登录|注册小魏的修行路Talkischeap.Showmethecode.透视变换(PerspectiveTransformation)是将图片投影到一个新的视平面(ViewingPlane)，也称作投影映射(ProjectiveMapping)。通用的变换公式为：u,v是原始图片左边，对应得到变换后的图片坐标x,y,其中。变换矩阵可以拆成4部分，表示线性变换，比如scaling，shearing和ratotion。用于平移，产生透视变换。所以可以理解成仿射等是透视变换的特殊形式。经过透视变换之后的图片通常不是平行四边形（除非映射视平面和原来平面平行的情况）。重写之前的变换公式可以得到：所以，已知变换对应的几个点就可以求取变换公式。反之，特定的变换公式也能新的变换后的图片。简单的看一个正方形到四边形的变换：变换的4组对应点可以表示成：根据变换公式得到：定义几个辅助变量：都为0时变换平面与原来是平行的，可以得到：不为0时，得到：求解出的变换矩阵就可以将一个正方形变换到四边形。反之，四边形变换到正方形也是一样的。于是，我们通过两次变换：四边形变换到正方形+正方形变换到四边形就可以将任意一个四边形变换到另一个四边形。看一段代码：[cpp]viewplaincopy1.PerspectiveTransform::PerspectiveTransform(floatinA11,floatinA21,2.floatinA31,floatinA12,3.floatinA22,floatinA32,4.floatinA13,floatinA23,5.floatinA33):6.a11(inA11),a12(inA12),a13(inA13),a21(inA21),a22(inA22),a23(inA23),7.a31(inA31),a32(inA32),a33(inA33){}8.9.PerspectiveTransformPerspectiveTransform::quadrilateralToQuadrilateral(floatx0,floaty0,floatx1,floaty1,10.floatx2,floaty2,floatx3,floaty3,floatx0p,floaty0p,floatx1p,floaty1p,floatx2p,floaty2p,11.floatx3p,floaty3p){12.PerspectiveTransformqToS=PerspectiveTransform::quadrilateralToSquare(x0,y0,x1,y1,x2,y2,x3,y3);13.PerspectiveTransformsToQ=14.PerspectiveTransform::squareToQuadrilateral(x0p,y0p,x1p,y1p,x2p,y2p,x3p,y3p);15.returnsToQ.times(qToS);16.}17.18.PerspectiveTransformPerspectiveTransform::squareToQuadrilateral(floatx0,floaty0,floatx1,floaty1,floatx2,19.floaty2,floatx3,floaty3){20.floatdx3=x0-x1+x2-x3;21.floatdy3=y0-y1+y2-y3;22.if(dx3==0.0f&&dy3==0.0f){23.PerspectiveTransformresult(PerspectiveTransform(x1-x0,x2-x1,x0,y1-y0,y2-y1,y0,0.0f,24.0.0f,1.0f));25.returnresult;26.}else{27.floatdx1=x1-x2;28.floatdx2=x3-x2;29.floatdy1=y1-y2;30.floatdy2=y3-y2;31.floatdenominator=dx1*dy2-dx2*dy1;32.floata13=(dx3*dy2-dx2*dy3)/denominator;33.floata23=(dx1*dy3-dx3*dy1)/denominator;34.PerspectiveTransformresult(PerspectiveTransform(x1-x0+a13*x1,x3-x0+a23*x3,x0,y1-y035.+a13*y1,y3-y0+a23*y3,y0,a13,a23,1.0f));36.returnresult;37.}38.}39.40.PerspectiveTransformPerspectiveTransform::quadrilateralToSquare(floatx0,floaty0,floatx1,floaty1,floatx2,41.floaty2,floatx3,floaty3){42.//Here,theadjointservesastheinverse:43.returnsquareToQuadrilateral(x0,y0,x1,y1,x2,y2,x3,y3).buildAdjoint();44.}45.46.PerspectiveTransformPerspectiveTransform::buildAdjoint(){47.//Adjointisthetransposeofthecofactormatrix:48.PerspectiveTransformresult(PerspectiveTransform(a22*a33-a23*a32,a23*a31-a21*a33,a21*a3249.-a22*a31,a13*a32-a12*a33,a11*a33-a13*a31,a12*a31-a11*a32,a12*a23-a13*a22,50.a13*a21-a11*a23,a11*a22-a12*a21));51.returnresult;52.}53.54.PerspectiveTransformPerspectiveTransform::times(PerspectiveTransformother){55.PerspectiveTransformresult(PerspectiveTransform(a11*other.a11+a21*other.a12+a31*other.a13,56.a11*other.a21+a21*other.a22+a31*other.a23,a11*other.a31+a21*other.a32+a3157.*other.a33,a12*other.a11+a22*other.a12+a32*other.a13,a12*other.a21+a2258.*other.a22+a32*other.a23,a12*other.a31+a22*other.a32+a32*other.a33,a1359.*other.a11+a23...
