TwistyPuzzleLib

    float fx,fy,fz,f;

        convertTo2Dcoords( mPoint, face, mCastedRotAxis[face][casted]);

        fx = mFaceAxis[face].get0();

        fy = mFaceAxis[face].get1();

        fz = mFaceAxis[face].get2();

        f  = mPoint[0]*fx + mPoint[1]*fy + mPoint[2]*fz;

        mCastedRotAxis4D[face][casted] = new Static4D( mPoint[0]-f*fx, mPoint[1]-f*fy, mPoint[2]-f*fz, 0);

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

// find the casted axis with which our move2D vector forms an angle closest to 90 deg.

  private int computeRotationIndex(float[][] rotAxis, float[] move2D, int[] enabled)

    {

    float cosAngle, minCosAngle = Float.MAX_VALUE;

    int minIndex=0, index;

    float m0 = move2D[0];

    float m1 = move2D[1];

    int numAxis = enabled[0];

    for(int axis=1; axis<=numAxis; axis++)

      {

      index = enabled[axis];

      cosAngle = m0*rotAxis[index][0] + m1*rotAxis[index][1];

      if( cosAngle<0 ) cosAngle = -cosAngle;

      if( cosAngle<minCosAngle )

        {

        minCosAngle=cosAngle;

        minIndex = index;

        }

      }

    return minIndex;

    }

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

// Convert the 3D point3D into a 2D point on the same face surface, but in a different

// coordinate system: a in-plane 2D coord where the origin is in the point where the axis intersects

// the surface, and whose Y axis points 'north' i.e. is in the plane given by the 3D origin, the

// original 3D Y axis and our 2D in-plane origin.

// If those 3 points constitute a degenerate triangle which does not define a plane - which can only

// happen if axis is vertical (or in theory when 2D origin and 3D origin meet, but that would have to

// mean that the distance between the center of the Object and its faces is 0) - then we arbitrarily

// decide that 2D Y = (0,0,-1) in the North Pole and (0,0,1) in the South Pole)

  private void convertTo2Dcoords(float[] point3D, int index , float[] output)

    {

    Static3D faceAxis = mFaceAxis[index];

    float y0,y1,y2; // base Y vector of the 2D coord system

    float a0 = faceAxis.get0();

    float a1 = faceAxis.get1();

    float a2 = faceAxis.get2();

    if( a0==0.0f && a2==0.0f )

      {

      y0=0; y1=0; y2=-a1;

      }

    else if( a1==0.0f )

      {

      y0=0; y1=1; y2=0;

      }

    else

      {

      float norm = (float)(-a1/Math.sqrt(1-a1*a1));

      y0 = norm*a0; y1= norm*(a1-1/a1); y2=norm*a2;

      }

    float x0 = y1*a2 - y2*a1;  //

    float x1 = y2*a0 - y0*a2;  // (2D coord baseY) x (axis) = 2D coord baseX

    float x2 = y0*a1 - y1*a0;  //

    float originAlpha = point3D[0]*a0 + point3D[1]*a1 + point3D[2]*a2;

    float origin0 = originAlpha*a0; // coords of the point where axis

    float origin1 = originAlpha*a1; // intersects surface plane i.e.

    float origin2 = originAlpha*a2; // the origin of our 2D coord system

    float v0 = point3D[0] - origin0;

    float v1 = point3D[1] - origin1;

    float v2 = point3D[2] - origin2;

    output[0] = v0*x0 + v1*x1 + v2*x2;

    output[1] = v0*y0 + v1*y1 + v2*y2;

    }

        convertTo2Dcoords(mTouch, mLastTouchedFace, mPoint2D);

    convertTo2Dcoords(mTouch, mLastTouchedFace, mMove2D);