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Constant Acceleration Motion Planning
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[-24.19218956,-97.0295726276,-17.3648177667,-98.4807753012,-100,0.0295705328734], | |
[-17.3648177667,-98.4807753012,-10.4528463268,-99.4521895368,-100,0.029948107127], | |
[-10.4528463268,-99.4521895368,-3.48994967025,-99.9390827019,-100,0.0303405249678], | |
[-3.48994967025,-99.9390827019,3.48994967025,-99.9390827019,-100,0.0307487852394], | |
[3.48994967025,-99.9390827019,10.4528463268,-99.4521895368,-100,0.0311739834966], | |
[10.4528463268,-99.4521895368,17.3648177667,-98.4807753012,-100,0.0316173243879], | |
[17.3648177667,-98.4807753012,24.19218956,-97.0295726276,-100,0.0320801360338], | |
[24.19218956,-97.0295726276,30.9016994375,-95.1056516295,-100,0.0325638867902], | |
[30.9016994375,-95.1056516295,37.4606593416,-92.7183854567,-100,0.0330702048819], | |
[37.4606593416,-92.7183854567,43.8371146789,-89.8794046299,-100,0.0336009015024], | |
[43.8371146789,-89.8794046299,50.0,-86.6025403784,-100,0.03415799813], | |
[50.0,-86.6025403784,55.9192903471,-82.9037572555,-100,0.0347437589998], | |
[55.9192903471,-82.9037572555,61.5661475326,-78.8010753607,-100,0.0353607299237], | |
[61.5661475326,-78.8010753607,66.9130606359,-74.3144825477,-100,0.0360117849773], | |
[66.9130606359,-74.3144825477,71.9339800339,-69.4658370459,-100,0.0367001830128], | |
[71.9339800339,-69.4658370459,76.6044443119,-64.2787609687,-100,0.0374296365383], | |
[76.6044443119,-64.2787609687,80.9016994375,-58.7785252292,-100,0.0382043962944], | |
[80.9016994375,-58.7785252292,84.8048096156,-52.9919264233,-100,0.0390293559412], | |
[84.8048096156,-52.9919264233,88.2947592859,-46.9471562786,-100,0.0399101827619], | |
[88.2947592859,-46.9471562786,91.3545457643,-40.6736643076,-100,0.0408534823895], | |
[91.3545457643,-40.6736643076,93.9692620786,-34.2020143326,-100,0.041867008546], | |
[93.9692620786,-34.2020143326,96.1261695938,-27.5637355817,-100,0.0429599330958], | |
[96.1261695938,-27.5637355817,97.8147600734,-20.7911690818,-100,0.0441431980494], | |
[97.8147600734,-20.7911690818,99.0268068742,-13.917310096,-100,0.045429980639], | |
[99.0268068742,-13.917310096,99.756405026,-6.97564737441,-100,0.0468363170735], | |
[99.756405026,-6.97564737441,100.0,-2.44929359829e-14,-100,0.0483819532264], | |
[100.0,-1.53979889652e-14,100,100,-100,1.30860649778], | |
[100,100,0.0,100.0,100,1.30860649778], | |
[0.0,100.0,-100,100,-100,1.30860649778], | |
[-100,100,-100.0,0.301776695297,100,1.30647742704], | |
[-100.0,0.301776695297,-100,-100,-100,1.41634583838], | |
]; |
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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 a = r[4]; | |
var t = r[5]; | |
pieces.push(new Piece(pieces, x1, y1, x2, y2, a, t)); | |
} | |
return pieces; | |
} | |
var Piece = function(parent, x1, y1, x2, y2, acceleration, duration) { | |
if (Array.isArray(parent)) { | |
parent = parent[parent.length - 1]; | |
} | |
this.x1 = x1; | |
this.y1 = y1; | |
this.x2 = x2; | |
this.y2 = y2; | |
this.acceleration = acceleration; | |
this.duration = duration; | |
this.length = dist(x1, y1, x2, y2); | |
if (parent) { | |
this.t0 = parent.t1; | |
this.t1 = this.t0 + duration; | |
this.v0 = parent.v(this.t0); | |
this.x0 = parent.x(this.t0); | |
} else { | |
this.t0 = 0; | |
this.t1 = duration; | |
this.v0 = 0; | |
this.x0 = 0; | |
} | |
} | |
Piece.prototype.hasT = function(t) { | |
return t >= this.t0 && t < this.t1; | |
} | |
Piece.prototype.a = function(t) { | |
return this.acceleration; | |
} | |
Piece.prototype.v = function(t) { | |
t -= this.t0; | |
return this.v0 + this.acceleration * t; | |
} | |
Piece.prototype.x = function(t) { | |
t -= this.t0; | |
t = min(t, this.duration); | |
return this.x0 + this.v0 * t + this.acceleration * t * t / 2; | |
} | |
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); | |
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 lastPiece = drawing.pieces[drawing.pieces.length - 1]; | |
var maxTime = lastPiece.t1; | |
var maxDistance = lastPiece.x(maxTime); | |
var maxVelocity = 250; | |
var maxAcceleration = 100; | |
background(255); | |
setStyle(window); | |
drawing.setTransform(window); | |
drawing.draw(window, time); | |
resetMatrix(); | |
noStroke(); | |
fill(0, 0, 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); | |
} |
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