[General] Get evenly weighted, random point in rectangle

[Serenity09]

I want to get an evenly weighted, random point in an angled rectangle. I was wondering if there are any libraries for shapes, particularly rectangles, available that can do that? Even better if it can also detect points being inside a rectangle. I don't have any big preference for how it defines rectangles internally. I don't think sampling random points and then rejecting ones outside the rectangle will work for performance reasons, but I could be overestimating things

The only thing I've found is Outside/Inside Polygon Detection System [Nhoek System] - Wc3C.net which might work, but I don't fully understand how it's implemented and the parts I do get make me a bit worried about how it'll do dynamically creating shapes. More importantly, I'm also not sure how I'd extend it's structure properly for my needs

 

[Noobsmoke]

You might wanna try this Line Segment Enumeration .v2.1a
If you use it wisely it you can achieve that.

 

[IcemanBo]

[vJASS] - [System] Polygon
^Flux has included much polygon logics which you might use, when you want to rotate, move expand, intercect with other rects, etc.

I'm not a maths pro, but I wouldn't know a fast and efficient way to just instantly get a random location inside a polygon-- for rects I would maybe try to get a non-angled point, with simply maths logics, and then rotate it by angle theta so it gets random into my rotated rect.

If you want include own logics, and don't need polygons, but really only basic rect logics, then you might write something like PurplePoot used here: PurplePoot - Prismatic Spray
(under "Geometry" trigger -- he creates a trigometric rect, and then make straight forward checks if it contains a point -- tequnique I would use same as I said above, and I also do this rotation trick inside the LineSegmentEnumeration)

 

[Dr Super Good]

The maths is very simple.

1. Find evenly weighted random point in non rotated rectangle. This is just a random X and Y between the minimum and maximum extents.
2. Rotate point around centre of the rectangle. This requires converting the point to be relative to the centre of the rectangle, multiplying it by a 2D rotation matrix and then offsetting it by the centre of the rectangle.

 

[Kaijyuu]

Matrix math is not "very simple" for most people xD

Still relatively easy with some trigonometry though. Multiply the line length (from the starting point) by the sin of the angle of rotation for the y offset, and and by the cos of the angle for the x offset.
(trig was my worst math subject so apologies if I messed up the formula)

 

[Serenity09]

Thanks everyone for your input. I'm going with the recommendation to generate a random point in a standard rect and rotate it after

 

[Dr Super Good]

Matrix math is not "very simple" for most people xD

The expansion of the rotation matrix with vector is used since it is only 2D and JASS does not support such maths natively.

As Wikipedia shows...

Or since the images do not work...
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)

Both only need simple high school mathematics, taught when you are around 12-13.