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

``````/**
* Calculates the tangent at a specific position along a bezier easing curve.
* For multidimensional curves, the tangent is the slope of each dimension at that point.
* See the example called extrudeAlongPath.js
*
* @example
* 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
* let tangent = bezier.tangentAt(t, b)
*
* @param {number} t : the position of which to calculate the bezier's tangent value; 0 < t < 1
* @param {Object} bezier : an array with at least 2 elements of either all numbers, or all arrays of numbers that are the same size.
* @return {array | number} the tangent at the requested position.
* @alias module:modeling/curves/bezier.tangentAt
*/
const tangentAt = (t, bezier) => {
if (t < 0 || t > 1) {
throw new Error('Bezier tangentAt() input must be between 0 and 1')
}
if (bezier.pointType === 'float_single') {
return bezierTangent(bezier, bezier.points, t)
} else {
const result = []
for (let i = 0; i < bezier.dimensions; i++) {
const singleDimensionPoints = []
for (let j = 0; j < bezier.points.length; j++) {
singleDimensionPoints.push(bezier.points[j][i])
}
result.push(bezierTangent(bezier, singleDimensionPoints, t))
}
return result
}
}

const bezierTangent = function (bezier, p, t) {
// from https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/bezier-der.html
const n = p.length - 1
let result = 0
for (let i = 0; i < n; i++) {
const q = n * (p[i + 1] - p[i])
result += bezier.tangentPermutations[i] * Math.pow(1 - t, n - 1 - i) * Math.pow(t, i) * q
}
return result
}

module.exports = tangentAt
``````