stoic ledge
Hi, I am looking to find a formula to calculate the number of vertices in a hexagon grid. I can't seem to find a pattern to how hexagonal count affects the number of vertices.
Is there a formula to determine vertice count so I may determine my vertices array size for my mesh or would the best way be to iterate through every hex and determine neighbouring hexagons to calculate vertex count?
rocky basin
@stoic ledge
If not mistaken, it will be:
Hexagons:
1 + 3 * r * (r +1)
Vertices:
6 * (1 + r * (r + 2))
I'm not sure what the value in brackets means.
Keep in mind that these formulas will work only for a particular shape type from your example. For other kinds of shapes, such as triangles or rectangles, you would need to reinvent the formulas.
stoic ledge
<@104169826615820288>
If not mistaken, it will be:
Hexagons:
`1 + 3 * r * (r +1...
Thank you so much. Is there a place to find such formulas or did you manage to work it out? Algebra is really not my strong suit.
The numbers in the brackets are just the exterior vertices I counted in some attempt of finding a pattern to the vertex count
rocky basin
Thank you so much. Is there a place to find such formulas or did you manage to w...
It's about noticing patterns. The shape you provided consists of 6 "triangles" that scale with radius. The formula for 1 + 2 + 3 + ... + n pattern is n * (n + 1) / 2. If we multiply this formula by 6 and add 1, we get the total hex count. If we reduce n by 1 and multiply it by 12, we will get the count of brown dots. If we multiply r by 6 * 3, we will end up with the white dot count. After summing both results with 6 dots from the middle hex, you will end up with the vertices formula.
stoic ledge
It's about noticing patterns. The shape you provided consists of 6 "triangles" t...
Thank you for the comprehensive explanation. I’ll try and digest this as much as I can. Appreciate the help a lot!