Fast way to check if a rectangle is inside a triangle (2D)

Question

Given vertices of rectangle and triangle, I can't find or figure out an algorithm that would check if a rectangle (2D, x-y axis aligned, not rotated) is inside a triangle (2D).

The only way I see it is to check if all rectangle points are inside the triangle, but I need the algorithm to be as fast as possible, so maybe there is a faster way to do this.

Consider posting on [scicomp.se], it might have a bigger target audience and visibility — Anton Menshov, Jan 20 '20 at 02:48
With "all rectangle points" do you mean the 4 vertices of the rectangle? Since rectangle and triangle are both convex figures this is sufficient. Is checking 4 points considered too much in your context? — Diego Mazzaro, Jan 20 '20 at 13:05

score 0 · Accepted Answer · answered Jan 20 '20 at 11:05

As both a rectangle and a triangle are convex polygons, it suffices to check that the four corners of the rectangle lie inside the triangle. This can be done by plugging the coordinates of the corners into the implicit equations of the sides and checking the signs.

Maybe using this answer: https://stackoverflow.com/a/21510010/1196549

Fast way to check if a rectangle is inside a triangle (2D)

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