Hi all,

 

In my work we have to run tests whose input parameters are in 3 dimensions, forming lines across a grid, like so:

 

What I want to know is, what is the best way of quantifying the spread of these lines?

If I were to use the extreme points to plot a cuboid I think that would overestimate the parameter space over which the experiments were run. I have also considered calculating the convex hull, using the extremes but I feel this might also lead to the same problem, albeit with a smaller overestimation.

I need to demonstrate that the lines are well spaced out from one another, perhaps by the angles between the lines.

 

Is there already a way of quantifying these types of things?

 

I'd really appreciate some help with this, it's a bit of a teaser for me with my limited maths abilities.

 

Thanks in advance

 

 

just guessing...

 

But it seems your points are on three lines converging at a point (17.5,1,3) - you could work out the volume constrained by the three planes that these lines define as a ratio of the maximum volume for this converging situation which would, as you mention, be the rectangular prism that contains all points.

 

Alternatively - two lines which converge will always lie on a single plane, so you could simplify to 3 comparisons of two variables in two dimension a|b a|c b|c

 

I am sure there is a way of producing a simple quantification of spread - hopefully someone will swing by who, unlike me, knows what they are talking about