Coordinate Transformation

Instructions

Your design company has primarily been working with CSS transformations to build webpages. After some discussion, a decision is made to start using JavaScript to perform some of the calculations dynamically. Some of your teammates are less experienced with JavaScript, so you decide to use a function closure to create reusable transformation for {x, y} coordinate pairs.

1. Translate the coordinates

Implement the translate2d function which returns a function making use of a closure to perform a repeatable 2d translation of a coordinate pair.

const moveCoordinatesRight2Px = translate2d(2, 0);
const result = moveCoordinatesRight2Px(4, 8);
// result => [6, 8]

2. Scale the coordinates

Implement the scale2d function which returns a function making use of a closure to perform a repeatable 2d scale of a coordinate pair.

For the purposes of this exercise, assume only positive scaling values.

const doubleScale = scale2d(2, 2);
const result = doubleScale(6, -3);
// result => [12, -6]

3. Compose transformation functions

Combine two transformation functions to perform a repeatable transformation. This is often called function composition, where the result of the first function 'f(x)' is used as the input to the second function 'g(x)'.

const moveCoordinatesRight2Px = translate2d(2, 0);
const doubleCoordinates = scale2d(2, 2);
const composedTransformations = composeTransformation(
  moveCoordinatesRight2Px,
  doubleCoordinates
);
const result = composedTransformations(0, 1);
// result => [4, 2]

4. Save the results of functions

Implement the memoizeTransform function. It takes a function to memoize, then returns a new function which remembers the inputs to the supplied function so that the last return value can be "remembered" and only calculated once if it is called again with the same arguments.

Memoizing is sometimes called dynamic programming, it allows for expensive operations to be done only once, since their result is remembered.

const tripleScale = scale2d(3, 3);
const memoizedScale = memoizeTransform(tripleScale);

memoizedScale(4, 3); // => [12, 9], this is computed since it hasn't been computed before for the arguments
memoizedScale(4, 3); // => [12, 9], this is remembered, since it was computed already