Tuesday, August 28, 2007

Exploring L-Systems with F# and C#

In this post I'm going to show a little program for displaying graphical representations of L-Systems using turtle graphics implemented in F#, C# and WPF.

First of all this program could be easily implemented using only F#, but for me is interesting to see the interaction between native F# type/structures and C#. Because of this, the code that performs the L-system rewrite is written in F# and the code that takes the result is written in C# and uses WPF.

The first thing we need is an implementation of the turtle. Since we want to use this library with several graphics toolkits, we define our own point type for the generated data.


namespace Langexplr.Lsystems

open System
open Microsoft.FSharp.Math.Vector

type Point =
{x : int; y : int }

module Funcs = begin

let my_create_vector(i,j) =
let result = (create 2 0.0)
result.[0] <- i
result.[1] <- j

type TurtleGraphics =
val mutable direction : vector
val mutable position : Point

new(iX,iY) = { position = {x = iX; y = iY};
direction = Funcs.my_create_vector(1.0,0.0)}

member t.Position
with get() = t.position and
set(v) = t.position <- {x = v.x; y = v.y }

member t.Direction
with get() = t.direction and
set(v) = t.direction <- v

member t.Advance(distance : int) =
let aX = int_of_float (t.direction.[0] * float_of_int distance)
let aY = int_of_float (t.direction.[1] * float_of_int distance)
t.position <- { x = aX+t.position.x;
y = aY+t.position.y }

member t.Rotate(angle) =
let nI = (t.direction.[0] * Math.Cos(angle)) - (t.direction.[1] * Math.Sin(angle))
let nJ = (t.direction.[0] * Math.Sin(angle)) + (t.direction.[1] * Math.Cos(angle))
t.direction <- Funcs.my_create_vector(nI,nJ)


Now we need to represent the elements required for the L-Systems. The following elements are required:

Start point or axiomthe initial sequence of elements
Rules L-system substitution rules
AngleThe angle used when rotating the turtle
Number of iterationsThe number of times the rules will be applied to the axiom
Size of the initial segmentThe size in pixels of the line that is drawn when the turtle moves forward

Also the elements inside the rule and the axiom must be translated to turtle graphics commands. The following commands are supported:

|Draws a line forward, the size of the line inversely proportional to the iteration number
+Turn left by the specified angle
-Right left by the specified angle
[Saves the position and direction of the turtle in a stack
]Restores the position and direction of the turtle from the stack
LetterIf activated, draws a line forward

The following code shows the implementation of this:


namespace Langexplr.Lsystems

open Langexplr.Lsystems

open System

type LsystemElement =
| Var of String
| Constant of String
| PipeCommand of int

type Rule =
| Rule of LsystemElement * LsystemElement list

module LsystemFuncs = begin
let rec gettingLsystemElements (str:string) i result =
if str.Length > i then
if System.Char.IsLetterOrDigit(str.[i]) then
gettingLsystemElements str (i+1) ((Var(str.[i].ToString()))::result)
gettingLsystemElements str (i+1) ((Constant(str.[i].ToString()))::result)
List.rev result
let getLsystemElements str =
gettingLsystemElements str 0 []

type TurtleGraphicsLsystemProcessor =
val start : LsystemElement list
val angle : double
val rules : Rule list
val seg_size : int
val mutable saved_positions : Point list
val mutable saved_directions : vector list
val mutable drawVariables : bool

new (a_start,a_angle,t_rules,s_size,drawVars) = {
start = a_start;
angle = (Math.PI/180.0)* a_angle;
rules = t_rules;
seg_size = s_size;
saved_positions = [];
saved_directions = [];
drawVariables = drawVars}

member lp.generate_for n current =
match n with
| 0 -> current
| o -> lp.generate_for (n - 1) (lp.apply_rules current n)

member lp.apply_rules elements iteration =
match elements with
| ((Var v)::rest) -> List.append (lp.apply_rule_for v) (lp.apply_rules rest iteration)
| ((Constant "|")::rest) -> (PipeCommand iteration)::(lp.apply_rules rest iteration)
| (e::rest) -> e::(lp.apply_rules rest iteration)
| [] -> elements

member lp.apply_rule_for v =
match (List.tryfind (fun r -> match r with
| Rule(Var vvar,_) when vvar = v -> true
| _ -> false)
lp.rules) with
| Some (Rule(_, result)) -> result
| None -> [Var v]

member lp.generate_iteration n (tg:TurtleGraphics)=
let final = lp.generate_for n lp.start
List.rev(lp.generate_points n final tg [tg.Position] [])

member lp.generate_points iterations elements (tg:TurtleGraphics) current lines =
match elements with
| ((Var _)::rest) ->
if (lp.drawVariables) then
lp.generate_points iterations rest tg (tg.Position::current) lines
lp.generate_points iterations rest tg current lines
| ((Constant "+")::rest) ->
lp.generate_points iterations rest tg current lines
| ((Constant "-")::rest) ->
lp.generate_points iterations rest tg current lines
| ((Constant "[")::rest) ->
lp.saved_directions <- tg.Direction::lp.saved_directions
lp.saved_positions <- tg.Position::lp.saved_positions
lp.generate_points iterations rest tg current lines
| ((Constant "]")::rest) ->
match (lp.saved_directions,lp.saved_positions) with
| (cdir::rest_dir,cpos::rest_pos) ->
lp.saved_directions <- rest_dir
lp.saved_positions <- rest_pos
tg.Position <- cpos
tg.Direction <- cdir
lp.generate_points iterations rest tg [tg.Position] (current::lines)
| _ -> lp.generate_points iterations rest tg current lines
| ((Constant "|")::rest) ->
tg.Advance(lp.seg_size / (iterations) )
lp.generate_points iterations rest tg (tg.Position::current) lines
| ((PipeCommand iteration)::rest) ->
tg.Advance(lp.seg_size / (iterations - iteration) )
lp.generate_points iterations rest tg (tg.Position::current) lines
| (_::rest) -> lp.generate_points iterations rest tg current lines
| [] -> current::lines


The generate_iteration method is the one that generates the line information. Its result is a list of lists of elements of type Point.

The C# code that takes this F# list of lists of Points and converts it to a group of Polyline instances is the following:

private void b_Click(object sender, RoutedEventArgs e)
string origin = this.originTB.Text;
int originX = 50;
int originY = 50;
string[] oparts = origin.Split(',');
if (oparts.Length == 2)
originX = int.Parse(oparts[0]);
originY = int.Parse(oparts[1]);

TurtleGraphics tg = new TurtleGraphics(originX, originY);
int iterations = int.Parse(this.iterationsTB.Text);


List<Rule> rules = GetRules();

TurtleGraphicsLsystemProcessor tgls =
new TurtleGraphicsLsystemProcessor(
Microsoft.FSharp.Collections.ListModule.of_IEnumerable<List<Rule>, Rule>(rules),
drawVariablesCB.IsChecked == true);

var pointCollections =
from pc in (tgls.generate_iteration(int.Parse(this.iterationsTB.Text))).Invoke(tg)
select (new PointCollection(
from p in pc
select new System.Windows.Point(p.x, p.y)));

foreach (PointCollection pcol in pointCollections)
Polyline pLine = new Polyline();

pLine.Points = pcol;
pLine.Stroke = this.colorButton.Background;

What is interesting to see is that the list generated in F# is easily manipulated using LINQ. The expression that sets the value of pointCollections takes the native list of lists of points and converts it to a list of PointCollection objects in one expression .

Another interesting thing about the interaction between F# and C# is that the definition of the generate_iteration says that it could be applied with one or two arguments (because of Currying) this is used in C# by invoking the result of calling the method with one argument: (tgls.generate_iteration(int.Parse(this.iterationsTB.Text))).Invoke(tg).

Executing the program with the following L-system (from Wikipedia):

Also with using the "|" command:

Code for this experiment can be found here.

Friday, August 17, 2007

Little JRuby experiment

Today I ran a Ruby program from a previous post with JRuby. I worked without modifications!

It's very nice to know that you can access Java libraries from within a Ruby. For example I decided to do a little experiment to create a TreeModel to display the contents of the loaded XSD definition in a JTree.

Here's an initial (and incomplete) implementation of the model:

require "java"
include_class 'javax.swing.JTree'
include_class 'javax.swing.JFrame'
include_class 'javax.swing.JScrollPane'
include_class 'java.awt.BorderLayout'
include_class 'javax.swing.tree.TreeModel'

class XsdTreeModel
include TreeModel
attr_reader :schema

def initialize(s)
@schema = s

def getChild(a,i)
case a
when XSDInfo::SchemaInformation
return a.elements.values[i]
when XSDInfo::SchemaElement
return a.element_type
when XSDInfo::SchemaComplexType
return a.attributes.values[i]
def getChildCount(a)
case a
when XSDInfo::SchemaInformation
return a.elements.length
when XSDInfo::SchemaElement
return 1
when XSDInfo::SchemaComplexType
return a.attributes.length
return 0
def getIndexOfChild(a,h)
case a
when XSDInfo::SchemaInformation
return a.elements.values.index(h)
when XSDInfo::SchemaElement
return 0
when XSDInfo::SchemaComplexType
return a.attributes.index(h)
return -1

def getRoot()
return @schema


def isLeaf(o)
return false

# Interface methods without implementation

def addTreeModelListener(l)
def removeTreeModelListener(l)
def valueForPathChanged(arg0, arg1)

Now we can use it:

sc = XSDInfo::SchemaCollection.new
sc.add_schema XSDInfo::SchemaInformation.new("xhtml1-strict.xsd")
sc.namespaces.each {|ns| sc[ns].solve_references sc}
a_schema = sc[sc.namespaces[0]]

f = JFrame.new

tree = JTree.new
sp = JScrollPane.new(tree)



Running this program generates the desired tree:

Thursday, August 16, 2007

Enjoying Netbeans Ruby integration

While listening to the Java Posse I noticed the work that Sun is doing with the Netbeans Ruby integration

This integration can be found in NetBeans IDE 6.0 Milestone 10 (M10). However, by reading Tor Norbye's blog I learned about nice features that are only available with the daily builds. So I decided to download a recent build and give it a try.

Here's some things that I found interesting and useful:


Nice debugger integration with the IDE.

Highlight block open/close element

This is a very useful feature to find out if nested blocks are closed.

Code navigator

To quickly program elements inside a file.


Display hints to improve the code or fix a bug. For example while editing a program from a previous post it showed me this:

Also it suggest a fix for that issue:

Very nice!

Tuesday, August 14, 2007

First steps to generate sample XML files from XSD with Ruby

As my first non-"hello world" program in Ruby I wanted to create something that was useful for me (or at least something entertaining). A couple of weeks ago I had the necessity of generating a sample file for a given XSD Schema . Eclipse already does something like this, but I thought it was a fun programming exercise.

I wanted to create something that loads the XSD Schema into a object structure that can be queried in order to the determine the elements that will be generated. I didn't look for a existing library that does this because it will be a much better exercise to try to build it myself. However creating something that support the full XSD specification like this or this is a HUGE task so I chose to support only a small subset of it.

For XML parsing and generation, I'm using REXML which is a very nice library for XML manipulation.

The basic strategy for loading the XSD Schema is to create a collection of classes that handles each part of the supported schema features. For example SchemaElement for supporting element declarations and SchemaComplexType was created for supporting the complexType declarations.

Since an XSD Schema is a common XSD document loading each element is done by using a load_from , for example for SchemaElement the load_from method looks like this:

class SchemaElement
def load_from(elementDefinition,prefixes)

@name = elementDefinition.attributes["name"]
if (elementDefinition.attributes["type"]) then
@element_type = Reference.new(elementDefinition.attributes["type"],prefixes)
if (elementDefinition.attributes["substitutionGroup"]) then
@substitution_group = Reference.new(elementDefinition.attributes["substitutionGroup"],prefixes)

elementDefinition.find_all {|e| !e.is_a?(REXML::Text)}.each{|e|
case e.name
when "complexType"
ct = SchemaComplexType.new
@element_type = ct
print ""Warning: ignoring #{e}"


As shown in the load_from method, there're relationships between schema elements, for example the type of the element could be a type defined elsewhere inside this schema or an imported schema. Once the schema is loaded, there's a process that takes the references and replace them with a real reference to the object. For the SchemaElement the solve_references_method looks like this:

class SchemaElement
def solve_references(collection)
if @substitution_group.is_a? (XSDInfo::Reference) then
@substitution_group = collection.get_type(

if @element_type.is_a?(XSDInfo::Reference) then
if(r = collection.get_type(@element_type.namespace,@element_type.name)) then
@element_type = r
print "Not found #{@element_type.namespace}.#{@element_type.name}\n"
if !@solving then
@solving = true
@element_type.solve_references(collection) unless @element_type == nil
@solving = false

Here collection points to a SchemaCollection object that holds all the loaded schemas.

Having all this we can load an XSD Schema and start querying for its parts, for example, we can get the list of attributes that apply to the b tag in the XHTML schema:

$ irb -r xsd/xsd.rb
irb(main):001:0> sc = XSDInfo::SchemaCollection.new
=> #<XSDInfo::SchemaCollection:0xb7b71170>
irb(main):002:0> sc.add_schema XSDInfo::SchemaInformation.new("../xhtml1-strict.xsd")
irb(main):003:0> sc.namespaces.each {|ns| sc[ns].solve_references sc}
=> ["http://www.w3.org/1999/xhtml"]
irb(main):004:0> sc["http://www.w3.org/1999/xhtml"].elements["b"].all_attributes.collect {|x| x.name}
=> ["onkeydown", "onkeypress", "onmouseover", "onkeyup", "onmousemove", "onmouseup", "ondblclick", "onmouseout", "onmousedown", "onclick", "title", "class", "id", "style", "dir", nil, "lang"]

Now, for generating the XML sample we can create a generate_sample for each part of the schema. For example the generate_sample for the SchemaComplexType looks like this:

## Sample Generation

def generate_sample_content(e,context)
atts = all_attributes.select {|x| x.name != nil && rand > 0.7}
atts.each {|att|
sample_length = 1 + (10*rand).to_i
sample_text = (1..sample_length).to_a.collect{ |p|
ltrs = ("a"[0].."z"[0]).to_a
e.attributes[att.name] = sample_text

self.all_content_parts.each {|p| p.generate_sample_content(e,context)}

The value of the attributes must be valid according to its simple type. However this is not supported right now.

Another example for the generate_sample method for the SchemaChoice class is the following:

def generate_sample_content(e,context)
if (@minOccurs == 1 && @maxOccurs == 1) then
element_to_gen = @elements[(rand*@elements.length).to_i]
elsif (@minOccurs == 0 && @maxOccurs == 1) then
element_to_gen = @elements[(rand*@elements.length).to_i]
element_to_gen.generate_sample_content(e,context) unless rand < 0.5
elsif (@maxOccurs == "unbounded") then
(1..(rand * 4).to_i).each {|i|
element_to_gen = @elements[(rand*@elements.length).to_i]
element_to_gen.generate_sample_content(e,context) unless rand < 0.5

Now with all this infrastructure we can generate some sample XML files:

def generate_sample_html_element name
sc = XSDInfo::SchemaCollection.new
sc.add_schema XSDInfo::SchemaInformation.new("../xhtml1-strict.xsd")
sc.namespaces.each {|ns| sc[ns].solve_references sc}
doc = REXML::Document.new
f = File.new("output.xml","w")
doc.elements << sc[sc.namespaces[0]].elements[name].a_sample
return sc

We call:

irb(main):006:0> generate_sample_html_element "b"


<b class="zlxzzyunen" onkeydown="uaqz" onkeypress="kqyqmqn" onmouseover="sevcgov" onkeyup="ezglfa" lang="ckn" ondblclick="gfaskd" onmousedown="jwed" onclick="m">
<del ondblclick="xeepat"/>
<del cite="ymtye" title="wldaeawdi" onmouseover="fnk" id="sd" onmouseup="bfqxp" onkeyup="esyfhq">
<a tabindex="lcofhfti" href="ffuuebwn" title="jxhl" onkeydown="fsdwqt" rev="btbsuhl" onmouseup="zerecv" onkeyup="agwsyz" shape="htswqoew" onmousedown="ny" onclick="hq">
<object codetype="xbzmtvzd" onkeydown="ibsuthweoa" archive="ivav" onkeypress="sbhvtgvds" onmousemove="ll" onmousedown="kgbpgzj" onmouseout="nrpdnipw" classid="qwqzkzd" onclick="cybmhyab" usemap="aubjg"/>

Generation is allways different because we're using the rand function for many parts of the process.

Code for this experiment can be found here.

Wednesday, August 8, 2007

Just started learning Ruby...

I'm starting to learn Ruby.

A nice start point is the Why's (Poignant) Guide to Ruby. Although to really enjoy this guide you have to take some time to read all the sections! It is really a different way to introduce a programming language.

Another useful resource is the Ruby Programming Wikibook.

For future posts I'll try to post more about experiences with Ruby.