ARFloat Tracker::rppMultiGetTransMat(ARMarkerInfo *marker_info, int marker_num, ARMultiMarkerInfoT *config) {
    rpp_float err = 1e+20;
    rpp_mat R, R_init;
    rpp_vec t;

    std::map<int, int> marker_id_freq;
    for (int i = 0; i < marker_num; i++) {
        const int m_patt_id = marker_info[i].id;
        if (m_patt_id >= 0) {
            std::map<int, int>::iterator iter = marker_id_freq.find(m_patt_id);

            if (iter == marker_id_freq.end()) {
                marker_id_freq.insert(std::make_pair(int(m_patt_id), 1));
            } else {
                ((*iter).second)++;
            }
        }
    }

    std::deque<std::pair<int, int> > config_patt_id;
    for (int j = 0; j < config->marker_num; j++)
        config_patt_id.push_back(std::make_pair(int(j), int(config->marker[j].patt_id)));

    std::map<int, int> m2c_idx;
    for (int m = 0; m < marker_num; m++) {
        const int m_patt_id = marker_info[m].id;
        bool ignore_marker = (m_patt_id < 0);
        std::map<int, int>::iterator m_iter = marker_id_freq.find(m_patt_id);
        if (m_iter != marker_id_freq.end())
            ignore_marker |= ((*m_iter).second > 1);
        if (!ignore_marker) {
            std::deque<std::pair<int, int> >::iterator c_iter = config_patt_id.begin();
            if (c_iter != config_patt_id.end())
                do {
                    const int patt_id = (*c_iter).second;
                    if (marker_info[m].id == patt_id) {
                        m2c_idx.insert(std::make_pair(int(m), int((*c_iter).first)));
                        config_patt_id.erase(c_iter);
                        c_iter = config_patt_id.end();
                        continue;
                    } else {
                        c_iter++;
                    }
                } while (c_iter != config_patt_id.end());
        }
    }

    // ----------------------------------------------------------------------
    const unsigned int n_markers = (unsigned int) m2c_idx.size();
    const unsigned int n_pts = 4 * n_markers;

    if (n_markers == 0)
        return (-1);

    rpp_vec *ppos2d = NULL, *ppos3d = NULL;
    arMalloc( ppos2d, rpp_vec, n_pts);
    arMalloc( ppos3d, rpp_vec, n_pts);
    memset(ppos2d, 0, sizeof(rpp_vec) * n_pts);
    memset(ppos3d, 0, sizeof(rpp_vec) * n_pts);

    const rpp_float iprts_z = 1;

    int p = 0;
    for (std::map<int, int>::iterator iter = m2c_idx.begin(); iter != m2c_idx.end(); iter++) {
        const int m = (*iter).first;
        const int c = (*iter).second;

        const int dir = marker_info[m].dir;
        const int v_idx[4] = { (4 - dir) % 4, (5 - dir) % 4, (6 - dir) % 4, (7 - dir) % 4 };

        for (int i = 0; i < 4; i++)
            for (int j = 0; j < 3; j++) {
                ppos2d[p + i][j] = (rpp_float) (j == 2 ? iprts_z : marker_info[m].vertex[v_idx[i]][j]);
                ppos3d[p + i][j] = (rpp_float) config->marker[c].pos3d[i][j];
            }

        p += 4;
    }

    const rpp_float cc[2] = { arCamera->mat[0][2], arCamera->mat[1][2] };
    const rpp_float fc[2] = { arCamera->mat[0][0], arCamera->mat[1][1] };

    robustPlanarPose(err, R, t, cc, fc, ppos3d, ppos2d, n_pts, R_init, true, 0, 0, 0);

    for (int k = 0; k < 3; k++) {
        config->trans[k][3] = (ARFloat) t[k];
        for (int j = 0; j < 3; j++)
            config->trans[k][j] = (ARFloat) R[k][j];
    }

    if (ppos2d != NULL)
        free(ppos2d);
    if (ppos3d != NULL)
        free(ppos3d);

    if (err > 1e+10)
        return (-1); // an actual error has occurred in robustPlanarPose()
    return (ARFloat(err)); // NOTE: err is a real number from the interval [0,1e+10]
}
 ARFloat
Tracker::arMultiGetTransMatHull(ARMarkerInfo *marker_info, int marker_num, ARMultiMarkerInfoT *config)
{
	//return arMultiGetTransMat(marker_info, marker_num, config);

	int numInPoints=0;
	std::vector<int> trackedMarkers;
	int trackedCenterX=-1,trackedCenterY=-1;

	//const int indices[4] = {idx0,idx1,idx2,idx3};
	//rpp_vec ppos2d[4];
	//rpp_vec ppos3d[4];

	const int maxHullPoints = 16;
	int indices[maxHullPoints];
	rpp_vec ppos2d[maxHullPoints];
	rpp_vec ppos3d[maxHullPoints];


	// create an array of 2D points and keep references
	// to the source points
	//
	for(int i=0; i<marker_num; i++)
	{
		int mId = marker_info[i].id;
		int configIdx = -1;

		for(int j=0; j<config->marker_num; j++)
			if(config->marker[j].patt_id==mId)
			{
				configIdx = j;
				break;
			}

		if(configIdx==-1)
			continue;

		trackedMarkers.push_back(i);

		for(int c=0; c<4; c++)
		{
			int dir = marker_info[i].dir;
			int cornerIdx = (c+4-dir)%4;
			hullInPoints[numInPoints].x = (MarkerPoint::coord_type)marker_info[i].vertex[cornerIdx][0];
			hullInPoints[numInPoints].y = (MarkerPoint::coord_type)marker_info[i].vertex[cornerIdx][1];
			hullInPoints[numInPoints].cornerIdx = c;
			hullInPoints[numInPoints].markerIdx = configIdx;
			numInPoints++;
		}

		if(numInPoints>=MAX_HULL_POINTS)
			break;
	}


	// next get the convex hull of all points
	// (decrease amount by one to ignore last point, which is identical to first point)
	//
	int numHullPoints = nearHull_2D(hullInPoints, numInPoints, numInPoints, hullOutPoints)-1;
	int idx0,idx1,idx2,idx3;


	if(hullTrackingMode==HULL_FOUR && numHullPoints != 0)
	{
		// find those points with furthest distance and that lie on
		// opposite parts of the hull. this fixes the first two points of our quad.
		//
		findLongestDiameter(hullOutPoints, numHullPoints, idx0,idx1);
		assert(iabs(idx0-idx1)>0);

		// find the point that is furthest away of the line
		// of our first two points. this fixes the third point of the quad
		findFurthestAway(hullOutPoints, numHullPoints, idx0,idx1, idx2);
		sortIntegers(idx0,idx1, idx2);

		// of all other points find the one that results in
		// a quad with the largest area.
		maximizeArea(hullOutPoints, numHullPoints, idx0,idx1,idx2,idx3);

		// now that we have all four points we must sort them...
		//
		sortInLastInteger(idx0,idx1,idx2, idx3);

		numHullPoints = 4;
		indices[0] = idx0;
		indices[1] = idx1;
		indices[2] = idx2;
		indices[3] = idx3;
	}
	else
	{
		if(numHullPoints>maxHullPoints)
			numHullPoints = maxHullPoints;

		for(int i=0; i<numHullPoints; i++)
			indices[i] = i;
	}

	assert(numHullPoints<=maxHullPoints);

	// create arrays of vertices for the 2D and 3D positions
	// 
	//const int indices[4] = {idx0,idx1,idx2,idx3};
	//rpp_vec ppos2d[4];
	//rpp_vec ppos3d[4];

	for(int i=0; i<numHullPoints; i++)
	{
		//int idx = indices[(i+1)%4];
		int idx = indices[i];
		const MarkerPoint& pt = hullOutPoints[idx];

		trackedCorners.push_back(CornerPoint(pt.x,pt.y));

		trackedCenterX += pt.x;
		trackedCenterY += pt.y;

		ppos2d[i][0] = pt.x;
		ppos2d[i][1] = pt.y;
		ppos2d[i][2] = 1.0f;

		assert(pt.markerIdx < config->marker_num);
		const ARMultiEachMarkerInfoT& markerInfo = config->marker[pt.markerIdx];
		int cornerIdx = pt.cornerIdx;

		ppos3d[i][0] = markerInfo.pos3d[cornerIdx][0];
		ppos3d[i][1] = markerInfo.pos3d[cornerIdx][1];
		ppos3d[i][2] = 0;
	}

	trackedCenterX /= 4;
	trackedCenterY /= 4;


	// prepare structures and data we need for input and output
	// parameters of the rpp functions
	const rpp_float cc[2] = {arCamera->mat[0][2],arCamera->mat[1][2]};
	const rpp_float fc[2] = {arCamera->mat[0][0],arCamera->mat[1][1]};
	rpp_float err = 1e+20;
	rpp_mat R, R_init;
	rpp_vec t;

	if(poseEstimator==POSE_ESTIMATOR_RPP)
	{
		robustPlanarPose(err,R,t,cc,fc,ppos3d,ppos2d,numHullPoints,R_init, true,0,0,0);
		if(err>1e+10)
			return(-1); // an actual error has occurred in robustPlanarPose()

		for(int k=0; k<3; k++)
		{
			config->trans[k][3] = (ARFloat)t[k];
			for(int j=0; j<3; j++)
				config->trans[k][j] = (ARFloat)R[k][j];
		}
	}
	else
	{
		ARFloat rot[3][3];

		int minIdx=-1, minDist=0x7fffffff;
		for(size_t i=0; i<trackedMarkers.size(); i++)
		{
			assert(trackedMarkers[i]>=0 && trackedMarkers[i]<marker_num);
			int idx = trackedMarkers[i];
			const ARMarkerInfo& mInfo = marker_info[idx];
			int dx = trackedCenterX-(int)mInfo.pos[0], dy = trackedCenterY-(int)mInfo.pos[1];
			int d = dx*dx + dy*dy;
			if(d<minDist)
			{
				minDist = d;
				minIdx = (int)idx;
			}
		}


		//trackedCorners.push_back(CornerPoint((int)marker_info[minIdx].pos[0],(int)marker_info[minIdx].pos[1]));

        if(minIdx >= 0) {
            return  -1;
        }

		if(arGetInitRot(marker_info+minIdx, arCamera->mat, rot )<0)
			return -1;


		// finally use the normal pose estimator to get the pose
		//
		ARFloat tmp_pos2d[maxHullPoints][2], tmp_pos3d[maxHullPoints][2];

		for(int i=0; i<numHullPoints; i++)
		{
			tmp_pos2d[i][0] = (ARFloat)ppos2d[i][0];
			tmp_pos2d[i][1] = (ARFloat)ppos2d[i][1];
			tmp_pos3d[i][0] = (ARFloat)ppos3d[i][0];
			tmp_pos3d[i][1] = (ARFloat)ppos3d[i][1];
		}

		for(int i=0; i<AR_GET_TRANS_MAT_MAX_LOOP_COUNT; i++ )
		{
			err = arGetTransMat3(rot, tmp_pos2d, tmp_pos3d, numHullPoints, config->trans, arCamera);
			if(err<AR_GET_TRANS_MAT_MAX_FIT_ERROR)
				break;
		}
	}

    return (ARFloat)err;
}
 ARFloat
Tracker::rppGetTransMat(ARMarkerInfo *marker_info, ARFloat center[2], ARFloat width, ARFloat conv[3][4])
{
	const bool initial_estimate_with_arGetInitRot = false; // only for testing
	
	rpp_float err = 1e+20;
	rpp_mat R, R_init;
	rpp_vec t;

	if(initial_estimate_with_arGetInitRot )
	{
		ARFloat  rot[3][3];
		if( arGetInitRot( marker_info, arCamera->mat, rot ) < 0 ) return -1;
		for(int i=0; i<3; i++)
			for(int j=0; j<3; j++)
				R_init[i][j] = (rpp_float)rot[i][j];
	}

	int dir = marker_info->dir;
	rpp_vec ppos2d[4];
	rpp_vec ppos3d[4];
	const unsigned int n_pts = 4;
	const rpp_float model_z =  0;
	const rpp_float iprts_z =  1;

	ppos2d[0][0] = marker_info->vertex[(4-dir)%4][0];
    ppos2d[0][1] = marker_info->vertex[(4-dir)%4][1];
	ppos2d[0][2] = iprts_z;
    ppos2d[1][0] = marker_info->vertex[(5-dir)%4][0];
    ppos2d[1][1] = marker_info->vertex[(5-dir)%4][1];
	ppos2d[1][2] = iprts_z;
    ppos2d[2][0] = marker_info->vertex[(6-dir)%4][0];
    ppos2d[2][1] = marker_info->vertex[(6-dir)%4][1];
	ppos2d[2][2] = iprts_z;
    ppos2d[3][0] = marker_info->vertex[(7-dir)%4][0];
    ppos2d[3][1] = marker_info->vertex[(7-dir)%4][1];
	ppos2d[3][2] = iprts_z;

	ppos3d[0][0] = center[0] - width*(ARFloat)0.5;
    ppos3d[0][1] = center[1] + width*(ARFloat)0.5;
	ppos3d[0][2] = model_z;
    ppos3d[1][0] = center[0] + width*(ARFloat)0.5;
    ppos3d[1][1] = center[1] + width*(ARFloat)0.5;
	ppos3d[1][2] = model_z;
    ppos3d[2][0] = center[0] + width*(ARFloat)0.5;
    ppos3d[2][1] = center[1] - width*(ARFloat)0.5;
	ppos3d[2][2] = model_z;
    ppos3d[3][0] = center[0] - width*(ARFloat)0.5;
    ppos3d[3][1] = center[1] - width*(ARFloat)0.5;
	ppos3d[3][2] = model_z;

	const rpp_float cc[2] = {arCamera->mat[0][2],arCamera->mat[1][2]};
	const rpp_float fc[2] = {arCamera->mat[0][0],arCamera->mat[1][1]};

	robustPlanarPose(err,R,t,cc,fc,ppos3d,ppos2d,n_pts,R_init, !initial_estimate_with_arGetInitRot,0,0,0);

	for(int i=0; i<3; i++)
	{
		conv[i][3] = (ARFloat)t[i];
		for(int j=0; j<3; j++)
			conv[i][j] = (ARFloat)R[i][j];
	}

	if(err > 1e+10) return(-1); // an actual error has occurred in robustPlanarPose()
	return(ARFloat(err)); // NOTE: err is a real number from the interval [0,1e+10]
}