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
• As game universes become more complex more
  worlds, more buildings, more rooms, with more
  polygons, textures, characters and so on
• Hiring game artists become 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..
• 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
  use of computer algorithms to dynamically
  generate terrain without manually hand drawn each
  of the terrain.

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Different Approaches to Procedural Generated
Terrain

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

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Fractal Landscape

• A fractal landscape is recursively self-similar,
  that appears similar at all scales of
  magnification.

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Fractal Landscape

• A way to create this fractal landscape is to
  employ random midpoint displacement algorithm.

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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.
• 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.
• This is used together with Perlin Noise to
  achieve nice-looking textures.

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Voronoi maps

• Voronoi maps choose a limited number of random
  specific points and calculates the distance of
  each grid cell from the nearest defined point.
• Each point creates territories around itself
  until it meets a neighbouring shape.

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Voronoi Maps

• The final image represent the boundaries or the
  graduated distances where the calculations can be
  varied to generate different results.

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Procedural Generation Methods used in Games

• One good example of a game that uses the
  procedurally generated content technology is a PC
  simulation game called Spore.
• Spore is a simulation game about life evolution.

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Procedural Methods used in Games

• Spore uses procedural generation methods where
  the game itself can generate its unique animation
  based from players creature design on the fly
  without game artists create them.

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Procedural Methods used in Games

• Spore implements procedural planet generation and
  a simulation of dynamic atmospheric scattering
  like the space phase of Spore.

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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
• 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  -
• axiom   A
• rules   (A ? B-A-B),
• (B ? ABA)
• angle   60º

• Evolution for n 2, n 4, n 6, n 9

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L-System Turtle Implementation

• L-Systems use string symbols to model elements of
  drawing on the computer screen as turtle graphics
  to produce screen images.
• The "turtle" is an imaginary pen that is given
  drawing commands, such as go forward and turn
  right to draw on the screen.

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L-systems used for creating cities

• 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 lacks support for real time
  interactively.
• However, this problem has been approached and
  refined by G. Stefan, P. Jeremy, S. Nigel and
  L.Geoff (2003) by creating a pseudo infinite
  virtual cities in real-time to the user.

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L-systems used for creating cities

• Real time procedural cities screenshots.

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Research Interest

• Both these L-System research work focus on
  modelling exterior look of buildings only but 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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L-Systems for Dynamic Creation of Building
Interiors

• Using L-systems as modeling structure, we defined
  an interior area by giving a different sets of
  rules.
• Considering the following example
• The axiom as been defined as F F F F
• to model a square shape
• The rewriting rules for F string would be
• F ? F W F
• Where W is another set of rules to draw internal
  walls
• W ? W W W W

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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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Creating L-System Interiors using Regular Polygons

• Using the same L-Systems rules, regular polygons
  from triangles to decagons are chosen to create
  interior textures.
• The result of the image are analyzed and compared
  with other regular polygon generated interiors.
• Interior textures issues like overlapping and
  collision detection are discussed.

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Example of L-System regular polygon interiors

• Triangle L-Systems string rules
• atom FFF
• Fstr FWF
• Wstr WW-WW
• angle 120

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Example of L-System regular polygon interiors

• Square L-Systems string rules
• atom FFFF
• Fstr FWF
• Wstr WW-WW
• angle 90

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Example of L-System regular polygon interiors

• Pentagon L-Systems string rules
• atom FFFFF
• Fstr FWF
• Wstr WW-WW
• angle 72

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Example of L-System regular polygon interiors

• Hexagon L-Systems string rules
• atom FFFFFF
• Fstr FWF
• Wstr WW-WW
• angle 60

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Example of L-System regular polygon interiors

• Heptagon L-Systems string rules
• atom FFFFFFF
• Fstr FWF
• Wstr WW-WW
• angle 51.42857143

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Example of L-System regular polygon interiors

• Octagon L-Systems string rules
• atom FFFFFFFF
• Fstr FWF
• Wstr WW-WW
• angle 45

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Example of L-System regular polygon interiors

• Nonagon L-Systems string rules
• atom FFFFFFFFF
• Fstr FWF
• Wstr WW-WW
• angle 40

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Example of L-System regular polygon interiors

• Decagon L-Systems string rules
• atom FFFFFFFFFF
• Fstr FWF
• Wstr WW-WW
• angle 36

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L-System Interiors Discussion

• Some regular polygons were considered suitable
  for modelling purposes like generating game maps.
• These polygons are squares and hexagons ? do not
  have overlapping and collision detections issues.

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L-System Interiors Discussion

• Squares are suitable candidates in generating
  city buildings architecture and game maps for
  tile-based strategy RPG.
• Each of the squares are arranged to adjacent to
  one another in the grid, and each of the tile
  usually represents a game terrain for that game
  map.

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L-System Interiors Discussion

• Examples of square-based game maps like Super
  Robot Wars and Disgaea

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L-System Interiors Discussion

• Hexagon is used to generate hexagonal game map
  grids called hex map. Most of the war strategy
  games use this layout to generate their game
  maps.
• The distance between the center of each hex cell
  and the center of all six adjacent hex cells
  remains constant.

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L-System Interiors Discussion

• Example of hex map game maps like Battle for
  Wesnoth.

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L-System Interiors Discussion

• The L-System examples can be further added
  graphics visually with different kinds of
  textures like doors, windows and picture frames
  to the system to become L-buildings.
• Different algorithms can be added within string
  production rules to create interesting building
  structure patterns.

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L-Buildings Examples

• Screenshots of L-buildings interior design

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L-System Versus Software Editor Tools

• Reason of using L-Systems for procedurally
  generating building interiors.
• L-System can achieve similar results of images to
  those images generated by graphic software
  editors like Maya.
• The models file size generated by L-Systems and
  Maya are reviewed and compared.

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L-System Versus Software Editor Tools
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L-System Versus Software Editor Tools
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L-System Versus Software Editor Tools
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L-System Versus Software Editor Tools
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L-System Versus Software Editor Tools

• L-System rules settings file rarely increase in
  file sizes and used up a very small storage space
  because it depend on computational algorithm
  method.
• For the Maya model files, it have significant
  increase in the file size depending on how many
  textures needed to be drawn on that screen.

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L-System Versus Software Editor Tools

• The level of efforts are easy for L-Systems
  string rules file.
• Maya models need to manually draw again the
  required model.
• L-Systems string rules only took a small amount
  of time to build the model .
• Maya models files needed to take a lot of time.

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Contributions to the Research and Games Community

• Reduce the workload of game level designers.
• Possibilities to create infinite game worlds.
• Generate random interior textures with ease and
  produce interesting design.
• Produce cheaper games while maintained the same
  or high standard quality of its gameplay.

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Future Work For This Research

• Complexity of the modelling task.
• No collision detection.
• More Randomness.

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Thank you

• Any Questions ?