Guided example
Recover 399 from the shape’s scale
Preset d = 399 and h = 1/100. The radii are 3.99, 1.35, 0.45, 0.15, 0.05, 0.01, and 0. The geometric construction identifier, scale unit, and identity pose stay in the record.
Start from radius 3.99, export the record, then recover the shape from that record alone.
Rounding merges possible inputs. The stored remainders identify the original trajectory. Q/S is the rational map, not λ = φ/(φ+π).
Domain: inside original 15 bit domain. Arithmetic: exact integer. h = 1/100.
| Step | d | radius h·d | remainder |
|---|---|---|---|
| 0 | 399 | 399/100 | 639958766566422 |
| 1 | 135 | 135/100 | 893219131545030 |
| 2 | 45 | 45/100 | 297739710515010 |
| 3 | 15 | 15/100 | 99246570171670 |
| 4 | 5 | 5/100 | 699748856723890 |
| 5 | 1 | 1/100 | 339949771344778 |
| 6 | 0 | 0/100 | — |
Integer trajectory complete; radius is zero. That terminal state is a point, not six landmarks.
a = 3.99
a = 1.35
a = 0.45
a = 0.15
a = 0.05
a = 0.01
a = 0