My Math Forum Calculate co-ordinates of embedded rectangle on rotation of parent rectangle

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March 30th, 2016, 03:44 AM   #1
Newbie

Joined: Mar 2016
From: Brisbane, Australia

Posts: 2
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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
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
Newbie

Joined: Feb 2016
From: israel

Posts: 17
Thanks: 3

iv'e attached an example for point A. you can do the same for each point

i'm assuming that both triangles rotate together
Attached Images
 20160330_164527.jpg (77.9 KB, 12 views)

 March 30th, 2016, 05:54 AM #3 Newbie   Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 important note: this Matrix is for counter clockwise revolution. for clockwise use a negative angle
 March 30th, 2016, 07:19 AM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587
 March 30th, 2016, 12:48 PM #5 Newbie   Joined: Mar 2016 From: Brisbane, Australia Posts: 2 Thanks: 0 Perfect! I'd forgotten about Matrices. Thankyou both : ) especially Shai for the old school penmanship

 Tags calculate, coordinates, embedded, parent, rectangle, rotation

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