opencv旋转图像

#include <opencv2opencv.hpp>


/*
@param o The customer origin
@param x The customer x

@Note 
The return matrix include translation
*/
cv::Mat ZRotationMatrix(const cv::Point2d o, const cv::Point2d x)
{
	cv::Mat Rz = cv::Mat::zeros(3, 3, CV_32FC1);
	Rz.at<float>(2, 2) = 1.0;

	double theta = std::atan((x.y - o.y) / (x.x - o.x));
	Rz.at<float>(0, 0) = std::cos(theta);
	Rz.at<float>(1, 0) = std::sin(theta);
	Rz.at<float>(0, 1) = -Rz.at<float>(1, 0);
	Rz.at<float>(1, 1) = Rz.at<float>(0, 0);

	// Adding Translation
	Rz.at<float>(0, 2) = static_cast<float>(x.x);
	Rz.at<float>(1, 2) = static_cast<float>(x.y);
	Rz.at<float>(2, 2) = 0;

	return Rz;
}

/*
Called by Rotation()
*/
std::pair<int, int> dstImageRegion(const cv::Mat points )
{
	CV_Assert(points.size() == cv::Size(4, 3));

	float maxRow(0.0), maxCol(0.0);
	for (size_t i=0; i<4; ++i)
	{
		// x
		maxCol = maxCol < points.at<float>(0, i) ? points.at<float>(0, i) : maxCol;
		
		// y
		maxRow = maxRow < points.at<float>(1, i) ? points.at<float>(1, i) : maxRow;
	}

	return {maxRow, maxCol};
}

/*
@Param Rz It includes the translation also!
*/
cv::Mat Rotation(const cv::Mat src, const cv::Mat Rz)
{
	// get region of dst
	cv::Mat Corners_src((cv::Mat_<float>(3,4) << 0, src.cols,	0,			src.cols,
												  0, 0,			src.rows,	src.rows,
												  1, 1,			1,			1
		));
	cv::Mat Corners_dst = Rz * Corners_src;

	std::pair<int, int> size_dst = dstImageRegion(Corners_dst);
	cv::Mat dst = cv::Mat::zeros(size_dst.first, size_dst.second, src.type());

	// Rz is the matrix from src to dst. The inverse matrix is needed to reconstruct dst.
	cv::Mat Rz_inv = Rz.clone();

	// The inverse matrix of Rotation is the same as its transpose matrix.
	Rz_inv.at<float>(0, 1) = Rz.at<float>(1, 0);
	Rz_inv.at<float>(1, 0) = Rz.at<float>(0, 1);

	// Set pixels value
	for (size_t j=0; j<dst.rows; ++j)
	{
		for (size_t i = 0; i < dst.cols; ++i)
		{
			cv::Mat tp_src = Rz_inv * cv::Mat((cv::Mat_<float>(3,1) << i,j,1));
			int Idx_src(cvRound(tp_src.at<float>(0))), Idy_src(cvRound(tp_src.at<float>(1)));
			
			if (Idx_src<0.0 || Idx_src>=src.cols || Idy_src<0.0 || Idy_src>=src.rows)
				continue;

			dst.at<float>(j, i) = src.at<float>(Idy_src, Idx_src);
		}

	}

	return dst;
}

int main()
{
	cv::Mat img = cv::imread("1.PNG", CV_LOAD_IMAGE_GRAYSCALE);
	img.convertTo(img, CV_32FC1);

	// 
	cv::Mat Rz = ZRotationMatrix(cv::Point2d(10,10), cv::Point2d(20, 5));
	cv::Mat img_d = Rotation(img, Rz);

	return 0;
}