Relative Split

For several reasons a designer might want to use ratios between geometric objects to describe a certain kind of geometric style. Therefore, the relative split can be used. The relative split operates on a scale between zero (0) and one (1).

Example 1: Cut in Half

The following figure shows the next applied rule. The "'0.5: X" introduces the relative split. It divides the actual scope by 2.

...
rel_example01 --> split(x){ '0.5: X | { ~1 :Y }* | 2 : Z | { ~1 :Y }* }
...

Example 2: Golden Section

Common design rules like the Golden Section can be quickly realized and branched. The following rules start with a decomposition of cuboid with a length of 10. Note that only the length ratio is promoted as a relative value. Rules a and b repeat the relative split with the Golden Section ratio.

...
rel_example02 --> split(x){ '.382: a | {  '.618: b } }
a --> split(x){ '.382: X | {  '.618:Y } }
b --> split(x){ '.382: X | {  '.618:Y } }
...

Example 3: Composed Golden Section

Further subdivisions can be made with a composition of the rules of example 2.

...
rel_example03 --> split(x){ '.382: a | {  '.618: b } }
a --> split(x){ '.382: a | {  '.618: c } }
b --> split(x){ '.382: b | {  '.618: d } }
c --> split(x){ '.382: X | {  '.618: Y } }
d --> split(x){ '.382: X | {  '.618: Y } }
...

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