How many hexagons fit in a hexagon?
How many hexagons fit in a hexagon?
The internal angle of the hexagon is 120 degrees so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane….
| Hexagonal tiling | |
|---|---|
| Face configuration | V3.3.3.3.3.3 (or V36) |
| Schläfli symbol(s) | {6,3} t{3,6} |
| Wythoff symbol(s) | 3 | 6 2 2 6 | 3 3 3 3 | |
| Coxeter diagram(s) |
How to calculate the distance on a hexagonal grid?
If dy / 2 > dx, you don’t have to do step two, so the distance is simply dy. Otherwise, the distance is dy + (dx – dy / 2). Unless I made a mistake. M H Rasel linked this post in his previous answer: Hexagonal Grids. Following this excellent post, I figured out that I needed cube coordinates; that gives the easiest way to calculate the distances.
How is the width and height of a hexagon determined?
In the pointy orientation, a hexagon has width w = sqrt (3) * size and height h = 2 * size. The sqrt (3) comes from sin (60°). The horizontal distance between adjacent hexagon centers is w. The vertical distance between adjacent hexagon centers is h * 3/4.
How are the directions on a hex grid related?
Each direction on the hex grid is a combination of two directions on the cube grid. For example, northwest on the hex grid lies between the +y and -z, so every step northwest involves adding 1 to y and subtracting 1 from z. We’ll use this property in the neighbors section.
How to find the distance between two hexes?
So, solving for distance using this system of equations gets you: distance = max( abs(dest.y – start.y), abs(ceil(dest.y / -2) + dest.x – ceil(start.y / -2) – start.x), abs(-dest.y – ceil(dest.y / -2) – dest.x + start.y + ceil(start.y / -2) + start.x) ) That will get you the Manhattan distance between two hexes…