Fix: is_simple_quad for triangles

[mcnick]

Problem

I discovered that the area_between_two_curves function is not symmetrical and could even find simple examples where the calculation is obviously wrong, e.g.

p = np.array([[0, 1, 2], [0, 1, 2]]).T
q = np.array([[0, 1, 2], [0, 0, 2]]).T
area_between_two_curves(p, q)  # Output: 0.0
area_between_two_curves(q, p)  # Output: 1.0

It turned out for triangles, i.e. having one vertex twice, the is_simple_quad function is False in case they are in clockwise order.

Changes

• fixed check for negativity of cross products
• added tests for triangles

What to look for

• The logic is still correct and makes sense
  • One could argue is_simple_quad does not need to work for triangles. But the change has no effect on quadrilaterals and for what it's used in this package it makes sense to correctly consider triangles.

[cjekel]

@mcnick Thanks for this! Sorry it's been long. I was unplugged for a couple weeks. My initial thought is something worried about preserving backwards compatibility with the old behavior. However, given that you point how out the old behavior was obviously wrong in some cases then this is a necessary bug fix!

[cjekel]

@mcnick LGTM!

I'm adding your simple triangle example as a basic unit test as well:

p = np.array([[0, 1, 2], [0, 1, 2]]).T
q = np.array([[0, 1, 2], [0, 0, 2]]).T
area_between_two_curves(p, q)  # Output: 0.0
area_between_two_curves(q, p)  # Output: 1.0

This change can be summarized as the old code would rearrange the formation of a natural triangle of four points. The rearrangement of four points fundamentally changes the shape, and therefore the area within those four points. The new code thanks to @mcnick now allows for the shoelace area to be calculated for a natural triangle of four points (i.e. a triangle where two of the four points are the same).