Student Name: Kae Thong Chew

1
Introduction

• Student Name Kae Thong Chew
• Presentation topic title Procedural Generation
  Terrains for Games using Fractals and L-systems.
• Supervisor Dr. Penny De Byl

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Why is this research important

• Computer games today are incredibly complex ?
  believable game object elements, intelligent,
  challenging and addictive game play to its
  players.
• As game universes become more complex more
  worlds, more buildings, more rooms, with more
  polygons, textures, characters and so on the
  man-hours required to design and model them grow
  exponentially.
• Hiring game artists becomes a very expensive
  exercise.

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Why is this research important

• As game worlds grow larger, so do the data files
  storing the game information game map designs,
  character models etc.. The amount of game data to
  store the game information has expanded in game
  file sizes throughout computer game history
• Example Castle Wolfenstein install file(1983)
  69kb but Return to Castle Wolfenstein (2001) demo
  install file 114.1 MB
• How to solve this problem
• Procedural terrain generation

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Procedural Terrain Generation

• Procedural terrain generation  is about making
  optimal use of system bandwidth and main memory
  by dynamically generating lower-level geometry
  data from statically stored higher-level scene
  data.

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Different Approaches to Procedural Generated
Terrain

• Some of the procedural methods used in
  contemporary games include
• Fractal landscape
• Perlin Noise
• Pseudo Random Number Generator (PRNG)
• L-systems

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Fractal Landscape

• A fractal landscape is essentially a
  two-dimensional form of the fractal coastline,
  with shape that is recursively constructed or
  self-similar, that is, a shape that appears
  similar at all scales of magnification and is
  therefore often referred to as "infinitely
  complex".

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Fractal Landscape

• A way to create this fractal landscape is to
  employ random midpoint displacement algorithm, in
  which a square is subdivided into four smaller
  equal squares and the center point is vertically
  offset by some random amount. The process is
  repeated on the four new squares, and so on,
  until the desired level of detail is reached.

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Fractal Landscape

• Another method is to divide and purturb.

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Fractal Landscapes
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Fractal Landscapes
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Perlin Noise

• Developed by Ken Perlin to create textures
  Perlin 84,85, 89.
• This is a function which uses interpolation
  between a large number of pre-calculated gradient
  vectors to construct a value that varies
  pseudo-randomly over space and/or time to create
  textures
• linear interpolation cosine
  interpolation

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Perlin Noise

• Two-dimensional Perlin noise.

• Salt and pepper noise, band-limited, and then
  up-sampled.

• Procedural marble texture

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Pseudo Random Number Generator (PRNG)

• A pseudorandom number generator (PRNG) is an
  algorithm that generates a sequence of numbers
  which are not truly random. The outputs of
  pseudorandom number generators only approximate
  some of the properties of random numbers
• It is given a seed and produces a very large set
  of semi-random numbers. If the seed is changed,
  the set of numbers produced will change
  drastically
• This is used together with Perlin Noise to
  achieve nice-looking textures.

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L-systems

• L-systems are a special kind of string rewriting
  grammars introduced by A.Lindenmayer in 1968 for
  modeling plants. They rewrite a given string (a
  sequence of symbols) according to a grammar, i.e.
  a set of rules. To give an example, the single
  rule
• a ? b a b
• transforms the string
• a b a c
• into
• b a b b b a b c

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Examples of L-systems

• Used for modelling tree plant branches
• Example using
• Axiom Xwhere rules F --gt FFrules X --gt
  F-XXFFX-Xangle 22.5
• (push) means saving a turtle cursor position
  and (pop) means return to that same saved
  position
• will produce the image

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Examples of L-systems

• Using turtle graphics, to draw images
• The Sierpinski triangle drawn using an L-system.
• variables  A B
• constants  -
• start   A
• rules   (A ? B-A-B),(B ? ABA)
• angle   60º
• Here, A and B mean both "draw forward", means
  "turn left by angle", and - means "turn right by
  angle" .

• Evolution for n 2, n 4, n 6, n 9

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L-systems used for creating cities

• Related research work on L-systems application
  which involved modelling building and cities are
  done by Parish and Müller (2001) procedurally
  using extended L-systems to build street maps and
  city buildings.

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L-systems used for creating cities

• This is useful for urban modelling and planning
  environment but this work lacks support for real
  time interactively to generate flyby those city
  buildings scenery.
• However, this problem has been approached and
  refined by G. Stefan, P. Jeremy, S. Nigel and
  L.Geoff (2003). They proposed methods using view
  frustum filling, pseudo random number generator
  and cached display lists to display a pseudo
  infinite virtual cities in real-time to the
  user.

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L-systems used for creating cities

• Framework architecture for this research work.

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L-systems used for creating cities

• Real time procedural cities screenshots

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Research Interest

• Both these research work focus on modelling
  exterior look of buildings only but so far no
  attempt has been made on creating the interior
  design of the buildings
• How do we determine the interior of buildings for
  game maps ?

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Research Interest

• Using L-systems as modelling structure, we
  defined an interior area by giving a different
  sets of rules to distinguish the interior wall
  from the exterior wall area.
• Considering the following example
• The axiom as been defined as FFFF
• to model a square shape
• The rewriting rules for F string would be
• F ? F W F
• Where W is another set of rules we defined to
  draw internal walls with different texture
  colour.
• W ? W W -W W
• And the rotation angle for (turn right) and
  (turn left) has been defined as 90 degrees.

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Example of Research Implementation Results

• The initial axiom screenshots for square shape.

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Example of Research Implementation Results

• After 1st iteration, interior walls which is
  grey texture are rendered within the square shape

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Example of Research Implementation Results

• At the 2nd iterations, more grey interior texture
  can be seen rendered within the square shape.

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Example of Research Implementation Results

• Another example for triangle shape
• The axiom as been defined as FFF
• to model a triangle shape
• The rewriting rules for F string would be
• F ? F W F
• Where W is another set of rules we defined to
  draw internal walls with different texture
  colour.
• W ? W W -W W
• And the rotation angle for (turn right) and
  (turn left) has been defined as 120 degrees.

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Example of Research Implementation Results

• The initial axiom screenshots for triangle shape.

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Example of Research Implementation Results

• After 1st iteration, interior walls which is
  grey texture are rendered within the triangle
  shape

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Example of Research Implementation Results

• At the 2nd iterations, more grey interior texture
  can be seen rendered within the triangle shape.

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Future work to complete in this research

• As for the future research work, the research
  will focus on rendering more random walls shape,
  using different interior textures and adding more
  than one story to the shape itself.

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Thank you

• Any Questions ?