by Goatmeal

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A Tutorial for Maintaining the Proper Thickness of 45º Angles. Cloning is HIGHLY recommended.

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## 19 Comments

While working on my "Alex Murphy Dings" font of OCP Logos,

Alex Murphy Dings

I, too, came upon the problem of trying to maintain the proper thickness while using 45º angles. This is where math — especially the Pythagorean Theorem — is your friend.

For a brick 1 unit long by 1 unit high, the diagonal length is 1.414 units long. So, to get a diagonal that is 1 unit in length (to match the brick height), the brick itself must be 0.7071 units long by 0.7071units high. Unfortunately, there is no 0.71 scale brick in FontStruct; everything is set to a 1-unit scale. However, we DO have a brick that has a diagonal length of 1.06 units, which is quite close to 1 unit!

I refer to them as diagonal units in the accompanying pictures:

1/4 Angle Brick = 0.35 --> "0.25" diagonal units

1/2 Angle Brick = 0.71 --> "0.50" diagonal units

3/4 Angle Brick = 1.06 --> "0.75" diagonal units

1 Full Brick = 1.414 --> "1.00" diagonal units

All you have to do is:

(1) Divide the Brick Height by 1.414 (the square root of 2)

(2) Round to the nearest 0.25; this gives you the "diagonal unit"

(3) Add the bricks listed above until they total the desired diagonal unit!

Here is a list of the first 10 Brick Heights and their corresponding Diagonal Units:

01 Brick High = 0.71 --> "0.75" Diagonal Units

02 Bricks High = 1.41 --> "1.50" Diagonal Units

03 Bricks High = 2.12 --> "2.00" Diagonal Units

04 Bricks High = 2.83 --> "2.75" Diagonal Units

05 Bricks High = 3.54 --> "3.50" Diagonal Units

06 Bricks High = 4.24 --> "4.25" Diagonal Units

07 Bricks High = 4.95 --> "5.00" Diagonal Units

08 Bricks High = 5.66 --> "5.75" Diagonal Units

09 Bricks High = 6.36 --> "6.25" Diagonal Units

10 Bricks High = 7.07 --> "7.00" Diagonal Units

And so on...

You can also do fractional bricks:

1.5 Bricks High = 1.06 --> "1.00" Diagonal Units

Of course, the bigger and more complex (and thus more) bricks you use in your FontStruct, the more accurate the thickness of your angle will become.

I understand that your tutorial uses current bricks for simplicity, but you may want to add the ones below as advanced options.

As soon as I get the chance, I will update this topic to add the advanced composite bricks for even greater accuracy! :^)

This is really good stuff! Proves that fontstruct goes far beyond fonts alone, and I've also always wondered how to solve this problem. Well executed, handy and informative. Definitely a tool to have around!

My clone "better 45 angles" uses the advanced 2, 3, 8 and 9 blocks.

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