWEVER, checking with AxisAngle4f and Quat4f equivalents, it was found that
- * BOTH of these sources produce inverted quaternions. So here we do an inversion.
- *
- * This correction was made in 11.5.42 6/19/2008 -- Bob Hanson
- *
- * former algorithm used:
- * /
-
- double tr = mat.m00 + mat.m11 + mat.m22; //Matrix trace
- double s;
- double[] q = new double[4];
- if (tr > 0) {
- s = Math.sqrt(tr + 1);
- q0 = (float) (0.5 * s);
- s = 0.5 / s; // = 1/q0
- q1 = (float) ((mat.m21 - mat.m12) * s);
- q2 = (float) ((mat.m02 - mat.m20) * s);
- q3 = (float) ((mat.m10 - mat.m01) * s);
- } else {
- float[][] m = new float[][] { new float[3], new float[3], new float[3] };
- mat.getRow(0, m[0]);
- mat.getRow(1, m[1]);
- mat.getRow(2, m[2]);
-
- //Find out the biggest element along the diagonal
- float max = Math.max(mat.m11, mat.m00);
- int i = (mat.m22 > max ? 2 : max == mat.m11 ? 1 : 0);
- int j = (i + 1) % 3;
- int k = (j + 1) % 3;
- s = -Math.sqrt(1 + m[i][i] - m[j][j] - m[k][k]);
- // 0 = 1 + (1-x^2)ct + x^2 -(1-y^2)ct - y^2 - (1-z^2)ct - z^2
- // 0 = 1 - ct + (x^2 - y^2 - z^2) - (x^2 - y^2 - z^2)ct
- // 0 = 1 - ct + 2x^2 - 1 - (2x^2)ct + ct
- // 0 = 2x^2(1 - ct)
- // theta = 0 (but then trace = 1 + 1 + 1 = 3)
- // or x = 0.
- q[i] = s * 0.5;
- if (s != 0)
- s = 0.5 / s; // = 1/q[i]
- q[j] = (m[i][j] + m[j][i]) * s;
- q[k] = (m[i][k] + m[k][i]) * s;
- q0 = (float) ((m[k][j] - m[j][k]) * s);
- q1 = (float) q[0]; // x
- q2 = (float) q[1]; // y
- q3 = (float) q[2]; // z
- }
-
- */
- }
-
- /*
- * if qref is null, "fix" this quaternion
- * otherwise, return a quaternion that is CLOSEST to the given quaternion
- * that is, one that gives a positive dot product
- *
- */
- public void setRef(Quat qref) {
- if (qref == null) {
- mul(getFixFactor());
- return;
- }
- if (dot(qref) >= 0)
- return;
- q0 *= -1;
- q1 *= -1;
- q2 *= -1;
- q3 *= -1;
- }
-
- /**
- * returns a quaternion frame based on three points (center, x, and any point in xy plane)
- * or two vectors (vA, vB).
- *
- * @param center (null for vA/vB option)
- * @param x
- * @param xy
- * @return quaternion for frame
- */
- public static final Quat getQuaternionFrame(P3 center, T3 x,
- T3 xy) {
- V3 vA = V3.newV(x);
- V3 vB = V3.newV(xy);
- if (center != null) {
- vA.sub(center);
- vB.sub(center);
- }
- return getQuaternionFrameV(vA, vB, null, false);
- }
-
- /**
- * Create a quaternion based on a frame
- * @param vA
- * @param vB
- * @param vC
- * @param yBased
- * @return quaternion
- */
- public static final Quat getQuaternionFrameV(V3 vA, V3 vB,
- V3 vC, boolean yBased) {
- if (vC == null) {
- vC = new V3();
- vC.cross(vA, vB);
- if (yBased)
- vA.cross(vB, vC);
- }
- V3 vBprime = new V3();
- vBprime.cross(vC, vA);
- vA.normalize();
- vBprime.normalize();
- vC.normalize();
- M3 mat = new M3();
- mat.setColumnV(0, vA);
- mat.setColumnV(1, vBprime);
- mat.setColumnV(2, vC);
-
- /*
- *
- * Verification tests using Quat4f and AngleAxis4f:
- *
- System.out.println("quaternion frame matrix: " + mat);
-
- Point3f pt2 = new Point3f();
- mat.transform(Point3f.new3(1, 0, 0), pt2);
- System.out.println("vA=" + vA + " M(100)=" + pt2);
- mat.transform(Point3f.new3(0, 1, 0), pt2);
- System.out.println("vB'=" + vBprime + " M(010)=" + pt2);
- mat.transform(Point3f.new3(0, 0, 1), pt2);
- System.out.println("vC=" + vC + " M(001)=" + pt2);
- Quat4f q4 = new Quat4f();
- q4.set(mat);
- System.out.println("----");
- System.out.println("Quat4f: {" + q4.w + " " + q4.x + " " + q4.y + " " + q4.z + "}");
- System.out.println("Quat4f: 2xy + 2wz = m10: " + (2 * q4.x * q4.y + 2 * q4.w * q4.z) + " = " + mat.m10);
-
- */
-
- Quat q = newM(mat);
-
- /*
- System.out.println("Quaternion mat from q \n" + q.getMatrix());
- System.out.println("Quaternion: " + q.getNormal() + " " + q.getTheta());
- AxisAngle4f a = new AxisAngle4f();
- a.set(mat);
- Vector3f v = Vector3f.new3(a.x, a.y, a.z);
- v.normalize();
- System.out.println("angleAxis: " + v + " "+(a.angle/Math.PI * 180));
- */
-
- return q;
- }
-
- public M3 getMatrix() {
- if (mat == null)
- setMatrix();
- return mat;
- }
-
- private void setMatrix() {
- mat = new M3();
- // q0 = w, q1 = x, q2 = y, q3 = z
- mat.m00 = q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3;
- mat.m01 = 2 * q1 * q2 - 2 * q0 * q3;
- mat.m02 = 2 * q1 * q3 + 2 * q0 * q2;
- mat.m10 = 2 * q1 * q2 + 2 * q0 * q3;
- mat.m11 = q0 * q0 - q1 * q1 + q2 * q2 - q3 * q3;
- mat.m12 = 2 * q2 * q3 - 2 * q0 * q1;
- mat.m20 = 2 * q1 * q3 - 2 * q0 * q2;
- mat.m21 = 2 * q2 * q3 + 2 * q0 * q1;
- mat.m22 = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3;
- }
-
- public Quat add(float x) {
- // scalar theta addition (degrees)
- return newVA(getNormal(), getTheta() + x);
- }
-
- public Quat mul(float x) {
- // scalar theta multiplication
- return (x == 1 ? new4(q1, q2, q3, q0) :
- newVA(getNormal(), getTheta() * x));
- }
-
- public Quat mulQ(Quat p) {
- return new4(
- q0 * p.q1 + q1 * p.q0 + q2 * p.q3 - q3 * p.q2,
- q0 * p.q2 + q2 * p.q0 + q3 * p.q1 - q1 * p.q3,
- q0 * p.q3 + q3 * p.q0 + q1 * p.q2 - q2 * p.q1,
- q0 * p.q0 - q1 * p.q1 - q2 * p.q2 - q3 * p.q3);
- }
-
- public Quat div(Quat p) {
- // unit quaternions assumed -- otherwise would scale by 1/p.dot(p)
- return mulQ(p.inv());
- }
-
- public Quat divLeft(Quat p) {
- // unit quaternions assumed -- otherwise would scale by 1/p.dot(p)
- return this.inv().mulQ(p);
- }
-
- public float dot(Quat q) {
- return this.q0 * q.q0 + this.q1 * q.q1 + this.q2 * q.q2 + this.q3 * q.q3;
- }
-
- public Quat inv() {
- return new4(-q1, -q2, -q3, q0);
- }
-
- public Quat negate() {
- return new4(-q1, -q2, -q3, -q0);
- }
-
- /**
- * ensures
- *
- * 1) q0 > 0
- * or
- * 2) q0 = 0 and q1 > 0
- * or
- * 3) q0 = 0 and q1 = 0 and q2 > 0
- * or
- * 4) q0 = 0 and q1 = 0 and q2 = 0 and q3 > 0
- *
- * @return 1 or -1
- *
- */
-
- private float getFixFactor() {
- return (q0 < 0 ||
- q0 == 0 && (q1 < 0 || q1 == 0 && (q2 < 0 || q2 == 0 && q3 < 0)) ? -1 : 1);
- }
-
- public V3 getVector(int i) {
- return getVectorScaled(i, 1f);
- }
-
- public V3 getVectorScaled(int i, float scale) {
- if (i == -1) {
- scale *= getFixFactor();
- return V3.new3(q1 * scale, q2 * scale, q3 * scale);
- }
- if (mat == null)
- setMatrix();
- V3 v = new V3();
- mat.getColumnV(i, v);
- if (scale != 1f)
- v.scale(scale);
- return v;
- }
-
- /**
- *
- * @return vector such that 0 <= angle <= 180
- */
- public V3 getNormal() {
- V3 v = getRawNormal(this);
- v.scale(getFixFactor());
- return v;
- }
-
- private static V3 getRawNormal(Quat q) {
- V3 v = V3.new3(q.q1, q.q2, q.q3);
- if (v.length() == 0)
- return V3.new3(0, 0, 1);
- v.normalize();
- return v;
- }
-
- /**
- *
- * @return 0 <= angle <= 180 in degrees
- */
- public float getTheta() {
- return (float) (Math.acos(Math.abs(q0)) * 2 * 180 / Math.PI);
- }
-
- public float getThetaRadians() {
- return (float) (Math.acos(Math.abs(q0)) * 2);
- }
-
- /**
- *
- * @param v0
- * @return vector option closest to v0
- *
- */
- public V3 getNormalDirected(V3 v0) {
- V3 v = getNormal();
- if (v.x * v0.x + v.y * v0.y + v.z * v0.z < 0) {
- v.scale(-1);
- }
- return v;
- }
-
- public V3 get3dProjection(V3 v3d) {
- v3d.set(q1, q2, q3);
- return v3d;
- }
-
- /**
- *
- * @param axisAngle
- * @return fill in theta of axisAngle such that
- */
- public P4 getThetaDirected(P4 axisAngle) {
- //fills in .w;
- float theta = getTheta();
- V3 v = getNormal();
- if (axisAngle.x * q1 + axisAngle.y * q2 + axisAngle.z * q3 < 0) {
- v.scale(-1);
- theta = -theta;
- }
- axisAngle.set4(v.x, v.y, v.z, theta);
- return axisAngle;
- }
-
- /**
- *
- * @param vector a vector, same as for getNormalDirected
- * @return return theta
- */
- public float getThetaDirectedV(V3 vector) {
- //fills in .w;
- float theta = getTheta();
- V3 v = getNormal();
- if (vector.x * q1 + vector.y * q2 + vector.z * q3 < 0) {
- v.scale(-1);
- theta = -theta;
- }
- return theta;
- }
-
- /**
- * Quaternions are saved as {q1, q2, q3, q0}
- *
- * While this may seem odd, it is so that for any point4 --
- * planes, axisangles, and quaternions -- we can use the
- * first three coordinates to determine the relavent axis
- * the fourth then gives us offset to {0,0,0} (plane),
- * rotation angle (axisangle), and cos(theta/2) (quaternion).
- * @return {x y z w} (unnormalized)
- */
- public P4 toPoint4f() {
- return P4.new4(q1, q2, q3, q0); // x,y,z,w
- }
-
- public A4 toAxisAngle4f() {
- double theta = 2 * Math.acos(Math.abs(q0));
- double sinTheta2 = Math.sin(theta/2);
- V3 v = getNormal();
- if (sinTheta2 < 0) {
- v.scale(-1);
- theta = Math.PI - theta;
- }
- return A4.newVA(v, (float) theta);
- }
-
- public T3 transform2(T3 pt, T3 ptNew) {
- if (mat == null)
- setMatrix();
- mat.rotate2(pt, ptNew);
- return ptNew;
- }
-
- public Quat leftDifference(Quat q2) {
- //dq = q.leftDifference(qnext);//q.inv().mul(qnext);
- Quat q2adjusted = (this.dot(q2) < 0 ? q2.negate() : q2);
- return inv().mulQ(q2adjusted);
- }
-
- public Quat rightDifference(Quat q2) {
- //dq = qnext.rightDifference(q);//qnext.mul(q.inv());
- Quat q2adjusted = (this.dot(q2) < 0 ? q2.negate() : q2);
- return mulQ(q2adjusted.inv());
- }
-
- /**
- *
- * Java axisAngle / plane / Point4f format
- * all have the format {x y z w}
- * so we go with that here as well
- *
- * @return "{q1 q2 q3 q0}"
- */
- @Override
- public String toString() {
- return "{" + q1 + " " + q2 + " " + q3 + " " + q0 + "}";
- }
-
- /**
- *
- * @param data1
- * @param data2
- * @param nMax > 0 --> limit to this number
- * @param isRelative
- *
- * @return pairwise array of data1 / data2 or data1 \ data2
- */
- public static Quat[] div(Quat[] data1, Quat[] data2, int nMax, boolean isRelative) {
- int n;
- if (data1 == null || data2 == null || (n = Math.min(data1.length, data2.length)) == 0)
- return null;
- if (nMax > 0 && n > nMax)
- n = nMax;
- Quat[] dqs = new Quat[n];
- for (int i = 0; i < n; i++) {
- if (data1[i] == null || data2[i] == null)
- return null;
- dqs[i] = (isRelative ? data1[i].divLeft(data2[i]) : data1[i].div(data2[i]));
- }
- return dqs;
- }
-
- public static Quat sphereMean(Quat[] data, float[] retStddev, float criterion) {
- // Samuel R. Buss, Jay P. Fillmore:
- // Spherical averages and applications to spherical splines and interpolation.
- // ACM Trans. Graph. 20(2): 95-126 (2001)
- if (data == null || data.length == 0)
- return new Quat();
- if (retStddev == null)
- retStddev = new float[1];
- if (data.length == 1) {
- retStddev[0] = 0;
- return newQ(data[0]);
- }
- float diff = Float.MAX_VALUE;
- float lastStddev = Float.MAX_VALUE;
- Quat qMean = simpleAverage(data);
- int maxIter = 100; // typically goes about 5 iterations
- int iter = 0;
- while (diff > criterion && lastStddev != 0 && iter < maxIter) {
- qMean = newMean(data, qMean);
- retStddev[0] = stdDev(data, qMean);
- diff = Math.abs(retStddev[0] - lastStddev);
- lastStddev = retStddev[0];
- //Logger.info(++iter + " sphereMean " + qMean + " stddev=" + lastStddev + " diff=" + diff);
- }
- return qMean;
- }
-
- /**
- * Just a starting point.
- * get average normal vector
- * scale normal by average projection of vectors onto it
- * create quaternion from this 3D projection
- *
- * @param ndata
- * @return approximate average
- */
- private static Quat simpleAverage(Quat[] ndata) {
- V3 mean = V3.new3(0, 0, 1);
- // using the directed normal ensures that the mean is
- // continually added to and never subtracted from
- V3 v = ndata[0].getNormal();
- mean.add(v);
- for (int i = ndata.length; --i >= 0;)
- mean.add(ndata[i].getNormalDirected(mean));
- mean.sub(v);
- mean.normalize();
- float f = 0;
- // the 3D projection of the quaternion is [sin(theta/2)]*n
- // so dotted with the normalized mean gets us an approximate average for sin(theta/2)
- for (int i = ndata.length; --i >= 0;)
- f += Math.abs(ndata[i].get3dProjection(v).dot(mean));
- if (f != 0)
- mean.scale(f / ndata.length);
- // now convert f to the corresponding cosine instead of sine
- f = (float) Math.sqrt(1 - mean.lengthSquared());
- if (Float.isNaN(f))
- f = 0;
- return newP4(P4.new4(mean.x, mean.y, mean.z, f));
- }
-
- private static Quat newMean(Quat[] data, Quat mean) {
- /* quaternion derivatives nicely take care of producing the necessary
- * metric. Since dq gives us the normal with the smallest POSITIVE angle,
- * we just scale by that -- using degrees.
- * No special normalization is required.
- *
- * The key is that the mean has been set up already, and dq.getTheta()
- * will always return a value between 0 and 180. True, for groupings
- * where dq swings wildly -- 178, 182, 178, for example -- there will
- * be problems, but the presumption here is that there is a REASONABLE
- * set of data. Clearly there are spherical data sets that simply cannot
- * be assigned a mean. (For example, where the three projected points
- * are equally distant on the sphere. We just can't worry about those
- * cases here. Rather, if there is any significance to the data,
- * there will be clusters of projected points, and the analysis will
- * be meaningful.
- *
- * Note that the hemisphere problem drops out because dq.getNormal() and
- * dq.getTheta() will never return (n, 182 degrees) but will
- * instead return (-n, 2 degrees). That's just what we want in that case.
- *
- * Note that the projection in this case is to 3D -- a set of vectors
- * in space with lengths proportional to theta (not the sin(theta/2)
- * that is associated with a quaternion map).
- *
- * This is officially an "exponential" or "hyperbolic" projection.
- *
- */
- V3 sum = new V3();
- V3 v;
- Quat q, dq;
- //System.out.println("newMean mean " + mean);
- for (int i = data.length; --i >= 0;) {
- q = data[i];
- dq = q.div(mean);
- v = dq.getNormal();
- v.scale(dq.getTheta());
- sum.add(v);
- }
- sum.scale(1f/data.length);
- Quat dqMean = newVA(sum, sum.length());
- //System.out.println("newMean dqMean " + dqMean + " " + dqMean.getNormal() + " " + dqMean.getTheta());
- return dqMean.mulQ(mean);
- }
-
- /**
- * @param data
- * @param mean
- * @return standard deviation in units of degrees
- */
- private static float stdDev(Quat[] data, Quat mean) {
- // the quaternion dot product gives q0 for dq (i.e. q / mean)
- // that is, cos(theta/2) for theta between them
- double sum2 = 0;
- int n = data.length;
- for (int i = n; --i >= 0;) {
- float theta = data[i].div(mean).getTheta();
- sum2 += theta * theta;
- }
- return (float) Math.sqrt(sum2 / n);
- }
-
- public float[] getEulerZYZ() {
- // http://www.swarthmore.edu/NatSci/mzucker1/e27/diebel2006attitude.pdf
- double rA, rB, rG;
- if (q1 == 0 && q2 == 0) {
- float theta = getTheta();
- // pure Z rotation - ambiguous
- return new float[] { q3 < 0 ? -theta : theta , 0, 0 };
- }
- rA = Math.atan2(2 * (q2 * q3 + q0 * q1), 2 * (-q1 * q3 + q0 * q2 ));
- rB = Math.acos(q3 * q3 - q2 * q2 - q1 * q1 + q0 * q0);
- rG = Math.atan2( 2 * (q2 * q3 - q0 * q1), 2 * (q0 * q2 + q1 * q3));
- return new float[] {(float) (rA / RAD_PER_DEG), (float) (rB / RAD_PER_DEG), (float) (rG / RAD_PER_DEG)};
- }
-
- public float[] getEulerZXZ() {
- // NOT http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
- // http://www.swarthmore.edu/NatSci/mzucker1/e27/diebel2006attitude.pdf
- double rA, rB, rG;
- if (q1 == 0 && q2 == 0) {
- float theta = getTheta();
- // pure Z rotation - ambiguous
- return new float[] { q3 < 0 ? -theta : theta , 0, 0 };
- }
- rA = Math.atan2(2 * (q1 * q3 - q0 * q2), 2 * (q0 * q1 + q2 * q3 ));
- rB = Math.acos(q3 * q3 - q2 * q2 - q1 * q1 + q0 * q0);
- rG = Math.atan2( 2 * (q1 * q3 + q0 * q2), 2 * (-q2 * q3 + q0 * q1));
- return new float[] {(float) (rA / RAD_PER_DEG), (float) (rB / RAD_PER_DEG), (float) (rG / RAD_PER_DEG)};
- }
-
-}
+/* $RCSfile$
+ * $Author: hansonr $
+ * $Date: 2007-04-05 09:07:28 -0500 (Thu, 05 Apr 2007) $
+ * $Revision: 7326 $
+ *
+ * Copyright (C) 2003-2005 The Jmol Development Team
+ *
+ * Contact: jmol-developers@lists.sf.net
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+package javajs.util;
+
+/*
+ * Standard UNIT quaternion math -- for rotation.
+ *
+ * All rotations can be represented as two identical quaternions.
+ * This is because any rotation can be considered from either end of the
+ * rotational axis -- either as a + rotation or a - rotation. This code
+ * is designed to always maintain the quaternion with a rotation in the
+ * [0, PI) range.
+ *
+ * This ensures that the reported theta is always positive, and the normal
+ * reported is always associated with a positive theta.
+ *
+ * @author Bob Hanson, hansonr@stolaf.edu 6/2008
+ *
+ */
+
+public class Quat {
+ public float q0, q1, q2, q3;
+ private M3 mat;
+
+ private final static P4 qZero = new P4();
+ private static final double RAD_PER_DEG = Math.PI / 180;
+
+ public Quat() {
+ q0 = 1;
+ }
+
+ public static Quat newQ(Quat q) {
+ Quat q1 = new Quat();
+ q1.set(q);
+ return q1;
+ }
+
+ public static Quat newVA(T3 v, float theta) {
+ Quat q = new Quat();
+ q.setTA(v, theta);
+ return q;
+ }
+
+ public static Quat newM(M3 mat) {
+ Quat q = new Quat();
+ q.setM(M3.newM3(mat));
+ return q;
+ }
+
+ public static Quat newAA(A4 a) {
+ Quat q = new Quat();
+ q.setAA(a);
+ return q;
+ }
+
+ public static Quat newP4(P4 pt) {
+ Quat q = new Quat();
+ q.setP4(pt);
+ return q;
+ }
+
+ /**
+ * Note that q0 is the last parameter here
+ *
+ * @param q1
+ * @param q2
+ * @param q3
+ * @param q0
+ * @return {q1 q2 q3 q0}
+ */
+ public static Quat new4(float q1, float q2, float q3, float q0) {
+ Quat q = new Quat();
+ if (q0 < -1) {
+ q.q0 = -1;
+ return q;
+ }
+ if (q0 > 1) {
+ q.q0 = 1;
+ return q;
+ }
+ q.q0 = q0;
+ q.q1 = q1;
+ q.q2 = q2;
+ q.q3 = q3;
+ return q;
+ }
+
+ public void set(Quat q) {
+ q0 = q.q0;
+ q1 = q.q1;
+ q2 = q.q2;
+ q3 = q.q3;
+ }
+
+ /**
+ * {x y z w} --> {q1 q2 q3 q0} and factored
+ *
+ * @param pt
+ */
+ private void setP4(P4 pt) {
+ float factor = (pt == null ? 0 : pt.distance4(qZero));
+ if (factor == 0) {
+ q0 = 1;
+ return;
+ }
+ q0 = pt.w / factor;
+ q1 = pt.x / factor;
+ q2 = pt.y / factor;
+ q3 = pt.z / factor;
+ }
+
+ /**
+ * q = (cos(theta/2), sin(theta/2) * n)
+ *
+ * @param pt
+ * @param theta
+ */
+ public void setTA(T3 pt, float theta) {
+ if (pt.x == 0 && pt.y == 0 && pt.z == 0) {
+ q0 = 1;
+ return;
+ }
+ double fact = (Math.sin(theta / 2 * RAD_PER_DEG) / Math.sqrt(pt.x
+ * pt.x + pt.y * pt.y + pt.z * pt.z));
+ q0 = (float) (Math.cos(theta / 2 * RAD_PER_DEG));
+ q1 = (float) (pt.x * fact);
+ q2 = (float) (pt.y * fact);
+ q3 = (float) (pt.z * fact);
+ }
+
+ public void setAA(A4 a) {
+ A4 aa = A4.newAA(a);
+ if (aa.angle == 0)
+ aa.y = 1;
+ setM(new M3().setAA(aa));
+ }
+
+ private void setM(M3 mat) {
+
+ /*
+ * Changed 7/16/2008 to double precision for 11.5.48.
+ *
+ *
+ *
+ * RayTrace Software Package, release 3.0. May 3, 2006.
+ *
+ * Mathematics Subpackage (VrMath)
+ *
+ * Author: Samuel R. Buss
+ *
+ * Software is "as-is" and carries no warranty. It may be used without
+ * restriction, but if you modify it, please change the filenames to
+ * prevent confusion between different versions. Please acknowledge
+ * all use of the software in any publications or products based on it.
+ *
+ * Bug reports: Sam Buss, sbuss@ucsd.edu.
+ * Web page: http://math.ucsd.edu/~sbuss/MathCG
+
+ // Use Shepperd's algorithm, which is stable, does not lose
+ // significant precision and uses only one sqrt.
+ // J. Guidance and Control, 1 (1978) 223-224.
+
+ *
+ *
+ * Except, that code has errors.
+ *
+ * CORRECTIONS (as noted below) of Quaternion.cpp. I have reported the bug.
+ *
+ * -- Bob Hanson
+ *
+ * theory:
+ * cos(theta/2)^2 = (cos(theta) + 1)/2
+ * and
+ * trace = (1-x^2)ct + (1-y^2)ct + (1-z^2)ct + 1 = 2cos(theta) + 1
+ * or
+ * cos(theta) = (trace - 1)/2
+ *
+ * so in general,
+ *
+ * w = cos(theta/2)
+ * = sqrt((cos(theta)+1)/2)
+ * = sqrt((trace-1)/4+1/2)
+ * = sqrt((trace+1)/4)
+ * = sqrt(trace+1)/2
+ *
+ * but there are precision issues, so we allow for other situations.
+ * note -- trace >= 0.5 when cos(theta) >= -0.25 (-104.48 <= theta <= 104.48).
+ * this code cleverly matches the precision in all four options.
+ *
+ */
+
+ this.mat = mat;
+
+ double trace = mat.m00 + mat.m11 + mat.m22;
+ double temp;
+ double w, x, y, z;
+ if (trace >= 0.5) {
+ w = Math.sqrt(1.0 + trace);
+ x = (mat.m21 - mat.m12) / w;
+ y = (mat.m02 - mat.m20) / w;
+ z = (mat.m10 - mat.m01) / w;
+ } else if ((temp = mat.m00 + mat.m00 - trace) >= 0.5) {
+ x = Math.sqrt(1.0 + temp);
+ w = (mat.m21 - mat.m12) / x;
+ y = (mat.m10 + mat.m01) / x;
+ z = (mat.m20 + mat.m02) / x;
+ } else if ((temp = mat.m11 + mat.m11 - trace) >= 0.5
+ || mat.m11 > mat.m22) {
+ y = Math.sqrt(1.0 + temp);
+ w = (mat.m02 - mat.m20) / y;
+ x = (mat.m10 + mat.m01) / y;
+ z = (mat.m21 + mat.m12) / y;
+ } else {
+ z = Math.sqrt(1.0 + mat.m22 + mat.m22 - trace);
+ w = (mat.m10 - mat.m01) / z;
+ x = (mat.m20 + mat.m02) / z; // was -
+ y = (mat.m21 + mat.m12) / z; // was -
+ }
+
+ q0 = (float) (w * 0.5);
+ q1 = (float) (x * 0.5);
+ q2 = (float) (y * 0.5);
+ q3 = (float) (z * 0.5);
+
+ /*
+ * Originally from http://www.gamedev.net/community/forums/topic.asp?topic_id=448380
+ * later algorithm was adapted from Visualizing Quaternions, by Andrew J. Hanson
+ * (Morgan Kaufmann, 2006), page 446
+ *
+ * HOWEVER, checking with AxisAngle4f and Quat4f equivalents, it was found that
+ * BOTH of these sources produce inverted quaternions. So here we do an inversion.
+ *
+ * This correction was made in 11.5.42 6/19/2008 -- Bob Hanson
+ *
+ * former algorithm used:
+ * /
+
+ double tr = mat.m00 + mat.m11 + mat.m22; //Matrix trace
+ double s;
+ double[] q = new double[4];
+ if (tr > 0) {
+ s = Math.sqrt(tr + 1);
+ q0 = (float) (0.5 * s);
+ s = 0.5 / s; // = 1/q0
+ q1 = (float) ((mat.m21 - mat.m12) * s);
+ q2 = (float) ((mat.m02 - mat.m20) * s);
+ q3 = (float) ((mat.m10 - mat.m01) * s);
+ } else {
+ float[][] m = new float[][] { new float[3], new float[3], new float[3] };
+ mat.getRow(0, m[0]);
+ mat.getRow(1, m[1]);
+ mat.getRow(2, m[2]);
+
+ //Find out the biggest element along the diagonal
+ float max = Math.max(mat.m11, mat.m00);
+ int i = (mat.m22 > max ? 2 : max == mat.m11 ? 1 : 0);
+ int j = (i + 1) % 3;
+ int k = (j + 1) % 3;
+ s = -Math.sqrt(1 + m[i][i] - m[j][j] - m[k][k]);
+ // 0 = 1 + (1-x^2)ct + x^2 -(1-y^2)ct - y^2 - (1-z^2)ct - z^2
+ // 0 = 1 - ct + (x^2 - y^2 - z^2) - (x^2 - y^2 - z^2)ct
+ // 0 = 1 - ct + 2x^2 - 1 - (2x^2)ct + ct
+ // 0 = 2x^2(1 - ct)
+ // theta = 0 (but then trace = 1 + 1 + 1 = 3)
+ // or x = 0.
+ q[i] = s * 0.5;
+ if (s != 0)
+ s = 0.5 / s; // = 1/q[i]
+ q[j] = (m[i][j] + m[j][i]) * s;
+ q[k] = (m[i][k] + m[k][i]) * s;
+ q0 = (float) ((m[k][j] - m[j][k]) * s);
+ q1 = (float) q[0]; // x
+ q2 = (float) q[1]; // y
+ q3 = (float) q[2]; // z
+ }
+
+ */
+ }
+
+ /*
+ * if qref is null, "fix" this quaternion
+ * otherwise, return a quaternion that is CLOSEST to the given quaternion
+ * that is, one that gives a positive dot product
+ *
+ */
+ public void setRef(Quat qref) {
+ if (qref == null) {
+ mul(getFixFactor());
+ return;
+ }
+ if (dot(qref) >= 0)
+ return;
+ q0 *= -1;
+ q1 *= -1;
+ q2 *= -1;
+ q3 *= -1;
+ }
+
+ /**
+ * returns a quaternion frame based on three points (center, x, and any point in xy plane)
+ * or two vectors (vA, vB).
+ *
+ * @param center (null for vA/vB option)
+ * @param x
+ * @param xy
+ * @return quaternion for frame
+ */
+ public static final Quat getQuaternionFrame(P3 center, T3 x,
+ T3 xy) {
+ V3 vA = V3.newV(x);
+ V3 vB = V3.newV(xy);
+ if (center != null) {
+ vA.sub(center);
+ vB.sub(center);
+ }
+ return getQuaternionFrameV(vA, vB, null, false);
+ }
+
+ /**
+ * Create a quaternion based on a frame
+ * @param vA
+ * @param vB
+ * @param vC
+ * @param yBased
+ * @return quaternion
+ */
+ public static final Quat getQuaternionFrameV(V3 vA, V3 vB,
+ V3 vC, boolean yBased) {
+ if (vC == null) {
+ vC = new V3();
+ vC.cross(vA, vB);
+ if (yBased)
+ vA.cross(vB, vC);
+ }
+ V3 vBprime = new V3();
+ vBprime.cross(vC, vA);
+ vA.normalize();
+ vBprime.normalize();
+ vC.normalize();
+ M3 mat = new M3();
+ mat.setColumnV(0, vA);
+ mat.setColumnV(1, vBprime);
+ mat.setColumnV(2, vC);
+
+ /*
+ *
+ * Verification tests using Quat4f and AngleAxis4f:
+ *
+ System.out.println("quaternion frame matrix: " + mat);
+
+ Point3f pt2 = new Point3f();
+ mat.transform(Point3f.new3(1, 0, 0), pt2);
+ System.out.println("vA=" + vA + " M(100)=" + pt2);
+ mat.transform(Point3f.new3(0, 1, 0), pt2);
+ System.out.println("vB'=" + vBprime + " M(010)=" + pt2);
+ mat.transform(Point3f.new3(0, 0, 1), pt2);
+ System.out.println("vC=" + vC + " M(001)=" + pt2);
+ Quat4f q4 = new Quat4f();
+ q4.set(mat);
+ System.out.println("----");
+ System.out.println("Quat4f: {" + q4.w + " " + q4.x + " " + q4.y + " " + q4.z + "}");
+ System.out.println("Quat4f: 2xy + 2wz = m10: " + (2 * q4.x * q4.y + 2 * q4.w * q4.z) + " = " + mat.m10);
+
+ */
+
+ Quat q = newM(mat);
+
+ /*
+ System.out.println("Quaternion mat from q \n" + q.getMatrix());
+ System.out.println("Quaternion: " + q.getNormal() + " " + q.getTheta());
+ AxisAngle4f a = new AxisAngle4f();
+ a.set(mat);
+ Vector3f v = Vector3f.new3(a.x, a.y, a.z);
+ v.normalize();
+ System.out.println("angleAxis: " + v + " "+(a.angle/Math.PI * 180));
+ */
+
+ return q;
+ }
+
+ public M3 getMatrix() {
+ if (mat == null)
+ setMatrix();
+ return mat;
+ }
+
+ private void setMatrix() {
+ mat = new M3();
+ // q0 = w, q1 = x, q2 = y, q3 = z
+ mat.m00 = q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3;
+ mat.m01 = 2 * q1 * q2 - 2 * q0 * q3;
+ mat.m02 = 2 * q1 * q3 + 2 * q0 * q2;
+ mat.m10 = 2 * q1 * q2 + 2 * q0 * q3;
+ mat.m11 = q0 * q0 - q1 * q1 + q2 * q2 - q3 * q3;
+ mat.m12 = 2 * q2 * q3 - 2 * q0 * q1;
+ mat.m20 = 2 * q1 * q3 - 2 * q0 * q2;
+ mat.m21 = 2 * q2 * q3 + 2 * q0 * q1;
+ mat.m22 = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3;
+ }
+
+ public Quat add(float x) {
+ // scalar theta addition (degrees)
+ return newVA(getNormal(), getTheta() + x);
+ }
+
+ public Quat mul(float x) {
+ // scalar theta multiplication
+ return (x == 1 ? new4(q1, q2, q3, q0) :
+ newVA(getNormal(), getTheta() * x));
+ }
+
+ public Quat mulQ(Quat p) {
+ return new4(
+ q0 * p.q1 + q1 * p.q0 + q2 * p.q3 - q3 * p.q2,
+ q0 * p.q2 + q2 * p.q0 + q3 * p.q1 - q1 * p.q3,
+ q0 * p.q3 + q3 * p.q0 + q1 * p.q2 - q2 * p.q1,
+ q0 * p.q0 - q1 * p.q1 - q2 * p.q2 - q3 * p.q3);
+ }
+
+ public Quat div(Quat p) {
+ // unit quaternions assumed -- otherwise would scale by 1/p.dot(p)
+ return mulQ(p.inv());
+ }
+
+ public Quat divLeft(Quat p) {
+ // unit quaternions assumed -- otherwise would scale by 1/p.dot(p)
+ return this.inv().mulQ(p);
+ }
+
+ public float dot(Quat q) {
+ return this.q0 * q.q0 + this.q1 * q.q1 + this.q2 * q.q2 + this.q3 * q.q3;
+ }
+
+ public Quat inv() {
+ return new4(-q1, -q2, -q3, q0);
+ }
+
+ public Quat negate() {
+ return new4(-q1, -q2, -q3, -q0);
+ }
+
+ /**
+ * ensures
+ *
+ * 1) q0 > 0
+ * or
+ * 2) q0 = 0 and q1 > 0
+ * or
+ * 3) q0 = 0 and q1 = 0 and q2 > 0
+ * or
+ * 4) q0 = 0 and q1 = 0 and q2 = 0 and q3 > 0
+ *
+ * @return 1 or -1
+ *
+ */
+
+ private float getFixFactor() {
+ return (q0 < 0 ||
+ q0 == 0 && (q1 < 0 || q1 == 0 && (q2 < 0 || q2 == 0 && q3 < 0)) ? -1 : 1);
+ }
+
+ public V3 getVector(int i) {
+ return getVectorScaled(i, 1f);
+ }
+
+ public V3 getVectorScaled(int i, float scale) {
+ if (i == -1) {
+ scale *= getFixFactor();
+ return V3.new3(q1 * scale, q2 * scale, q3 * scale);
+ }
+ if (mat == null)
+ setMatrix();
+ V3 v = new V3();
+ mat.getColumnV(i, v);
+ if (scale != 1f)
+ v.scale(scale);
+ return v;
+ }
+
+ /**
+ *
+ * @return vector such that 0 <= angle <= 180
+ */
+ public V3 getNormal() {
+ V3 v = getRawNormal(this);
+ v.scale(getFixFactor());
+ return v;
+ }
+
+ private static V3 getRawNormal(Quat q) {
+ V3 v = V3.new3(q.q1, q.q2, q.q3);
+ if (v.length() == 0)
+ return V3.new3(0, 0, 1);
+ v.normalize();
+ return v;
+ }
+
+ /**
+ *
+ * @return 0 <= angle <= 180 in degrees
+ */
+ public float getTheta() {
+ return (float) (Math.acos(Math.abs(q0)) * 2 * 180 / Math.PI);
+ }
+
+ public float getThetaRadians() {
+ return (float) (Math.acos(Math.abs(q0)) * 2);
+ }
+
+ /**
+ *
+ * @param v0
+ * @return vector option closest to v0
+ *
+ */
+ public V3 getNormalDirected(V3 v0) {
+ V3 v = getNormal();
+ if (v.x * v0.x + v.y * v0.y + v.z * v0.z < 0) {
+ v.scale(-1);
+ }
+ return v;
+ }
+
+ public V3 get3dProjection(V3 v3d) {
+ v3d.set(q1, q2, q3);
+ return v3d;
+ }
+
+ /**
+ *
+ * @param axisAngle
+ * @return fill in theta of axisAngle such that
+ */
+ public P4 getThetaDirected(P4 axisAngle) {
+ //fills in .w;
+ float theta = getTheta();
+ V3 v = getNormal();
+ if (axisAngle.x * q1 + axisAngle.y * q2 + axisAngle.z * q3 < 0) {
+ v.scale(-1);
+ theta = -theta;
+ }
+ axisAngle.set4(v.x, v.y, v.z, theta);
+ return axisAngle;
+ }
+
+ /**
+ *
+ * @param vector a vector, same as for getNormalDirected
+ * @return return theta
+ */
+ public float getThetaDirectedV(V3 vector) {
+ //fills in .w;
+ float theta = getTheta();
+ V3 v = getNormal();
+ if (vector.x * q1 + vector.y * q2 + vector.z * q3 < 0) {
+ v.scale(-1);
+ theta = -theta;
+ }
+ return theta;
+ }
+
+ /**
+ * Quaternions are saved as {q1, q2, q3, q0}
+ *
+ * While this may seem odd, it is so that for any point4 --
+ * planes, axisangles, and quaternions -- we can use the
+ * first three coordinates to determine the relavent axis
+ * the fourth then gives us offset to {0,0,0} (plane),
+ * rotation angle (axisangle), and cos(theta/2) (quaternion).
+ * @return {x y z w} (unnormalized)
+ */
+ public P4 toPoint4f() {
+ return P4.new4(q1, q2, q3, q0); // x,y,z,w
+ }
+
+ public A4 toAxisAngle4f() {
+ double theta = 2 * Math.acos(Math.abs(q0));
+ double sinTheta2 = Math.sin(theta/2);
+ V3 v = getNormal();
+ if (sinTheta2 < 0) {
+ v.scale(-1);
+ theta = Math.PI - theta;
+ }
+ return A4.newVA(v, (float) theta);
+ }
+
+ public T3 transform2(T3 pt, T3 ptNew) {
+ if (mat == null)
+ setMatrix();
+ mat.rotate2(pt, ptNew);
+ return ptNew;
+ }
+
+ public Quat leftDifference(Quat q2) {
+ //dq = q.leftDifference(qnext);//q.inv().mul(qnext);
+ Quat q2adjusted = (this.dot(q2) < 0 ? q2.negate() : q2);
+ return inv().mulQ(q2adjusted);
+ }
+
+ public Quat rightDifference(Quat q2) {
+ //dq = qnext.rightDifference(q);//qnext.mul(q.inv());
+ Quat q2adjusted = (this.dot(q2) < 0 ? q2.negate() : q2);
+ return mulQ(q2adjusted.inv());
+ }
+
+ /**
+ *
+ * Java axisAngle / plane / Point4f format
+ * all have the format {x y z w}
+ * so we go with that here as well
+ *
+ * @return "{q1 q2 q3 q0}"
+ */
+ @Override
+ public String toString() {
+ return "{" + q1 + " " + q2 + " " + q3 + " " + q0 + "}";
+ }
+
+ /**
+ *
+ * @param data1
+ * @param data2
+ * @param nMax > 0 --> limit to this number
+ * @param isRelative
+ *
+ * @return pairwise array of data1 / data2 or data1 \ data2
+ */
+ public static Quat[] div(Quat[] data1, Quat[] data2, int nMax, boolean isRelative) {
+ int n;
+ if (data1 == null || data2 == null || (n = Math.min(data1.length, data2.length)) == 0)
+ return null;
+ if (nMax > 0 && n > nMax)
+ n = nMax;
+ Quat[] dqs = new Quat[n];
+ for (int i = 0; i < n; i++) {
+ if (data1[i] == null || data2[i] == null)
+ return null;
+ dqs[i] = (isRelative ? data1[i].divLeft(data2[i]) : data1[i].div(data2[i]));
+ }
+ return dqs;
+ }
+
+ public static Quat sphereMean(Quat[] data, float[] retStddev, float criterion) {
+ // Samuel R. Buss, Jay P. Fillmore:
+ // Spherical averages and applications to spherical splines and interpolation.
+ // ACM Trans. Graph. 20(2): 95-126 (2001)
+ if (data == null || data.length == 0)
+ return new Quat();
+ if (retStddev == null)
+ retStddev = new float[1];
+ if (data.length == 1) {
+ retStddev[0] = 0;
+ return newQ(data[0]);
+ }
+ float diff = Float.MAX_VALUE;
+ float lastStddev = Float.MAX_VALUE;
+ Quat qMean = simpleAverage(data);
+ int maxIter = 100; // typically goes about 5 iterations
+ int iter = 0;
+ while (diff > criterion && lastStddev != 0 && iter < maxIter) {
+ qMean = newMean(data, qMean);
+ retStddev[0] = stdDev(data, qMean);
+ diff = Math.abs(retStddev[0] - lastStddev);
+ lastStddev = retStddev[0];
+ //Logger.info(++iter + " sphereMean " + qMean + " stddev=" + lastStddev + " diff=" + diff);
+ }
+ return qMean;
+ }
+
+ /**
+ * Just a starting point.
+ * get average normal vector
+ * scale normal by average projection of vectors onto it
+ * create quaternion from this 3D projection
+ *
+ * @param ndata
+ * @return approximate average
+ */
+ private static Quat simpleAverage(Quat[] ndata) {
+ V3 mean = V3.new3(0, 0, 1);
+ // using the directed normal ensures that the mean is
+ // continually added to and never subtracted from
+ V3 v = ndata[0].getNormal();
+ mean.add(v);
+ for (int i = ndata.length; --i >= 0;)
+ mean.add(ndata[i].getNormalDirected(mean));
+ mean.sub(v);
+ mean.normalize();
+ float f = 0;
+ // the 3D projection of the quaternion is [sin(theta/2)]*n
+ // so dotted with the normalized mean gets us an approximate average for sin(theta/2)
+ for (int i = ndata.length; --i >= 0;)
+ f += Math.abs(ndata[i].get3dProjection(v).dot(mean));
+ if (f != 0)
+ mean.scale(f / ndata.length);
+ // now convert f to the corresponding cosine instead of sine
+ f = (float) Math.sqrt(1 - mean.lengthSquared());
+ if (Float.isNaN(f))
+ f = 0;
+ return newP4(P4.new4(mean.x, mean.y, mean.z, f));
+ }
+
+ private static Quat newMean(Quat[] data, Quat mean) {
+ /* quaternion derivatives nicely take care of producing the necessary
+ * metric. Since dq gives us the normal with the smallest POSITIVE angle,
+ * we just scale by that -- using degrees.
+ * No special normalization is required.
+ *
+ * The key is that the mean has been set up already, and dq.getTheta()
+ * will always return a value between 0 and 180. True, for groupings
+ * where dq swings wildly -- 178, 182, 178, for example -- there will
+ * be problems, but the presumption here is that there is a REASONABLE
+ * set of data. Clearly there are spherical data sets that simply cannot
+ * be assigned a mean. (For example, where the three projected points
+ * are equally distant on the sphere. We just can't worry about those
+ * cases here. Rather, if there is any significance to the data,
+ * there will be clusters of projected points, and the analysis will
+ * be meaningful.
+ *
+ * Note that the hemisphere problem drops out because dq.getNormal() and
+ * dq.getTheta() will never return (n, 182 degrees) but will
+ * instead return (-n, 2 degrees). That's just what we want in that case.
+ *
+ * Note that the projection in this case is to 3D -- a set of vectors
+ * in space with lengths proportional to theta (not the sin(theta/2)
+ * that is associated with a quaternion map).
+ *
+ * This is officially an "exponential" or "hyperbolic" projection.
+ *
+ */
+ V3 sum = new V3();
+ V3 v;
+ Quat q, dq;
+ //System.out.println("newMean mean " + mean);
+ for (int i = data.length; --i >= 0;) {
+ q = data[i];
+ dq = q.div(mean);
+ v = dq.getNormal();
+ v.scale(dq.getTheta());
+ sum.add(v);
+ }
+ sum.scale(1f/data.length);
+ Quat dqMean = newVA(sum, sum.length());
+ //System.out.println("newMean dqMean " + dqMean + " " + dqMean.getNormal() + " " + dqMean.getTheta());
+ return dqMean.mulQ(mean);
+ }
+
+ /**
+ * @param data
+ * @param mean
+ * @return standard deviation in units of degrees
+ */
+ private static float stdDev(Quat[] data, Quat mean) {
+ // the quaternion dot product gives q0 for dq (i.e. q / mean)
+ // that is, cos(theta/2) for theta between them
+ double sum2 = 0;
+ int n = data.length;
+ for (int i = n; --i >= 0;) {
+ float theta = data[i].div(mean).getTheta();
+ sum2 += theta * theta;
+ }
+ return (float) Math.sqrt(sum2 / n);
+ }
+
+ public float[] getEulerZYZ() {
+ // http://www.swarthmore.edu/NatSci/mzucker1/e27/diebel2006attitude.pdf
+ double rA, rB, rG;
+ if (q1 == 0 && q2 == 0) {
+ float theta = getTheta();
+ // pure Z rotation - ambiguous
+ return new float[] { q3 < 0 ? -theta : theta , 0, 0 };
+ }
+ rA = Math.atan2(2 * (q2 * q3 + q0 * q1), 2 * (-q1 * q3 + q0 * q2 ));
+ rB = Math.acos(q3 * q3 - q2 * q2 - q1 * q1 + q0 * q0);
+ rG = Math.atan2( 2 * (q2 * q3 - q0 * q1), 2 * (q0 * q2 + q1 * q3));
+ return new float[] {(float) (rA / RAD_PER_DEG), (float) (rB / RAD_PER_DEG), (float) (rG / RAD_PER_DEG)};
+ }
+
+ public float[] getEulerZXZ() {
+ // NOT http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
+ // http://www.swarthmore.edu/NatSci/mzucker1/e27/diebel2006attitude.pdf
+ double rA, rB, rG;
+ if (q1 == 0 && q2 == 0) {
+ float theta = getTheta();
+ // pure Z rotation - ambiguous
+ return new float[] { q3 < 0 ? -theta : theta , 0, 0 };
+ }
+ rA = Math.atan2(2 * (q1 * q3 - q0 * q2), 2 * (q0 * q1 + q2 * q3 ));
+ rB = Math.acos(q3 * q3 - q2 * q2 - q1 * q1 + q0 * q0);
+ rG = Math.atan2( 2 * (q1 * q3 + q0 * q2), 2 * (-q2 * q3 + q0 * q1));
+ return new float[] {(float) (rA / RAD_PER_DEG), (float) (rB / RAD_PER_DEG), (float) (rG / RAD_PER_DEG)};
+ }
+
+}