-
Notifications
You must be signed in to change notification settings - Fork 4
/
particle_system_rb.html
410 lines (358 loc) · 12 KB
/
particle_system_rb.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
<!doctype html>
<html class="no-js" lang="en">
<head>
<meta charset="utf-8">
<style>
body {font-family: Helvetica, sans-serif;}
table {background-color:#CCDDEE;text-align:left}
</style>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
processEscapes: true
},
"HTML-CSS": { fonts: ["TeX"] }
});
</script>
<script type="text/javascript" aync src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js"></script>
<title>Particle System - Rigid Bodies</title>
</head>
<body>
<main>
<h1 style="text-align:center">Particle System - Rigid Bodies</h1>
<table style="align_center;border-radius: 20px;padding: 20px;margin:auto">
<col width="1100">
<col width="400">
<tr>
<td>
<canvas id="simCanvas" width="1024" height="768" style="border:2px solid #000000;border-radius: 20px;background-color:#EEEEEE">Your browser does not support the HTML5 canvas tag.</canvas>
</td>
<td>
<table>
<col width="180" style="padding-right:10px">
<col width="100">
<tr>
<td><label>Current time</label></td>
<td><span id="time">0.00</span> s</td>
</tr>
<tr>
<td><label>Time per sim. step</label></td>
<td><span id="timePerStep">0.00</span> ms</td>
</tr>
<tr>
<td><label># rigid bodies</label></td>
<td><span id="numRigidBodies">0</span></td>
</tr>
<tr>
<td><label for="timeStepSizeInput">Time step size</label></td>
<td><input onchange="gui.sim.timeStepSize=parseFloat(value)" id="timeStepSizeInput" type="number" value="0.005" step="0.001"></td>
</tr>
<tr>
<td><label for="gravityInput">Gravity</label></td>
<td><input onchange="gui.sim.gravity=parseFloat(value)" id="gravityInput" type="number" value="-9.81" step="0.01"></td>
</tr>
<tr>
<td><label for="rbEmissionInput">Rigid body emission</label></td>
<td><input onchange="gui.sim.rbEmission=parseInt(value)" id="rbEmissionInput" type="number" value="5" step="1"></td>
</tr>
<tr>
<td><label for="maxLifeTimeInput">Max. lifetime</label></td>
<td><input onchange="gui.sim.maxLifeTime=parseFloat(value)" id="maxLifeTimeInput" type="number" value="3" step="0.1"></td>
</tr>
<tr>
<td></td>
<td><button onclick="gui.restart()" type="button" id="restart">Restart</button></td>
</tr>
<tr>
<td></td>
<td><button onclick="gui.doPause()" type="button" id="Pause">Pause</button></td>
</tr>
</table>
</td>
</tr>
<tr><td>
<h2>Particle system algorithm:</h2>
This example shows a simple particle system where each particle is represented by a rigid body with a rotation and an angular velocity:
<ol>
<li>remove rigid bodies with age > max. life time</li>
<li>generate new rigid bodies by emitters</li>
<li>compute forces for all rigid bodies</li>
<li>time integration to get new rigid body positions, rotations and velocities</li>
</ol>
<h3>1. Remove rigid bodies with age > max. life time</h3>
<p>The life time of each rigid body is set to 0 when a rigid body is generated. In each simulation step the life time is increased by the time step size $\Delta t$. When a rigid body's life time is greater than a predefined maximum life time, the rigid body is removed from the simulation.</p>
<p>Note that the life time can be used for rendering effects. In our case the transparency is increased depending on the life time to fade out the rigid bodies.</p>
<h3>2. Generate new rigid bodies by emitters</h3>
<p>In each simulation step new rigid bodies are generated at the position of the emitter. Typically they are initialized with some predefined values and sometimes some random values are added to obtain more natural results.</p>
<p>In our simulation the rigid bodies are generated with a velocity pointing upwards. Moreover, the velocity in x- and y-direction is modified by some random values. The starting position of the body is at the emitter and it has a random rotation and angular velocity.</p>
<h3>3. Compute forces for all rigid bodies</h3>
<p>In each step forces are determined for the rigid bodies, e.g. gravity, wind etc. In our simple example only gravity is applied.</p>
<h3>4. Time integration</h3>
Finally, the rigid bodies are advected by numerical time integration. In our case we use a symplectic Euler method:
$$\begin{align*}
\mathbf v(t + \Delta t) &= \mathbf v(t) + \frac{\Delta t}{m} \mathbf f^{\text{ext}} \\
\mathbf x(t + \Delta t) &= \mathbf x(t) + \Delta t \mathbf v(t + \Delta t) \\
\alpha(t + \Delta t) &= \alpha(t) + \Delta t \omega,
\end{align*}$$
where $\mathbf f^{\text{ext}}$ are the external forces, $\omega$ is the (in our example constant) angular velocity and $\alpha$ is the rotation angle.
</td></tr>
</table>
</main>
<script id="simulation_code" type="text/javascript">
class RigidBody
{
constructor (x, y, vx, vy, rot, angVel)
{
this.x = x;
this.y = y;
this.fx = 0.0;
this.fy = 0.0;
this.vx = vx;
this.vy = vy;
this.rotation = rot;
this.omega = angVel;
this.lifeTime = 0.0;
}
}
class Simulation
{
constructor()
{
this.rigidBodies = [];
this.mass = 1.0;
this.inertiaInverse = 1.0;
this.gravity = -9.81;
this.timeStepSize = 0.05;
this.time = 0;
this.maxLifeTime = 3;
this.rbEmission = 5;
this.emitter_x = 0.0;
this.emitter_y = 0.0;
}
emitRigidBodies()
{
// emit new rigid bodies
for (let i = 0; i < this.rbEmission; i++)
{
// use random variation of velocity
let vx = -5 + Math.random()*10.0;
let vy = 10.0 + Math.random()*5.0/2.0;
// random rotation
let angVel = -15 + Math.random()*30.0;
let rot = 180.0*Math.random() * (Math.PI / 180.0);
this.rigidBodies.push(new RigidBody(this.emitter_x, this.emitter_y, vx, vy, rot, angVel));
}
}
// simulation step
simulationStep()
{
let dt = this.timeStepSize;
// remove bodies where lifeTime > maxLifeTime
for (let i = 0; i < this.rigidBodies.length; i++)
{
let rb = this.rigidBodies[i];
rb.lifeTime += this.timeStepSize;
if (rb.lifeTime > this.maxLifeTime)
{
this.rigidBodies.splice(i, 1);
i--;
}
}
// emit new rigid bodies
this.emitRigidBodies();
// Symplectic Euler
for (let i = 0; i < this.rigidBodies.length; i++)
{
let rb = this.rigidBodies[i];
// integrate velocity considering gravitational acceleration and other forces
rb.vx = rb.vx + dt * rb.fx / this.mass;
rb.vy = rb.vy + dt * (rb.fy / this.mass + this.gravity);
// integrate position
rb.x = rb.x + dt * rb.vx;
rb.y = rb.y + dt * rb.vy;
// integrate rotation
rb.rotation = rb.rotation + dt * rb.omega;
}
// update simulation time
this.time = this.time + dt;
}
}
class GUI
{
constructor()
{
this.canvas = document.getElementById("simCanvas");
this.c = this.canvas.getContext("2d");
this.requestID = -1;
this.timeSum = 0.0;
this.counter = 0;
this.pause = false;
this.origin = { x : this.canvas.width / 2, y : this.canvas.height/2};
this.zoom = 50;
this.rigidBodySize = 0.3;
this.selected = false;
// register mouse event listeners (zoom/selection)
this.canvas.addEventListener("mousedown", this.mouseDown.bind(this), false);
this.canvas.addEventListener("mousemove", this.mouseMove.bind(this), false);
this.canvas.addEventListener("mouseup", this.mouseUp.bind(this), false);
this.canvas.addEventListener("wheel", this.wheel.bind(this), false);
}
// set simulation parameters from GUI and start mainLoop
restart()
{
window.cancelAnimationFrame(this.requestID);
delete this.sim;
this.sim = new Simulation();
this.timeSum = 0.0;
this.counter = 0;
this.sim.rbEmission = parseFloat(document.getElementById('rbEmissionInput').value);
this.sim.maxLifeTime = parseFloat(document.getElementById('maxLifeTimeInput').value);
this.sim.gravity = parseFloat(document.getElementById('gravityInput').value);
this.sim.timeStepSize = parseFloat(document.getElementById('timeStepSizeInput').value);
document.getElementById("numRigidBodies").innerHTML = this.sim.rigidBodies.length;
this.mainLoop();
}
drawCoordinateSystem()
{
// draw x-axis
this.c.strokeStyle = "#FF0000";
this.c.beginPath();
this.c.moveTo(this.origin.x, this.origin.y);
this.c.lineTo(this.origin.x+1*this.zoom, this.origin.y);
this.c.stroke();
// draw y-axis
this.c.strokeStyle = "#00FF00";
this.c.beginPath();
this.c.moveTo(this.origin.x, this.origin.y);
this.c.lineTo(this.origin.x, this.origin.y-1*this.zoom);
this.c.stroke();
}
draw()
{
this.c.clearRect(0, 0, this.canvas.width, this.canvas.height);
this.drawCoordinateSystem();
let r = this.rigidBodySize;
let s = r * this.zoom;
let s2 = 0.5*s;
// draw rigid bodies as boxes
for (let i = 0; i < this.sim.rigidBodies.length; i++)
{
let rb = this.sim.rigidBodies[i];
//this.c.fillStyle = "#0000FF";
let alpha = 1.0 - rb.lifeTime/this.sim.maxLifeTime;
this.c.strokeStyle = "rgba(0, 0, 0, " + alpha + ")";
this.c.fillStyle = "rgba(0, 30, 200, " + alpha + ")";
let px = this.origin.x + rb.x * this.zoom;
let py = this.origin.y - rb.y * this.zoom;
this.c.save();
this.c.beginPath();
this.c.translate(px, py);
this.c.rotate(rb.rotation);
this.c.translate(-s2, -s2);
this.c.rect(0, 0, s, s);
this.c.closePath();
this.c.fill();
this.c.stroke();
this.c.restore();
}
r = 1.5*this.rigidBodySize;
s = r * this.zoom;
s2 = 0.5*s;
if (this.selected)
this.c.fillStyle = "#FF0000";
else
this.c.fillStyle = "#00BB00";
let px = this.origin.x + this.sim.emitter_x * this.zoom;
let py = this.origin.y - this.sim.emitter_y * this.zoom;
this.c.save();
this.c.beginPath();
this.c.translate(px-s2, py-s2);
this.c.rect(0, 0, s, s);
this.c.closePath();
this.c.fill();
this.c.stroke();
this.c.restore();
}
mainLoop()
{
// perform multiple sim steps per render step
for (let i=0; i < 8; i++)
{
let t0 = performance.now();
this.sim.simulationStep();
let t1 = performance.now();
this.timeSum += t1 - t0;
this.counter += 1;
if (this.counter % 50 == 0)
{
this.timeSum /= this.counter;
document.getElementById("timePerStep").innerHTML = this.timeSum.toFixed(2);
document.getElementById("numRigidBodies").innerHTML = this.sim.rigidBodies.length;
this.timeSum = 0.0;
this.counter = 0;
}
document.getElementById("time").innerHTML = this.sim.time.toFixed(2);
}
this.draw();
if (!this.pause)
this.requestID = window.requestAnimationFrame(this.mainLoop.bind(this));
}
doPause()
{
this.pause = !this.pause;
if (!this.pause)
this.mainLoop();
}
mouseDown(event)
{
// left mouse button down
if (event.which == 1)
{
let mousePos = this.getMousePos(this.canvas, event);
let px = this.origin.x + this.sim.emitter_x * this.zoom;
let py = this.origin.y - this.sim.emitter_y * this.zoom;
let dx = px - mousePos.x
let dy = py - mousePos.y
let dist2 = Math.sqrt(dx * dx + dy * dy)
if (dist2 < 10)
this.selected = true;
}
}
getMousePos(canvas, event)
{
let rect = canvas.getBoundingClientRect();
return {
x: event.clientX - rect.left,
y: event.clientY - rect.top
};
}
mouseMove(event)
{
if (this.selected)
{
let mousePos = this.getMousePos(this.canvas, event);
this.sim.emitter_x = (mousePos.x - this.origin.x) / this.zoom;
this.sim.emitter_y = -(mousePos.y - this.origin.y) / this.zoom;
}
}
mouseUp(event)
{
this.selected = false;
}
wheel(event)
{
event.preventDefault();
this.zoom += event.deltaY * -0.05;
if (this.zoom < 1)
this.zoom = 1;
}
}
gui = new GUI();
gui.restart();
</script>
</body>
</html>