# Squared curves

A quarter arc sits in a box whose corner is where its two end tangents meet. The handle fraction f is how far each handle reaches toward that corner.

## The numbers

| Curve | Handle fraction f | Superellipse exponent n |
|---|---|---|
| Circle | 0.552 | 2.00 |
| Katagami Text | 0.59 | 2.13 |
| Katagami Round | 0.69 | 2.43 |
| Katagami Sans | 0.73 | 2.62 |

A larger f reaches further toward the corner and reads as squarer. The exponent n of the superellipse with the same reach is `n = -1 / log2(0.375 f + 0.5)`.

## How Katagami squares a bowl

The build moves each curve's handles toward the corner by a share of the remaining distance. In Katagami Sans the share is 0.36 in capitals and 0.32 in lowercase. The build also condenses round letters, so the squared corners carry the area that the narrower width removes. The [Curves table on the home page](https://katagami.kevinliu.studio/#curves) measures f from the outlines in your browser.

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Source: https://katagami.kevinliu.studio/learn/squared-curves