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March 30th, 2016, 03:44 AM   #1
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Calculate co-ordinates of embedded rectangle on rotation of parent rectangle

OK... too many years since school but I want to know the mathematical formulae to calulcate the co-ordinates of the green rectangle (X,Y of each corner) when he known values are:
Width and Height of parent (blue) rectangle
Rotation in degrees or radians about the centre of the rectangle
Initial co-ordinates of the small rectangle are relative to the larger one
e.g. Blue is 2000 x 1500 pixels (points) Top Left is 0,0 Bottom right is 2000,1500 in an X,Y co-ordinate system
Green has four corners defined where each has a defined X,Y co-ordinate.
I can work with a formulae relating to distances in mm instead of pixels, and angles; and can convert them.
Note; I need to know the change in location (A --> B) of each corner in relation to either the Centre (D), or the original 0,0 (C)

Hope someone can help : )
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March 30th, 2016, 05:49 AM   #2
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iv'e attached an example for point A. you can do the same for each point

i'm assuming that both triangles rotate together
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March 30th, 2016, 05:54 AM   #3
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important note: this Matrix is for counter clockwise revolution. for clockwise use a negative angle
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March 30th, 2016, 07:19 AM   #4
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Wolfram|Alpha Widgets: "Rotation Matrices Calculator MyAlevelMathsTut" - Free Widget Gallery Widget
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March 30th, 2016, 12:48 PM   #5
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Perfect! I'd forgotten about Matrices. Thankyou both : ) especially Shai for the old school penmanship
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