Predict future state in TagPro.

tagpro-box2d-prediction.js

var dt = (1.0 / 60);
var damping = 0.5;
// Scale between Box2d physics and tagpro physics.
var scale = 100;
// Damping factor.
var d = 1 - damping * dt;
/**
 * Get predicted velocity along one axis.
 * @param {number} v0 - Initial velocity
 * @param {number} a - Acceleration
 * @param {integer} n - The number of steps ahead.
 * @return {number} - The predicted velocity
 */
function getVelocity(v0, a, n) {
  /*
   * Expansion of \sum_{i=0}^{n-1} ad^{n-i}
   * + initial velocity term.
   */
  return v0 * Math.pow(d, n) + // Initial velocity term
    a * ((d - Math.pow(d, n + 1)) / (1 - d));
}

/**
 * Get predicted displacement along one axis.
 * @param {number} v0 - Initial velocity
 * @param {number} a - Acceleration
 * @param {integer} n - The number of steps ahead.
 * @return {number} - The predicted position
 */
function getPosition(v0, a, n) {
  // Expansion of \sum_{i=1}^n scale * dt * getVelocity(n)
  var sum = (d - Math.pow(d, n + 1)) / (1 - d);
  return scale * dt * (v0 * sum + (a / (1 - d)) * (d * n - d * sum));
}

/**
 * Given an initial velocity, target velocity, and acceleration, gives
 * the number of steps necessary to reach that target velocity.
 * @param {number} v0 - Initial velocity. It must be possible to reach
 *   target velocity from initial velocity with given acceleration.
 * @param {number} a - Acceleration, -1 < a < 1, a != 0
 * @param {number} v - The target velocity
 * @return {number} - The number of steps required to reach the
 *   target velocity, or null if there was a constraint violation.
 *   Likely float, use floor/ceil as appropriate.
 */
function getSteps(v0, a, v) {
  if (a === 0) {
    if (v0 === v) {
      return 0;
    } else {
      return null;
    }
  }
  if (v0 > v && a >= 0) return null;
  if (v0 < v && a <= 0) return null;
  // Inverse of v = getVelocity(n).
  return (Math.log(v * (1 - d) - a * d) - Math.log(v0 * ( 1 - d) - a * d)) /
    Math.log(d);
}

module.exports = {
  getPosition: getPosition,
  getVelocity: getVelocity,
  getSteps: getSteps
};

function getSteps() return NaN when a>0.004.

https://jsfiddle.net/c44y4ook/1/

So you can only calculate deceleration, which is what you probably need.

Thanks for these great functions. I would never have figured them out by myself.

/Rojale