Fast Sine and Cosine Approximation
let t = 0, cos, sin, x, y;
const PI = Math.PI;
const TWO_PI = PI * 2;
const HALF_PI = PI / 2;
const tA = 4 / PI;
const tB = 4 / PI ** 2;
const canvas = document.body.appendChild(document.createElement('canvas'));
const c = canvas.getContext('2d');
canvas.width = canvas.height = 300;
function loop() {
// low precision sine/cosine// always wrap input angle to -PI..PIt += 0.1;
if (t < -PI) {
t += TWO_PI;
} else if (t > PI) {
t -= TWO_PI;
}// compute sineif (t < 0) {
sin = tA * t + tB * t * t;
} else {
sin = tA * t - tB * t * t;
}// compute cosine: sin(t + PI/2) = cos(t)t += HALF_PI;
if (t > PI) {
t -= TWO_PI;
}if (t < 0) {
cos = tA * t + tB * t * t;
} else {
cos = tA * t - tB * t * t;
}t -= HALF_PI; // move the shape
x = 110 + 100 * cos;
y = 110 + 100 * sin;
c.fillStyle = 'rgba(100, 100, 20, .5)';
c.fillRect(x, y, 10, 10);
window.requestAnimationFrame(loop);
}loop();
This is an old trick for fast sine/cosine approximation. I learned about it from Michael Baczynski’s blog which now seems to be down. Here is a wayback link for the original article and another one to a more in-depth discussion about it:
original post
original thread
It’s unlikely that the speed gain (if there even is one here) makes sense in javascript. This is really more for fun… a quick search will turn up all kinds of cool info about fast sine/cosine stuff.
