hw4 helper22

spring-mass-damper system

by SunnyHsu

HTML

<div id="info">Spring (hw4 helper) <br/>
    <a href="javascript:reset();">reset</a>
</div>
<div id="euler">Euler </div>
<div id="midpt">MidPoint </div>
<div id="rk4">RK4 </div>
<div id="implicit">ImplicitEuler </div>

<script src="http://cdnjs.cloudflare.com/ajax/libs/three.js/r70/three.min.js"></script>

CSS

#info {
    position: absolute;
    top: 0px;
    width: 100%;
    padding: 10px;
    text-align: center;
    color: #ffff00
}
#euler{
  position: absolute;
  top:50%;
  left:10%;
  color: red;
}
#midpt{
  position: absolute;
  top:35%;
  left:10%;
  color: red;
}
#rk4{
  position: absolute;
  top:65%;
  left:10%;
  color: red;
}
#implicit{
  position: absolute;
  top:80%;
  left:10%;
  color: red;
}
body {
    overflow: hidden;
}

JavaScript

var camera, scene, renderer;
var mesh, border;
var clock = new THREE.Clock();
var mesh1,mesh2,mesh3;
var m = 1, k = 5, c = .51;
var x = [];//euler
var x1 = [];//midPoint
var x2 =[];//rk4
var x3 = [];//implicitEuler

function reset() {
	x[0] = 40, x[1] = 0;
  x1[0] = 40, x1[1] = 0;
  x2[0] = 40, x2[1] = 0;
  x3[0] = 40, x3[1] = 0;
}

function deriv (x) {
	var ff = [];
    ff.push (x[1]);                  // x_dot = v;
    ff.push (-(c*x[1] + k*x[0])/m);  // v_dot = 1/m *(-cx_dot -kx)
    return ff;
}

function ODESolver (dt) {
   
	var n = x.length;
    var f = deriv (x);
    
    for (var i = 0; i < n; i++) {//ch5_p25_Euler
        x[i] += f[i]*dt;
    } 
    
     var midpt=[];//ch5_p33_Midpoint
    for(var i = 0; i < n ;i++){
    		midpt[i] = x1[i] + f[i]*dt/2;
    }
    var ff=deriv(midpt);
    for(var i=0; i < n;i++){
    		x1[i] += ff[i]*dt;
    }
   
     for(var i = 0; i < n ;i++){//ch5_p44_RK4
    	var k1=f[i];
      var k2=f[ i + (dt/2) ];
      var k3=f[ i + (dt/2) ];
      var k4=f[i+dt];
      x2[i] += (k1 + 2*k2 + 2*k3 + k4)*dt/6;
    }
   
    for (var i = 0; i < n; i++) {//ch5_p25_Euler
        x3[i] += f[i+1]*dt;
    }  
    // fake version // let x[0] be a sine function
   /*  
    this.time = this.time + dt || 0;
    x[0] = 20*Math.sin(5*this.time);  // fake....  */
}
	
init();
animate();

function init() {
    scene = new THREE.Scene();

    camera = new THREE.OrthographicCamera(-50, 50, 50, -50, -10, 10);
    camera.position.z = 10;
    scene.add(camera);

    mesh = new THREE.Mesh(new THREE.CircleGeometry(1, 10), new THREE.MeshBasicMaterial());
    scene.add(mesh);
		mesh1 = mesh.clone();
  	scene.add (mesh1);
   mesh2 = mesh.clone();
   scene.add (mesh2);
    mesh3 = mesh.clone();
   scene.add (mesh3);
    
  
    var material = new THREE.LineBasicMaterial({
        color: 0x0000ff
    });

    var geometry = new THREE.Geometry();
    geometry.vertices.push(
    new THREE.Vector3(-40, -0, 0),
    new THREE.Vector3(40, 0, 0));

    var border...