## Combining UTM zones into one solid map

I have an area, example 4000m x 4000m. So, 4x4km. The origin can be placed anywhere, maybe in center, maybe on the top-left, nevermind.

Now, I want to fill this area with some stuff from OSM. I read a lot about UTM, zones, etc. UTM quadrant is divided into 6×10 100km squares, this squares are divided into 10×10 10x10km squares, this squares are divided to 10×10 1x1km squares and so on.

Getting back to my 4kmx4km square. How do I convert coordinates to place objects in my square and the position responds to reality?

To make it harder, let’s say that I want to put on the square objects from squares from different UTM quadrants from different zones, for example: most southern-east 1×1 from 34V, most southern-west from 35V, most northern-west from 35U and most northern-east from 35U.

Additional question: Is it possible to create one continuous maps (builded from smaller pieces), which covers the region composed of several UTM zones (for example, from 29W to 34S).

How to translate UTM coordinates properly?

**EDIT**

Ok, I implement Albers, Lambert and Equidistant projections for some tests. Input args: a = 6378206.4 m, e = 0.00676866, e2 = 0.0822719 Standard parallels: 55.0, 49.0 Origin: 52.205746, 22.514281

And results:

Albers : x = -489.71509; y = -2291.5

Lambert : x = -489.15250; y = -1653.5

Equidistant: x = -489.71533; y = -2289.5

I checked the algorithms and are ok, the results agree with the sample data. What is the reason that the result of the Lambert projection stands out from the rest? Does this mean that Lambert is better to applied to larger areas than the other two?