Linear Interpolation

lerp.js

/**
 * Linearly interpolate, or produce a point that is a given fraction of the way
 * between two other points.
 *
 * This is equivalent to the weighted arithmetic mean of the two points,
 * where t is the weight.
 *
 * @param {number} v0 the starting bound, returned when t=0
 * @param {number} v1 the ending bound, returned when t=1
 * @param {number} t the fraction between the given data points, also called the interpolant
 * @returns a number that is some fraction t between the values v0 and v1
 */
export function lerp(v0, v1, t) {
  return (1 - t) * v0 + t * v1;
}

/**
 * Linearly map a data point in one interval to the corresponding place in
 * another interval.
 *
 * For example, suppose there's a volume slider control and the goal is to
 * determine the current volume level from the position of the slider. It has a
 * track that's 128 pixels long and the slider is currently at a position 24
 * pixels from the start. So, 24 is in the range of 0 to 128. Determining the
 * volume level from 0 to 100 would be the result from
 * linearRemap(0, 128, 0, 100, 24). This is a volume level of 18.75.
 *
 * @param {number} xMin the lower bound of the starting interval
 * @param {number} xMax the upper bound of the starting interval
 * @param {number} yMin the lower bound of the ending interval
 * @param {number} yMax the upper bound of the ending interval
 * @param {number} x the value in the starting interval
 * @returns a value "y" in the ending interval
 */
export function linearRemap(xMin, xMax, yMin, yMax, x) {
  return lerp(yMin, yMax, unlerp(xMin, xMax, x));
}

/**
 * The inverse of lerp. Determine the fraction of the way along an interval that
 * a given point is.
 * 
 * @param {number} v0 the start value
 * @param {number} v1 the end value
 * @param {number} x the value between v0 and v1
 * @returns a fraction representing how far between v0 and v1 a given point x is
 */
export function unlerp(v0, v1, x) {
  return (x - v0) / (v1 - v0);
}