ABSTRACT
We have relied on regular polygons to eliminate the need to think about where vertices are located. They are equally spaced around the circle, and that is that. In our new world, we eliminate the parameters n and J and replace them with a single parameter, V , together with ( x , y ) coordinates that are user-provided (in the four-color version of the model). The differences are set forth in this table. (Note: This is based on the Erfle and Erfle Bridges 2020 paper, which does not italicize letters.)
| What changesWhat does not | Polygons String Art model | Beyond Polygons model ( Excel file name: 4ColorAestheometry.xlsx) |
| How vertices are determined | Click n | User types in their own ( x , y ) coordinates of each vertex (up to 40 per color) |
| How the VF is determined | Click n and J | User types in how many coordinates to use, V |
| Calculation of VCF | VCF = GCD( n , J ) | There is no VCF as the only move is a "jump" of 1 |
| Number of Vertex Frame (VF) lines | V used = n /VCF | V (As we see below, V can be less than vertices provided.) |
| Subdivisions, S | No change ( S and P values are entered by typing (like Four Colors files) rather than by arrow keys.) | |
| Number of Subdivisions per line, P | ||
| Calculation of SCF | SCF = GCD( P , S · V used ) | SCF = GCD( P , S · V ) |
| Lines in image | n /SCF· S /SCF = V used ·S /SCF | V · S /SCF |
