Great that at least some one else thought of this. To bad I only encounter this page several years later. However, I am going to answer your question for the basic hexagons instead. The pictures that have been shown until now are not 100%. And on a 1 meter map the grid will be out of shape. Meaning no 60 degree turn possible.
I have been experimenting on:
Different sizes of hexagons: Which triangle (in pixels) basis gives the highest accuracy on 1 meter maps once printed out. This includes having them as perfect as possible when turning them 60 degree's. Also when turning them 180 degree's for refitting.
Different combined layers of hexagons.
Single hexagons for cutting out high detailed pictures (RAM = insufficient at big maps).
The exact limits of my computer plus what I feel is allowable.
I did not experiment yet on having elevation by making different shaped hexagons. But I do know that the basis needs to be correct before making the elevation.
Summary:
Accuracy of 1 mm or less on a 1 meter map. The 60 degree rule.
I need lines that can fit themselves when turned 180 degree´s.
I need the triangle to fit on my screen with maximum zoom.
I narrowed down my selection to 3 with these rules:
Small:
Size; +26 x +45, 27 x 46 pixels
Inaccuracy on 1 meter; 0,74 mm
Sequence; 131213131312131
Medium:
Size; +41 x +71, 42 x 72 pixels
Inaccuracy on 1 meter; 0,20 mm
Sequence; 1312131313121313131312131
Large:
Size; +56 x +97, 57 x 98 pixels
Inaccuracy on 1 meter; 0,05 mm
Sequence; 1312131313121313131213131312131
The one's are 1 pixel.
The two's and three's are groups of 2 pixels. A 2 is 4 pixels in total and A 3 is 6 pixels in total.
If you add a sequence up, you will see that they are the width in pixels. If you add them up and counting 4 and 6 instead of 2 and 3. You get the hight in pixels.
The + numbers are what you add in pixels when you place 2 triangles on top of each other or against each other.
Feel free to ask questions. On my email.