How to determine if a point is inside a 2D convex polygon?

Question

I have a convex polygon (typically just a rotated square), and I know all of 4 points. How do I determine if a given point (yellow/green) is inside the polygon?

Answer 1

Assuming that your point is at Y coordinate y, simply calculate the x positions where each of the polygon's (non-horizontal) lines cross y. Count the number of x positions that are less than the x position of your point. If the number of x positions is odd, your point is inside the polygon. Note: this works for all polygons, not just convex. Think of it this way: draw a line from infinitely far away straight in to your point. When that line crosses a polygon line, it is now inside the polygon. Cross the line again, outside. Cross again, inside (and so forth). Hope this helps!