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### WebGL Experiment Demonstrates Barnes-Hut N-Body Simulation of a Growing Watermelon in a Box

BY MARKUS SPRUNCK

Japan produces watermelons which have a cubic shape. USA Today reported in 2013 that these melons have been sold for up to 850\$ in Moscow [1] - quite expensive for a simple melon. To produce this unusual shape the young melon fruits are put into a box.
The growing melons are then forced into the cubic shape.

In the following WebGL experiment this growth into a cubic shape is simulated with an N-Body-SimulationThis WebGL experiment demonstrates how to simulate a growing watermelon in a web browser. You may start the web application with a WebGL enabled browser here http://webgl-examples.appspot.com/square-melon/melon.html. The complete source code is available on GitHub

### Expected Result

The WebGL simulation is not a simple geometrical transformation from a sphere to a cube. It uses an N-Body-Simulation which calculates the forces between the nodes of a sphere.

Figure 1: Start of Simulation

Figure 2: End of
Simulation

The underlying model for the melon has 400 nodes and 420 links between the nodes. All nodes repulse each other and the links work as springs to keep them together.

Figure 3: Model of N-Body Simulation with 400 vertices/nodes

### Why Barnes-Hut-Algorithm is needed?

A simple three.js sphere with 400 nodes is used to render the melon. To calculate all repulsive forces between the nodes would need 400*(400-1)/2 or 79800 single calculations - a quite CPU intensive task.

One solution to improve performance is to reduce the number of calculations with an approximation of the repulsive forces. Groups of nodes which are far away can be handled as a single node. This can be done with an optimal data structure. One approach to do this, is the so called Barnes-Hut-Algorithm designed for astronomical problems. You may find an excellent description of two dimensional Barnes-Hut-Algorithm in the article http://arborjs.org/docs/barnes-hutFor the growing watermelon the Barnes-Hut-Algorithm is implemented for three dimensions in JavaScript.

### Implementation

In the file melon.simulator.js (line 1 - 469) the core of the N-Body Simulation is implemented.

 ``` 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469``` ```/** * Options for n-body simulation and rendering */ function SimulationOptions() { "use strict"; return { RUN_SIMULATION : true, SPHERE_RADIUS : 1200.0, SPHERE_RADIUS_MINIMUM : 25.0, CHARGE : 25.0, THETA : 0.8, SPRING : 8.0, // Parameters for rendering SHOW_MELON_TEXTURE : true, DISPLAY_CUBE : true }; } /** * Node element with information for simulation and rendering */ function NNode(node) { "use strict"; this.id = node.id; this.masterNode = null; this.x = node.x; this.y = node.y; this.z = node.z; this.force_x = 0.0; this.force_y = 0.0; this.force_z = 0.0; // Rendering elements this.sphere = {}; this.sphereCreated = false; } NNode.prototype.getRadius = function() { "use strict"; return MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM; }; function NLink(source, target) { "use strict"; this.source = (source.masterNode == null) ? source : source.masterNode; this.target = (target.masterNode == null) ? target : target.masterNode; this.default_distance = this.getDistance(); // Rendering elements this.threeElement = {}; this.linkWebGLCreated = false; } NLink.prototype.getDistance = function() { "use strict"; var deltaX = (this.source.x - this.target.x); var deltaY = (this.source.y - this.target.y); var deltaZ = (this.source.z - this.target.z); return Math.sqrt(deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ); } function initRandomPosition(node) { var gamma = 2 * Math.PI * Math.random(); var delta = Math.PI * Math.random(); var radius = MELONE_SimulationOptions.SPHERE_RADIUS * 0.95; node.x = radius * Math.sin(delta) * Math.cos(gamma); node.y = radius * Math.sin(delta) * Math.sin(gamma); node.z = radius * Math.cos(delta); }; /** * Implementation of Barnes-Hut algorithm for a three-dimensional simulation of * charge */ BarnesHutAlgorithmOctTree = function(options) { "use strict"; // Parameter needed for the simulation if (typeof (options) !== "undefined") { if (typeof (options.SPHERE_RADIUS) !== "undefined") { MELONE_SimulationOptions.SPHERE_RADIUS = options.SPHERE_RADIUS; } if (typeof (options.SPHERE_RADIUS_MINIMUM) !== "undefined") { MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM = options.SPHERE_RADIUS_MINIMUM; } if (typeof (options.CHARGE) !== "undefined") { MELONE_SimulationOptions.CHARGE = options.CHARGE; } if (typeof (options.THETA) !== "undefined") { MELONE_SimulationOptions.THETA = options.THETA; } } BarnesHutAlgorithmOctTree.prototype.run = function(nodes) { var size = MELONE_SimulationOptions.SPHERE_RADIUS; MELONE_OctTreeRoot = new BarnesHutAlgorithmOctNode(-size, size, -size, size, -size, size); var node; if (nodes.length > 1) { for ( var i = 0; i < nodes.length; i++) { node = nodes[i]; MELONE_OctTreeRoot.addNode(node); } MELONE_OctTreeRoot.calculateAveragesAndSumOfMass(); for (i = 0; i < nodes.length; i++) { node = nodes[i]; MELONE_OctTreeRoot.calculateForces(node); } } }; }; BarnesHutAlgorithmOctNode = function(xMin, xMax, yMin, yMax, zMin, zMax) { "use strict"; this.xMin = xMin; this.xMax = xMax; this.yMin = yMin; this.yMax = yMax; this.zMin = zMin; this.zMax = zMax; this.sum_mass = 0; this.sum_x = 0; this.sum_y = 0; this.sum_z = 0; this.node = null; this.children = null; this.diameter = (((xMax - xMin) + (yMax - yMin) + (zMax - zMin)) / 3); }; BarnesHutAlgorithmOctNode.prototype.isFilled = function() { "use strict"; return (this.node != null); }; BarnesHutAlgorithmOctNode.prototype.isParent = function() { "use strict"; return (this.children != null); }; BarnesHutAlgorithmOctNode.prototype.isFitting = function(node) { "use strict"; return ((node.x >= this.xMin) && (node.x <= this.xMax) && (node.y >= this.yMin) && (node.y <= this.yMax) && (node.z >= this.zMin) && (node.z <= this.zMax)); }; BarnesHutAlgorithmOctNode.prototype.addNode = function(new_node) { "use strict"; if (this.isFilled() || this.isParent()) { var relocated_node; if (MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM > this.diameter) { var radius = Math.sqrt(new_node.x * new_node.x + new_node.y * new_node.y + new_node.z * new_node.z); var factor = (radius - MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM) / radius; new_node.x *= factor; new_node.y *= factor; new_node.z *= factor; relocated_node = this.node; this.node = null; this.sum_mass = 0; this.sum_x = 0; this.sum_y = 0; this.sum_z = 0; MELONE_OctTreeRoot.addNode(relocated_node); return; } if (!this.isParent()) { var xMiddle = (this.xMin + this.xMax) / 2; var yMiddle = (this.yMin + this.yMax) / 2; var zMiddle = (this.zMin + this.zMax) / 2; // create children this.children = []; this.children.push(new BarnesHutAlgorithmOctNode(xMiddle, this.xMax, yMiddle, this.yMax, zMiddle, this.zMax)); this.children.push(new BarnesHutAlgorithmOctNode(this.xMin, xMiddle, yMiddle, this.yMax, zMiddle, this.zMax)); this.children.push(new BarnesHutAlgorithmOctNode(this.xMin, xMiddle, this.yMin, yMiddle, zMiddle, this.zMax)); this.children.push(new BarnesHutAlgorithmOctNode(xMiddle, this.xMax, this.yMin, yMiddle, zMiddle, this.zMax)); this.children.push(new BarnesHutAlgorithmOctNode(xMiddle, this.xMax, yMiddle, this.yMax, this.zMin, zMiddle)); this.children.push(new BarnesHutAlgorithmOctNode(this.xMin, xMiddle, yMiddle, this.yMax, this.zMin, zMiddle)); this.children.push(new BarnesHutAlgorithmOctNode(this.xMin, xMiddle, this.yMin, yMiddle, this.zMin, zMiddle)); this.children.push(new BarnesHutAlgorithmOctNode(xMiddle, this.xMax, this.yMin, yMiddle, this.zMin, zMiddle)); // re-locate old node (add into children) relocated_node = this.node; this.node = null; this.sum_mass = 0; this.sum_x = 0; this.sum_y = 0; this.sum_z = 0; this.addChildNode(relocated_node); } // now add new node into children if (this.isParent()) { this.addChildNode(new_node); } } else { this.node = new_node; this.sum_mass = 1.0; this.sum_x = this.node.x; this.sum_y = this.node.y; this.sum_z = this.node.z; this.node.force_x = 0.0; this.node.force_y = 0.0; this.node.force_z = 0.0; } }; BarnesHutAlgorithmOctNode.prototype.addChildNode = function(node) { "use strict"; if (this.isParent()) { for ( var index = 0; index < 8; index++) { var child = this.children[index]; if (child.isFitting(node)) { child.addNode(node); return; } } } // Unable to add node -> has to be relocated initRandomPosition(node); MELONE_OctTreeRoot.addNode(node); }; BarnesHutAlgorithmOctNode.prototype.calculateForces = function(new_node) { "use strict"; if (this.sum_mass > 0.01 || this.isFilled()) { var deltaX, deltaY, deltaZ; if (this.isFilled()) { deltaX = (this.node.x - new_node.x); deltaY = (this.node.y - new_node.y); deltaZ = (this.node.z - new_node.z); } else { deltaX = (this.sum_x / this.sum_mass - new_node.x) * new_node.mass; deltaY = (this.sum_y / this.sum_mass - new_node.y) * new_node.mass; deltaZ = (this.sum_z / this.sum_mass - new_node.z) * new_node.mass; } var radius = Math.sqrt(deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ); var radius_squared = Math.pow((radius > 1e-6) ? radius : 1e-6, 2); var treatInternalNodeAsSingleBody = this.diameter / radius < MELONE_SimulationOptions.THETA; if (this.isFilled() || treatInternalNodeAsSingleBody) { new_node.force_x -= (deltaX * MELONE_SimulationOptions.CHARGE) / radius_squared; new_node.force_y -= (deltaY * MELONE_SimulationOptions.CHARGE) / radius_squared; new_node.force_z -= (deltaZ * MELONE_SimulationOptions.CHARGE) / radius_squared; } else if (this.isParent()) { for ( var index = 0; index < 8; index++) { var child = this.children[index]; if (child.isFilled() || this.isParent()) { child.calculateForces(new_node); } } } } }; BarnesHutAlgorithmOctNode.prototype.calculateAveragesAndSumOfMass = function() { "use strict"; if (this.isParent()) { var child; for ( var index = 0; index < 8; index++) { child = this.children[index]; child.calculateAveragesAndSumOfMass(); } this.sum_mass = 0; this.sum_x = 0; this.sum_y = 0; this.sum_z = 0; for (index = 0; index < 8; index++) { child = this.children[index]; if (child.isFilled() || this.isParent()) { this.sum_mass += child.sum_mass; this.sum_x += child.sum_x; this.sum_y += child.sum_y; this.sum_z += child.sum_z; } } } }; /** * n-body simulator makes the Branes-Hut simulation and adds the link forces. */ var NBodySimulator = function() { "use strict"; // all existing nodes and links this.node_list = []; this.node_list_simulate = []; this.link_list = []; this.octTree = new BarnesHutAlgorithmOctTree(); NBodySimulator.prototype.simulateAllForces = function() { var me = this; this.node_list_simulate = []; this.node_list.forEach(function(node) { if (node.masterNode == null) { me.node_list_simulate.push(node); } }); // Execute Barnes-Hut simulation this.octTree = new BarnesHutAlgorithmOctTree(); this.octTree.run(this.node_list_simulate); // Calculate link forces this.link_list.forEach(function(link) { me.calcLinkForce(link); }); this.node_list_simulate.forEach(function(node) { me.applyForces(node); me.scaleToBeInSphere(node); me.resetForces(node); }); // Scale and apply all forces this.node_list.forEach(function(node) { if (node.masterNode != null) { node.x = node.masterNode.x; node.y = node.masterNode.y; node.z = node.masterNode.z; } }); }; NBodySimulator.prototype.updateMelon = function(sphere) { "use strict"; var vertices = sphere.geometry.vertices; for ( var i = 0; i < vertices.length; i++) { vertices[i].x = this.node_list[i].x; vertices[i].y = this.node_list[i].y; vertices[i].z = this.node_list[i].z; } sphere.geometry.verticesNeedUpdate = true; } NBodySimulator.prototype.createModelFromSphere = function(sphere) { "use strict"; var vertices = sphere.geometry.vertices; for ( var i = 0; i < vertices.length; i++) { var newNode = { "id" : i, "alias" : ('id' + i), "x" : vertices[i].x, "y" : vertices[i].y, "z" : vertices[i].z }; this.node_list.push(new NNode(newNode)); } // Merge double nodes for ( var k = 1; k <= sphere.geometry.widthSegments; k++) { this.node_list[k].masterNode = this.node_list[0]; } for ( var k = 1; k < sphere.geometry.heightSegments; k++) { var indexNode1 = (sphere.geometry.widthSegments) + k * (sphere.geometry.widthSegments + 1); var indexNode2 = (sphere.geometry.widthSegments + 1) + (k - 1) * (sphere.geometry.widthSegments + 1); this.node_list[indexNode1].masterNode = this.node_list[indexNode2]; } for ( var k = 1; k <= sphere.geometry.widthSegments; k++) { var indexNode1 = vertices.length - 1 - k; var indexNode2 = vertices.length - 1; this.node_list[indexNode1].masterNode = this.node_list[indexNode2]; } var faces = sphere.geometry.faces; for ( var k = 0; k < faces.length; k++) { // Create links var sourceNode = this.node_list[faces[k].a]; var targetNode = this.node_list[faces[k].b]; this.link_list.push(new NLink(sourceNode, targetNode)); // Create last row of links if (k >= faces.length - sphere.geometry.widthSegments) { sourceNode = this.node_list[faces[k].b]; targetNode = this.node_list[faces[k].c]; this.link_list.push(new NLink(sourceNode, targetNode)); } } }; /** * Each link acts as simple spring. There are two types of nodes and links. */ NBodySimulator.prototype.calcLinkForce = function(link) { var deltaX = (link.source.x - link.target.x); var deltaY = (link.source.y - link.target.y); var deltaZ = (link.source.z - link.target.z); var radius = Math.sqrt(deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ); if (radius > 1e-6) { var factor = (radius - link.default_distance) / radius / radius * MELONE_SimulationOptions.SPRING; link.source.force_x -= (deltaX) * factor; link.source.force_y -= (deltaY) * factor; link.source.force_z -= (deltaZ) * factor; link.target.force_x += (deltaX) * factor; link.target.force_y += (deltaY) * factor; link.target.force_z += (deltaZ) * factor; } }; /** * Ensure that the new position is in the sphere. Nodes which leave the * sphere would be ignored by OctTree (Barnes-Hut-Algorithm). */ NBodySimulator.prototype.scaleToBeInSphere = function(node) { node.x = Math.min(Math.max(1 - MELONE_SimulationOptions.SPHERE_RADIUS, node.x), MELONE_SimulationOptions.SPHERE_RADIUS - 1); node.y = Math.min(Math.max(1 - MELONE_SimulationOptions.SPHERE_RADIUS, node.y), MELONE_SimulationOptions.SPHERE_RADIUS - 1); node.z = Math.min(Math.max(1 - MELONE_SimulationOptions.SPHERE_RADIUS, node.z), MELONE_SimulationOptions.SPHERE_RADIUS - 1); }; /** * Move the nodes depending of the forces */ NBodySimulator.prototype.applyForces = function(node) { node.x += node.force_x; node.y += node.force_y; node.z += node.force_z; }; /** * Reset all forces of the node to zero */ NBodySimulator.prototype.resetForces = function(node) { node.force_x = 0; node.force_y = 0; node.force_z = 0; }; }; /** * global variables */ var MELONE_SimulationOptions = new SimulationOptions(); var MELONE_OctTreeRoot = {}; var MELONE_NBodySimulator = new NBodySimulator(); ```

In file melon.main.js (lines 1 - 328) all the rendering of the melon happens and a simple GUI is implemented.

 ``` 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``` ```/** * Global constants */ var BORDER_LEFT = 10; var BORDER_TOP = 10; var BORDER_RIGHT = 10; var BORDER_BOTTOM = 60; /** * Global variables for rendering */ var g_panelWidthWebGL; var g_panelHeightWebGL; var g_scene; var g_cube_wireframe; var g_camera; var g_renderer; var g_control; var g_gui; var g_melon; /** * Initialize WebGL */ function initWebGL() { "use strict"; // Container for WebGL rendering var container = document.getElementById('graphic-container'); container.style.background = "#252525"; initDatGui(container); // Size of drawing g_panelWidthWebGL = window.innerWidth - BORDER_RIGHT - BORDER_LEFT; g_panelHeightWebGL = window.innerHeight - BORDER_BOTTOM - BORDER_TOP; // Create g_camera g_camera = new THREE.PerspectiveCamera(40, g_panelWidthWebGL / g_panelHeightWebGL, 1, 40000); resetCamera(); // Create g_scene g_scene = new THREE.Scene(); g_scene.add(g_camera); // Create g_renderer if (Detector.webgl) { g_renderer = new THREE.WebGLRenderer({ antialias : true }); } else { container.appendChild(Detector.getWebGLErrorMessage()); return; } g_renderer.setSize(g_panelWidthWebGL, g_panelHeightWebGL); container.appendChild(g_renderer.domElement); // LIGHTS var light = new THREE.DirectionalLight( 0xffffff, 1.475 ); light.position.set( -1000, 1000, 1000 ); g_scene.add( light ); var hemiLight = new THREE.HemisphereLight( 0xffffff, 0xffffff, 0.3 ); hemiLight.position.set( 0, 5000, 0 ); g_scene.add( hemiLight ); // Support window resize var resizeCallback = function() { g_panelWidthWebGL = window.innerWidth - BORDER_RIGHT - BORDER_LEFT; g_panelHeightWebGL = window.innerHeight - BORDER_BOTTOM - BORDER_TOP; var devicePixelRatio = window.devicePixelRatio || 1; g_renderer.setSize(g_panelWidthWebGL * devicePixelRatio, g_panelHeightWebGL * devicePixelRatio); g_renderer.domElement.style.width = g_panelWidthWebGL + 'px'; g_renderer.domElement.style.height = g_panelHeightWebGL + 'px'; resetCamera(); g_camera.updateProjectionMatrix(); g_gui.domElement.style.position = 'absolute'; g_gui.domElement.style.left = '' + (BORDER_LEFT) + 'px'; g_gui.domElement.style.top = '' + (BORDER_TOP) + 'px'; }; window.addEventListener('resize', resizeCallback, false); resizeCallback(); g_control = new THREE.TrackballControls(g_camera, g_renderer.domElement); g_control.target.set(0, 0, 0); g_control.rotateSpeed = 1.0; g_control.zoomSpeed = 1.2; g_control.panSpeed = 0.8; g_control.noZoom = false; g_control.noPan = false; g_control.staticMoving = false; g_control.dynamicDampingFactor = 0.15; g_control.keys = [ 65, 83, 68 ]; g_control.addEventListener('change', renderer); // create melone with texture var loader = new THREE.TextureLoader(); loader.load('melon.jpg', function(texture) { var geometry = new THREE.SphereGeometry(800, 16, 20); var material = new THREE.MeshLambertMaterial({ map : texture, depthTest : true, overdraw : true, castShadow : true, shininess: 20, shading : THREE.SmoothShading }); g_melon = new THREE.Mesh(geometry, material); g_melon.geometry.dynamic = true; if (MELONE_SimulationOptions.SHOW_MELON_TEXTURE) { g_scene.add(g_melon); } MELONE_NBodySimulator.createModelFromSphere(g_melon); }); // Start animation animate(); } /** * Render WebGL with about 60 fames per second if possible */ function animate() { "use strict"; requestAnimationFrame(animate); g_control.update(); // simulate forces if (MELONE_SimulationOptions.RUN_SIMULATION) { for (var i = 0; i < 3; i++) { MELONE_NBodySimulator.simulateAllForces(); } } // update position of the melone if (null != g_melon) { MELONE_NBodySimulator.updateMelon(g_melon); } // re-draw the box renderCubeWithDottedHiddenLines(); // update wire frame var nodes = MELONE_NBodySimulator.node_list; for ( var i = 0; i < nodes.length; i++) { renderNodeSphere(nodes[i]); } var links = MELONE_NBodySimulator.link_list; for (i = 0; i < links.length; i++) { renderLineElementForLink(links[i]); } renderer(); } function renderer() { "use strict"; g_renderer.render(g_scene, g_camera); } /** * Render a cube with hidden dotted lines. It is necessary to render the cube * several times to make all hidden lines dotted and the visible lines solid. */ function renderCubeWithDottedHiddenLines() { "use strict"; if (typeof (g_cube_wireframe) !== "undefined") { g_scene.remove(g_cube_wireframe); } if (MELONE_SimulationOptions.DISPLAY_CUBE) { // Create geometries var a = (MELONE_SimulationOptions.SPHERE_RADIUS + MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM) * 2; var cube_geometry = new THREE.CubeGeometry(a, a, a); var cube_geometry_wire = convertCubeGeometry2LineGeometry(cube_geometry); // Create materials var material_solid_wireframe = new THREE.MeshBasicMaterial({ color : 0x666666, depthTest : true, wireframe : true, polygonOffset : true, polygonOffsetFactor : 1, polygonOffsetUnits : 1 }); // Render four cubes with same geometry g_cube_wireframe = new THREE.Line(cube_geometry_wire, material_solid_wireframe, THREE.LinePieces); g_scene.add(g_cube_wireframe); } } /** * Helper to create a line-geometry from a cube-geometry */ function convertCubeGeometry2LineGeometry(input) { "use strict"; var geometry = new THREE.Geometry(); var vertices = geometry.vertices; for ( var i = 0; i < input.faces.length; i += 2) { var face1 = input.faces[i]; var face2 = input.faces[i + 1]; var c1 = input.vertices[face1.c].clone(); var a1 = input.vertices[face1.a].clone(); var a2 = input.vertices[face2.a].clone(); var b2 = input.vertices[face2.b].clone(); var c2 = input.vertices[face2.c].clone(); vertices.push(c1, a1, a2, b2, b2, c2); } geometry.computeLineDistances(); return geometry; } /** * Renders sphere for the node */ function renderNodeSphere(node) { "use strict"; if (node.sphereCreated) { // Update position node.sphere.position.x = node.x; node.sphere.position.z = node.z; node.sphere.position.y = node.y; node.sphere.visible = !MELONE_SimulationOptions.SHOW_MELON_TEXTURE; } else { // Create sphere var material = new THREE.MeshLambertMaterial({ reflectivity : 0.9, ambient : 0x3A3A3A, depthTest : true, transparent : true, color : 0xAAAAAA }); node.sphere = new THREE.Mesh(new THREE.SphereGeometry( MELONE_SimulationOptions.SPHERE_RADIUS_MINIMUM), material); node.sphere.position.x = node.x; node.sphere.position.z = node.z; node.sphere.position.y = node.y; node.sphere.visible = false; g_scene.add(node.sphere); node.sphereCreated = true; } } /** * Renders a link - optional with arrow head */ function renderLineElementForLink(link) { "use strict"; // Center position of the nodes var source_position = new THREE.Vector3(link.source.x, link.source.y, link.source.z); var target_position = new THREE.Vector3(link.target.x, link.target.y, link.target.z); if (link.linkWebGLCreated) { // Move existing line link.threeElement.geometry.vertices[0] = source_position; link.threeElement.geometry.vertices[1] = target_position; link.threeElement.geometry.verticesNeedUpdate = true; link.threeElement.visible = !MELONE_SimulationOptions.SHOW_MELON_TEXTURE; } else { // Create line var line_geometry = new THREE.Geometry(); line_geometry.vertices.push(source_position); line_geometry.vertices.push(target_position); var line_material = new THREE.LineBasicMaterial({ depthTest : true, transparent : true, opacity : 1.0, color: 0xAAAAAA }); line_material.transparent = true; var line = new THREE.Line(line_geometry, line_material); line.visible = false; link.threeElement = line; link.linkWebGLCreated = true; g_scene.add(line); } } function resetCamera() { "use strict"; g_camera.position.x = MELONE_SimulationOptions.SPHERE_RADIUS * 2.5; g_camera.position.y = MELONE_SimulationOptions.SPHERE_RADIUS * 2.5; g_camera.position.z = MELONE_SimulationOptions.SPHERE_RADIUS * 4; g_camera.lookAt(new THREE.Vector3(0, 0, 0)); } /** * User interface to change parameters */ function initDatGui(container) { g_gui = new dat.GUI({ autoPlace : false }); f1 = g_gui.addFolder('Render Options'); f1.add(MELONE_SimulationOptions, 'SHOW_MELON_TEXTURE').name('Show Texture') .onChange(function(value) { if (value) { g_scene.add(g_melon); } else { g_scene.remove(g_melon); } }); f1.add(MELONE_SimulationOptions, 'DISPLAY_CUBE').name('Show Box'); f1.open(); f3 = g_gui.addFolder('N-Body Simulation'); f3.add(MELONE_SimulationOptions, 'RUN_SIMULATION').name('Run'); f3.add(MELONE_SimulationOptions, 'SPRING', 5.0, 20.0).step(1.0).name( 'Spring Link'); f3.add(MELONE_SimulationOptions, 'CHARGE', 5, 40).step(1.0).name('Charge'); f3.open(); container.appendChild(g_gui.domElement); } /** * Call initialization */ initWebGL(); ```

File melon.html (lines 1 - 53) is the entry for the web application.

 ``` 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``` ``` Square Watermelon
N-Body Simulation of a Growing Watermelon in a Box, by Markus Sprunck
find sources on GitHub
```

It is strongly recommended to use a modern browser like Google Chrome 39 and/or Firefox 34. The application also runs with MS Internet Explorer 11, but the performance is not satisfying with IE.