How to minimize a midpoint of a 3D line to a 3D data set?

I have two points pt1 = (36.77, 11.63, -38.82) pt2 = (31.77, 14.61, -31.09). I also have a set of data points that I need to use to "connect" these two points.

a = [44.16 17.609 -28.523;
     43.491 15.957 -30.258;
     45.491 16.502 -31.569;
     45.337 17.206 -33.948;
     44.864 14.849 -33.304]

I wanted to connect the points by first making a line between them. I can use the two points to make a vector that would connect them, then I can divide that in half and then find the midpoint between these points. Once I have the mid point I want to "move" it so that it resides "in" the data. To move it in I was going to find the smallest distance from the midpoint of the line and a data point then move the midpoint there. I want to iterate this until I have enough lines that fit the data well. I wanted to do this with fmincon, but I am having a hard time with the parameters. Any suggestions?

Answer 1

[Matt J]

You don't need fmincon for something so simple as finding separation distances of points. It can all be done algebraically,

mindpoint=(pt1+pt2)/2;

[minDistance,minloc]=min(sum(  (a-midpoint).^2   ,2)  ), %R2016b or higher