org.simantics.g3d/src/org/simantics/g3d/math/MathTools.java

   1 /*******************************************************************************
   2  * Copyright (c) 2012, 2013 Association for Decentralized Information Management in
   3  * Industry THTH ry.
   4  * All rights reserved. This program and the accompanying materials
   5  * are made available under the terms of the Eclipse Public License v1.0
   6  * which accompanies this distribution, and is available at
   7  * http://www.eclipse.org/legal/epl-v10.html
   8  *
   9  * Contributors:
  10  *     VTT Technical Research Centre of Finland - initial API and implementation
  11  *******************************************************************************/
  12 package org.simantics.g3d.math;
  13
  14 import javax.vecmath.AxisAngle4d;
  15 import javax.vecmath.Matrix3d;
  16 import javax.vecmath.Matrix4d;
  17 import javax.vecmath.Quat4d;
  18 import javax.vecmath.Tuple2d;
  19 import javax.vecmath.Tuple3d;
  20 import javax.vecmath.Tuple4d;
  21 import javax.vecmath.Vector2d;
  22 import javax.vecmath.Vector2f;
  23 import javax.vecmath.Vector3d;
  24
  25 import org.simantics.g3d.math.EulerTools.Order;
  26
  27
  28 /**
  29  * Some useful geometry related math functions. Beware, methods may modify their input parameters!
  30  *
  31  * @author Marko Luukkainen
  32  *
  33  */
  34 public class MathTools {
  35
  36         public static double NEAR_ZERO = 0.000000001;
  37         public static double NEAR_HALF = 0.499999999;
  38
  39         public static final Vector3d Z_AXIS = new Vector3d(0.0,0.0,1.0);
  40         public static final Vector3d Y_AXIS = new Vector3d(0.0,1.0,0.0);
  41         public static final Vector3d X_AXIS = new Vector3d(1.0,0.0,0.0);
  42         public static final Vector3d ORIGIN = new Vector3d(0.0,0.0,0.0);
  43
  44         final static double EPS = 1.0e-12;
  45
  46
  47         public static boolean equals(double d1, double d2) {
  48                 return Math.abs(d1-d2) < EPS;
  49         }
  50
  51         public static boolean equals(Tuple3d p1, Tuple3d p2) {
  52                 return distanceSquared(p1, p2) < NEAR_ZERO;
  53         }
  54
  55         public static boolean equals(Tuple4d p1, Tuple4d p2) {
  56                 return distanceSquared(p1, p2) < NEAR_ZERO;
  57         }
  58
  59         public static double distance(Tuple3d p1, Tuple3d p2) {
  60                 double dx, dy, dz;
  61
  62                 dx = p2.x - p1.x;
  63                 dy = p2.y - p1.y;
  64                 dz = p2.z - p1.z;
  65                 return Math.sqrt(dx*dx+dy*dy+dz*dz);
  66         }
  67
  68         public static double distance(Tuple4d p1, Tuple4d p2) {
  69                 double dx, dy, dz, dw;
  70
  71                 dx = p2.x - p1.x;
  72                 dy = p2.y - p1.y;
  73                 dz = p2.z - p1.z;
  74                 dw = p2.w - p1.w;
  75                 return Math.sqrt(dx*dx+dy*dy+dz*dz+dw*dw);
  76         }
  77
  78         public static double distanceSquared(Tuple3d p1, Tuple3d p2) {
  79                 double dx, dy, dz;
  80
  81                 dx = p2.x - p1.x;
  82                 dy = p2.y - p1.y;
  83                 dz = p2.z - p1.z;
  84                 return dx*dx+dy*dy+dz*dz;
  85         }
  86
  87         public static double distanceSquared(Tuple4d p1, Tuple4d p2) {
  88                 double dx, dy, dz, dw;
  89
  90                 dx = p2.x - p1.x;
  91                 dy = p2.y - p1.y;
  92                 dz = p2.z - p1.z;
  93                 dw = p2.w - p1.w;
  94                 return dx*dx+dy*dy+dz*dz+dw*dw;
  95         }
  96
  97         public static boolean isValid(Tuple3d t) {
  98                 return !(Double.isInfinite(t.x) || Double.isNaN(t.x) ||
  99                          Double.isInfinite(t.y) || Double.isNaN(t.y) ||
 100                          Double.isInfinite(t.z) || Double.isNaN(t.z));
 101         }
 102
 103         public static Vector3d closestPointOnEdge(Vector3d point, Vector3d edgePoint1, Vector3d edgePoint2) {
 104                 point.sub(edgePoint1);
 105                 Vector3d v = new Vector3d(edgePoint2);
 106                 v.sub(edgePoint1);
 107                 double t = v.dot(point);
 108                 t /= v.lengthSquared();
 109                 if (t <= 0.0f)
 110                         return edgePoint1;
 111                 if (t >= 1.0f)
 112                         return edgePoint2;
 113                 v.scale(t);
 114                 v.add(edgePoint1);
 115                 return v;
 116         }
 117
 118         public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir) {
 119                 Vector3d v = new Vector3d(point);
 120                 v.sub(straightPoint);
 121                 double t = straightDir.dot(v);
 122                 t /= straightDir.lengthSquared();
 123                 v.set(straightDir);
 124                 v.scale(t);
 125                 v.add(straightPoint);
 126                 return v;
 127         }
 128
 129         public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir, double u[]) {
 130                 Vector3d v = new Vector3d(point);
 131                 v.sub(straightPoint);
 132                 u[0] = straightDir.dot(v);
 133                 u[0] /= straightDir.lengthSquared();
 134                 v.set(straightDir);
 135                 v.scale(u[0]);
 136                 v.add(straightPoint);
 137                 return v;
 138         }
 139
 140         public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, Tuple3d planePoint) {
 141                 point.sub(planePoint);
 142
 143                 return planeNormal.dot(point);
 144         }
 145
 146         public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, float d) {
 147                 return (planeNormal.dot(point) + d);
 148         }
 149
 150         public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Tuple3d intersectPoint) {
 151                 intersectPoint.set(planePoint);
 152                 intersectPoint.sub(linePoint);
 153                 double u = planeNormal.dot(new Vector3d(intersectPoint));
 154                 double v = planeNormal.dot(lineDir);
 155                 if (Math.abs(v) < NEAR_ZERO)
 156                         return false;
 157                 u /= v;
 158                 intersectPoint.set(lineDir);
 159                 intersectPoint.scale(u);
 160                 intersectPoint.add(linePoint);
 161                 return true;
 162         }
 163
 164         public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Vector3d intersectPoint, double[] u) {
 165                 intersectPoint.set(planePoint);
 166                 intersectPoint.sub(linePoint);
 167                 u[0] = planeNormal.dot(intersectPoint);
 168                 double v = planeNormal.dot(lineDir);
 169                 if (Math.abs(v) < NEAR_ZERO)
 170                         return false;
 171                 u[0] /= v;
 172                 intersectPoint.set(lineDir);
 173                 intersectPoint.scale(u[0]);
 174                 intersectPoint.add(linePoint);
 175                 return true;
 176         }
 177
 178         public static boolean intersectLineLine(Tuple3d l1_start,Tuple3d l1_end,Tuple3d l2_start,Tuple3d l2_end,Tuple3d l1_pos, Tuple3d l2_pos) {
 179                         Vector3d p13 = new Vector3d();
 180                         Vector3d p43 = new Vector3d();
 181                         Vector3d p21 = new Vector3d();
 182                         double d1343,d4321,d1321,d4343,d2121;
 183                         double numer,denom;
 184                         p13.sub(l1_start, l2_start);
 185                         p43.sub(l2_end,l2_start);
 186                         if (Math.abs(p43.x)  < NEAR_ZERO && Math.abs(p43.y)  < NEAR_ZERO && Math.abs(p43.z)  < NEAR_ZERO)
 187                                 return false;
 188                         p21.sub(l1_end,l1_start);
 189                         if (Math.abs(p21.x)  < NEAR_ZERO && Math.abs(p21.y)  < NEAR_ZERO && Math.abs(p21.z)  < NEAR_ZERO)
 190                                 return false;
 191
 192                         d1343 = p13.dot(p43);
 193                         d4321 = p43.dot(p21);
 194                         d1321 = p13.dot(p21);
 195                         d4343 = p43.lengthSquared();
 196                         d2121 = p21.lengthSquared();
 197
 198                         denom = d2121 * d4343 - d4321 * d4321;
 199                         if (Math.abs(denom) < NEAR_ZERO)
 200                                 return false;
 201                         numer = d1343 * d4321 - d1321 * d4343;
 202
 203                         double mua = numer / denom;
 204                         double mub = (d1343 + d4321 * mua) / d4343;
 205
 206                         l1_pos.x = l1_start.x + mua * p21.x;
 207                         l1_pos.y = l1_start.y + mua * p21.y;
 208                         l1_pos.z = l1_start.z + mua * p21.z;
 209                         l2_pos.x = l2_start.x + mub * p43.x;
 210                         l2_pos.y = l2_start.y + mub * p43.y;
 211                         l2_pos.z = l2_start.z + mub * p43.z;
 212
 213                         return true;
 214         }
 215
 216         public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb) {
 217                 Vector3d p13 = new Vector3d();
 218
 219                 double d1343,d4321,d1321,d4343,d2121;
 220                 double numer,denom;
 221
 222                 p13.sub(p1, p3);
 223                 if (Math.abs(p43.x)  < NEAR_ZERO && Math.abs(p43.y)  < NEAR_ZERO && Math.abs(p43.z)  < NEAR_ZERO)
 224                         return false;
 225                 if (Math.abs(p21.x)  < NEAR_ZERO && Math.abs(p21.y)  < NEAR_ZERO && Math.abs(p21.z)  < NEAR_ZERO)
 226                         return false;
 227
 228                 d1343 = p13.dot(p43);
 229                 d4321 = p43.dot(p21);
 230                 d1321 = p13.dot(p21);
 231                 d4343 = p43.lengthSquared();
 232                 d2121 = p21.lengthSquared();
 233
 234                 denom = d2121 * d4343 - d4321 * d4321;
 235                 if (Math.abs(denom) < NEAR_ZERO)
 236                         return false;
 237                 numer = d1343 * d4321 - d1321 * d4343;
 238
 239                 double mua = numer / denom;
 240                 double mub = (d1343 + d4321 * mua) / d4343;
 241
 242                 pa.x = p1.x + mua * p21.x;
 243                 pa.y = p1.y + mua * p21.y;
 244                 pa.z = p1.z + mua * p21.z;
 245                 pb.x = p3.x + mub * p43.x;
 246                 pb.y = p3.y + mub * p43.y;
 247                 pb.z = p3.z + mub * p43.z;
 248
 249                 return true;
 250         }
 251
 252         /**
 253          * Calculate the line segment PaPb that is the shortest route between
 254          *  two lines P1P2 and P3P4. Calculate also the values of mua and mub where
 255          *  Pa = P1 + mua (P2 - P1)
 256          *  Pb = P3 + mub (P4 - P3)
 257          * @param p1
 258          * @param p21
 259          * @param p3
 260          * @param p43
 261          * @param pa
 262          * @param pb
 263          * @param mu
 264          * @return
 265          */
 266         public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb, double mu[]) {
 267                 Vector3d p13 = new Vector3d();
 268
 269                 double d1343,d4321,d1321,d4343,d2121;
 270                 double numer,denom;
 271                 double EPS = 0.001;
 272                 p13.sub(p1, p3);
 273                 if (Math.abs(p43.x)  < EPS && Math.abs(p43.y)  < EPS && Math.abs(p43.z)  < EPS)
 274                         return false;
 275                 if (Math.abs(p21.x)  < EPS && Math.abs(p21.y)  < EPS && Math.abs(p21.z)  < EPS)
 276                         return false;
 277
 278                 d1343 = p13.dot(p43);
 279                 d4321 = p43.dot(p21);
 280                 d1321 = p13.dot(p21);
 281                 d4343 = p43.lengthSquared();
 282                 d2121 = p21.lengthSquared();
 283
 284                 denom = d2121 * d4343 - d4321 * d4321;
 285                 if (Math.abs(denom) < EPS)
 286                         return false;
 287                 numer = d1343 * d4321 - d1321 * d4343;
 288
 289                 mu[0] = numer / denom;
 290                 mu[1] = (d1343 + d4321 * mu[0]) / d4343;
 291
 292                 pa.x = p1.x + mu[0] * p21.x;
 293                 pa.y = p1.y + mu[0] * p21.y;
 294                 pa.z = p1.z + mu[0] * p21.z;
 295                 pb.x = p3.x + mu[1] * p43.x;
 296                 pb.y = p3.y + mu[1] * p43.y;
 297                 pb.z = p3.z + mu[1] * p43.z;
 298
 299                 return true;
 300         }
 301
 302
 303
 304         public static void rotate(Quat4d q, Tuple3d in, Tuple3d out) {
 305                 // p' = q * p * q'
 306                 double tw =             - q.x*in.x - q.y*in.y - q.z*in.z;
 307                 double tx =  q.w*in.x            + q.y*in.z - q.z*in.y;
 308                 double ty =  q.w*in.y - q.x*in.z            + q.z*in.x;
 309                 double tz =  q.w*in.z + q.x*in.y - q.y*in.x           ;
 310
 311                 //temp * q' -> x = -x, y = -y z = -z
 312                 //out.w = tw*q.w + tx*q.x + ty*q.y + tz*q.z;
 313                 out.x =  -tw*q.x + tx*q.w - ty*q.z + tz*q.y;
 314                 out.y =  -tw*q.y + tx*q.z + ty*q.w - tz*q.x;
 315                 out.z =  -tw*q.z - tx*q.y + ty*q.x + tz*q.w;
 316         }
 317
 318         public static void getMatrix(Quat4d quat, Matrix3d m) {
 319                         m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
 320                         m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
 321                         m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
 322                         m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
 323                         m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
 324                         m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
 325                         m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
 326                         m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
 327                         m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
 328
 329         }
 330
 331         public static void getMatrix(Quat4d quat, Matrix4d m) {
 332                 m.setZero();
 333                 m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
 334                 m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
 335                 m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
 336                 m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
 337                 m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
 338                 m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
 339                 m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
 340                 m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
 341                 m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
 342                 m.m33 = 1.0;
 343         }
 344
 345         private static double q[] = new double[3];
 346         private static int nxt[] = { 1, 2, 0 };
 347         /**
 348          * Converts Matrix to Quaternion
 349          *
 350          * Note: non-thread safe.
 351          *
 352          * @param mat
 353          * @param quat
 354          */
 355         public static void getQuat(Matrix3d mat, Quat4d quat) {
 356                 double tr = mat.m00 + mat.m11 + mat.m22;
 357                 if (tr > 0.0) {
 358                         double s = Math.sqrt(tr + 1.0);
 359                         quat.w = 0.5 * s;
 360                         s = 0.5 / s;
 361                         quat.x = (mat.m21 - mat.m12) * s;
 362                         quat.y = (mat.m02 - mat.m20) * s;
 363                         quat.z = (mat.m10 - mat.m01) * s;
 364                 } else {
 365                         int i = 0, j, k;
 366                         if (mat.m11 > mat.m00)
 367                                 i = 1;
 368                         if (mat.m22 > mat.getElement(i, i))
 369                                 i = 2;
 370
 371
 372                         j = nxt[i];
 373                         k = nxt[j];
 374
 375                         double s = Math.sqrt((mat.getElement(i, i) - (mat.getElement(j, j) + mat.getElement(k, k))) + 1.0);
 376
 377                         q[i] = s * 0.5;
 378
 379                         if (Math.abs(s) > 0.001)
 380                                 s = 0.5 / s;
 381
 382                         quat.w = (mat.getElement(k, j) - mat.getElement(j, k)) * s;
 383                         q[j] = (mat.getElement(j, i) + mat.getElement(i, j)) * s;
 384                         q[k] = (mat.getElement(k, i) + mat.getElement(i, k)) * s;
 385
 386                         quat.x = q[0];
 387                         quat.y = q[1];
 388                         quat.z = q[2];
 389                 }
 390         }
 391
 392         public static Quat4d getQuat(Matrix3d mat) {
 393                 Quat4d q = new Quat4d();
 394                 getQuat(mat, q);
 395                 return q;
 396         }
 397
 398         public static AxisAngle4d getFromPseudoEuler(Vector3d euler) {
 399                 AxisAngle4d aa = new AxisAngle4d();
 400                 aa.angle = euler.length();
 401                 Vector3d normal = new Vector3d(euler);
 402                 if (aa.angle > NEAR_ZERO) {
 403                         normal.normalize();
 404                         aa.x = normal.x;
 405                         aa.y = normal.y;
 406                         aa.z = normal.z;
 407                 } else {
 408                         aa.x = 1.0;
 409                         aa.y = 0.0;
 410                         aa.z = 0.0;
 411                 }
 412
 413                 return aa;
 414         }
 415
 416         public static Vector3d getPseudoEuler(AxisAngle4d aa) {
 417                 Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);
 418                 euler.scale(aa.angle);
 419                 return euler;
 420         }
 421
 422
 423         public static void getQuat(Vector3d euler, Quat4d quat)  {
 424                 Quat4d q = EulerTools.getQuatFromEuler(Order.YXZ, euler.y,euler.x,euler.z);
 425                 quat.set(q);
 426         // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
 427         // Using the x-convention, the 3-1-3 Euler angles phi, theta and psi (around the Z, X and again the Z-axis)
 428 //         quat.x = -Math.cos((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
 429 //         quat.y = -Math.sin((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
 430 //         quat.z = -Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
 431 //         quat.w = Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
 432
 433                 // http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
 434                 // Y, Z, X order
 435 //          double c1 = Math.cos(euler.y*0.5);
 436 //          double s1 = Math.sin(euler.y*0.5);
 437 //          double c2 = Math.cos(euler.z*0.5);
 438 //          double s2 = Math.sin(euler.z*0.5);
 439 //          double c3 = Math.cos(euler.x*0.5);
 440 //          double s3 = Math.sin(euler.x*0.5);
 441 //          double c1c2 = c1*c2;
 442 //          double s1s2 = s1*s2;
 443 //          quat.w =c1c2*c3 - s1s2*s3;
 444 //          quat.x =c1c2*s3 + s1s2*c3;
 445 //          quat.y =s1*c2*c3 + c1*s2*s3;
 446 //          quat.z =c1*s2*c3 - s1*c2*s3;
 447
 448 //          Quat4d q2 = EulerTools.getQuatFromEuler(Order.YZX, euler.y,euler.z,euler.x);
 449 //          System.out.println("Q " + quat + " Q2 " + q2);
 450 //         double c1 = Math.cos(euler.y);
 451 //          double s1 = Math.sin(euler.y);
 452 //          double c2 = Math.cos(euler.z);
 453 //          double s2 = Math.sin(euler.z);
 454 //          double c3 = Math.cos(euler.x);
 455 //          double s3 = Math.sin(euler.x);
 456 //          quat.w = Math.sqrt(1.0 + c1 * c2 + c1*c3 - s1 * s2 * s3 + c2*c3) / 2.0;
 457 //          double w4 = (4.0 * quat.w);
 458 //          quat.x = (c2 * s3 + c1 * s3 + s1 * s2 * c3) / w4 ;
 459 //          quat.y = (s1 * c2 + s1 * c3 + c1 * s2 * s3) / w4 ;
 460 //          quat.z = (-s1 * s3 + c1 * s2 * c3 +s2) / w4 ;
 461         }
 462
 463
 464
 465
 466         public static void getEuler(Quat4d quat,Vector3d euler)  {
 467                 Vector3d e = EulerTools.getEulerFromQuat(Order.YXZ, quat);
 468                 euler.x = e.y;
 469                 euler.y = e.x;
 470                 euler.z = e.z;
 471
 472                 // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
 473 //         euler.x = Math.atan2(quat.x * quat.z + quat.y* quat.w, quat.y*quat.z - quat.x * quat.w);
 474 //         euler.y = Math.acos(-square(quat.x) - square(quat.y) + square(quat.z) + square(quat.w));
 475 //         euler.z = -Math.atan2(quat.x * quat.z - quat.y* quat.w, quat.y*quat.z + quat.x * quat.w);
 476
 477                 // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm
 478         // Y, Z, X order
 479 //         double test = quat.x * quat.y + quat.z * quat.w;
 480 //         if (test > NEAR_HALF) {
 481 //                 euler.y = 2.0 * Math.atan2(quat.x,quat.w);
 482 //                 euler.z = Math.PI * 0.5;
 483 //                 euler.x = 0.0;
 484 //         } else if (test < -NEAR_HALF) {
 485 //                 euler.y = -2.0 * Math.atan2(quat.x,quat.w);
 486 //                 euler.z = -Math.PI * 0.5;
 487 //                 euler.x = 0.0;
 488 //         } else {
 489 //                 double sqx = square(quat.x);
 490 //                 double sqy = square(quat.y);
 491 //                 double sqz = square(quat.z);
 492 //                 euler.y = Math.atan2(2.0*(quat.y*quat.w-quat.x*quat.z), 1.0 - 2.0*(sqy-sqz));
 493 //                 euler.z = Math.asin(2.0*test);
 494 //                 euler.x = Math.atan2(2.0*(quat.x*quat.w-quat.y*quat.z), 1.0 - 2.0*(sqx-sqz));
 495 //                 System.out.println(euler + " " + EulerTools.getEulerFromQuat(Order.YXZ, quat) +  " " + quat);
 496 //         }
 497 //         double sqw = quat.w*quat.w;
 498 //          double sqx = quat.x*quat.x;
 499 //          double sqy = quat.y*quat.y;
 500 //          double sqz = quat.z*quat.z;
 501 //              double unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor
 502 //              double test = quat.x*quat.y + quat.z*quat.w;
 503 //              if (test > 0.499*unit) { // singularity at north pole
 504 //                      euler.y = 2 * Math.atan2(quat.x,quat.w);
 505 //                      euler.z = Math.PI/2;
 506 //                      euler.x = 0;
 507 //                      return;
 508 //              }
 509 //              if (test < -0.499*unit) { // singularity at south pole
 510 //                      euler.y = -2 * Math.atan2(quat.x,quat.w);
 511 //                      euler.z = -Math.PI/2;
 512 //                      euler.x = 0;
 513 //                      return;
 514 //              }
 515 //              euler.y = Math.atan2(2*quat.y*quat.w-2*quat.x*quat.z , sqx - sqy - sqz + sqw);
 516 //              euler.z = Math.asin(2*test/unit);
 517 //              euler.x = Math.atan2(2*quat.x*quat.w-2*quat.y*quat.z , -sqx + sqy - sqz + sqw);
 518         }
 519
 520         public static Quat4d getQuat(Vector3d euler) {
 521                 Quat4d q = new Quat4d();
 522                 getQuat(euler,q);
 523                 return q;
 524         }
 525
 526
 527         public static Vector3d getEuler(Quat4d quat) {
 528                 Vector3d v = new Vector3d();
 529                 getEuler(quat, v);
 530                 return v;
 531         }
 532
 533         public static Quat4d getQuat(AxisAngle4d aa) {
 534                 Quat4d q = new Quat4d();
 535                 getQuat(aa, q);
 536                 return q;
 537         }
 538
 539         public static AxisAngle4d getAxisAngle(Quat4d q) {
 540                 AxisAngle4d aa = new AxisAngle4d();
 541                 double mag = q.x * q.x + q.y * q.y + q.z * q.z;
 542
 543                 if (mag > EPS) {
 544                         mag = Math.sqrt(mag);
 545                         aa.angle = 2.0 * Math.atan2(mag, q.w);
 546                         mag = 1.0 / mag;
 547                         aa.x = q.x * mag;
 548                         aa.y = q.y * mag;
 549                         aa.z = q.z * mag;
 550
 551                 } else {
 552                         aa.x = 0.0;
 553                         aa.y = 1.0;
 554                         aa.z = 0.0;
 555                         aa.angle = 0.0;
 556                 }
 557                 // aa.set(q);
 558                 return aa;
 559         }
 560
 561         public static Quat4d getIdentityQuat() {
 562                 return new Quat4d(0, 0, 0, 1);
 563         }
 564
 565         public static void getQuat(AxisAngle4d aa, Quat4d q) {
 566                 double mag,amag;
 567                 // Quat = cos(theta/2) + sin(theta/2)(roation_axis)
 568
 569                 amag = Math.sqrt( aa.x*aa.x + aa.y*aa.y + aa.z*aa.z);
 570                 if( amag < NEAR_ZERO ) {
 571                         q.w = 1.0;
 572                         q.x = 0.0;
 573                         q.y = 0.0;
 574                         q.z = 0.0;
 575                 } else {
 576                         amag = 1.0/amag;
 577                         double a2 = aa.angle * 0.5;
 578                         mag = Math.sin(a2);
 579                         q.w = Math.cos(a2);
 580                         q.x = aa.x*amag*mag;
 581                         q.y = aa.y*amag*mag;
 582                         q.z = aa.z*amag*mag;
 583                 }
 584         }
 585
 586
 587         /*
 588          * Cohen-Sutherland
 589          */
 590
 591         private static final int IN = 0;
 592         private static final int LEFT = 1;
 593         private static final int RIGHT = 2;
 594         private static final int BOTTOM = 4;
 595         private static final int TOP = 8;
 596
 597
 598         private static int bitcode(Vector2f p1, Vector2f min, Vector2f max) {
 599                 int code = IN;
 600                 if (p1.x < min.x)
 601                         code |= LEFT;
 602                 else if (p1.x > max.x)
 603                         code |= RIGHT;
 604                 if (p1.y < min.y)
 605                         code |= BOTTOM;
 606                 else if (p1.y > max.y)
 607                         code |= TOP;
 608                 return code;
 609         }
 610
 611         public static boolean clipLineRectangle(Vector2f p1,Vector2f p2, Vector2f min, Vector2f max, Vector2f r1, Vector2f r2) {
 612                 while (true) {
 613                         int o1 = bitcode(p1, min, max);
 614                         int o2 = bitcode(p2, min, max);
 615                         int and = o1 & o2;
 616                         int or = o1 | o2;
 617                         if (and != IN) {
 618                                 return false;
 619                         }
 620                         if (or == IN) {
 621                                 r1.set(p1);
 622                                 r2.set(p2);
 623                                 return true;
 624                         }
 625                         if (o1 == IN) {
 626                                 Vector2f t = p1;
 627                                 p1 = p2;
 628                                 p2 = t;
 629                                 int t2 = o1;
 630                                 o1 = o2;
 631                                 o2 = t2;
 632                         }
 633                         if ((o1 & TOP) != IN) {
 634                                 float t = (max.y - p1.y) / (p2.y - p1.y);
 635                                 p1.x += t * (p2.x - p1.x);
 636                                 p1.y = max.y;
 637                         } else if ((o1 & BOTTOM) != IN) {
 638                                 float t = (min.y - p1.y) / (p2.y - p1.y);
 639                                 p1.x += t * (p2.x - p1.x);
 640                                 p1.y = min.y;
 641                         } else if ((o1 & LEFT) != IN) {
 642                                 float t = (min.x - p1.x) / (p2.x - p1.x);
 643                                 p1.y += t * (p2.y - p1.y);
 644                                 p1.x = min.x;
 645                         } else if ((o1 & RIGHT) != IN) {
 646                                 float t = (max.x - p1.x) / (p2.x - p1.x);
 647                                 p1.y += t * (p2.y - p1.y);
 648                                 p1.x = max.x;
 649                         } else {
 650                                 throw new RuntimeException("Error in clipping code");
 651                         }
 652                 }
 653
 654         }
 655
 656         public static double square(double d) {
 657                 return d * d;
 658         }
 659
 660
 661         public static void multiplyOrientation(AxisAngle4d aa, AxisAngle4d rot)  {
 662                 Quat4d q1 = new Quat4d();
 663                 getQuat(aa, q1);
 664                 Quat4d q2 = new Quat4d();
 665                 getQuat(rot, q2);
 666                 q2.mul(q1);
 667                 rot.set(q2);
 668         }
 669
 670         public static double radToDeg(double rad) {
 671                 return (rad / Math.PI) * 180.0;
 672         }
 673
 674         public static double degToRad(double deg) {
 675                 return (deg / 180.0) * Math.PI;
 676         }
 677
 678         public static double clamp(double min, double max,double v) {
 679                 if (v < min)
 680                         return min;
 681                 if (v > max)
 682                         return max;
 683                 return v;
 684         }
 685
 686         public static AxisAngle4d createRotation(Vector3d original, Vector3d rotated) {
 687                 AxisAngle4d result = new AxisAngle4d();
 688                 if (createRotation(original, rotated, result))
 689                         return result;
 690                 return null;
 691         }
 692
 693
 694         public static void setIdentity(Quat4d q) {
 695                 q.w = 1.0;
 696                 q.x = 0.0;
 697                 q.y = 0.0;
 698                 q.z = 0.0;
 699         }
 700
 701         public static void setIdentity(AxisAngle4d aa) {
 702                 aa.angle = 0.0;
 703                 aa.x = 0.0;
 704                 aa.y = 1.0;
 705                 aa.z = 0.0;
 706         }
 707
 708         public static void set(Matrix3d mat, double m00, double m01, double m02,
 709                         double m10, double m11, double m12, double m20, double m21,
 710                         double m22) {
 711                 mat.m00 = m00;
 712                 mat.m01 = m01;
 713                 mat.m02 = m02;
 714
 715                 mat.m10 = m10;
 716                 mat.m11 = m11;
 717                 mat.m12 = m12;
 718
 719                 mat.m20 = m20;
 720                 mat.m21 = m21;
 721                 mat.m22 = m22;
 722         }
 723
 724         public static void set(Matrix4d mat, double[] v) {
 725                 mat.m00 = v[0];
 726                 mat.m01 = v[1];
 727                 mat.m02 = v[2];
 728                 mat.m03 = v[3];
 729
 730                 mat.m10 = v[4];
 731                 mat.m11 = v[5];
 732                 mat.m12 = v[6];
 733                 mat.m13 = v[7];
 734
 735                 mat.m20 = v[8];
 736                 mat.m21 = v[9];
 737                 mat.m22 = v[10];
 738                 mat.m23 = v[11];
 739
 740                 mat.m30 = v[12];
 741                 mat.m31 = v[13];
 742                 mat.m32 = v[14];
 743                 mat.m33 = v[15];
 744
 745         }
 746
 747         public static boolean createRotation(Vector3d original, Vector3d rotated, AxisAngle4d result) {
 748
 749                         if (rotated.lengthSquared() > 0.01)
 750                                 rotated.normalize();
 751                         else
 752                                 return false;
 753                         double d = original.dot(rotated);
 754                         if (d > 0.9999) {
 755                                 // original and rotated are parallel, pointing at the same direction
 756                                 result.angle = 0.0;
 757                                 result.x = 0.0;
 758                                 result.y = 1.0;
 759                                 result.z = 0.0;
 760                         } else if (d < -0.9999) {
 761                                 // original and rotated are parallel, pointing at the opposite direction
 762                                 Vector3d a = Z_AXIS;
 763                                 if (Math.abs(a.dot(original)) > 0.8 )
 764                                         a = Y_AXIS;
 765                                 result.set(a, Math.PI);
 766                         } else {
 767                                 double angle = original.angle(rotated);
 768                                 Vector3d axis = new Vector3d();
 769                                 axis.cross(original, rotated);
 770                                 result.set(axis,angle);
 771                         }
 772                         return true;
 773                 }
 774
 775         public static boolean createRotation(Vector3d original, Vector3d rotated, Quat4d result) {
 776
 777                         if (rotated.lengthSquared() > 0.01)
 778                                 rotated.normalize();
 779                         else
 780                                 return false;
 781                         double d = original.dot(rotated);
 782                         if (d > 0.9999) {
 783                                 // original and rotated are parallel, pointing at the same direction
 784                                 result.w = 1.0;
 785                                 result.x = 0.0;
 786                                 result.y = 0.0;
 787                                 result.z = 0.0;
 788                         } else if (d < -0.9999) {
 789                                 // original and rotated are parallel, pointing at the opposite direction
 790                                 Vector3d a = Z_AXIS;
 791                                 if (Math.abs(a.dot(original)) > 0.8 )
 792                                         a = Y_AXIS;
 793                                 getQuat(a, Math.PI, result);
 794
 795                         } else {
 796                                 double angle = original.angle(rotated);
 797                                 Vector3d axis = new Vector3d();
 798                                 axis.cross(original, rotated);
 799                                 getQuat(axis, angle, result);
 800                         }
 801                         return true;
 802                 }
 803
 804         public static void getQuat(Vector3d axis, double angle, Quat4d q)
 805         {
 806                 double mag,amag;
 807                 // Quat = cos(theta/2) + sin(theta/2)(roation_axis)
 808
 809                 amag = Math.sqrt( axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
 810                 if( amag < EPS ) {
 811                         q.w = 1.0;
 812                         q.x = 0.0;
 813                         q.y = 0.0;
 814                         q.z = 0.0;
 815                 } else {
 816                         amag = 1.0/amag;
 817                         double a2 = angle*0.5;
 818                         mag = Math.sin(a2);
 819                         q.w = Math.cos(a2);
 820                         q.x = axis.x*amag*mag;
 821                         q.y = axis.y*amag*mag;
 822                         q.z = axis.z*amag*mag;
 823                 }
 824
 825         }
 826
 827         /**
 828          * Linear interpolation of quaternions. Result IS set to q1.
 829          * @param q1
 830          * @param q2
 831          * @param alpha
 832          */
 833         public static void lip(Quat4d q1, Quat4d q2, double alpha) {
 834                 double s1 = 1.0 - alpha;
 835                 double s2 = alpha;
 836                 q1.scale(s1);
 837                 mad(q1,q2,s2);
 838                 q1.normalize();
 839         }
 840
 841         public static double dot(Quat4d q1, Quat4d q2) {
 842                 return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
 843         }
 844
 845         public static void mad(Tuple3d q1, Tuple3d q2, double s2) {
 846                 q1.x += q2.x * s2;
 847                 q1.y += q2.y * s2;
 848                 q1.z += q2.z * s2;
 849         }
 850
 851         public static void mad(Quat4d q1, Quat4d q2, double s2) {
 852                 q1.x += q2.x * s2;
 853                 q1.y += q2.y * s2;
 854                 q1.z += q2.z * s2;
 855                 q1.w += q2.w * s2;
 856         }
 857
 858         /**
 859          * Slerp
 860          *
 861          * Sets results to q1. Modifies q2.
 862          *
 863          * @param q1
 864          * @param q2
 865          * @param alpha
 866          */
 867         public static void sip(Quat4d q1, Quat4d q2, double alpha) {
 868                 double cosom = dot(q1,q2);
 869                 if (cosom < 0.0) {
 870                         cosom = -cosom;
 871                         q2.negate();
 872                 }
 873
 874                 if (cosom > 0.9999) {
 875                         q2.sub(q1);
 876                         q2.scale(alpha);
 877                         q1.add(q2);
 878                         q1.normalize();
 879                         return;
 880                 }
 881                 double theta_0 = Math.acos(cosom);
 882                 double theta = theta_0 * alpha;
 883                 Quat4d t = new Quat4d(q1);
 884                 t.scale(-cosom);
 885                 t.add(q2);
 886                 t.normalize();
 887                 t.scale(Math.sin(theta));
 888                 q1.scale(Math.cos(theta));
 889                 q1.add(t);
 890         }
 891
 892
 893         public static void rotate(double angle, Tuple2d v1, Tuple2d v2) {
 894                 // TODO : verify implementation
 895                 double sin = Math.sin(angle);
 896                 if (sin == 1.0) {
 897                         v2.x = v1.y;
 898                         v2.y = -v1.x;
 899                 } else if (sin == -1.0) {
 900                         v2.x = -v1.y;
 901                         v2.y = v1.x;
 902                 } else {
 903                         double cos = Math.cos(angle);
 904                         if (cos == -1.0) {
 905                                 v2.x = -v1.x;
 906                                 v2.y = -v1.y;
 907                         } else if (cos != 1.0) {
 908                                 v2.x= v1.x * cos + v1.y * -sin;
 909                                 v2.y= v1.x* sin + v1.y *cos;
 910                         }
 911                 }
 912         }
 913
 914         public static Tuple3d getPosRot(double m3x2[]) {
 915                 Vector3d t = new Vector3d();
 916                 t.x = m3x2[4];
 917                 t.y = m3x2[5];
 918
 919
 920                 Vector2d v2 = new Vector2d(1,0);
 921                 Vector2d v = new Vector2d();
 922                 // use rotation of (1,0) to calculate the rotation component
 923                 v.x  =  m3x2[0];
 924                 v.y  =  m3x2[2];
 925                 double a1 = v2.angle(v);
 926                 if (v.y < 0) {
 927                         t.z = a1;
 928                 } else {
 929                         t.z = Math.PI*2.0 - a1;
 930                 }
 931                 return t;
 932         }
 933
 934         public static Matrix4d glFrustum(double l, double r, double b, double t, double n, double f) {
 935                 Matrix4d mat = new Matrix4d();
 936                 mat.m00 = 2.0 * n / (r - l);
 937                 mat.m11 = 2.0 * n / (t - b);
 938                 mat.m02 = (r+l) / (r-l);
 939                 mat.m12 = (t+b) / (t-b);
 940                 mat.m22 = -(f+n) / (f-n);
 941                 mat.m23 = -(2.0 *f * n) / (f-n);
 942                 mat.m32 = -1.0;
 943                 return mat;
 944         }
 945
 946         public static Matrix4d glOrtho(double l, double r, double b, double t, double n, double f) {
 947                 Matrix4d mat = new Matrix4d();
 948                 mat.m00 = 2.0 / (r - l);
 949                 mat.m11 = 2.0 / (t - b);
 950                 mat.m22 = -2.0 / (f-n);
 951                 mat.m33 =  1.0;
 952                 mat.m03 = -(r+l)/(r-l);
 953                 mat.m13 = -(t+b)/(t-b);
 954                 mat.m23 = -(f+n)/(f-n);
 955                 return mat;
 956         }
 957 }