Maximum perpendicular distance from line to convex hull boundary

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Kwek Lawrence on 9 Sep 2019
Commented: Kwek Lawrence on 12 Sep 2019
I'm looking to find the max perpendicular distance of the 2 faces of a 2D convex hull perpendicular to a symmetry line (y=x). There are 3 possible scenarios
(1) convhull intersects with symline and max perpendicular distance occurs within the symline intersection
(2) convhull intersects with symline but max perpendicular distance to symline does not occur within the symline intersection
(3) convhull does not intersect with symline.
Would like to know how to do so in each of those cases.
Kwek Lawrence on 12 Sep 2019
I think I should rephrase my question.
The ultimate goal is to find the maximum width of a 2D convex hull in the direction perpendicular to the symmetry line. A figure of what I want to achieve and sample data are as attached.
I have convex hull generated based on x and y waveform coordinates.
k=convhull(x,y)
t=linspace(0,140,14001)
My thoughts: (1) Generate perpendicular lines from points on t, (2) determinine a set of 2 intersections with the convex hull for each line (3) Find largest distance between sets of intersections.
Would appreciate any help with this, or any other suggestions to achieve my initial objective.

Neuropragmatist on 10 Sep 2019
I had to do something similar to this some time ago, sorry I don't really remember the specifics but I used rayTriGPU:
To find the intersection between a ray and all of the faces of a convex hull. There is some explanation in the code as to how to do this.
You could adapt this very easily I think to do what you want.
Hope this helps,
NP.
Kwek Lawrence on 12 Sep 2019
Yea that helped. Thanks for your input!