Will points on path with width intersect

Question

I want to be able to check if a list of points will hit a screwed rectangle (rhombus i think).

I start out with 2 point P and T, i want to create a rectangle between the 2 points. I have used https://stackoverflow.com/questions/7854043/drawing-rectangle-between-two-points-with-arbitrary-width to do this. This gives me 4 points A, B, C and D of the new rectangle.

I then want to check if the point M is withing this rectangle.

The two black dots are my points P and T, the black box is the rectangle i want to generate between the two dots, being X wide. I then want to test if the red dots are withing the black box.

Answer 1

There are lots of algorithms to check whether a point is inside or outside a polygon. The simplest being the ray casting algorithm.

The idea is, you cast a ray (assume a line) from your point to either the left or the right. Then for each side of your polygon, you test whether the ray intersects it, and if it does, you add 1 to a counter. At last, if the number of times the ray intersected with a side is odd (that is if counter % 2 == 1), your point lies inside the polygon.