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copied!<p>Look up <code>"quad to quad" transform</code>, e.g. <a href="http://threeblindmiceandamonkey.com/?p=16" rel="nofollow noreferrer">threeblindmiceandamonkey</a>.<br> A 3x3 transform on 2d homogeneous coordinates can transform any 4 points (a quad) to any other quad; conversely, any fromquad and toquad, such as the corners of your truck and a target rectangle, give a 3 x 3 transform.</p> <p>Qt has <a href="http://doc.trolltech.com/4.5/qtransform.html#quadToQuad" rel="nofollow noreferrer">quadToQuad</a> and can transform pixmaps with it, but I guess you don't have Qt ?<br> Added 10Jun: from <a href="http://labs.trolltech.com/page/Graphics/Examples" rel="nofollow noreferrer">labs.trolltech.com/page/Graphics/Examples</a> there's a nice demo which quad-to-quads a pixmap as you move the corners:</p> <h2><img src="https://imgur.com/zdVtz.png" alt="alt text"></h2> <p>Added 11Jun: @Will, here's translate.h in Python (which you know a bit ? """ ...""" are multiline comments.)<br> <code>perstrans()</code> is the key; hope that makes sense, if not ask. </p> <p>Bytheway, you <em>could</em> map the pixels one by one, mapQuadToQuad( target rect, orig quad ), but without pixel interpolation it'll look terrible; OpenCV does it all.</p> <pre><code>#!/usr/bin/env python """ square <-> quad maps from http://threeblindmiceandamonkey.com/?p=16 matrix.h """ from __future__ import division import numpy as np __date__ = "2010-06-11 jun denis" def det2(a, b, c, d): return a*d - b*c def mapSquareToQuad( quad ): # [4][2] SQ = np.zeros((3,3)) px = quad[0,0] - quad[1,0] + quad[2,0] - quad[3,0] py = quad[0,1] - quad[1,1] + quad[2,1] - quad[3,1] if abs(px) < 1e-10 and abs(py) < 1e-10: SQ[0,0] = quad[1,0] - quad[0,0] SQ[1,0] = quad[2,0] - quad[1,0] SQ[2,0] = quad[0,0] SQ[0,1] = quad[1,1] - quad[0,1] SQ[1,1] = quad[2,1] - quad[1,1] SQ[2,1] = quad[0,1] SQ[0,2] = 0. SQ[1,2] = 0. SQ[2,2] = 1. return SQ else: dx1 = quad[1,0] - quad[2,0] dx2 = quad[3,0] - quad[2,0] dy1 = quad[1,1] - quad[2,1] dy2 = quad[3,1] - quad[2,1] det = det2(dx1,dx2, dy1,dy2) if det == 0.: return None SQ[0,2] = det2(px,dx2, py,dy2) / det SQ[1,2] = det2(dx1,px, dy1,py) / det SQ[2,2] = 1. SQ[0,0] = quad[1,0] - quad[0,0] + SQ[0,2]*quad[1,0] SQ[1,0] = quad[3,0] - quad[0,0] + SQ[1,2]*quad[3,0] SQ[2,0] = quad[0,0] SQ[0,1] = quad[1,1] - quad[0,1] + SQ[0,2]*quad[1,1] SQ[1,1] = quad[3,1] - quad[0,1] + SQ[1,2]*quad[3,1] SQ[2,1] = quad[0,1] return SQ #............................................................................... def mapQuadToSquare( quad ): return np.linalg.inv( mapSquareToQuad( quad )) def mapQuadToQuad( a, b ): return np.dot( mapQuadToSquare(a), mapSquareToQuad(b) ) def perstrans( X, t ): """ perspective transform X Nx2, t 3x3: [x0 y0 1] t = [a0 b0 w0] -> [a0/w0 b0/w0] [x1 y1 1] t = [a1 b1 w1] -> [a1/w1 b1/w1] ... """ x1 = np.vstack(( X.T, np.ones(len(X)) )) y = np.dot( t.T, x1 ) return (y[:-1] / y[-1]) .T #............................................................................... if __name__ == "__main__": np.set_printoptions( 2, threshold=100, suppress=True ) # .2f sq = np.array([[0,0], [1,0], [1,1], [0,1]]) quad = np.array([[171, 72], [331, 93], [333, 188], [177, 210]]) print "quad:", quad print "square to quad:", perstrans( sq, mapSquareToQuad(quad) ) print "quad to square:", perstrans( quad, mapQuadToSquare(quad) ) dw, dh = 300, 250 rect = np.array([[0, 0], [dw, 0], [dw, dh], [0, dh]]) quadquad = mapQuadToQuad( quad, rect ) print "quad to quad transform:", quadquad print "quad to rect:", perstrans( quad, quadquad ) """ quad: [[171 72] [331 93] [333 188] [177 210]] square to quad: [[ 171. 72.] [ 331. 93.] [ 333. 188.] [ 177. 210.]] quad to square: [[-0. 0.] [ 1. 0.] [ 1. 1.] [ 0. 1.]] quad to quad transform: [[ 1.29 -0.23 -0. ] [ -0.06 1.79 -0. ] [-217.24 -88.54 1.34]] quad to rect: [[ 0. 0.] [ 300. 0.] [ 300. 250.] [ 0. 250.]] """ </code></pre>

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