DESCRIPTION

Ariana-Lua (name probably will change!) is a research project. :)

The idea is to have the Lua scripting language to plot mathematical functions in the browser.

This currently:

1. Extends Lua with some mathematical functions (the cephes library).
2. Extends Lua with some functions that will eventually call the javascript plotting functions.
3. Compile the whole shebang to WebAssembly.

DOCUMENTATION

The screen has four panels (parameters, script, plots and output). You can choose which panels to see at a given time. Normally you would write a few lines in the script panel and observe the plots.

Scripts are written in Lua 5.4. But the language is so simple that you can have a look at a couple of the examples and do what you need.

It has a package ariana that extends the language with:

• Transcendental functions (Bessel functions)
• Function Plotting capabilities.
• Canvas manipulation
• Creation of parameters

A simple example:

-- We import Ariana's tools
local ariana = require "ariana"

-- We can create a slider!
-- Has value 1, a minimum of 0 and maximum of 5.
-- We give it a name so we can identify it
local a = ariana.Slider(1, 0, 5, 'a')

-- Define the function we want to draw
local function sinc(x)
  return math.sin(a*x)/x
end

-- We define options and the functions we want to plot
local options = {
  xmin=-20,
  xmax=20
}
local functions = {
  {name=sinc, color="red", width=1},
}

-- And plot them
ariana.plot(functions, options)

Note the glaring naming inconsistencies (ariana.plot lowercase p vs ariana.Slider sign of a research project under heavy refactoring). now you can activate the parameters panel and change the Slider to see how your plot depends on that particular parameter.

You can plot as many functions as you want, just add them to the list.

Currently the supported options for the plot are not many:

local plot_defaults = {
  points=1000,
  xmin=-5,
  xmax=5,
  padding={
    left=10,
    right=10,
    top=10,
    bottom=10
  },
  gridcolor='#ccc',
  gridwidth=1,
  axiscolor='#ccc',
  axiswidth=2
}

But I will work on that. Most notably you cannot set a title of the plot or axis.

A plot command returns a canvas context:

local ctx = ariana.plot(functions, options)

-- We get back a handle to the canvas
-- We can get the width and height of the canvas
width = ctx.width()
height = ctx.height()

ctx.font = '48px serif';
ctx.fillText('A Bessel function!', width/2 - 100, 50);

So, as you can see you can use the full power of canvas to add things to your plot. Currently, this is very limited though, it would be very though to center something on the screen, for instance.

You can have a canvas context without a plot. See the Mandelbrot example. That example will teach you a bit of the performance hit taken by all this technology, there is right now a factor of 10 (a pure javascript being ten times faster than this Lua implementation)

DESIGN CHOICES

On a first look it would seem that implementing the whole thing in javascript and a bunch of high speed function in WebAssembly would be a better way to go. Indeed it would take not a lot of time to reproduce all this in a jsbin in javascript.

But I wanted to see how far can I go with a different language. An old dream of mine is to create a full fledged Computer Algebra System (CAS), that is a little bit out of my reach right now because of time considerations. One of the fist steps in that direction would be to create my own programming language (I call it the K programming language) that would be well suited for mathematical expressions.

Lua is not that kind of a language, but it is a very minimal language that can be embedded anywhere. It is versatile and expressive and has been around since 1993. So after javascript Lua is a very nice second choice. And it is probably more user friendly than javascript. It is also a very easy to extend language, it was build that way. So I thought, let's go ahead and give this a try.

What all this means is that when you load the webpage the whole Lua virtual machine is downloaded from the server and running in your browser.

Why the name?

Ariana is the middle name of my ex-wife whom I love deeply. You might find a repo with that name in my account with an earlier attempt with the K-programming Language (after my father's name Keith and the K-theory in mathematics).

Lua means Moon in the Portuguese language and is an exceedingly beautiful and well orchestrated piece of C code and an early love of mine. Pff topic, Lua-jit is a fantastic place to start learning Just In Time compilers and is a testament of how humans working together can build tools that exceed expectations. Regrettably I cannot port that to the web right now.

Until I can find something that rolls better in the mouth and convey all these feelings we are stuck with ariana-lua.

ROADMAP

I would like to reach a stage (stage 0) in which the tool is usable. That means:

• Clean code, bug free
• Complete implementations
• Documentation of Lua extensions
• A few examples
• UI polishing and functionality (probably not made by myself)
• Not yet implemented but could be there for stage 0:
  • ODE solvers
  • Matrix manipulations
  • Big ints and arbitrary precision arithmetic
  • ...

A further stage 1 would add the possibility of saving and sharing scripts

BUILD INSTRUCTIONS

Install emscripten, build and serve the docs folder

# Get the emsdk repo
$ git clone https://github.com/juj/emsdk.git

# Enter that directory
$ cd emsdk

# Fetch the latest registry of available tools.
emsdk$ ./emsdk update

# Download and install the latest SDK tools.
emsdk$ ./emsdk install latest

# Make the "latest" SDK "active" for the current user. (writes ~/.emscripten file)
emsdk$ ./emsdk activate latest

# Activate PATH and other environment variables in the current terminal
emsdk$ source ./emsdk_env.sh

# go to the ariana-lua folder
ariana-lua$ make

# serve the output folder
ariana-lua/docs$ go run server.go

EXTERNAL DEPENDENCIES

Note that they are included in this repository

• Lua
• Cephes (node-cephes)
• Lua json (https://github.com/rxi/json.lua)