A function that allows you to convert a 2d vector into a single byte and back into a vector. Useful when you want to send player joystick input over the network.

vec2ToByte.js

import { mod, Vec2 } from "https://cdn.jsdelivr.net/npm/[email protected]/dist/renda.min.js";

const RING_SEGMENTS = 36;
const RING_COUNT = 7;

// https://www.desmos.com/calculator/zpob0tj445

/**
 * Normalizes a Vec2 (between -1 and 1) and returns a byte (a value between 0 and 255)
 * which can be used to turn it back into a Vec2 using {@linkcode byteToVec2d}.
 * Naturally, a lot of precision is lost when using this operation.
 * @param {import("$renda").Vec2} vec
 */
export function vec2dToByte(vec) {
	if (vec.magnitude == 0) return 0;
	const theta = vec.clockwiseAngleTo(new Vec2(-1, 0));
	const ba = mod(Math.round(((Math.PI - theta) / (2 * Math.PI)) * RING_SEGMENTS - 1), RING_SEGMENTS) + 1;
	const bb = Math.round(vec.magnitude * RING_COUNT) * RING_SEGMENTS - RING_SEGMENTS;
	return ba + bb;
}

/**
 * Converts a byte which was generated by {@linkcode vec2dToByte} back into a Vec2.
 * Naturally, a lot of precision is lost when using this operation.
 * @param {number} byte
 */
export function byteToVec2d(byte) {
	const radius = Math.floor(((byte - 1) / RING_SEGMENTS) + 1) / RING_COUNT;
	const theta = byte / RING_SEGMENTS * Math.PI * 2;
	return new Vec2(Math.cos(theta) * radius, Math.sin(theta) * radius);
}

z_vec2dToByte.test.js

import { byteToVec2d, vec2dToByte } from "./vec2ToByte.js";
import { assertVecAlmostEquals, Vec2 } from "https://cdn.jsdelivr.net/npm/[email protected]/dist/renda.min.js";

/**
 * @param {number} byte
 */
function assertIsByte(byte) {
	if (Math.round(byte) != byte) {
		throw new Error(`${byte} is not an integer`);
	}
	if (byte < 0 || byte > 255) {
		throw new Error(`${byte} is not within the 0-255 range`);
	}
}

Deno.test({
	name: "Some common vectors stay exactly the same",
	fn() {
		const tests = [
			new Vec2(),
			new Vec2(0, 1),
			new Vec2(0, -1),
			new Vec2(1, 0),
			new Vec2(-1, 0),
		];

		for (const test of tests) {
			const byte = vec2dToByte(test);
			assertIsByte(byte);
			const vec = byteToVec2d(byte);
			assertVecAlmostEquals(vec, test);
		}
	},
});

Deno.test({
	name: "Other vectors stay roughly the same",
	fn() {
		const tests = [
			new Vec2(),
			new Vec2(0, 1),
			new Vec2(0, -1),
			new Vec2(1, 0),
			new Vec2(-1, 0),
		];

		for (const test of tests) {
			const byte = vec2dToByte(test);
			assertIsByte(byte);
			const vec = byteToVec2d(byte);
			assertVecAlmostEquals(vec, test);
		}
	},
});