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How can i get the get upper-left, upper-right, lower-left and lower-right corners XY coordinates from a rectangle shape when i have the following data available to me?


Is there an easy way of doing this?


the rectangle is being rotated at positionX and positionY, the upper left corner when no rotation is applied (rotation=0).

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Are positionX and positionY the coordinates of the center? –  Alex Becker Jul 14 '12 at 8:01
No, that is the position of the upper left corner of the rectangle when no rotation is applied. –  netbrain Jul 14 '12 at 8:02
About which point are you rotating? The origin? The centre of the rectangle? –  Aneesh Karthik C Jul 14 '12 at 8:08
How is the rectangle being rotated? About the upper left corner, or about the center? –  Zev Chonoles Jul 14 '12 at 8:08
the rectangle is being rotated at positionX and positionY, so the upper left corner when no rotation is applied –  netbrain Jul 14 '12 at 8:12
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2 Answers

up vote 3 down vote accepted

First, let me take these smaller notifications:

  • positionX = $x$
  • positionY = $y$
  • width = $w$
  • height = $h$
  • rotation = $\theta$ Thus, our top-left point is $(x,y)$. The other 3 points will be(without rotation): $(x+w, y)$, $(x+w, y-h)$ and $(x, y-h)$.

Since we are rotating the complete geometry about point $(x,y)$ by an angle of $\theta$, we'll have new points given as:

  1. $(x, y)$
  2. $(x + w*\cos(\theta), y + w*\sin(\theta))$
  3. $(x + w*\cos(\theta) + h*\cos(\frac{3\pi}{2}-\theta), y + w*\sin(\theta) + h*\sin(\frac{3\pi}{2}-\theta))$
  4. $(x + h*\cos(\frac{3\pi}{2}+\theta), y + h*\sin(\frac{3\pi}{2}+\theta))$

which, on simplification give us the co-ordinates

  1. $(x, y)$
  2. $(x + w*\cos(\theta), y + w*\sin(\theta))$
  3. $(x + w*\cos(\theta) - h*\sin(\theta), y + w*\sin(\theta) - h*\cos(\theta))$
  4. $(x + h*\sin(\theta), y - h*\cos\theta))$

I am not entirely sure of the conversion I did for $\sin(\frac{3\pi}{2}±\theta)$ or $\cos(\frac{3\pi}{2}±\theta)$

KEY: 1. -> Top-Left corner, 2. -> Top-Right Corner, 3. -> Bottom-Right Corner and 4. -> Bottom-Left Corner.

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You state that (x,y) will always be the upper left corner. This is not true. if you rotate the rectangle a full 180 degrees, then in fact the (x,y) would be the bottom right corner? –  netbrain Jul 14 '12 at 11:02
Yes, it will be so, but in that case, you'll have to rotate your view too(so that +ve Y-Axis goes back to top). –  hjpotter92 Jul 14 '12 at 11:04
Im not sure i follow. my requirement for this is to be able to identify the upper-right, upper-left, bottom-right and bottom-left corner regardless of the rectangles rotation. –  netbrain Jul 14 '12 at 11:11
With the logic you've given; you can't say which corner goes to which position unless you rotate your view also such that the Y-Axis goes down-to-up(from negative to positive). Otherwise, in my solution, the original top-left will remain at the same co-ordinate value and others will change. Position can't be determined. –  hjpotter92 Jul 14 '12 at 11:13
The bottom-right corner doesn`t seem to be correct. I dont't have the time right now to investigate, but ill look at it later. –  netbrain Jul 14 '12 at 12:59
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Let the coordinate of upper left corner be $(a,b)$ and width and hight are $w$ and $h$ respectively. Now if the rotation angle is $0$ then upper right corner is $(a+w,b)$, lower left corner is $(a,b-h)$, lower right corner is $(a+w,b-h)$. Now translate your origin to $(a,b)$ and rotate the coordinate axes by $\theta$ say, then you can compute the transformed coordinates using the formulas given here and here ${} {} {}$

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