@kaliber/math

A set of useful math functions!

Motivation

Some math problems are just way easier to reason about if you have access to some higher level abstractions. This library provides some of these abstractions in a clear, consistent API.

Installation

yarn add @kaliber/math

Reference

1. lerp
2. unlerp
3. clamp
4. sequence
5. randomNumberGenerator
6. pseudoRandom

Common usecases

lerp

lerp({ start: number, end: number, amount: number, clamp: boolean = false }): number

Linearly interpolates between points.

| Argument | Type | | | --- | --- | --- | | start | Number | Start of the input range. | | end | Number | End of the input range. | | input | Number | Value indicating where to interpolate. If you want your result to lie between start and end, you should provide an input between 0 and 1. | | clamp | Boolean (default is false) | Whether to clamp the output value between the start and end values. |

const rotZ = lerp({ start: -45, end: 45, input: 0.5 })

unlerp

unlerp({ start: number, end: number, input: number, clamp: boolean = false })

Normalizes a number to a value between 0 and 1, given an input range.

| Argument | Type | | | --- | --- | --- | | start | Number | Start of the input range. | | end | Number | End of the input range. | | input | Number | The value to normalize. If the given input lies between start and end, your output value will always be between 0 and 1. | | clamp | Boolean (default is false) | Whether to clamp the output value between 0 and 1. |

const normalizedMouseX = unlerp({ start: 0, end: window.innerWidth, input: mouseX })

clamp

clamp({ min: number, max: number, input: number }) : number

Constrain a number between two boundary values. The boundary arguments are called min and max to make them easy to memorize, but swapping them has no consequences.

| Argument | Type | | | --- | --- | --- | | min | Number | First boundary value | | max | Number | Second boundary value | | input | Number | Number to constrain |

const clamped = clamp({ min: 0, max: 1, input: normalizedMouseX })

sequence

sequence(length: number) : array

Return an array of length consequtive numbers, starting with 0.

| Argument | Type | | | --- | --- | --- | | length | Number | The length of the sequence |

sequence(10).map(index => {
  // ...
})

randomNumberGenerator

randomNumberGenerator(seed: string | number) : function

Creates a random number generator that deterministically generates a (seemingly) random number, based on the input seed. Will always return the same sequence of numbers, given the same seed. The output values fall between 0 (inclusive) and 1 (exclusive).

| Argument | Type | | | --- | --- | --- | | seed | String \| Number | A string or number |

const random = randomNumberGenerator('hello world')

pseudoRandom

pseudoRandom(seed: string | number) : number

Deterministically generate a (seemingly) random number. Uses randomNumberGenerator internally, based on the input seed. Will always return the same number, given the same seed. The output value falls between 0 (inclusive) and 1 (exclusive).

The seed is salted, to make sure the first value returned by a randomNumberGenerator generator is different, given the same seed.

| Argument | Type | | | --- | --- | --- | | seed | String \| Number | A string or number |

const seeminglyRandomNumber = pseudoRandom('hello world')

Common usecases

lerp & unlerp

lerp and unlerp are exact opposites. This fact can help you build some intuition around them:

  lerp({ start: 0, end: 10, input: 0.7 }) === 7
unlerp({ start: 0, end: 10, input: 7   }) === 0.7

  lerp({ start: a, end: b, input: c }) === d
unlerp({ start: a, end: b, input: d }) === c

They are often applied in tandem to remap values:

// Input
const normalizedMouseX = unlerp({ start: 0, end: window.innerWidth, input: mouseX })

// Output
const rotZ = lerp({ start: -20, end: 20, input: normalizedMouseX })

// Apply output
element.style.transform = `rotateZ(${rotZ}deg)`

lerp

lerp in itself is very useful if you have a library that returns normalized values (values between 0 and 1). You can use lerp to map these values to other useful values. For instance:

const { ref: viewportPositionRef } = useNormalizedPositionInViewport({
  startViewportPercentage: 0,
  endViewportPercentage: 50,
  onChange(n) {
    setSpring({
      opacity: lerp({ start: 0, end: 1, input: n }),
      clip: lerp({ start: 50, end: 100, input: n })
    })
  }
})

sequence

sequence is often useful in React if you want to render n items, but your starting point is a number:

const amountOfItems = 5

return (
  <ul>
    {sequence(amountOfItems).map(i => (
      <li>Item {i + 1}</li>
    ))}
  </ul>
)

pseudoRandom

Sometimes you want elements to appear random, but they shouldn't really change. In this case, you can use a pseudo random number. Returns a number between 0 and 1, including 0 but excluding 1.

<div>
  {items.map(x => <Item rotation={lerp(-10, 10, pseudoRandom(x.id))} />)}
</div>

Disclaimer

This library is intended for internal use, we provide no support, use at your own risk.

This library is not transpiled.