@jscad/modeling/src/curves/bezier/valueAt.js

Constructive Solid Geometry (CSG) Library for JSCAD

/**
 * Calculates the value 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 to see this in use.
 * Math and explanation comes from {@link https://www.freecodecamp.org/news/nerding-out-with-bezier-curves-6e3c0bc48e2f/}
 *
 * @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 position = bezier.valueAt(t,b) // where 0 < t < 1
 *
 * @param {number} t : the position of which to calculate the value; 0 < t < 1
 * @param {Object} bezier : a bezier curve created with bezier.create().
 * @returns {array | number} the value at the requested position.
 * @alias module:modeling/curves/bezier.valueAt
 */
const valueAt = (t, bezier) => {
  if (t < 0 || t > 1) {
    throw new Error('Bezier valueAt() input must be between 0 and 1')
  }
  if (bezier.pointType === 'float_single') {
    return bezierFunction(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(bezierFunction(bezier, singleDimensionPoints, t))
    }
    return result
  }
}

const bezierFunction = function (bezier, p, t) {
  const n = p.length - 1
  let result = 0
  for (let i = 0; i <= n; i++) {
    result += bezier.permutations[i] * Math.pow(1 - t, n - i) * Math.pow(t, i) * p[i]
  }
  return result
}

module.exports = valueAt