Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span equals an integer number of pixels).

====================

Thankfully, in programming, there's really no reason to make the hexes absolutely perfect. As long as they look good, opposing sides are of same length (e.g. top right == lower left) and the hexes are drawn at minimum processing, they work.

Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span equals an integer number of pixels).

====================

Thankfully, in programming, there's really no reason to make the hexes absolutely perfect. As long as they look good, the opposing sides are the same length and the hexes are drawn at minimum processing, they work.

Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span equals an integer number of pixels).

====================

Thankfully, in programming, there's usually no reason to make the hexes absolutely perfect. As long as they look good, the opposing sides are the same length and the hexes are drawn at minimum processing, they work.

Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span equals an integer number of pixels).

====================

Thankfully, in programming, there's usually no reason to make the hexes absolutely perfect. As long as they look good and are drawn fast, they work.

Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span amounts to an integer number of pixels).

====================

Thankfully, in programming, there's usually no reason to make the hexes absolutely perfect. As long as they look good and are drawn fast, they work.

Here's a simple algorithm on adding an "almost-perfect" hex (it just looks good, but isn't actually perfect - the diagonal lines are about 10% longer than the vertical ones):

For a vertical (pointy) hexagon w/ an outer diameter of 100 pixels (length between two opposing angles):

1. Start drawing a line from x, y-50 (x and y = center of hex) ==> x-50, y-25. (top left diagonal)
2. Draw a line from x-50, y-25 ==> x-50, y+25. (left vertical)
3. Draw a line from x-50, y+25 ==> x, y+50. (bottom left diagonal)
4. Draw a line from x, y+50 ==> x+50, y+25. (bottom right diagonal)
5. Draw a line from x+50, y+25 ==> x+50, y-25. (right vertical)
6. Draw a line from x+50, y-25 ==> x, y-50. (top right diagonal)

Notice how you can apply this to any size (+/- 25 is 25% of outer diameter, while +/-50 is 50%, so for a 40-pixel hexagon this would be +/- 10px and +/- 20px, respectively). Note however, that the smaller a hexagon is, the more difference there'll be between vertical/horizontal sides and diagonal sides, because a vertical/horizontal line cannot be a decimal number of pixels in length (although diagonal lines can, as long as both its x and y span amounts to a non-decimal number of pixels).

====================

Thankfully, in programming, there's usually no reason to make the hexes absolutely perfect. As long as they look good and are drawn fast, they work.