# Index : Eulerian path Generators

### Quad Mesh

Size Width   Height   Border

### Star Mesh

Computes intersections of lines from vertex i to vertex i + 2 to create a graph solved by Hierholzer
Size sides   random pc   Border

### Simple Star

Connecting vertex i to vertex i + (side separation) - complete if sides and side_separation are relatively prime or
use Hierholzer to make a fully connected star
Size sides   side separation   random pc   Border   fully connected (if sides odd)

### cardioid

Connecting vertex i to vertex 2*i mod sides - complete if sides is a primitive root of 2 see Sequence A167791
Size sides   Border

### Circles

Path step size degrees. required steps per segment computed steps per segment Columns rows radius separation #sides polygon radius circle separation inscribed circle inscribed radius #n circles radius centre radius centre radius centre radius centre radius centre radius centre

### Knight's tour

size n - board is n x n Border an array of arrays of order position in the tour [ [56,53,12,5,44,51,14,17], [11,6,55,52,13,16,45,50], [54,57,4,9,48,43,18,15], [3,10,7,24,31,46,49,42], [58,33,30,47,8,23,26,19], [63,2,61,32,25,20,41,38], [34,59,64,29,36,39,22,27], [1,62,35,60,21,28,37,40] ]

### Infill

Perimeter - Polygon sides   sides per strut Radius inset