algorithm that openGL uses to construct 3D surface from vertices a 3D model is a collection of points, and basically a 3D software has algorithm to find out how those points connect to make surfaces.
I'm searching for what those algorithms are called, that can use a set of points and properly fill in the dots to create the accurate 3D model from the set of points to create the 3D object intended.
Please mention the name of the algorithm if it's a general approach, if it's file specific then please assume for .obj files. Any links or references would also be highly appreciated.
Most 3D models are not just collections of points; they’re also the information about how those points are connected. Those are polygon meshes. What you’re describing sounds like a point cloud, which is what processes like 3D scanning often produce. That article has a “conversion to 3D surfaces” section; if you search for “point cloud meshing” elsewhere you should also find a bunch of information about ways to do this. One new-ish technique worth looking at, which is more robust than a lot of older approaches to the problem: Fast Winding Numbers for Soups and Clouds.
For OBJ files in particular, polygons are specified with a list of vertices using the f command as described here.