Automatic creation of polygons from Feature Class points in ArcGIS for Desktop?

Question

I have two point feature classes, let's call them A and B. They are well-spaced and the points are non-overlapping:

My objective is to create a topology using these two sets of points by connecting the minimum number of A points together to form polygons each of which contains one B point. The result would look something like this:

I am familiar with how to use the Topology rules within a Feature Dataset to ensure that the polygons do not overlap and that the A points appear on the edges of the polygons, whereas the B points are properly contained.

I am not familiar with any way to automatically calculate/draw the edges of the polygons themselves in ArcGIS. Is there a tool (or sequence of tools) I could use to automatically group the A feature class points into the vertices of polygons and then produce an output feature class of polygons?

If not, then the solution I'll have to pursue will be to write a toolbox script to process the A and B feature classes and generate a new polygon output class. If there is a "quick" way to do this, without having to write my own Python interacting with arcPy, I'd love to know.

Answer 1

Triangulate points A:

Create Thiessen proximity polygons for points B:

Intersect 2 layers. Add field area and populate it by polygons’ area. Sort table in descending order using area field. From sorted table remove duplicate (not first) records using field Tri_Index:

Join above table to triangles using Tri_Index for joining. Use field B_ID (points B id field) to show triangles:

I hope the rest is obvious and I also want to hope that pattern of points relative to each other is similar for the rest of study area