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GetPerspectiveTransform mathematical explanation

Hi guys! I'm doing a course project devoted to perspective transformations. I have a ready opencv function GetPerspectiveTransform that takes my source array CvPoint2D32f srcQuad[4] and gets destination array CvPoint2D32f dstQuad[4] using a matrix of perspective transformation CvMat* warp_matrix = cvCreateMat(3,3,CV_32FC1); But is there a mathematical analogue of this function? I mean can I using some mathematical formulas replace ready function GetPerspectiveTransform? Thank you very much for any assistance.