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Title	Challenge: Modeling Accretion Disks
ID	1180451277
Created	Unknown
Updated	11 years ago, 1388682447413
Code	/*********************************************************** * A roughly spherical cloud of particles collapsing * and coalescing under its own gravity to form a star. * * I've implemented one of Sal's suggestions, so the * initial cloud now starts the simulation spinning. * The system now evolves more slowly, but a lot more * interestingly. A sort of disc is created and there * are often several small systems of orbits orbiting * each other. You can often get planets orbiting the sun * which have satellites of their own. * * Use the mouse to rotate the universe * Move the to the bottom of the screen for more controls. * * The red line shows the normal to the mean angular momentum, * centred on the centre of mass of the universe. * * The histogram shows the distribution of particle masses * on a log base 2 scale. The final column is the count of * all particle > 2048 mass units. * * The most distant particle is the one furthest from the * centre of the universe's mass. * * Note that scaling does no affect particle size to make * it easier to follow particles at extreme scales. **********************************************************/ // Reduce this number if simulation is too slow. var numParticles = 250; var initialMassRange = [2, 12]; var initialMaxDistance = 600; // This gives the cloud some initial rotation var startWithRotation = true; var initialSpin = 1.8; var GRAVITATIONAL_CONSTANT = 0.8; // How close particles have to be for a collision var collisionThreshold = 1.5; // How much mass a particle needs for it to become a star var sunThreshold = 500; // Display variables var backgroundColour = color(10, 10, 20); var particleColour = color(240, 240, 220); var sunColour = color(255, 153, 0); var myFont = createFont("times", 12); var angularMomentumLineHeight = 120; var toolbarHeight = 80; var sliderX = 20; var sliderY = 350; var sliderWidth = 80; var buttonY = 365; var rotateRate = 1; // Speed of rotation using mouse var running = true; var mouseOverButton = false; var currentScale = 3; var colourScale = initialMaxDistance currentScale; var maxScale = 100; var centreX = 200; var centreY = 200; // These values are filled in later var totalMass = 0; var maxMass = 0; var massHistogram = []; for (var h=0; h<12; h++) { massHistogram.push(0); } // Take the logarithm base two of the mass var binMass = function(mass) { for (var i=massHistogram.length-1; i>=0; i--){ if (mass > pow(2, i)) { return i; } } }; var Particle = function(x, y, z, v, m) { this.position = [x, y, z]; this.velocity = v; this.mass = m; this.combineWith = []; // Radius is the cube root of mass this.getRadius = function() { this.radius = pow(this.mass, 1/3); }; this.getRadius(); this.draw = function() { var c; if (this.mass < sunThreshold) { // Particles are darker the further away they are var d = constrain((this.position[2] + 0.5 * colourScale) / colourScale, 0.05, 1); c = lerpColor(backgroundColour, particleColour, d); } else { c = sunColour; } fill(c); var r = this.radius * 2 * currentScale / log(currentScale); if (r < 1) { point(this.position[0], this.position[1]); } else { ellipse(this.position[0], this.position[1], r, r); } }; this.move = function() { this.position[0] += this.velocity[0]; this.position[1] += this.velocity[1]; this.position[2] += this.velocity[2]; }; this.attract = function(that) { var dx = this.position[0] - that.position[0]; var dy = this.position[1] - that.position[1]; var dz = this.position[2] - that.position[2]; var d2 = dx * dx + dy * dy + dz * dz; var d = sqrt(d2); if (d<(this.radius+that.radius)collisionThreshold) { this.combineWith.push(that); return; } var force = GRAVITATIONAL_CONSTANT this.massthat.mass / d2; var accel1 = force / this.mass; var accel2 = force / that.mass; dx /= d; dy /= d; dz /= d; this.velocity[0] -= accel1 dx; this.velocity[1] -= accel1 * dy; this.velocity[2] -= accel1 * dz; that.velocity[0] += accel2 * dx; that.velocity[1] += accel2 * dy; that.velocity[2] += accel2 * dz; }; this.mergeWith = function(that) { var mass2 = this.mass + that.mass; var proportion = this.mass / mass2; for (var i=0; i<3; i++) { this.position[i] = this.position[i] * proportion + that.position[i] * (1 - proportion); this.velocity[i] = this.velocity[i] * proportion + that.velocity[i] * (1 - proportion); } // Update histogram massHistogram[binMass(this.mass)]--; massHistogram[binMass(mass2)]++; this.mass = mass2; if (this.mass > maxMass) { maxMass = this.mass; } this.getRadius(); this.combineWith = []; }; }; var initialiseParticles = function(n) { var particles = []; var massRange = initialMassRange[1]-initialMassRange[0]; totalMass = 0; for (var i=0; i<n; i++) { // Randomly distribute within sphere var phi = random() * 360; var theta = acos( random() * 2 - 1 ); var r = initialMaxDistance * pow(random(), 1/3); var x = r * sin(theta) * cos(phi); var y = r * sin(theta) * sin(phi); var z = r * cos(theta); var v; if (startWithRotation) { var d = initialSpin / sqrt(xx + yy); v = [random() * d * y, random() * d * -x, random() * 0.2 - 0.1]; } else { v = [random()-0.5, random()-0.5, random()-0.5]; } var m = initialMassRange[0] + random() * massRange; if (m > maxMass) { maxMass = m; } totalMass += m; massHistogram[binMass(m)] += 1; particles.push(new Particle(x, y, z, v, m)); } return particles; }; var particles = initialiseParticles(numParticles); // Adjust to keep centred on the centre of mass // But maybe this never changes var centreParticles = function(particles) { var mid = [0, 0, 0]; var i; for (var d=0; d<3; d++) { for (i=0; i<particles.length; i++) { var p = particles[i]; if (p !== undefined) { mid[d] += p.mass * p.position[d]; } } mid[d] /= totalMass; for (i=0; i<particles.length; i++) { particles[i].position[d] -= mid[d]; } } resetMatrix(); translate(centreX, centreY); scale(1/currentScale, 1/currentScale); }; var drawSlider = function(x, y) { strokeWeight(1); fill(20, 20, 50); textAlign(LEFT, CENTER); textFont(myFont, 14); textSize(12); text("Scale 1:" + round(currentScale * 10)/10, x, y-16); rect(x, y, sliderWidth, 3, 4); stroke(160, 160, 160); line(x + 1, y, x + sliderWidth - 2, y); fill(180, 180, 180); stroke(50, 50, 50); var proportion = (currentScale - 0.5) / (maxScale - 0.5); var buttonX = x + sliderWidth * proportion - 5; rect(buttonX, y-7, 10, 16, 3); line(buttonX + 3, y - 2, buttonX + 7, y - 2); line(buttonX + 3, y + 1, buttonX + 7, y + 1); line(buttonX + 3, y + 4, buttonX + 7, y + 4); }; var drawHistogram = function() { var barWidth = 9; var x = 265; var y = 400 - 18; var i; // Axis stroke(10,10,10); var axisLength = massHistogram.length * (barWidth+1) + 2; line(x, y, x + axisLength, y); // Label fill(10, 10, 20); textFont(myFont, 11); textAlign(CENTER, BASELINE); text("log(mass) distribution", x + axisLength/2, y+12); // Bars noStroke(); var maxHeight = 5; for(i=0; i<massHistogram.length; i++) { if (massHistogram[i] > maxHeight) { maxHeight = massHistogram[i]; } } var scaleHeight = (toolbarHeight - 35) / maxHeight; textFont(myFont, 10); for(i=0; i<massHistogram.length; i++) { var barHeight = round(massHistogram[i] * scaleHeight); fill(250, 250, 255, 180); rect(x+1, y-barHeight, barWidth, barHeight); fill(10, 10, 20); text(massHistogram[i], x+barWidth/2, y-barHeight-2); x += barWidth + 1; } }; var findMeanAngularMomentum = function() { var angularM = [0,0,0]; for (var p=0; p<particles.length; p++) { var a = particles[p].position; var b = particles[p].velocity; var x = a[1] * b[2] - a[2] * b[1]; var y = a[2] * b[0] - a[0] * b[2]; var z = a[0] * b[1] - a[1] * b[0]; var d = sqrt(xx + yy + zz) / (angularMomentumLineHeight currentScale); // Normalise and scale by mass //var m = particles[p].mass / d; var m = 10 / d; angularM[0] += x * m; angularM[1] += y * m; angularM[2] += z * m; } angularM[0] /= totalMass; angularM[1] /= totalMass; angularM[2] /= totalMass; return angularM; }; var drawAngularMomentum = function() { var am = findMeanAngularMomentum(); stroke(255, 0, 0); strokeWeight(currentScale2); line(-am[0], -am[1], am[0], am[1]); }; var findMostDistanceParticle = function() { var maxDistance = 0; for (var i = 0; i < particles.length; i++) { var p = particles[i]; var d = p.position[0] p.position[0]; d += p.position[1] * p.position[1]; d += p.position[2] * p.position[2]; d = sqrt(d); if (d > maxDistance) { maxDistance = d; } } return maxDistance; }; var handleMouseEvents = function() { var y = 400 - toolbarHeight; mouseOverButton = false; if (mouseY > y) { resetMatrix(); fill(200, 200, 200, 100); rect(0, y, 400, toolbarHeight); strokeWeight(2); stroke(200, 200, 200); line(0, y, 400, y); drawSlider(sliderX, sliderY); fill(20, 20, 50); textAlign(LEFT, CENTER); text("Number of bodies: " + particles.length, 120, y+20); text("Most massive body: " + round(maxMass), 120, y+40); text("Most distant body: "+round(findMostDistanceParticle()), 120, y+60); drawHistogram(); strokeWeight(1); fill(200, 200, 200, 100); // Mouseover effect if (mouseY > buttonY && mouseX > 60 && mouseX < 75) { fill(240, 240, 240); mouseOverButton = true; } if (running) { // Pause button rect(60, buttonY, 5, 20, 5); rect(69, buttonY, 5, 20, 5); } else { triangle(60.5, buttonY, 74, buttonY + 8, 60.5, buttonY + 16); } } }; var rotateY3D = function(theta){ var ct = cos(theta); var st = sin(theta); var x, z; for (var i = 0; i < particles.length; i+=1) { var p = particles[i]; x = p.position[0]; z = p.position[2]; p.position = [ct * x + st * z, p.position[1], -st * x + ct * z]; x = p.velocity[0]; z = p.velocity[2]; p.velocity = [ct * x + st * z, p.velocity[1], -st * x + ct * z]; } }; var rotateX3D = function(theta){ var ct = cos(theta); var st = sin(theta); var y, z; for (var i = 0; i < particles.length; i++) { var p = particles[i]; y = p.position[1]; z = p.position[2]; p.position = [p.position[0], cty - stz, sty + ctz]; y = p.velocity[1]; z = p.velocity[2]; p.velocity = [p.velocity[0], cty - stz, sty + ctz]; } }; var sortByZ = function(a, b) { return a.position[2] - b.position[2]; }; var draw = function() { var i, j; if (running) { // Gravitational attraction for (i=0; i<particles.length; i++) { for (j=i+1; j<particles.length; j++) { particles[i].attract(particles[j]); } } // Combining particles var particles_to_remove = []; for (i=0; i<particles.length; i++) { for (j=0; j<particles[i].combineWith.length; j++) { var p = particles[i].combineWith[j]; particles[i].mergeWith(p); particles_to_remove.push(particles.indexOf(p)); } } // Remove particles particles_to_remove.sort(); for (i=0; i<particles_to_remove.length; i++) { var r = particles_to_remove[i]; var particle = particles[r]; if (particle !== undefined) { massHistogram[binMass(particle.mass)]--; particles.splice(r, 1); } } particles_to_remove = []; // Moving for (i=0; i<particles.length; i++) { particles[i].move(); } //particles.sort(sortByZ); } centreParticles(particles); background(backgroundColour); drawAngularMomentum(); noStroke(); for (i=0; i<particles.length; i++) { particles[i].draw(); } handleMouseEvents(); }; var mouseClicked = function() { if (mouseOverButton) { if (running) { running = false; } else { running = true; } } }; var mouseDragged = function() { if (mouseY < 400 - toolbarHeight) { // Rotate universe rotateY3D(-(pmouseX - mouseX) * rotateRate); rotateX3D( (pmouseY - mouseY) * rotateRate); } else if (mouseX > sliderX && mouseX < sliderX + sliderWidth && mouseY > sliderY - 7 && mouseY < sliderY + 9) { // Drag slider for scale var proportion = (mouseX - sliderX)/sliderWidth; currentScale = 0.3+proportion(maxScale - 0.3); colourScale = initialMaxDistance currentScale; } }; var mouseOut = function(){ mouseIsPressed = false; }; var keyPressed = function() { switch (keyCode) { case 37: centreX += 20; break; case 38: centreY += 20; break; case 39: centreX -= 20; break; case 40: centreY -= 20; break; } }; rotateX3D(90);
Folds
Fork	false
Key	ag5zfmtoYW4tYWNhZGVteXIUCxIKU2NyYXRjaHBhZBjNg_GyBAw
Votes	3593
Spin-Offs	854
Type
Width	400
Height	400
User Flagged	false
Origin Scratchpad	{"id":"1176457365","title":"Challenge: Modeling Accretion Disks","deleted":"false","official":"false"}
Hidden From Hotlist	false
Restricted Posting	true
By Child	false
Author Nick	Peter Collingridge
Author Name	peterwcollingridge
Author ID	kaid_1128810778687926889052316
Author Profile Access	COACH

Archive Data

Added	1 years ago, 1707881042225
Updated	1 years ago, 1707882948861
Source Deleted	unknown