View source for Ping pong ball dispay

== Introduction ==

<gallery>
Pingpongballtesselation.svg
271_hex_layout.svg|
271_hex_layout_A4.pdf|A3 PDF version to be printed
</gallery>

Ping Pong ball (table tennis) display using WS2812B and Raspberry Pi Camera.

16 × 16 = 256 balls, or hexagonal grid, tesselation?
* More visually interesting
*Uniform neighbors
*Natural expansion
*No diagonal-neighbor ambiguity: 
*The geometry feels less rigid:

https://wiki.luntti.net/index.php?title=File:271_hex_layout_A4.pdf

Hexagonal 1 + 6 + 12 + 18 + 24 + 30, always six (6) more. Thus <math>T(n) = 1 + 6 + 12 + \cdots + 6n = 1 + 6(1+2+\cdots n) = 1 + 6 \frac{n(n+1)}2 = 1 + 3n(n+1)</math>

{| class="wikitable"
! Layer ''n''
! Added
! Total
|-
| 0
| 1
| 1
|-
| 1
| 6
| 7
|-
| 2
| 12
| 19
|-
| 3
| 18
| 37
|-
| 4
| 24
| 61
|-
| 5
| 30
| 91
|-
| 6
| 36
| 127
|-
| 7
| 42
| 169
|-
| 8
| 48
| 217
|-
| 9
| 54
| 271
|}

<youtube>EZEMK-C-nSo</youtube>

== Mechanical structure ==

<gallery>
Hex displayPlans.svg| The dimensions and picture. The dimensions are on the other layer, so those can be hidden. Inkscape shows the texts on the right position.
</gallery>

Diameter of ping pong ball is 40 mm. Centers 40 mm apart horizontally and 34.641016 mm apart vertically.

Inner hexagon:
*center → flat side: 331.769 mm
*center → corner: 383.094 mm
*flat side length: 383.094 mm
*across flats: 663.538 mm
*across corners: 766.188 mm
Outer hexagon:
*center → flat side: 356.769 mm
*center → corner: 411.944 mm
*flat side length: 411.944 mm
*across flats: 713.538 mm
*across corners: 823.888 mm
*Distance between the two hexagons: 25 mm