I am building a simulator in Javascript and struggling to understand the basics of the physics and kinematic since it's been a while since I graduated. Anyways, I have a loop that should simulate the time and every iteration of the loop is equal to 1 second and I have an object that I want to move from point A ( [150, 50] ) to point B ( [1, 1] ). The object has a max speed of 10, acceleration of 4.9 and deceleration of -4.9. I'm recalculating the target position every iteration of the loop ( 1 sec. ) but it doesn't work when I have to decelerate because at some point the velocity is negative. Is there any formula I can use to calculate the interpolation considering both acceleration and deceleration every x seconds moving from point A to point B?
Here's the current state of my code:
const math = require('mathjs');
const { distance } = require('mathjs');
let currentPos = [150, 51];
const targetPosition = [1, 1];
const MAX_SPEED = 10;
const BASE_ACCELERATION = 4.9;
let currentVelocity= 0;
let stopping = false;
const interpolate = (pos, velocity, target, acceleration, t) => {
const d = math.distance(target, pos);
const delta = math.subtract(target, pos);
const ratio = math.divide(delta, d);
const v = Math.min(velocity + (acceleration * t), MAX_SPEED);
const newPos = move(pos, ratio, lerp(velocity, v, t));
return { pos: newPos, d , v, ratio };
};
const move = (pos, ratio, velocity) => {
return math.chain(ratio)
.multiply(velocity)
.add(pos)
.done();
};
const lerp = (v0, v1, t) => {
return v0 + t * (v1 - v0);
};
const getStopDistance = (v0, a) => v0 / 2 * a;
// Let's say I'm simulating 15 seconds
for (let i = 0; i < 15; i++) {
console.log(`####### sec ${i} #######`);
console.log(`currentPos -> `, currentPos);
console.log(`currentVelocity -> `, currentVelocity);
console.log(`stopping -> `, stopping);
const sd = getStopDistance(currentVelocity, BASE_ACCELERATION);
const a = (stopping) ? -BASE_ACCELERATION : BASE_ACCELERATION;
const it = interpolate(currentPos, currentVelocity, targetPosition, a, 1);
if (it.d == 0)
break;
console.log('sd -> ', sd);
console.log('it -> ', it);
if (!stopping && sd >= it.d) {
// Trying to break it down in 2 equations within 1 sec. The first with the current velocity and accelerations and the rest should be the time I should start stopping ?**strong text**
const d1 = sd - it.d;
const t1 = (2 * d1) / (currentVelocity + currentVelocity);
const i1 = interpolate(currentPos, currentVelocity, targetPosition, BASE_ACCELERATION, t1);
const t2 = 1 - t1;
const i2 = interpolate(i1.pos, i1.v, targetPosition, -BASE_ACCELERATION, t2);
console.log('d1 -> ', d1);
console.log('t1 -> ', t1);
console.log('i1 -> ', i1);
console.log('t2 -> ', t2);
console.log('i2 -> ', i2);
stopping = true;
currentPos = i2.pos;
currentVelocity = i2.v;
} else {
currentPos = it.pos;
currentVelocity = it.v;
}
}
