Assignment 1: Introduction to node.js and JavaScript

For this first assignment, your goal is to set up node.js and npm on your system, and to get familiar with the basics of how to use modules. The intention here is to just focus on understanding the basics, and so it is going to be a little more structured than usual. Also unlike in future assignments, this assignment will be broken up into stages.

Stage 1 (due 9/13/13)

In the first stage, your goal is to implement an extremely simplified physics simulation. You will be modeling the motion of a collection of non-interacting moving particles in a box. You can assume that there is no friction and no external forces (ie gravity).

To do this, you should make a module which defines a function that integrates the state of the system forward by some time step. You should export this function as a module. Here is a method signature to help get you started

module.exports = function(position, velocity, ground, dt) {

  var nextPosition = new Array(position.length)
  var nextVelocity = new Array(velocity.length)
  
  // Compute next state here

  return {
    position: nextPosition,
    velocity: nextVelocity
  }
}

The arguments for the method are as follows:

• position is an array of length 2 arrays of numbers representing the position of each particle
• velocity is an array of length 2 arrays of numbers representing the velocity of each particle
• ground is a length 2 array of numbers representing the normal direction for the bottom of the box
• dt is the amount of time to step the simulation forward

For each particle, you should update the system using the rule that:

position[i] += dt * velocity[i]

If a particle hits one of the sides of the box or crosses the ground side, then the position is integrated up to the time of intersection and the velocity is reflected by the normal of the side. The shape of the box is determined by the following system of inequalities:

• -1 < x < 1
• y < 1
• ground[0] * x + ground[1] * y > 0

You can assume that:

• The position of all particles will be within the box
• The second component of the ground normal will always be greater than 0.

In this project you can use any modules on npm that you would like, or if you prefer you can also write and publish your own modules if you think they will help you with this assignment.

Deliverables

For the first part of this assignment, you should submit an archive that has the following things:

• All the code you wrote to make your project work (excluding code within node_modules/)
• A package.json file that lists all dependencies within your project and has a reference to the entry point to your project.
• A collection of test cases contained in the test/ folder

Testing

To verify that your modules is working as intended, you should write at least a couple of test cases. To get you started, here is a simple example:

var assert = require("assert")
var stepSimulator = require("./mysimulator.js")

var position = [[0, 0.5]]
var velocity = [[0, 1.0]]
var ground   = [0, 1]
var dt       = 0.1

for(var t=0.0; t<1.0; t+=dt) {
  var nstate = stepSimulator(position, velocity, ground, dt)
  position = nstate.position
  velocity = nstate.velocity
  assert.ok(Math.abs(position[0]) < 1e-6)
  assert.ok(Math.abs(position[1] - 1.0 + Math.abs(t - 0.5)) < 1e-6)
}

You should write at least two different test cases of your own to supplement this.

Submission

To submit your assignment, use moodle and upload a zipped archive of all the above files.

Some hints

To figure out how to reflect the velocities, think back to the first lecture. Recall that if we have a vector and we want to reflect it about a normal n, the formula is:

v_reflected = v - 2 * n * dot(n, v) / dot(n, n)

For more information, see the following wiki article:

• Reflection across a line in a plane

To figure out when a particle intersects one of the bounding lines, you need to do a bit of algebra. Remember that the position of the particle at time $t$ is given by,

p(t) = p_0 + t * v_0

Where p_0 is the initial position at the start of the time step and v_0 is the initial velocity. To figure out the point in time when the particle hits one of the walls, we need to solve for t in the following equation:

dot(p(t) - d * n, n) = 0

where d is the distance from the line to the origin and n is the unit normal of the line.

Stage 2 (due 9/20/13)

The goal for the second part of this assignment is to cover the remaining tools. Your main objective here is to create an account on github, upload your project, and to build a visualization for the simulation.

Visualization requirements

Your visualization will display an animation showing the state of the simulation as the particles evolve over time. At minimum, it should have the following features:

• An input where the initial position of the particles can be specified
• An input where the initial velocity of the particles can be specified
• An input where the ground normal can be specified
• An input where the time step per tick is specified
• A button that resets the state of all the particles to the initial conditions
• A canvas object that renders the state of the simulation

Your animation should advance the state of the system using the module you wrote in part 1 by a the input time step. In the canvas object, you should draw at minimum:

• The position of all the particles
• The 4 sides of the box containing the particles

Publishing to GitHub

Unlike in stage 1, for the second part of assignment 1, you will submit your code by publishing it on GitHub. To do this, you will need to create an account on GitHub (you can find instructions on how to do this here). Once this is done, you should create a repository following the instructions in lecture 3 with all of your code. Once this is done, email me a link to your project with the complete repository.

Some hints

For instructions on how to run your modules within a browser, you should follow the notes from lecture 4. Regarding making the HTML5 interface, you may find the textarea and input tags useful.

Questions

For any questions on this assignment, you should open an issue on github, using the link on the sidebar.