Rotopic group notation (EntityClass, 3)
From Hi.gher. Space
In group notation, letters are used to represent dimensions.
- A normal letter represents that the object is extruded in that dimension.
- A superscript letter represents that the object is tapered in that direction.
- A pair of parentheses represents that the object is spherated.
Conversions
To digit notation
- Change every letter (subscript or not) to a number 1.
- If there is a sequence (111...) with n 1s and nothing else inside the parentheses, change the entire sequence, including parentheses, to the number n.
- If there is a sequence of superscript 1s, change the sequence to the number of 1s in the sequence, retaining the superscript.
To surface equation
Marek14 found a way to convert group notation to a surface equation, edited here for ease of use:
Using the example (((xy)z)w):
- Make a square of each variable and add terms within parenthesis: (((x2+y2)+z2)+w2)
- Replace each parenthesis with a square root function: sqrt(sqrt(sqrt(x2+y2)+z2)+w2)
- Immediately outside of each square root function, subtract a parameter and square this: (sqrt((sqrt((sqrt(x2+y2)-A)2+z2)-B)2+w2)-C)2
- Remove the outermost square and parentheses, and form an equation with this expression as the LHS and zero as the RHS: sqrt((sqrt((sqrt(x2+y2)-A)2+z2)-B)2+w2)-C = 0