Distorted Android

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2023 Leszek Koltunski  leszek@koltunski.pl                                          //

//                                                                                               //

// This file is part of Distorted.                                                               //

//                                                                                               //

// 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 Street, Fifth Floor, Boston, MA  02110-1301  USA                //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.library.helpers;

///////////////////////////////////////////////////////////////////////////////////////////////////

public class MatrixHelper

  {

  public static void setIdentity(float[] output)

    {

    output[ 0] = 1;

    output[ 1] = 0;

    output[ 2] = 0;

    output[ 3] = 0;

    output[ 4] = 0;

    output[ 5] = 1;

    output[ 6] = 0;

    output[ 7] = 0;

    output[ 8] = 0;

    output[ 9] = 0;

    output[10] = 1;

    output[11] = 0;

    output[12] = 0;

    output[13] = 0;

    output[14] = 0;

    output[15] = 1;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void multiply(float[] output, float[] m1, float[] m2)

    {

    output[ 0] = m1[ 0]*m2[ 0] + m1[ 4]*m2[ 1] + m1[ 8]*m2[ 2] + m1[12]*m2[ 3];

    output[ 1] = m1[ 1]*m2[ 0] + m1[ 5]*m2[ 1] + m1[ 9]*m2[ 2] + m1[13]*m2[ 3];

    output[ 2] = m1[ 2]*m2[ 0] + m1[ 6]*m2[ 1] + m1[10]*m2[ 2] + m1[14]*m2[ 3];

    output[ 3] = m1[ 3]*m2[ 0] + m1[ 7]*m2[ 1] + m1[11]*m2[ 2] + m1[15]*m2[ 3];

    output[ 4] = m1[ 0]*m2[ 4] + m1[ 4]*m2[ 5] + m1[ 8]*m2[ 6] + m1[12]*m2[ 7];

    output[ 5] = m1[ 1]*m2[ 4] + m1[ 5]*m2[ 5] + m1[ 9]*m2[ 6] + m1[13]*m2[ 7];

    output[ 6] = m1[ 2]*m2[ 4] + m1[ 6]*m2[ 5] + m1[10]*m2[ 6] + m1[14]*m2[ 7];

    output[ 7] = m1[ 3]*m2[ 4] + m1[ 7]*m2[ 5] + m1[11]*m2[ 6] + m1[15]*m2[ 7];

    output[ 8] = m1[ 0]*m2[ 8] + m1[ 4]*m2[ 9] + m1[ 8]*m2[10] + m1[12]*m2[11];

    output[ 9] = m1[ 1]*m2[ 8] + m1[ 5]*m2[ 9] + m1[ 9]*m2[10] + m1[13]*m2[11];

    output[10] = m1[ 2]*m2[ 8] + m1[ 6]*m2[ 9] + m1[10]*m2[10] + m1[14]*m2[11];

    output[11] = m1[ 3]*m2[ 8] + m1[ 7]*m2[ 9] + m1[11]*m2[10] + m1[15]*m2[11];

    output[12] = m1[ 0]*m2[12] + m1[ 4]*m2[13] + m1[ 8]*m2[14] + m1[12]*m2[15];

    output[13] = m1[ 1]*m2[12] + m1[ 5]*m2[13] + m1[ 9]*m2[14] + m1[13]*m2[15];

    output[14] = m1[ 2]*m2[12] + m1[ 6]*m2[13] + m1[10]*m2[14] + m1[14]*m2[15];

    output[15] = m1[ 3]*m2[12] + m1[ 7]*m2[13] + m1[11]*m2[14] + m1[15]*m2[15];

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void frustum(float[] output, float l, float r, float b, float t, float n, float f)

    {

    output[0]  =  2 * n / (r - l);

    output[1]  =  0;

    output[2]  =  0;

    output[3]  =  0;

    output[4]  =  0;

    output[5]  =  2 * n / (t - b);

    output[6]  =  0;

    output[7]  =  0;

    output[8]  =  (r + l) / (r - l);

    output[9]  =  (t + b) / (t - b);

    output[10] = -(f + n) / (f - n);

    output[11] = -1;

    output[12] =  0;

    output[13] =  0;

    output[14] = -(2 * f * n) / (f - n);

    output[15] =  0;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void ortho(float[] output, float l, float r, float b, float t, float n, float f)

    {

    output[0]  =  2 / (r - l);

    output[1]  =  0;

    output[2]  =  0;

    output[3]  =  0;

    output[4]  =  0;

    output[5]  =  2 / (t - b);

    output[6]  =  0;

    output[7]  =  0;

    output[8]  =  0;

    output[9]  =  0;

    output[10] = -2 / (f - n);

    output[11] =  0;

    output[12] = -(r + l) / (r - l);

    output[13] = -(t + b) / (t - b);

    output[14] = -(f + n) / (f - n);

    output[15] =  1;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void setLookAt(float[] output, float eyeX , float eyeY , float eyeZ ,

                                               float lookX, float lookY, float lookZ,

                                               float upX  , float upY  , float upZ  )

    {

    // TODO

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// this is android.opengl.Matrix.rotateM(), but with pre-computed sin and cos of the angle

// and also we have to pre-allocate and pass here two temp arrays.

  public static void rotateSinCos(float[] output, float[] tmp1, float[] tmp2, float sin, float cos, float x, float y, float z)

    {

    tmp1[0]  = (1-cos)*x*x + cos;

    tmp1[1]  = (1-cos)*x*y + sin*z;

    tmp1[2]  = (1-cos)*x*z - sin*y;

    tmp1[3]  = 0;

    tmp1[4]  = (1-cos)*x*y - sin*z;

    tmp1[5]  = (1-cos)*y*y + cos;

    tmp1[6]  = (1-cos)*y*z + sin*x;

    tmp1[7]  = 0;

    tmp1[8]  = (1-cos)*x*z + sin*y;

    tmp1[9]  = (1-cos)*y*z - sin*x;

    tmp1[10] = (1-cos)*z*z + cos;

    tmp1[11] = 0;

    tmp1[12] = 0;

    tmp1[13] = 0;

    tmp1[14] = 0;

    tmp1[15] = 1;

    tmp2[0]  =  output[ 0];

    tmp2[1]  =  output[ 1];

    tmp2[2]  =  output[ 2];

    tmp2[3]  =  output[ 3];

    tmp2[4]  =  output[ 4];

    tmp2[5]  =  output[ 5];

    tmp2[6]  =  output[ 6];

    tmp2[7]  =  output[ 7];

    tmp2[8]  =  output[ 8];

    tmp2[9]  =  output[ 9];

    tmp2[10] =  output[10];

    tmp2[11] =  output[11];

    tmp2[12] =  output[12];

    tmp2[13] =  output[13];

    tmp2[14] =  output[14];

    tmp2[15] =  output[15];

    multiply(output,tmp2,tmp1);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void translate(float[] output, float dx, float dy, float dz)

    {

    output[12] += ( output[ 0]*dx + output[ 4]*dy + output[ 8]*dz);

    output[13] += ( output[ 1]*dx + output[ 5]*dy + output[ 9]*dz);

    output[14] += ( output[ 2]*dx + output[ 6]*dy + output[10]*dz);

    output[15] += ( output[ 3]*dx + output[ 7]*dy + output[11]*dz);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static void scale(float[] output, float sx, float sy, float sz)

    {

    output[ 0] *= sx;

    output[ 1] *= sx;

    output[ 2] *= sx;

    output[ 3] *= sx;

    output[ 4] *= sy;

    output[ 5] *= sy;

    output[ 6] *= sy;

    output[ 7] *= sy;

    output[ 8] *= sz;

    output[ 9] *= sz;

    output[10] *= sz;

    output[11] *= sz;

    }

  }

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2021 Leszek Koltunski  leszek@koltunski.pl                                          //

//                                                                                               //

// This file is part of Distorted.                                                               //

//                                                                                               //

// 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 Street, Fifth Floor, Boston, MA  02110-1301  USA                //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.library.helpers;

import org.distorted.library.type.Static4D;

///////////////////////////////////////////////////////////////////////////////////////////////////

public class QuatHelper

  {

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat1*quat2

  public static Static4D quatMultiply( Static4D quat1, Static4D quat2 )

    {

    float qx = quat1.get0();

    float qy = quat1.get1();

    float qz = quat1.get2();

    float qw = quat1.get3();

    float rx = quat2.get0();

    float ry = quat2.get1();

    float rz = quat2.get2();

    float rw = quat2.get3();

    float tx = rw*qx - rz*qy + ry*qz + rx*qw;

    float ty = rw*qy + rz*qx + ry*qw - rx*qz;

    float tz = rw*qz + rz*qw - ry*qx + rx*qy;

    float tw = rw*qw - rz*qz - ry*qy - rx*qx;

    return new Static4D(tx,ty,tz,tw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat1*quat2

  public static void quatMultiply( float[] ret, Static4D quat1, Static4D quat2 )

    {

    float qx = quat1.get0();

    float qy = quat1.get1();

    float qz = quat1.get2();

    float qw = quat1.get3();

    float rx = quat2.get0();

    float ry = quat2.get1();

    float rz = quat2.get2();

    float rw = quat2.get3();

    ret[0] = rw*qx - rz*qy + ry*qz + rx*qw;

    ret[1] = rw*qy + rz*qx + ry*qw - rx*qz;

    ret[2] = rw*qz + rz*qw - ry*qx + rx*qy;

    ret[3] = rw*qw - rz*qz - ry*qy - rx*qx;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat1*quat(rx,ry,rz,rw)

    public static void quatMultiply( float[] ret, Static4D quat1, float rx, float ry, float rz, float rw )

      {

      float qx = quat1.get0();

      float qy = quat1.get1();

      float qz = quat1.get2();

      float qw = quat1.get3();

      ret[0] = rw*qx - rz*qy + ry*qz + rx*qw;

      ret[1] = rw*qy + rz*qx + ry*qw - rx*qz;

      ret[2] = rw*qz + rz*qw - ry*qx + rx*qy;

      ret[3] = rw*qw - rz*qz - ry*qy - rx*qx;

      }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat1*quat2

  public static float[] quatMultiply( float[] quat1, float[] quat2 )

    {

    float qx = quat1[0];

    float qy = quat1[1];

    float qz = quat1[2];

    float qw = quat1[3];

    float rx = quat2[0];

    float ry = quat2[1];

    float rz = quat2[2];

    float rw = quat2[3];

    float tx = rw*qx - rz*qy + ry*qz + rx*qw;

    float ty = rw*qy + rz*qx + ry*qw - rx*qz;

    float tz = rw*qz + rz*qw - ry*qx + rx*qy;

    float tw = rw*qw - rz*qz - ry*qy - rx*qx;

    return new float[] {tx,ty,tz,tw};

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat1*(rx,ry,rz,rw)

  public static Static4D quatMultiply( Static4D quat, float rx, float ry, float rz, float rw )

    {

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    float tx = rw*qx - rz*qy + ry*qz + rx*qw;

    float ty = rw*qy + rz*qx + ry*qw - rx*qz;

    float tz = rw*qz + rz*qw - ry*qx + rx*qy;

    float tw = rw*qw - rz*qz - ry*qy - rx*qx;

    return new Static4D(tx,ty,tz,tw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return (qx,qy,qz,qw)*quat

  public static Static4D quatMultiply( float qx, float qy, float qz, float qw, Static4D quat )

    {

    float rx = quat.get0();

    float ry = quat.get1();

    float rz = quat.get2();

    float rw = quat.get3();

    float tx = rw*qx - rz*qy + ry*qz + rx*qw;

    float ty = rw*qy + rz*qx + ry*qw - rx*qz;

    float tz = rw*qz + rz*qw - ry*qx + rx*qy;

    float tw = rw*qw - rz*qz - ry*qy - rx*qx;

    return new Static4D(tx,ty,tz,tw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return (qx,qy,qz,qw)*(rx,ry,rz,rw)

  public static Static4D quatMultiply( float qx, float qy, float qz, float qw, float rx, float ry, float rz, float rw )

    {

    float tx = rw*qx - rz*qy + ry*qz + rx*qw;

    float ty = rw*qy + rz*qx + ry*qw - rx*qz;

    float tz = rw*qz + rz*qw - ry*qx + rx*qy;

    float tw = rw*qw - rz*qz - ry*qy - rx*qx;

    return new Static4D(tx,ty,tz,tw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)

  public static void quatMultiply( float[] ret, float[] q, float[] r )

    {

    ret[0] = r[3]*q[0] - r[2]*q[1] + r[1]*q[2] + r[0]*q[3];

    ret[1] = r[3]*q[1] + r[2]*q[0] + r[1]*q[3] - r[0]*q[2];

    ret[2] = r[3]*q[2] + r[2]*q[3] - r[1]*q[0] + r[0]*q[1];

    ret[3] = r[3]*q[3] - r[2]*q[2] - r[1]*q[1] - r[0]*q[0];

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)

  public static void quatMultiply( float[] ret, Static4D q, float[] r )

    {

    float q0 = q.get0();

    float q1 = q.get1();

    float q2 = q.get2();

    float q3 = q.get3();

    ret[0] = r[3]*q0 - r[2]*q1 + r[1]*q2 + r[0]*q3;

    ret[1] = r[3]*q1 + r[2]*q0 + r[1]*q3 - r[0]*q2;

    ret[2] = r[3]*q2 + r[2]*q3 - r[1]*q0 + r[0]*q1;

    ret[3] = r[3]*q3 - r[2]*q2 - r[1]*q1 - r[0]*q0;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)

  public static void quatMultiply( float[] ret, float[] q, Static4D r )

    {

    float r0 = r.get0();

    float r1 = r.get1();

    float r2 = r.get2();

    float r3 = r.get3();

    ret[0] = r3*q[0] - r2*q[1] + r1*q[2] + r0*q[3];

    ret[1] = r3*q[1] + r2*q[0] + r1*q[3] - r0*q[2];

    ret[2] = r3*q[2] + r2*q[3] - r1*q[0] + r0*q[1];

    ret[3] = r3*q[3] - r2*q[2] - r1*q[1] - r0*q[0];

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)

  public static void quatMultiply( float[] ret, float qx, float qy, float qz, float qw, float rx, float ry, float rz, float rw )

    {

    ret[0] = rw*qx - rz*qy + ry*qz + rx*qw;

    ret[1] = rw*qy + rz*qx + ry*qw - rx*qz;

    ret[2] = rw*qz + rz*qw - ry*qx + rx*qy;

    ret[3] = rw*qw - rz*qz - ry*qy - rx*qx;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)

  private static void quatMultiply( float[] ret, int index, float qx, float qy, float qz, float qw, float rx, float ry, float rz, float rw )

    {

    ret[index  ] = rw*qx - rz*qy + ry*qz + rx*qw;

    ret[index+1] = rw*qy + rz*qx + ry*qw - rx*qz;

    ret[index+2] = rw*qz + rz*qw - ry*qx + rx*qy;

    ret[index+3] = rw*qw - rz*qz - ry*qy - rx*qx;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate (x1,x2,x3,x4) by quat  ( i.e. return quat*vector*(quat^-1) )

  public static Static4D rotateVectorByQuat(float x, float y, float z, float w, Static4D quat)

    {

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    Static4D tmp = quatMultiply(qx,qy,qz,qw,x,y,z,w);

    return quatMultiply(tmp,-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate (x1,x2,x3,x4) by quat  ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, float x, float y, float z, float w, Static4D quat)

    {

    float[] tmp = new float[4];

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    quatMultiply(tmp,qx,qy,qz,qw,x,y,z,w);

    quatMultiply(output,tmp[0],tmp[1],tmp[2],tmp[3],-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate (x1,x2,x3,x4) by quat  ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, int index, float x, float y, float z, float w, Static4D quat)

    {

    float[] tmp = new float[4];

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    quatMultiply(tmp,qx,qy,qz,qw,x,y,z,w);

    quatMultiply(output,index,tmp[0],tmp[1],tmp[2],tmp[3],-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate (x1,x2,x3,x4) by quat  ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, float x, float y, float z, float w, float[] quat)

    {

    float[] tmp = new float[4];

    float qx = quat[0];

    float qy = quat[1];

    float qz = quat[2];

    float qw = quat[3];

    quatMultiply(tmp,qx,qy,qz,qw,x,y,z,w);

    quatMultiply(output,tmp[0],tmp[1],tmp[2],tmp[3],-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate (x1,x2,x3,x4) by quat  ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, int index, float x, float y, float z, float w, float[] quat)

    {

    float[] tmp = new float[4];

    float qx = quat[0];

    float qy = quat[1];

    float qz = quat[2];

    float qw = quat[3];

    quatMultiply(tmp,qx,qy,qz,qw,x,y,z,w);

    quatMultiply(output,index,tmp[0],tmp[1],tmp[2],tmp[3],-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate vec by quat ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, float[] vec, float[] quat)

    {

    float[] tmp = new float[4];

    quatMultiply(tmp,quat,vec);

    quat[0] = -quat[0];

    quat[1] = -quat[1];

    quat[2] = -quat[2];

    quatMultiply(output,tmp,quat);

    quat[0] = -quat[0];

    quat[1] = -quat[1];

    quat[2] = -quat[2];

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate vec by quat ( i.e. return quat*vector*(quat^-1) )

  public static void rotateVectorByQuat(float[] output, float[] vec, Static4D quat)

    {

    float[] tmp = new float[4];

    quatMultiply(tmp,quat,vec);

    float x1 = quat.get0();

    float y1 = quat.get1();

    float z1 = quat.get2();

    float w1 = quat.get3();

    quat.set(-x1,-y1,-z1,w1);

    quatMultiply(output,tmp,quat);

    float x2 = quat.get0();

    float y2 = quat.get1();

    float z2 = quat.get2();

    float w2 = quat.get3();

    quat.set(-x2,-y2,-z2,w2);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate 'vector' by quat  ( i.e. return quat*vector*(quat^-1) )

  public static Static4D rotateVectorByQuat(Static4D vector, Static4D quat)

    {

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    Static4D tmp = quatMultiply(qx,qy,qz,qw,vector);

    return quatMultiply(tmp,-qx,-qy,-qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate 'vector' by quat^(-1)  ( i.e. return (quat^-1)*vector*quat )

  public static Static4D rotateVectorByInvertedQuat(Static4D vector, Static4D quat)

    {

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    Static4D tmp = quatMultiply(-qx,-qy,-qz,qw,vector);

    return quatMultiply(tmp,qx,qy,qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate 'vector' by quat^(-1)  ( i.e. return (quat^-1)*vector*quat )

    public static void rotateVectorByInvertedQuat(float[] output, float x, float y, float z, float w, float[] quat)

      {

      float[] tmp = new float[4];

      float qx = quat[0];

      float qy = quat[1];

      float qz = quat[2];

      float qw = quat[3];

      quatMultiply(tmp,-qx,-qy,-qz,qw,x,y,z,w);

      quatMultiply(output,tmp[0],tmp[1],tmp[2],tmp[3],qx,qy,qz,qw);

      }

///////////////////////////////////////////////////////////////////////////////////////////////////

// rotate 'vector' by quat^(-1)  ( i.e. return (quat^-1)*vector*quat )

  public static void rotateVectorByInvertedQuat(float[] output, float x, float y, float z, float w, Static4D quat)

    {

    float[] tmp = new float[4];

    float qx = quat.get0();

    float qy = quat.get1();

    float qz = quat.get2();

    float qw = quat.get3();

    quatMultiply(tmp,-qx,-qy,-qz,qw,x,y,z,w);

    quatMultiply(output,tmp[0],tmp[1],tmp[2],tmp[3],qx,qy,qz,qw);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static Static4D quatFromDrag(float dragX, float dragY)

    {

    float axisX = dragY;  // inverted X and Y - rotation axis is perpendicular to (dragX,dragY)

    float axisY = dragX;  // Why not (-dragY, dragX) ? because Y axis is also inverted!

    float axisZ = 0;

    float axisL = (float)Math.sqrt(axisX*axisX + axisY*axisY + axisZ*axisZ);

    if( axisL>0 )

      {

      axisX /= axisL;

      axisY /= axisL;

      axisZ /= axisL;

      float ratio = axisL;

      ratio = ratio - (int)ratio;     // the cos() is only valid in (0,Pi)

      float cosA = (float)Math.cos(Math.PI*ratio);

      float sinA = (float)Math.sqrt(1-cosA*cosA);

      return new Static4D(axisX*sinA, axisY*sinA, axisZ*sinA, cosA);

      }

    return new Static4D(0f, 0f, 0f, 1f);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static double computeCos(double oldX, double oldY, double newX, double newY, double len1, double len2)

    {

    double ret= (oldX*newX+oldY*newY) / (len1*len2);

    if( ret<-1.0 ) return -1.0;

    if( ret> 1.0 ) return  1.0;

    return ret;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// sin of (signed!) angle between vectors 'old' and 'new', counterclockwise!

  public static double computeSin(double oldX, double oldY, double newX, double newY, double len1, double len2)

    {

    double ret= (newX*oldY-oldX*newY) / (len1*len2);

    if( ret<-1.0 ) return -1.0;

    if( ret> 1.0 ) return  1.0;

    return ret;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return quat Q that turns 3D vector A=(ax,ay,az) to another 3D vector B=(bx,by,bz)

// take care of double-cover by ensuring that always Q.get3() >=0

  public static Static4D retRotationQuat(float ax, float ay, float az, float bx, float by, float bz)

    {

    float nx = ay*bz - az*by;

    float ny = az*bx - ax*bz;

    float nz = ax*by - ay*bx;

    float sin = (float)Math.sqrt(nx*nx + ny*ny + nz*nz);

    float cos = ax*bx + ay*by + az*bz;

    if( sin!=0 )

      {

      nx /= sin;

      ny /= sin;

      nz /= sin;

      }

    // Why sin<=0 and cos>=0 ?

    // 0<angle<180 -> 0<halfAngle<90 -> both sin and cos are positive.

    // But1: quats work counterclockwise -> negate cos.

    // But2: double-cover, we prefer to have the cos positive (so that unit=(0,0,0,1))

    // so negate again both cos and sin.

    float sinHalf =-(float)Math.sqrt((1-cos)/2);

    float cosHalf = (float)Math.sqrt((1+cos)/2);

    return new Static4D(nx*sinHalf,ny*sinHalf,nz*sinHalf,cosHalf);

    }

  }