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 Vector3d projectToPlane(Vector3d v, Vector3d planeNormal) {
 151             //v.normalize();
 152             //planeNormal.normalize();
 153             Vector3d t = new Vector3d();
 154             t.cross(v,planeNormal);
 155             t.cross(planeNormal, t);
 156             return t;
 157
 158         }
 159
 160         public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Tuple3d intersectPoint) {
 161                 intersectPoint.set(planePoint);
 162                 intersectPoint.sub(linePoint);
 163                 double u = planeNormal.dot(new Vector3d(intersectPoint));
 164                 double v = planeNormal.dot(lineDir);
 165                 if (Math.abs(v) < NEAR_ZERO)
 166                         return false;
 167                 u /= v;
 168                 intersectPoint.set(lineDir);
 169                 intersectPoint.scale(u);
 170                 intersectPoint.add(linePoint);
 171                 return true;
 172         }
 173
 174         public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Vector3d intersectPoint, double[] u) {
 175                 intersectPoint.set(planePoint);
 176                 intersectPoint.sub(linePoint);
 177                 u[0] = planeNormal.dot(intersectPoint);
 178                 double v = planeNormal.dot(lineDir);
 179                 if (Math.abs(v) < NEAR_ZERO)
 180                         return false;
 181                 u[0] /= v;
 182                 intersectPoint.set(lineDir);
 183                 intersectPoint.scale(u[0]);
 184                 intersectPoint.add(linePoint);
 185                 return true;
 186         }
 187
 188         public static boolean intersectLineLine(Tuple3d l1_start,Tuple3d l1_end,Tuple3d l2_start,Tuple3d l2_end,Tuple3d l1_pos, Tuple3d l2_pos) {
 189                         Vector3d p13 = new Vector3d();
 190                         Vector3d p43 = new Vector3d();
 191                         Vector3d p21 = new Vector3d();
 192                         double d1343,d4321,d1321,d4343,d2121;
 193                         double numer,denom;
 194                         p13.sub(l1_start, l2_start);
 195                         p43.sub(l2_end,l2_start);
 196                         if (Math.abs(p43.x)  < NEAR_ZERO && Math.abs(p43.y)  < NEAR_ZERO && Math.abs(p43.z)  < NEAR_ZERO)
 197                                 return false;
 198                         p21.sub(l1_end,l1_start);
 199                         if (Math.abs(p21.x)  < NEAR_ZERO && Math.abs(p21.y)  < NEAR_ZERO && Math.abs(p21.z)  < NEAR_ZERO)
 200                                 return false;
 201
 202                         d1343 = p13.dot(p43);
 203                         d4321 = p43.dot(p21);
 204                         d1321 = p13.dot(p21);
 205                         d4343 = p43.lengthSquared();
 206                         d2121 = p21.lengthSquared();
 207
 208                         denom = d2121 * d4343 - d4321 * d4321;
 209                         if (Math.abs(denom) < NEAR_ZERO)
 210                                 return false;
 211                         numer = d1343 * d4321 - d1321 * d4343;
 212
 213                         double mua = numer / denom;
 214                         double mub = (d1343 + d4321 * mua) / d4343;
 215
 216                         l1_pos.x = l1_start.x + mua * p21.x;
 217                         l1_pos.y = l1_start.y + mua * p21.y;
 218                         l1_pos.z = l1_start.z + mua * p21.z;
 219                         l2_pos.x = l2_start.x + mub * p43.x;
 220                         l2_pos.y = l2_start.y + mub * p43.y;
 221                         l2_pos.z = l2_start.z + mub * p43.z;
 222
 223                         return true;
 224         }
 225
 226         public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb) {
 227                 Vector3d p13 = new Vector3d();
 228
 229                 double d1343,d4321,d1321,d4343,d2121;
 230                 double numer,denom;
 231
 232                 p13.sub(p1, p3);
 233                 if (Math.abs(p43.x)  < NEAR_ZERO && Math.abs(p43.y)  < NEAR_ZERO && Math.abs(p43.z)  < NEAR_ZERO)
 234                         return false;
 235                 if (Math.abs(p21.x)  < NEAR_ZERO && Math.abs(p21.y)  < NEAR_ZERO && Math.abs(p21.z)  < NEAR_ZERO)
 236                         return false;
 237
 238                 d1343 = p13.dot(p43);
 239                 d4321 = p43.dot(p21);
 240                 d1321 = p13.dot(p21);
 241                 d4343 = p43.lengthSquared();
 242                 d2121 = p21.lengthSquared();
 243
 244                 denom = d2121 * d4343 - d4321 * d4321;
 245                 if (Math.abs(denom) < NEAR_ZERO)
 246                         return false;
 247                 numer = d1343 * d4321 - d1321 * d4343;
 248
 249                 double mua = numer / denom;
 250                 double mub = (d1343 + d4321 * mua) / d4343;
 251
 252                 pa.x = p1.x + mua * p21.x;
 253                 pa.y = p1.y + mua * p21.y;
 254                 pa.z = p1.z + mua * p21.z;
 255                 pb.x = p3.x + mub * p43.x;
 256                 pb.y = p3.y + mub * p43.y;
 257                 pb.z = p3.z + mub * p43.z;
 258
 259                 return true;
 260         }
 261
 262         /**
 263          * Calculate the line segment PaPb that is the shortest route between
 264          *  two lines P1P2 and P3P4. Calculate also the values of mua and mub where
 265          *  Pa = P1 + mua (P2 - P1)
 266          *  Pb = P3 + mub (P4 - P3)
 267          * @param p1
 268          * @param p21
 269          * @param p3
 270          * @param p43
 271          * @param pa
 272          * @param pb
 273          * @param mu
 274          * @return
 275          */
 276         public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb, double mu[]) {
 277                 Vector3d p13 = new Vector3d();
 278
 279                 double d1343,d4321,d1321,d4343,d2121;
 280                 double numer,denom;
 281                 double EPS = 0.001;
 282                 p13.sub(p1, p3);
 283                 if (Math.abs(p43.x)  < EPS && Math.abs(p43.y)  < EPS && Math.abs(p43.z)  < EPS)
 284                         return false;
 285                 if (Math.abs(p21.x)  < EPS && Math.abs(p21.y)  < EPS && Math.abs(p21.z)  < EPS)
 286                         return false;
 287
 288                 d1343 = p13.dot(p43);
 289                 d4321 = p43.dot(p21);
 290                 d1321 = p13.dot(p21);
 291                 d4343 = p43.lengthSquared();
 292                 d2121 = p21.lengthSquared();
 293
 294                 denom = d2121 * d4343 - d4321 * d4321;
 295                 if (Math.abs(denom) < EPS)
 296                         return false;
 297                 numer = d1343 * d4321 - d1321 * d4343;
 298
 299                 mu[0] = numer / denom;
 300                 mu[1] = (d1343 + d4321 * mu[0]) / d4343;
 301
 302                 pa.x = p1.x + mu[0] * p21.x;
 303                 pa.y = p1.y + mu[0] * p21.y;
 304                 pa.z = p1.z + mu[0] * p21.z;
 305                 pb.x = p3.x + mu[1] * p43.x;
 306                 pb.y = p3.y + mu[1] * p43.y;
 307                 pb.z = p3.z + mu[1] * p43.z;
 308
 309                 return true;
 310         }
 311
 312
 313
 314         public static void rotate(Quat4d q, Tuple3d in, Tuple3d out) {
 315                 // p' = q * p * q'
 316                 double tw =             - q.x*in.x - q.y*in.y - q.z*in.z;
 317                 double tx =  q.w*in.x            + q.y*in.z - q.z*in.y;
 318                 double ty =  q.w*in.y - q.x*in.z            + q.z*in.x;
 319                 double tz =  q.w*in.z + q.x*in.y - q.y*in.x           ;
 320
 321                 //temp * q' -> x = -x, y = -y z = -z
 322                 //out.w = tw*q.w + tx*q.x + ty*q.y + tz*q.z;
 323                 out.x =  -tw*q.x + tx*q.w - ty*q.z + tz*q.y;
 324                 out.y =  -tw*q.y + tx*q.z + ty*q.w - tz*q.x;
 325                 out.z =  -tw*q.z - tx*q.y + ty*q.x + tz*q.w;
 326         }
 327
 328         public static void getMatrix(Quat4d quat, Matrix3d m) {
 329                         m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
 330                         m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
 331                         m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
 332                         m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
 333                         m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
 334                         m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
 335                         m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
 336                         m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
 337                         m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
 338
 339         }
 340
 341         public static void getMatrix(Quat4d quat, Matrix4d m) {
 342                 m.setZero();
 343                 m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
 344                 m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
 345                 m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
 346                 m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
 347                 m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
 348                 m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
 349                 m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
 350                 m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
 351                 m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
 352                 m.m33 = 1.0;
 353         }
 354
 355         private static double q[] = new double[3];
 356         private static int nxt[] = { 1, 2, 0 };
 357         /**
 358          * Converts Matrix to Quaternion
 359          *
 360          * Note: non-thread safe.
 361          *
 362          * @param mat
 363          * @param quat
 364          */
 365         public static void getQuat(Matrix3d mat, Quat4d quat) {
 366                 double tr = mat.m00 + mat.m11 + mat.m22;
 367                 if (tr > 0.0) {
 368                         double s = Math.sqrt(tr + 1.0);
 369                         quat.w = 0.5 * s;
 370                         s = 0.5 / s;
 371                         quat.x = (mat.m21 - mat.m12) * s;
 372                         quat.y = (mat.m02 - mat.m20) * s;
 373                         quat.z = (mat.m10 - mat.m01) * s;
 374                 } else {
 375                         int i = 0, j, k;
 376                         if (mat.m11 > mat.m00)
 377                                 i = 1;
 378                         if (mat.m22 > mat.getElement(i, i))
 379                                 i = 2;
 380
 381
 382                         j = nxt[i];
 383                         k = nxt[j];
 384
 385                         double s = Math.sqrt((mat.getElement(i, i) - (mat.getElement(j, j) + mat.getElement(k, k))) + 1.0);
 386
 387                         q[i] = s * 0.5;
 388
 389                         if (Math.abs(s) > 0.001)
 390                                 s = 0.5 / s;
 391
 392                         quat.w = (mat.getElement(k, j) - mat.getElement(j, k)) * s;
 393                         q[j] = (mat.getElement(j, i) + mat.getElement(i, j)) * s;
 394                         q[k] = (mat.getElement(k, i) + mat.getElement(i, k)) * s;
 395
 396                         quat.x = q[0];
 397                         quat.y = q[1];
 398                         quat.z = q[2];
 399                 }
 400         }
 401
 402         public static Quat4d getQuat(Matrix3d mat) {
 403                 Quat4d q = new Quat4d();
 404                 getQuat(mat, q);
 405                 return q;
 406         }
 407
 408         public static AxisAngle4d getFromPseudoEuler(Vector3d euler) {
 409                 AxisAngle4d aa = new AxisAngle4d();
 410                 aa.angle = euler.length();
 411                 Vector3d normal = new Vector3d(euler);
 412                 if (aa.angle > NEAR_ZERO) {
 413                         normal.normalize();
 414                         aa.x = normal.x;
 415                         aa.y = normal.y;
 416                         aa.z = normal.z;
 417                 } else {
 418                         aa.x = 1.0;
 419                         aa.y = 0.0;
 420                         aa.z = 0.0;
 421                 }
 422
 423                 return aa;
 424         }
 425
 426         public static Vector3d getPseudoEuler(AxisAngle4d aa) {
 427                 Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);
 428                 euler.scale(aa.angle);
 429                 return euler;
 430         }
 431
 432
 433         public static void getQuat(Vector3d euler, Quat4d quat)  {
 434                 Quat4d q = EulerTools.getQuatFromEuler(Order.YXZ, euler.y,euler.x,euler.z);
 435                 quat.set(q);
 436         // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
 437         // Using the x-convention, the 3-1-3 Euler angles phi, theta and psi (around the Z, X and again the Z-axis)
 438 //         quat.x = -Math.cos((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
 439 //         quat.y = -Math.sin((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
 440 //         quat.z = -Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
 441 //         quat.w = Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
 442
 443                 // http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
 444                 // Y, Z, X order
 445 //          double c1 = Math.cos(euler.y*0.5);
 446 //          double s1 = Math.sin(euler.y*0.5);
 447 //          double c2 = Math.cos(euler.z*0.5);
 448 //          double s2 = Math.sin(euler.z*0.5);
 449 //          double c3 = Math.cos(euler.x*0.5);
 450 //          double s3 = Math.sin(euler.x*0.5);
 451 //          double c1c2 = c1*c2;
 452 //          double s1s2 = s1*s2;
 453 //          quat.w =c1c2*c3 - s1s2*s3;
 454 //          quat.x =c1c2*s3 + s1s2*c3;
 455 //          quat.y =s1*c2*c3 + c1*s2*s3;
 456 //          quat.z =c1*s2*c3 - s1*c2*s3;
 457
 458 //          Quat4d q2 = EulerTools.getQuatFromEuler(Order.YZX, euler.y,euler.z,euler.x);
 459 //          System.out.println("Q " + quat + " Q2 " + q2);
 460 //         double c1 = Math.cos(euler.y);
 461 //          double s1 = Math.sin(euler.y);
 462 //          double c2 = Math.cos(euler.z);
 463 //          double s2 = Math.sin(euler.z);
 464 //          double c3 = Math.cos(euler.x);
 465 //          double s3 = Math.sin(euler.x);
 466 //          quat.w = Math.sqrt(1.0 + c1 * c2 + c1*c3 - s1 * s2 * s3 + c2*c3) / 2.0;
 467 //          double w4 = (4.0 * quat.w);
 468 //          quat.x = (c2 * s3 + c1 * s3 + s1 * s2 * c3) / w4 ;
 469 //          quat.y = (s1 * c2 + s1 * c3 + c1 * s2 * s3) / w4 ;
 470 //          quat.z = (-s1 * s3 + c1 * s2 * c3 +s2) / w4 ;
 471         }
 472
 473
 474
 475
 476         public static void getEuler(Quat4d quat,Vector3d euler)  {
 477                 Vector3d e = EulerTools.getEulerFromQuat(Order.YXZ, quat);
 478                 euler.x = e.y;
 479                 euler.y = e.x;
 480                 euler.z = e.z;
 481
 482                 // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
 483 //         euler.x = Math.atan2(quat.x * quat.z + quat.y* quat.w, quat.y*quat.z - quat.x * quat.w);
 484 //         euler.y = Math.acos(-square(quat.x) - square(quat.y) + square(quat.z) + square(quat.w));
 485 //         euler.z = -Math.atan2(quat.x * quat.z - quat.y* quat.w, quat.y*quat.z + quat.x * quat.w);
 486
 487                 // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm
 488         // Y, Z, X order
 489 //         double test = quat.x * quat.y + quat.z * quat.w;
 490 //         if (test > NEAR_HALF) {
 491 //                 euler.y = 2.0 * Math.atan2(quat.x,quat.w);
 492 //                 euler.z = Math.PI * 0.5;
 493 //                 euler.x = 0.0;
 494 //         } else if (test < -NEAR_HALF) {
 495 //                 euler.y = -2.0 * Math.atan2(quat.x,quat.w);
 496 //                 euler.z = -Math.PI * 0.5;
 497 //                 euler.x = 0.0;
 498 //         } else {
 499 //                 double sqx = square(quat.x);
 500 //                 double sqy = square(quat.y);
 501 //                 double sqz = square(quat.z);
 502 //                 euler.y = Math.atan2(2.0*(quat.y*quat.w-quat.x*quat.z), 1.0 - 2.0*(sqy-sqz));
 503 //                 euler.z = Math.asin(2.0*test);
 504 //                 euler.x = Math.atan2(2.0*(quat.x*quat.w-quat.y*quat.z), 1.0 - 2.0*(sqx-sqz));
 505 //                 System.out.println(euler + " " + EulerTools.getEulerFromQuat(Order.YXZ, quat) +  " " + quat);
 506 //         }
 507 //         double sqw = quat.w*quat.w;
 508 //          double sqx = quat.x*quat.x;
 509 //          double sqy = quat.y*quat.y;
 510 //          double sqz = quat.z*quat.z;
 511 //              double unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor
 512 //              double test = quat.x*quat.y + quat.z*quat.w;
 513 //              if (test > 0.499*unit) { // singularity at north pole
 514 //                      euler.y = 2 * Math.atan2(quat.x,quat.w);
 515 //                      euler.z = Math.PI/2;
 516 //                      euler.x = 0;
 517 //                      return;
 518 //              }
 519 //              if (test < -0.499*unit) { // singularity at south pole
 520 //                      euler.y = -2 * Math.atan2(quat.x,quat.w);
 521 //                      euler.z = -Math.PI/2;
 522 //                      euler.x = 0;
 523 //                      return;
 524 //              }
 525 //              euler.y = Math.atan2(2*quat.y*quat.w-2*quat.x*quat.z , sqx - sqy - sqz + sqw);
 526 //              euler.z = Math.asin(2*test/unit);
 527 //              euler.x = Math.atan2(2*quat.x*quat.w-2*quat.y*quat.z , -sqx + sqy - sqz + sqw);
 528         }
 529
 530         public static Quat4d getQuat(Vector3d euler) {
 531                 Quat4d q = new Quat4d();
 532                 getQuat(euler,q);
 533                 return q;
 534         }
 535
 536
 537         public static Vector3d getEuler(Quat4d quat) {
 538                 Vector3d v = new Vector3d();
 539                 getEuler(quat, v);
 540                 return v;
 541         }
 542
 543         public static Quat4d getQuat(AxisAngle4d aa) {
 544                 Quat4d q = new Quat4d();
 545                 getQuat(aa, q);
 546                 return q;
 547         }
 548
 549         public static AxisAngle4d getAxisAngle(Quat4d q) {
 550                 AxisAngle4d aa = new AxisAngle4d();
 551                 double mag = q.x * q.x + q.y * q.y + q.z * q.z;
 552
 553                 if (mag > EPS) {
 554                         mag = Math.sqrt(mag);
 555                         aa.angle = 2.0 * Math.atan2(mag, q.w);
 556                         mag = 1.0 / mag;
 557                         aa.x = q.x * mag;
 558                         aa.y = q.y * mag;
 559                         aa.z = q.z * mag;
 560
 561                 } else {
 562                         aa.x = 0.0;
 563                         aa.y = 1.0;
 564                         aa.z = 0.0;
 565                         aa.angle = 0.0;
 566                 }
 567                 // aa.set(q);
 568                 return aa;
 569         }
 570
 571         public static Quat4d getIdentityQuat() {
 572                 return new Quat4d(0, 0, 0, 1);
 573         }
 574
 575         public static void getQuat(AxisAngle4d aa, Quat4d q) {
 576                 double mag,amag;
 577                 // Quat = cos(theta/2) + sin(theta/2)(roation_axis)
 578
 579                 amag = Math.sqrt( aa.x*aa.x + aa.y*aa.y + aa.z*aa.z);
 580                 if( amag < NEAR_ZERO ) {
 581                         q.w = 1.0;
 582                         q.x = 0.0;
 583                         q.y = 0.0;
 584                         q.z = 0.0;
 585                 } else {
 586                         amag = 1.0/amag;
 587                         double a2 = aa.angle * 0.5;
 588                         mag = Math.sin(a2);
 589                         q.w = Math.cos(a2);
 590                         q.x = aa.x*amag*mag;
 591                         q.y = aa.y*amag*mag;
 592                         q.z = aa.z*amag*mag;
 593                 }
 594         }
 595
 596
 597         /*
 598          * Cohen-Sutherland
 599          */
 600
 601         private static final int IN = 0;
 602         private static final int LEFT = 1;
 603         private static final int RIGHT = 2;
 604         private static final int BOTTOM = 4;
 605         private static final int TOP = 8;
 606
 607
 608         private static int bitcode(Vector2f p1, Vector2f min, Vector2f max) {
 609                 int code = IN;
 610                 if (p1.x < min.x)
 611                         code |= LEFT;
 612                 else if (p1.x > max.x)
 613                         code |= RIGHT;
 614                 if (p1.y < min.y)
 615                         code |= BOTTOM;
 616                 else if (p1.y > max.y)
 617                         code |= TOP;
 618                 return code;
 619         }
 620
 621         public static boolean clipLineRectangle(Vector2f p1,Vector2f p2, Vector2f min, Vector2f max, Vector2f r1, Vector2f r2) {
 622                 while (true) {
 623                         int o1 = bitcode(p1, min, max);
 624                         int o2 = bitcode(p2, min, max);
 625                         int and = o1 & o2;
 626                         int or = o1 | o2;
 627                         if (and != IN) {
 628                                 return false;
 629                         }
 630                         if (or == IN) {
 631                                 r1.set(p1);
 632                                 r2.set(p2);
 633                                 return true;
 634                         }
 635                         if (o1 == IN) {
 636                                 Vector2f t = p1;
 637                                 p1 = p2;
 638                                 p2 = t;
 639                                 int t2 = o1;
 640                                 o1 = o2;
 641                                 o2 = t2;
 642                         }
 643                         if ((o1 & TOP) != IN) {
 644                                 float t = (max.y - p1.y) / (p2.y - p1.y);
 645                                 p1.x += t * (p2.x - p1.x);
 646                                 p1.y = max.y;
 647                         } else if ((o1 & BOTTOM) != IN) {
 648                                 float t = (min.y - p1.y) / (p2.y - p1.y);
 649                                 p1.x += t * (p2.x - p1.x);
 650                                 p1.y = min.y;
 651                         } else if ((o1 & LEFT) != IN) {
 652                                 float t = (min.x - p1.x) / (p2.x - p1.x);
 653                                 p1.y += t * (p2.y - p1.y);
 654                                 p1.x = min.x;
 655                         } else if ((o1 & RIGHT) != IN) {
 656                                 float t = (max.x - p1.x) / (p2.x - p1.x);
 657                                 p1.y += t * (p2.y - p1.y);
 658                                 p1.x = max.x;
 659                         } else {
 660                                 throw new RuntimeException("Error in clipping code");
 661                         }
 662                 }
 663
 664         }
 665
 666         public static double square(double d) {
 667                 return d * d;
 668         }
 669
 670
 671         public static void multiplyOrientation(AxisAngle4d aa, AxisAngle4d rot)  {
 672                 Quat4d q1 = new Quat4d();
 673                 getQuat(aa, q1);
 674                 Quat4d q2 = new Quat4d();
 675                 getQuat(rot, q2);
 676                 q2.mul(q1);
 677                 rot.set(q2);
 678         }
 679
 680         public static double radToDeg(double rad) {
 681                 return (rad / Math.PI) * 180.0;
 682         }
 683
 684         public static double degToRad(double deg) {
 685                 return (deg / 180.0) * Math.PI;
 686         }
 687
 688         public static double clamp(double min, double max,double v) {
 689                 if (v < min)
 690                         return min;
 691                 if (v > max)
 692                         return max;
 693                 return v;
 694         }
 695
 696         public static AxisAngle4d createRotation(Vector3d original, Vector3d rotated) {
 697                 AxisAngle4d result = new AxisAngle4d();
 698                 if (createRotation(original, rotated, result))
 699                         return result;
 700                 return null;
 701         }
 702
 703
 704         public static void setIdentity(Quat4d q) {
 705                 q.w = 1.0;
 706                 q.x = 0.0;
 707                 q.y = 0.0;
 708                 q.z = 0.0;
 709         }
 710
 711         public static void setIdentity(AxisAngle4d aa) {
 712                 aa.angle = 0.0;
 713                 aa.x = 0.0;
 714                 aa.y = 1.0;
 715                 aa.z = 0.0;
 716         }
 717
 718         public static void set(Matrix3d mat, double m00, double m01, double m02,
 719                         double m10, double m11, double m12, double m20, double m21,
 720                         double m22) {
 721                 mat.m00 = m00;
 722                 mat.m01 = m01;
 723                 mat.m02 = m02;
 724
 725                 mat.m10 = m10;
 726                 mat.m11 = m11;
 727                 mat.m12 = m12;
 728
 729                 mat.m20 = m20;
 730                 mat.m21 = m21;
 731                 mat.m22 = m22;
 732         }
 733
 734         public static void set(Matrix4d mat, double[] v) {
 735                 mat.m00 = v[0];
 736                 mat.m01 = v[1];
 737                 mat.m02 = v[2];
 738                 mat.m03 = v[3];
 739
 740                 mat.m10 = v[4];
 741                 mat.m11 = v[5];
 742                 mat.m12 = v[6];
 743                 mat.m13 = v[7];
 744
 745                 mat.m20 = v[8];
 746                 mat.m21 = v[9];
 747                 mat.m22 = v[10];
 748                 mat.m23 = v[11];
 749
 750                 mat.m30 = v[12];
 751                 mat.m31 = v[13];
 752                 mat.m32 = v[14];
 753                 mat.m33 = v[15];
 754
 755         }
 756
 757         public static boolean createRotation(Vector3d original, Vector3d rotated, AxisAngle4d result) {
 758
 759                 if (rotated.lengthSquared() > 0.01)
 760                         rotated.normalize();
 761                 else
 762                         return false;
 763                 double d = original.dot(rotated);
 764                 if (d > 0.9999) {
 765                         // original and rotated are parallel, pointing at the same direction
 766                         result.angle = 0.0;
 767                         result.x = 0.0;
 768                         result.y = 1.0;
 769                         result.z = 0.0;
 770                 } else if (d < -0.9999) {
 771                         // original and rotated are parallel, pointing at the opposite direction
 772                         Vector3d a = Z_AXIS;
 773                         if (Math.abs(a.dot(original)) > 0.8 )
 774                                 a = Y_AXIS;
 775                         result.set(a, Math.PI);
 776                 } else {
 777                         double angle = original.angle(rotated);
 778                         Vector3d axis = new Vector3d();
 779                         axis.cross(original, rotated);
 780                         result.set(axis,angle);
 781                 }
 782                 return true;
 783         }
 784
 785         public static boolean createRotation(Vector3d original, Vector3d rotated, Quat4d result) {
 786
 787                 if (rotated.lengthSquared() > 0.01)
 788                         rotated.normalize();
 789                 else
 790                         return false;
 791                 double d = original.dot(rotated);
 792                 if (d > 0.9999) {
 793                         // original and rotated are parallel, pointing at the same direction
 794                         result.w = 1.0;
 795                         result.x = 0.0;
 796                         result.y = 0.0;
 797                         result.z = 0.0;
 798                 } else if (d < -0.9999) {
 799                         // original and rotated are parallel, pointing at the opposite direction
 800                         Vector3d a = Z_AXIS;
 801                         if (Math.abs(a.dot(original)) > 0.8 )
 802                                 a = Y_AXIS;
 803                         getQuat(a, Math.PI, result);
 804
 805                 } else {
 806                         double angle = original.angle(rotated);
 807                         Vector3d axis = new Vector3d();
 808                         axis.cross(original, rotated);
 809                         getQuat(axis, angle, result);
 810                 }
 811                 return true;
 812         }
 813
 814         public static boolean createRotation(Vector3d original, Vector3d rotated, Vector3d axis, AxisAngle4d result) {
 815
 816         if (rotated.lengthSquared() > 0.01)
 817             rotated.normalize();
 818         else
 819             return false;
 820         if (original.lengthSquared() > 0.01)
 821             original.normalize();
 822         else
 823             return false;
 824         if (axis.lengthSquared() > 0.01)
 825             axis.normalize();
 826         else
 827             return false;
 828         double d = original.dot(rotated);
 829         if (d > 0.9999) {
 830             // original and rotated are parallel, pointing at the same direction
 831             result.angle = 0.0;
 832             result.x = axis.x;
 833             result.y = axis.y;
 834             result.z = axis.z;
 835         } else if (d < -0.9999) {
 836             // original and rotated are parallel, pointing at the opposite direction
 837             result.angle = Math.PI;
 838             result.x = axis.x;
 839             result.y = axis.y;
 840             result.z = axis.z;
 841         } else {
 842             // Project vectors to Axis plane
 843             Vector3d p1 = projectToPlane(original, axis);
 844             Vector3d p2 = projectToPlane(rotated, axis);
 845             // Create vectors where z-axis is plane normal
 846             Quat4d q = getQuat(createRotation(axis, Z_AXIS));
 847             Vector3d t1 = new Vector3d();
 848             Vector3d t2 = new Vector3d();
 849             rotate(q, p1, t1);
 850             rotate(q, p2, t2);
 851             // Calculate angles on z-axis plane.
 852             double a1 = Math.atan2(t1.y, t1.x);
 853             double a2 = Math.atan2(t2.y, t2.x);
 854             result.set(axis,a2-a1);
 855
 856         }
 857         return true;
 858     }
 859
 860         public static void getQuat(Vector3d axis, double angle, Quat4d q)
 861         {
 862                 double mag,amag;
 863                 // Quat = cos(theta/2) + sin(theta/2)(roation_axis)
 864
 865                 amag = Math.sqrt( axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
 866                 if( amag < EPS ) {
 867                         q.w = 1.0;
 868                         q.x = 0.0;
 869                         q.y = 0.0;
 870                         q.z = 0.0;
 871                 } else {
 872                         amag = 1.0/amag;
 873                         double a2 = angle*0.5;
 874                         mag = Math.sin(a2);
 875                         q.w = Math.cos(a2);
 876                         q.x = axis.x*amag*mag;
 877                         q.y = axis.y*amag*mag;
 878                         q.z = axis.z*amag*mag;
 879                 }
 880
 881         }
 882
 883         /**
 884          * Linear interpolation of quaternions. Result IS set to q1.
 885          * @param q1
 886          * @param q2
 887          * @param alpha
 888          */
 889         public static void lip(Quat4d q1, Quat4d q2, double alpha) {
 890                 double s1 = 1.0 - alpha;
 891                 double s2 = alpha;
 892                 q1.scale(s1);
 893                 mad(q1,q2,s2);
 894                 q1.normalize();
 895         }
 896
 897         public static double dot(Quat4d q1, Quat4d q2) {
 898                 return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
 899         }
 900
 901         public static void mad(Tuple3d q1, Tuple3d q2, double s2) {
 902                 q1.x += q2.x * s2;
 903                 q1.y += q2.y * s2;
 904                 q1.z += q2.z * s2;
 905         }
 906
 907         public static void mad(Quat4d q1, Quat4d q2, double s2) {
 908                 q1.x += q2.x * s2;
 909                 q1.y += q2.y * s2;
 910                 q1.z += q2.z * s2;
 911                 q1.w += q2.w * s2;
 912         }
 913
 914         /**
 915          * Slerp
 916          *
 917          * Sets results to q1. Modifies q2.
 918          *
 919          * @param q1
 920          * @param q2
 921          * @param alpha
 922          */
 923         public static void sip(Quat4d q1, Quat4d q2, double alpha) {
 924                 double cosom = dot(q1,q2);
 925                 if (cosom < 0.0) {
 926                         cosom = -cosom;
 927                         q2.negate();
 928                 }
 929
 930                 if (cosom > 0.9999) {
 931                         q2.sub(q1);
 932                         q2.scale(alpha);
 933                         q1.add(q2);
 934                         q1.normalize();
 935                         return;
 936                 }
 937                 double theta_0 = Math.acos(cosom);
 938                 double theta = theta_0 * alpha;
 939                 Quat4d t = new Quat4d(q1);
 940                 t.scale(-cosom);
 941                 t.add(q2);
 942                 t.normalize();
 943                 t.scale(Math.sin(theta));
 944                 q1.scale(Math.cos(theta));
 945                 q1.add(t);
 946         }
 947
 948
 949         public static void rotate(double angle, Tuple2d v1, Tuple2d v2) {
 950                 // TODO : verify implementation
 951                 double sin = Math.sin(angle);
 952                 if (sin == 1.0) {
 953                         v2.x = v1.y;
 954                         v2.y = -v1.x;
 955                 } else if (sin == -1.0) {
 956                         v2.x = -v1.y;
 957                         v2.y = v1.x;
 958                 } else {
 959                         double cos = Math.cos(angle);
 960                         if (cos == -1.0) {
 961                                 v2.x = -v1.x;
 962                                 v2.y = -v1.y;
 963                         } else if (cos != 1.0) {
 964                                 v2.x= v1.x * cos + v1.y * -sin;
 965                                 v2.y= v1.x* sin + v1.y *cos;
 966                         }
 967                 }
 968         }
 969
 970         public static Tuple3d getPosRot(double m3x2[]) {
 971                 Vector3d t = new Vector3d();
 972                 t.x = m3x2[4];
 973                 t.y = m3x2[5];
 974
 975
 976                 Vector2d v2 = new Vector2d(1,0);
 977                 Vector2d v = new Vector2d();
 978                 // use rotation of (1,0) to calculate the rotation component
 979                 v.x  =  m3x2[0];
 980                 v.y  =  m3x2[2];
 981                 double a1 = v2.angle(v);
 982                 if (v.y < 0) {
 983                         t.z = a1;
 984                 } else {
 985                         t.z = Math.PI*2.0 - a1;
 986                 }
 987                 return t;
 988         }
 989
 990         public static Matrix4d glFrustum(double l, double r, double b, double t, double n, double f) {
 991                 Matrix4d mat = new Matrix4d();
 992                 mat.m00 = 2.0 * n / (r - l);
 993                 mat.m11 = 2.0 * n / (t - b);
 994                 mat.m02 = (r+l) / (r-l);
 995                 mat.m12 = (t+b) / (t-b);
 996                 mat.m22 = -(f+n) / (f-n);
 997                 mat.m23 = -(2.0 *f * n) / (f-n);
 998                 mat.m32 = -1.0;
 999                 return mat;
1000         }
1001
1002         public static Matrix4d glOrtho(double l, double r, double b, double t, double n, double f) {
1003                 Matrix4d mat = new Matrix4d();
1004                 mat.m00 = 2.0 / (r - l);
1005                 mat.m11 = 2.0 / (t - b);
1006                 mat.m22 = -2.0 / (f-n);
1007                 mat.m33 =  1.0;
1008                 mat.m03 = -(r+l)/(r-l);
1009                 mat.m13 = -(t+b)/(t-b);
1010                 mat.m23 = -(f+n)/(f-n);
1011                 return mat;
1012         }
1013 }