c++ - Convert a point on an inclined image to a non-inclined point -

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i have image of image, inner image inclined , has own coordinate table (visible on edges):

enter image description here

now need convert point of actual image (x cm, y cm) point on inclined image. say, want know (x cm, y cm) coordinates bottom left corner ((0, img.height())) of actual image has. is, if inner image's coordinate table extrapolated.

i know:

  • the angle a of inclined image
  • two points p1 , p2 selected manually inclined image
  • the cm coordinates p1cm , p2cm these 2 points

i can scale of image comparing 2 points , getting ratio between cm distance , actual distance:

double dcmx = p1cm.x() - p2cm.x(); double dcmy = p1cm.y() - p2cm.y(); double dcm = sqrt(pow(dcmx, 2) + pow(dcmy, 2))  double dpointx = p1.x() - p2.x(); double dpointy = p1.y() - p2.y(); double dpoint = sqrt(pow(dpointx, 2) + pow(dpointy, 2))  double scale = dpoint / dcm;

but have no idea how coordinates of left bottom corner in cm coordinates.

this kind of transformation (using scale , tilt angle) called affine transformation. might want use opencv libraries simplicity. code simple:

double scale = dpoint / dcm;   point center = point( img.cols/2, img.rows/2); mat warpmat = getrotationmatrix2d( center, angle, scale ); point2f src[1]; point2f dst[1]; src[0] = point2f(src_x, src_y); transform(src, dst, warpmat);

then have result inside dst. can of course make src array larger , give transform method more points @ once.
see this more information opencv , affine transformation.

if don't want use opencv can still take @ documentation pages of getrotationmatrix2d , warpaffine , implement yourself, quite simple:

enter image description here

build matrix (warpmat):

enter image description here

and then, each point (x,y) build vector [x,y,1] , matrix multiplication between warpmat , [x,y,1]:

enter image description here


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