Seeking method for determining survey points?

I'm trying to write software to create a topographic map, my goal is to select several points of interest and create a minimal mapping that is inclusive of the points and interpolates the topography.

Is there a standard algorithm / approach for progressively selecting additional points?

Update (1): @JoshC

My goal is to produce a mesh, but I'm not as interested in the x,y offset being consistent.

the simple case is with 2 points of interest

Let's say we have a point at (2,2,0) [elevation of 0] and another point of interest at (4,4,8).

The parameters of my algorithm will determine that a z delta of 8 units over a distance of 5.6 units is 'significant' and warrants additional exploration. I'll use the midpoint for this (4,4,?). So the software will recommend that I find z @ (4,4). Let's say I find that to be (4,4,2). From here, my algorithm will decide that a z delta of 2 over the distance of 2.8 [(2,2,0),(4,4,2)] is 'insignificant' but that the 6 unit increase over a distance of 2.8 [(4,4,2),(6,6,8)] is 'significant' and warrants additional exploration ie. surveying (5,5,?)

I'm satisfied with assuming radial topography, by minimal mapping I mean that I'll 'zoom' to a window of [(2,2),(6,6)]  The black box is the viewing window.

My thought is to then 'fill' the colored spaces with the weighted average of the z value and it's distance from the corresponding survey markers.

What I've described above is the algorithm I'm thinking about implementing, but I'm curious if there is already an industry standard (this is generalized, the solution needs to allow for an arbitrary number of points of interest / not just 2)

I'm new to this domain.

• When you say "interpolates the topography", can you elaborate a little on what you're aiming to produce from this? Are you talking about generating elevation surfaces? Do you want to generate a raster or a mesh layer? And what is a "minimal mapping"? May 25 '19 at 1:12
• @JoshC I've updated the question in reply - thanks for taking a look! May 25 '19 at 1:46
• Have you considered using a TIN? May 25 '19 at 2:18
• @Kirk another great term! A TIN might be exactly what I need, is there a standard implementation that recommends survey points to optimize fidelity - any conventions? My application is much less a - I have the data and want to represent the surface, and more a - what data do I need to collect to represent the surface May 25 '19 at 3:51
• More terminology: Digital Elevation Model (DEM) Digital Terrain Model (DTM), TIN breakline. May 25 '19 at 17:52