Reference Talk:Tiling Pattern

• Adding a table of unit square normalization scales.

The tiling pattern creates a series tiles in the x-z plane. See the image below for examples of the twenty-seven available patterns.

The syntax is as follows:

pigment {
  tiling Pattern_Number
  [PATTERN_MODIFIERS...]
  }

The various tiling patterns annotated by tiling pattern and tiling type respectively

For each pattern, each individual tile of the pattern has the same beveling as the other tiles in that pattern, allowing regular caulking to be defined. For a pattern with N tile types (where N is the tiling type noted in the above image) the main color/texture of the tiles are at x/N with x going from 0 to N-1, and the extreme color/texture caulk for these tiles are at (x+1)/N. The bevel covers the range between these two values.

To begin exploring the tiling pattern right away, see the distribution file ~scenes/textures/pattern/tiling.pov. It uses obvious colors to better illustrate how the feature works, and you can optionally write it's color_map to a text file. Once you get a feel for the break points, you can always define you own map!

The scale required to fit the core repeated tile into a unit square size for each tiling pattern is given in the table below.

Tiling Number	Unit square normalization scale
1	<1,1,1>
2	<2/3,1,1/sqrt(3)>
3	<1,1,2/sqrt(3)>
4	<1,1,2/sqrt(3)>
5	<2/3,1,1/sqrt(3)>
6	<1/4,1,1/4>
7	<1/(sqrt(2)+1),1,1/(sqrt(2)+1)>
8	<1,1,1/(sqrt(3)+2)>
9	<1/2,1,1/(2*sqrt(3))>
10	<1,1,1/2>
11	<1/3,1,1/3>
12	<1/3,1,1/3>
13	<1/(sqrt(3)+1),1,1/(sqrt(3)+1)>
14	<1/(sqrt(3)+1),1,1/(sqrt(3)+1)>
15	<1/5,1,1/5>
16	<1/(sqrt(3)+3),1,1/((sqrt(3)+1.0)*2.0)>
17	<1/(sqrt(3)+3),1,1/((sqrt(3)+1.0)*2.0)>
18	<1/4,1,1/4>
19	<1/2,1,1/((sqrt(3)/2)*3)>
20	<1/2,1,1/((sqrt(3)/2)*3)>
21	<1/(1+sqrt(3)),1,1/(1+sqrt(3))>
22	<1/(2+sqrt(3)),1,1/(3+(2*sqrt(3)))>
23	<1/(3+sqrt(3)),1,1/(3+(3*sqrt(3)))>
24	<1/(3+sqrt(3)),1,1/(3+(3*sqrt(3)))>
25	<1/(4*sqrt(2)),1,1/(4*sqrt(2))> (*)
26	<1/(4*sqrt(2)),1,1/(4*sqrt(2))> (*)
27	<1/(4*sqrt(2)),1,1/(4*sqrt(2))> (*)
(*) - Unit square scaling not possible with penrose tiling. Scaling given useful to see all tiles in a way symmetrical in z.