Mapping values to sequential range

Question

I get values in the Range of -360 to 360 that should be mapped to a sequence corresponding to fractions of 45. (Or any other value, Im really more interested in the mapping algorithm than the use case here).

IN	-360	-315	-270	-225	-180	-135	-90	-45	0	45	90	135	180	225	270	325	360
STEP	0	1	0	-1	0	1	0	-1	0	1	0	-1	0	1	0	-1	0
OUT	0	45	0	-45	0	45	0	-45	0	45	0	-45	0	45	0	-45	0

Is there a linear Transformation I can/should use? Or how do I set up a mapping like:

var mapRange = function(base_range, target_range, s) {
  return target_range[0] + (s - base_range[0]) * (target_range[1] - target_range[0]) / (base_range[1] - base_range[0]);
};

for this?

edit: Added the desired output. Thought breaking it down to a -1 to 1 range would imply the trivial *45

Answer 1

What you are looking for is a triangle wave, which can be computed using this formula:

4 * a / p * abs(((i - p / 4) % p) - p / 2) - a

Note that % in the formula is modulo, not remainder, so in JavaScript we need to define a function to return the expected result (see the docs, and some sample functions here).

In your case, a (the amplitude) is 1, and p (the period) is 180. You can write a function to compute the value and then use it to compute individual values:

const mod = (n, m) => ((n % m) + m) % m

const triWave = (i, a, p) => 4 * a / p * Math.abs(mod(i - p / 4, p) - p / 2) - a

console.log(triWave(22.5, 1, 180))
console.log(triWave(-56.25, 1, 180))

const inp = Array.from({ length: 17 }, (_, i) => -360 + 45 * i)
const steps = inp.map(i => triWave(i, 1, 180))

console.log(steps)