Magic Cube

  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);

    }

  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 quatInverted= new Static4D(-qx,-qy,-qz,qw);

    Static4D tmp = quatMultiply(quat,vector);

    return quatMultiply(tmp,quatInverted);

    }

  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 quatInverted= new Static4D(-qx,-qy,-qz,qw);

    Static4D tmp = quatMultiply(quatInverted,vector);

    return quatMultiply(tmp,quat);

    }

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  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);

    }