given a list of 3d points, what are the simplest ways to display them as a surface?

is it essential to first translate the points to triangles or polygons? if so, are there codes that i can use? the number of points i refer to is quite large (~40,000), will that be a problem?

You should look at Delaunay triangulation algorithms… Or convex hull of a cloud of points. In fact, when you’ve got one, you’ve got the other (and for you, the first one is what is important).

Basically, those algorithms enable you to create a set of triangles from a set of unorganized points (and here is your surface !).

The thing is, if you really want to understand the underlying mathematics and code the algorithm yourself, you should be prepared for some headache !

Eric

P.S. : you will find hundreds of things about this on the net.