Is there a typo in hull.py

[Phonicavi]

Sorry for bothering! I was wondering whether there is a typo in the hull.py file, line:190:
in function def distLine(pointA, pointB, pointX)

	vec1 = pointX - pointA
	vec2 = pointX - pointB
	vec3 = pointB - pointA
	vec4 = cross(vec1, vec2)
	if vec2.length() == 0:
		return None

	else:
		return vec4.length()/vec2.length()

You have calculated vec3 but never use it. I think for a line-segment from pointA to pointB, the distance from pointX should be:

	if vec3.length() == 0:
		return None

	else:
		return vec4.length()/vec3.length()

:)

[swapnil96]

Looking at this after a long time so I might be rusty in coordinate geometry now

But it seems
What you have written is correct along with that vec4 = cross(vec1, vec3)
I don't know why it didn't come up during testing or not pointed by anyone till now.

Can you create a pull request with necessary changes

1. Remove vec2
2. Rename vec3 as vec2, vec4 as vec3
3. Accordingly the if-else thing

[Phonicavi]

Thanks for your replying.

Suppose we have a triangle denoted as ABX, with vectors vec1 = \vec{AX}, vec2 = \vec{BX}, vec3 = \vec{AB}, and vec4 = cross(vec1, vec2).
Let \theta be the angle between \vec{XA} and \vec{XB}, the norm of vec4 is actually |AX| * |BX| * sin(\theta).
Consider the area of triangle ABX, suppose the distance from point X to line AB is d, then the area T = 0.5 * |AB| * d, where the base |AB| is the norm of vec3. Again the area of the triangle can also be computed by T = 0.5 * |AX| * |BX| * sin(\theta), see https://en.wikipedia.org/wiki/Law_of_sines#Relationship_to_the_area_of_the_triangle.

Thus d can be computed as |AX| * |BX| * sin(\theta) / |AB|, which is exactly the norm of vec4 / the norm of vec3. Besides if the norm of vec3 is zero (i.e. point A and point B converge into the same position) there is no line segment any more. :)

[swapnil96]

Yep, correct again, so there are 2 ways to close this issue

1. Either we implement the way I mentioned last time, it will take more changes but it will use only 2 vectors and a cross product, not that it matters for time complexity or such, just that it will use the area of a parallelogram formula

2. We just change the typo of vec2 to vec3 and we are done.

I think I will also go with method 2. If that is all I will close the issue by making that change

[Phonicavi]

Method 2 looks good to me, thank you!

[swapnil96]

22e3e3a