I've a need to compute the area of single elements (dice) of a matrix like this:
https://i.stack.imgur.com/EKVSz.jpg
The matrix is composed by 'c' columns and 'r' rows and every element/rectangle has the same height and width of any other.
knowing the element (x,y) center, I can know if its vertex are: - All out of circle area - All inside the circle area or - Partially inside the circle area (ray = 75.000 micron)
My problem is how I can compute the area of dice that are intersectated by the circle and more in deep how I can can compute the area of the portion of dice dice inside the circle.
So, to make an example, to work on, I've a dice with
CenterX , CenterY [ 29870.4 , 67144.9 ]
DieDimensionX, DieDimensionY [ 5430.52 , 4320.54 ]
Coord of upper left corner (A) [ 27155.14 , 69305.17 ]
Coord of upper rightcorner (B) [ 32585.66 , 69305.17 ]
Coord of lower left corner (C) [ 27155.14 , 64984.63 ]
Coord of lower right corner (D) [ 32585.66 , 64984.63 ]
For each coord I've computed the segment lenght from axis origin and 1 corner (on 4) is out of circle:
sqrt( (x^2) + (y^2) )
A: 74435.261920332
B: 76583.495783129 == >75.000
C: 70430.133924738
D: 72696.81818259
Which is the area of this dice inside the circle? Or else: which is the percentage of the area of dice inside the reticule compared with a full dice? I've read something about 'Simpson rule' that could help me but I don't know (a) if this is the correct approach (b) neither how to apply it on my example.
Thanks to anyone that would be able to help me.
Ciao, Stefano