Find 3d orientation from a plane knowing the 2d position of 4 corners - solvePnpRansac / coplanar posit

advanced
#1

Using the nice addons ofxFern for augmented reality I get 4 corners points as 2d coordinates, I am trying to find the 3d orientation as euler angles in order to use 3d assets with the AR tracking.
I have something almost working using cv::solvePnpRansac, sometime the rotation works but is not very accurate, maybe I am not using solvePnpRansac correctly?

ofPoint getOrientation(ofPoint pts[4]) {

    ofxCv::Calibration calibration;
    calibration.load("kinect-color.yml");

	vector<cv::Point2f> cornersp;
	cornersp.push_back(cv::Point2f(pts[0].x, pts[0].y));
	cornersp.push_back(cv::Point2f(pts[1].x, pts[1].y));
	cornersp.push_back(cv::Point2f(pts[2].x, pts[2].y));
	cornersp.push_back(cv::Point2f(pts[3].x, pts[3].y));


	float pageWidth = (ofDist(pts[1].x, pts[1].y, pts[2].x, pts[2].y) + ofDist(pts[0].x, pts[0].y, pts[3].x, pts[3].y)) / 2;
	float pageHeight = (ofDist(pts[0].x, pts[0].y, pts[1].x, pts[1].y) + ofDist(pts[2].x, pts[2].y, pts[3].x, pts[3].y)) / 2;

	vector<cv::Point3f> objp;
	objp.push_back(cv::Point3f(0, pageHeight,0));
	objp.push_back(cv::Point3f(0, 0, 0));
	objp.push_back(cv::Point3f(pageWidth, 0, 0));
	objp.push_back(cv::Point3f(pageWidth, pageHeight, 0));

	cv::Mat cameraMatrix = calibration.getDistortedIntrinsics().getCameraMatrix();
	cv::Mat distortion = calibration.getDistCoeffs();
	cv::Mat translation;
	cv::Mat rotation;
	cv::solvePnPRansac(objp, cornersp, cameraMatrix, distortion, rotation, translation, false);


	ofPoint euler(ofRadToDeg(rotation.at<double>(0)), ofRadToDeg(rotation.at<double>(1)), ofRadToDeg(rotation.at<double>(2)));
	return euler;
}

I read ‘coplanar posit’ could also do the job, maybe there are other suggestion?