TerrainosaurusTerrainosaurusTerrain Generation Terrain Generation Using Genetic AlgorithmsUsing Genetic Algorithms

Ryan SaundersRyan Saunders

Texas A&M Student Research WeekTexas A&M Student Research Week

03/29/200503/29/2005

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OverviewOverview

IntroductionIntroductionMotivationMotivation

Applications of terrain generationApplications of terrain generationCharacteristics of an idealized t-gen methodologyCharacteristics of an idealized t-gen methodology

BackgroundBackgroundCurrent methodsCurrent methodsTerrain model representationTerrain model representationGenetic algorithmsGenetic algorithms

The algorithmThe algorithmPhase I:Phase I: Construct a terrain type databaseConstruct a terrain type databasePhase II:Phase II: Design the terrain layoutDesign the terrain layoutPhase III:Phase III: Generate the heightfieldGenerate the heightfield

Discussion & future workDiscussion & future work

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TerrainosaurusTerrainosaurusTerrain generation for dummiesTerrain generation for dummies

A novel approach to terrain generationA novel approach to terrain generationUser-orientedUser-oriented

Physically-basedPhysically-based

ExtensibleExtensible

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Potential ApplicationsPotential ApplicationsWhy would you want to do this?Why would you want to do this?

ArtArt

Architectural Architectural renderingrendering

Military training Military training exercisesexercises

CG moviesCG movies

GamesGames

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Idealized Terrain GenerationIdealized Terrain GenerationIn a perfect world…In a perfect world…

Allowing a high degree of control, but requiring Allowing a high degree of control, but requiring only a low baseline amount of inputonly a low baseline amount of input

Easy to use, with only intuitive user inputsEasy to use, with only intuitive user inputs

Able to produce a wide variety of recognizable Able to produce a wide variety of recognizable types of terrain, in believable relation to each othertypes of terrain, in believable relation to each other

Realistic, providing a plausible simulation of the Realistic, providing a plausible simulation of the real worldreal world

Extensible, to support new types of terrainExtensible, to support new types of terrain

Useful at arbitrary levels-of-detail (LOD)Useful at arbitrary levels-of-detail (LOD)

Fast enough to run in real-timeFast enough to run in real-time

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Current Terrain Generation Current Terrain Generation MethodsMethodsStrengths & WeaknessesStrengths & Weaknesses

GIS Data Sculpting (e.g., Terragen)

Procedural (e.g., fractals) Simulation (e.g., erosion)

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Terrain Model RepresentationTerrain Model RepresentationHeightfields & other thingsHeightfields & other things

Heightfield – the most commonHeightfield – the most common2D grid of elevations2D grid of elevations h=f(x,y)h=f(x,y)

Precludes representation of caves & overhangsPrecludes representation of caves & overhangs

Real-world surveying data availableReal-world surveying data available

Ideal for optimized rendering and collision Ideal for optimized rendering and collision detectiondetection

Other possible representationsOther possible representationsPolygonal meshPolygonal mesh

Implicit functionImplicit function

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Genetic AlgorithmsGenetic AlgorithmsHow to solve really hard problemsHow to solve really hard problems

Genetic algorithm (GA):Genetic algorithm (GA): any of a family of techniques for any of a family of techniques for solving difficult optimization problems by analogy to solving difficult optimization problems by analogy to Darwinian natural selectionDarwinian natural selection

GAs are useful for finding GAs are useful for finding approximateapproximate solutions when the solutions when the optimaloptimal solution is unknown or infeasible to calculate solution is unknown or infeasible to calculateA candidate solution (a A candidate solution (a chromosomechromosome, in GA parlance) is , in GA parlance) is decomposed into interchangeable subunits called decomposed into interchangeable subunits called genesgenesA A population population of such chromosomes is evolved for some of such chromosomes is evolved for some number of generations, allowing multiple potential solutions to number of generations, allowing multiple potential solutions to be explored simultaneouslybe explored simultaneouslyThe “goodness” of a solution is measured by an objective The “goodness” of a solution is measured by an objective function (the function (the fitnessfitness function), and the more promising function), and the more promising solutions are “cross-bred” and “mutated” to explore nearby solutions are “cross-bred” and “mutated” to explore nearby solutions which might be even bettersolutions which might be even better

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Phase IPhase IConstructing a terrain libraryConstructing a terrain library

The user creates a database of heightfield data The user creates a database of heightfield data (normally from a GIS data provider), classified (normally from a GIS data provider), classified into logical into logical terrain typesterrain types (e.g., “Sierra Nevada (e.g., “Sierra Nevada mountains”, “midwest prairie”, “sand dunes”)mountains”, “midwest prairie”, “sand dunes”)

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Phase IIPhase IILaying out the terrainLaying out the terrain

The user expresses his The user expresses his design for the terrain design for the terrain by sketching a 2D by sketching a 2D map of polygonal map of polygonal terrain regions, terrain regions, providing the size, providing the size, shape and relative shape and relative placement of the placement of the different terrain typesdifferent terrain types

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Phase IIPhase IIRefining region boundariesRefining region boundaries

In order to prevent the appearance of noticeable artifacts in the In order to prevent the appearance of noticeable artifacts in the generated heightfield (caused by the unnaturally straight generated heightfield (caused by the unnaturally straight boundaries drawn by the user), the user’s boundaries are replaced boundaries drawn by the user), the user’s boundaries are replaced with irregular, GA-generated boundaries. The shape of the with irregular, GA-generated boundaries. The shape of the generated boundary can be controlled by a generated boundary can be controlled by a smoothnesssmoothness parameter to the GA.parameter to the GA.

High smoothness value Low smoothness value

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Phase IIIPhase IIIThe general ideaThe general idea

Construct progressively higher-resolution versions of the heightfield, with Construct progressively higher-resolution versions of the heightfield, with each successive version based on the previouseach successive version based on the previous

By using the previous LOD as a rough “pattern” to approximate, we ensure that By using the previous LOD as a rough “pattern” to approximate, we ensure that macro-level details of the heightfield are fixed before we worry about the micro-macro-level details of the heightfield are fixed before we worry about the micro-level detailslevel details

We do this using a genetic algorithm that searches for an arrangement of We do this using a genetic algorithm that searches for an arrangement of high-resolution chunks of elevation data that:high-resolution chunks of elevation data that:

““fit” the shape of the lower-resolution heightfieldfit” the shape of the lower-resolution heightfielddisplay the appropriate terrain type characteristics in each regiondisplay the appropriate terrain type characteristics in each region

Resample Replace

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Phase IIIPhase IIIThe heightfield refinement GAThe heightfield refinement GA

A heightfield can be A heightfield can be represented as a represented as a chromosomechromosome containing a containing a 2D, rectangular grid of 2D, rectangular grid of overlapping, circular overlapping, circular genesgenes of of a certain radius, in which each a certain radius, in which each gene holds a chunk of gene holds a chunk of elevation data from one of the elevation data from one of the input samplesinput samples

The genes may be mutated The genes may be mutated independently and traded independently and traded between chromosomesbetween chromosomesWhen we’re done, we can turn When we’re done, we can turn a chromosome back into a a chromosome back into a heightfield with standard heightfield with standard image compositing operationsimage compositing operations

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Phase IIIPhase IIIMutation & crossover operatorsMutation & crossover operators

Just as a heightfield can be interpreted as a grayscale Just as a heightfield can be interpreted as a grayscale image (and vice versa), the mutation and crossover gene image (and vice versa), the mutation and crossover gene operations correspond to image manipulation operationsoperations correspond to image manipulation operations

The effect of these operations diminishes towards the The effect of these operations diminishes towards the boundary of the gene due to blending between adjacent genesboundary of the gene due to blending between adjacent genes

Original heightfield Vertical offset mutation Rotate mutation

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Phase IIIPhase IIIThe fitness functionThe fitness function

The The fitness functionfitness function is a scalar function is a scalar function returning [0,1], giving an evaluation of how returning [0,1], giving an evaluation of how “good” a particular chromosome is. Our fitness “good” a particular chromosome is. Our fitness function is:function is:

G

N

c

RA

AR

G

T

Rff 1

fR the fitness of region R

cG the compatibility of gene G with the pattern heightfield

α relative weighting factor

AR area of region R

AT total area of heightfield

N number of genes

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Phase IIIPhase IIIFitness evaluation: the fitness of an individual Fitness evaluation: the fitness of an individual regionregion

To measure the characteristics of a region To measure the characteristics of a region of terrain, we use a number of different of terrain, we use a number of different techniquestechniques

Simple statistics (min, max, mean, variance) of Simple statistics (min, max, mean, variance) of physical quantities such as elevation and slopephysical quantities such as elevation and slopePhysical features (edges, peaks, etc.) extracted Physical features (edges, peaks, etc.) extracted with conventional computer vision techniqueswith conventional computer vision techniquesFrequency spectrum coefficients of the FFTFrequency spectrum coefficients of the FFT

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Phase IIIPhase IIIFitness evaluation: gene compatibilityFitness evaluation: gene compatibility

The compatibility of a gene with its local The compatibility of a gene with its local environment is a measure of its environment is a measure of its divergence from the mean elevation and divergence from the mean elevation and gradient of the pattern heightfield it is gradient of the pattern heightfield it is trying to matchtrying to match

Compatibility is measured with a 1D Gaussian Compatibility is measured with a 1D Gaussian function centered over the target function centered over the target elevation/gradientelevation/gradient

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EvaluationEvaluationHow well we met our goalsHow well we met our goals

Low amount of user input requiredLow amount of user input required(+) Single terrain-type case is trivial(+) Single terrain-type case is trivial

Moderate degree of user control affordedModerate degree of user control afforded(+) User can create arbitrarily complex terrain regions(+) User can create arbitrarily complex terrain regions

(-) User has little control over location and orientation of (-) User has little control over location and orientation of features (e.g., cliffs, individual mountain peaks)features (e.g., cliffs, individual mountain peaks)

Easy to use, with intuitive inputsEasy to use, with intuitive inputs(+) User design is done visually (2D map) and by (+) User design is done visually (2D map) and by example (terrain library)example (terrain library)

(+) Most free parameters are quality-related (GA (+) Most free parameters are quality-related (GA population size, number of cycles, level-of-detail)population size, number of cycles, level-of-detail)

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EvaluationEvaluationHow well we met our goalsHow well we met our goals

Extensible, able to produce diverse terrain typesExtensible, able to produce diverse terrain types(+) New terrain types can be added simply by finding (+) New terrain types can be added simply by finding new sample heightfieldsnew sample heightfields

(-) Terrain type analysis is too sensitive to oddities in the (-) Terrain type analysis is too sensitive to oddities in the input samples (e.g., lakes)input samples (e.g., lakes)

Computer-aided terrain-type classification and Computer-aided terrain-type classification and segmentation could reduce or eliminate this problemsegmentation could reduce or eliminate this problem

(-) Terrain types characterized by large variations in (-) Terrain types characterized by large variations in feature content (e.g, Monument Valley) are not likely to feature content (e.g, Monument Valley) are not likely to be well reproduced with the current fitness functionbe well reproduced with the current fitness function

A more detailed analysis of the terrain feature model might A more detailed analysis of the terrain feature model might yield a more complete fitness functionyield a more complete fitness function

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EvaluationEvaluationHow well we met our goalsHow well we met our goals

RealisticRealistic(+) Real-world data is used as the raw material for (+) Real-world data is used as the raw material for generating the terrain, resulting in plausible detail at generating the terrain, resulting in plausible detail at both low and high frequenciesboth low and high frequencies(-) Semantic constraints (e.g., rivers must flow downhill) (-) Semantic constraints (e.g., rivers must flow downhill) are not enforced are not enforced

Arbitrary level-of-detail (LOD)Arbitrary level-of-detail (LOD)(+) Can generate at any LOD for which data can be (+) Can generate at any LOD for which data can be providedprovided

Fast enough to run in real-timeFast enough to run in real-time(-) Not exactly…in fact, it’s rather slow(-) Not exactly…in fact, it’s rather slow(+) Many of the operations are inherently parallelizable, (+) Many of the operations are inherently parallelizable, suggesting that a GPU-centric implementation might suggesting that a GPU-centric implementation might offer a significant speed boostoffer a significant speed boost