Calculation field matrix ART algo

Hellow, i'm not good in matlab so i hope anyone can really help me and not just give a link to matlab help :p The goal is to implement the art algoritm but therefore i need to have a field where in the image will come with inputparameter LengthX and LengthY and the pixelwidth for the resolution. Further there must be an variable amount of projections. => i can calculate the angle every time from it. so the angle = 360 / projections. Now i have to calculate for each projection witch cells of the field covers a standard default ray with width equal to one cell that stays always horizontal. So the output must be vectors (amount is equal to the amount of projections) with values between 0 en 1 how mutch the standard ray covers the cells from the field.
For example for projection 5 the cell 128 hits the standard ray for half the area so vector5 element 128 must be 0.5. I really hope someone can help me because i'm quite desperate.
In the attachment you see an example for a example how it works.

So the inputparameters must be LengthX , LengthY , angle , pixelwidth. Output must be the amount of projections in vectors that covers the field LengthX x LengthY long.

Thx in advance
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