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Constant Jerk Motion Planning
Raw
index.html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<style>body {padding: 0; margin: 0; overflow: hidden;}</style>
</head>
<body>
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.5.5/p5.min.js"></script>
<script src="pieces.js"></script>
<script src="sketch.js"></script>
</body>
</html>
Raw
pieces.js
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];
Raw
sketch.js
function makePieces(records) {
var pieces = [];
for (var i = 0; i < records.length; i++) {
var r = records[i];
var x1 = r[0] * 1;
var y1 = r[1] * 1;
var x2 = r[2] * 1;
var y2 = r[3] * 1;
var j = r[4];
var t = r[5];
pieces.push(new Piece(pieces, x1, y1, x2, y2, j, t));
}
return pieces;
}
var Piece = function(parent, x1, y1, x2, y2, jerk, duration) {
if (Array.isArray(parent)) {
parent = parent[parent.length - 1];
}
this.x1 = x1;
this.y1 = y1;
this.x2 = x2;
this.y2 = y2;
this.jerk = jerk;
this.duration = duration;
this.length = dist(x1, y1, x2, y2);
if (parent) {
this.t0 = parent.t1;
this.t1 = this.t0 + duration;
this.a0 = parent.a(this.t0);
this.v0 = parent.v(this.t0);
this.x0 = parent.x(this.t0);
} else {
this.t0 = 0;
this.t1 = duration;
this.a0 = 0;
this.v0 = 0;
this.x0 = 0;
}
}
Piece.prototype.hasT = function(t) {
return t >= this.t0 && t < this.t1;
}
Piece.prototype.j = function(t) {
return this.jerk;
}
Piece.prototype.a = function(t) {
t = min(t - this.t0, this.duration);
return this.a0 + this.jerk * t;
}
Piece.prototype.v = function(t) {
t = min(t - this.t0, this.duration);
return this.v0 + this.a0 * t + this.jerk * t * t / 2;
}
Piece.prototype.x = function(t) {
t = min(t - this.t0, this.duration);
return this.x0 + this.v0 * t + this.a0 * t * t / 2 + this.jerk * t * t * t / 6;
}
function evaluate(pieces, n, t) {
for (var i = 0; i < pieces.length; i++) {
if (pieces[i].hasT(t) || i == pieces.length - 1) {
switch (n) {
case 0: return pieces[i].x(t);
case 1: return pieces[i].v(t);
case 2: return pieces[i].a(t);
case 3: return pieces[i].j(t);
default: return 0;
}
}
}
return 0;
}
function computeBounds(pieces) {
var p = pieces[0];
var minx = p.x1;
var maxx = p.x1;
var miny = p.y1;
var maxy = p.y1;
for (var i = 0; i < pieces.length; i++) {
var piece = pieces[i];
minx = min(minx, piece.x1, piece.x2);
maxx = max(maxx, piece.x1, piece.x2);
miny = min(miny, piece.y1, piece.y2);
maxy = max(maxy, piece.y1, piece.y2);
}
var width = maxx - minx;
var height = maxy - miny;
return {
minx: minx, miny: miny, maxx: maxx, maxy: maxy,
width: width, height: height,
}
}
function drawPiece(dc, piece) {
dc.vertex(piece.x1, piece.y1);
dc.vertex(piece.x2, piece.y2);
}
function drawPieceLength(dc, piece, length) {
var x1 = piece.x1;
var y1 = piece.y1;
var x2 = lerp(piece.x1, piece.x2, length / piece.length);
var y2 = lerp(piece.y1, piece.y2, length / piece.length);
dc.vertex(x1, y1);
dc.vertex(x2, y2);
}
function drawPieces(dc, pieces, length) {
dc.beginShape();
for (var i = 0; i < pieces.length; i++) {
if (length <= 0) {
break;
}
var piece = pieces[i];
if (piece.length < length) {
drawPiece(dc, piece);
} else {
drawPieceLength(dc, piece, length);
}
length -= piece.length;
}
dc.endShape();
}
function Drawing(pieces) {
this.pieces = pieces;
this.bounds = computeBounds(pieces);
}
Drawing.prototype.setTransform = function(dc) {
var bounds = this.bounds;
var sx = dc.width / (bounds.width + 40);
var sy = dc.height / (bounds.height + 40);
var s = min(sx, sy);
var dx = (dc.width - bounds.width * s) / 2;
var dy = (dc.height - bounds.height * s) / 2;
dc.resetMatrix();
dc.translate(dx, dy);
dc.scale(s);
dc.translate(-bounds.minx, -bounds.miny);
}
Drawing.prototype.draw = function(dc, t) {
var length = evaluate(this.pieces, 0, t);
drawPieces(window, this.pieces, length);
}
var drawing;
function setup() {
drawing = new Drawing(makePieces(PIECES));
createCanvas(windowWidth, windowHeight);
restart();
}
function windowResized() {
resizeCanvas(windowWidth, windowHeight);
restart();
}
function setStyle(dc) {
dc.stroke(0);
dc.strokeWeight(1);
dc.strokeJoin(ROUND);
dc.noFill();
}
function restart() {
background(255);
}
function draw() {
var time = millis() / 1000;
var distance = evaluate(drawing.pieces, 0, time);
var velocity = evaluate(drawing.pieces, 1, time);
var acceleration = evaluate(drawing.pieces, 2, time);
var jerk = evaluate(drawing.pieces, 3, time);
var lastPiece = drawing.pieces[drawing.pieces.length - 1];
var maxTime = lastPiece.t1;
var maxDistance = lastPiece.x(maxTime);
var maxVelocity = 200;
var maxAcceleration = 200;
var maxJerk = 1000;
background(255);
setStyle(window);
drawing.setTransform(window);
drawing.draw(window, time);
resetMatrix();
noStroke();
fill(0);
rect(0, 0, time / maxTime * width, 10);
fill(255, 0, 0);
rect(0, height - 10, distance / maxDistance * width, 10);
fill(0, 255, 0);
rect(0, height - 20, velocity / maxVelocity * width, 10);
fill(0, 0, 255);
var w = acceleration / maxAcceleration * width / 2;
rect(width / 2, height - 30, w, 10);
fill(128);
var w = jerk / maxJerk * width / 2;
rect(width / 2, height - 40, w, 10);
}
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