# modeling/src/curves/bezier/create.js

``````/**
* Represents a bezier easing function.
* @typedef {Object} bezier
* @property {Array} points - The control points for the bezier curve. The first and last point will also be the start and end of the curve
* @property {string} pointType - A reference to the type and dimensionality of the points that the curve was created from
* @property {number} dimensions - The dimensionality of the bezier
* @property {Array} permutations - A pre-calculation of the bezier algorithm's co-efficients
* @property {Array} tangentPermutations - A pre-calculation of the bezier algorithm's tangent co-efficients
*
*/

/**
* Creates an object representing a bezier easing curve.
* Curves can have both an arbitrary number of control points, and an arbitrary number of dimensions.
*
* @example
* const b = bezier.create([0,10]) // a linear progression from 0 to 10
* const b = bezier.create([0, 0, 10, 10]) // a symmetrical cubic easing curve that starts slowly and ends slowly from 0 to 10
* const b = bezier.create([0,0,0], [0,5,10], [10,0,-5], [10,10,10]]) // a cubic 3 dimensional easing curve that can generate position arrays for modelling
* // Usage
* let position = bezier.valueAt(t,b) // where 0 < t < 1
* let tangent = bezier.tangentAt(t,b) // where 0 < t < 1
*
* @param {Array} points An array with at least 2 elements of either all numbers, or all arrays of numbers that are the same size.
* @returns {bezier} a new bezier data object
* @alias module:modeling/curves/bezier.create
*/
const create = (points) => {
if (!Array.isArray(points)) throw new Error('Bezier points must be a valid array/')
if (points.length < 2) throw new Error('Bezier points must contain at least 2 values.')
const pointType = getPointType(points)

return {
points: points,
pointType: pointType,
dimensions: pointType === 'float_single' ? 0 : points[0].length,
permutations: getPermutations(points.length - 1),
tangentPermutations: getPermutations(points.length - 2)
}
}

const getPointType = function (points) {
let firstPointType = null
points.forEach((point) => {
let pType = ''
if (Number.isFinite(point)) {
pType = 'float_single'
} else if (Array.isArray(point)) {
point.forEach((val) => {
if (!Number.isFinite(val)) throw new Error('Bezier point values must all be numbers.')
})
pType = 'float_' + point.length
} else throw new Error('Bezier points must all be numbers or arrays of number.')
if (firstPointType == null) {
firstPointType = pType
} else {
if (firstPointType !== pType) {
throw new Error('Bezier points must be either all numbers or all arrays of numbers of the same size.')
}
}
})
return firstPointType
}

const getPermutations = function (c) {
const permutations = []
for (let i = 0; i <= c; i++) {
permutations.push(factorial(c) / (factorial(i) * factorial(c - i)))
}
return permutations
}

const factorial = function (b) {
let out = 1
for (let i = 2; i <= b; i++) {
out *= i
}
return out
}

module.exports = create
``````