Computer graphics & visualization Interactive Terrain Synthesis.

computer graphics & visualization

Image Synthesis

Interactive Terrain Synthesis


Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Fractal Terrain Synthesis• Goals:– Generation of fractal terrain– Non-repetitive, infinite extent– Interactive frame rates– Real-time editable

• Methods– Rescale & Add on GPU



Fractal terrain synthesis• Stochastic Fractals– „Statistical“ Self-Similarity (Stochastic Fractals)

• If blown up in scale, any part appears statistically similar to the whole

– Simulation of Fractal Brownian motion (FBm)• Movement of small particles of solid matter in liquid• Probability as a tool for modelling

– Modelling of (dynamic) natural phenomena• Terrains, clouds, water etc.

– Modelling and rendering of solid textures• Marble, wood etc.• Procedural shaders



Rescale-and-AddNoise synthesis by point evaluation – Summation of scaled and dilated noise functions



Rescale-and-AddAdd weighted noise octaves to simulate 1/f-noise– 1/f noise: as frequency increases, amplitude decreases

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Rescale-and-AddAnother method to simulate 1/f-noise– Generate noisy copies on-the-fly from a base random

texture

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Rescale-and-Add

H(x,y): synthesized height fieldF(x,y): basis function n: number of octaves



Rescale And Add• Basis function(s) F:

– Filtered white noise, Perlin noise, images, …– Affects basic appearance of terrain

• Reformulation yields more intuitive parameters:– r: roughness– l: lacunarity (fractal gap)– o: octaves



Rescale And Add - ParametersRoughness r



Rescale And Add - ParametersLacunarity l



Rescale And Add - ParametersOctaves o



Multifractals and other tricks…Substitute basis function by convex combination:

with and

More editing possibilities,more realism• Add low frequency base geometry

– Edit basic terrain via base geometry– Edit appearance via basis functions– Close to spatial and frequency domain

editing paradigm

• Use „odd“ lacunarity / roughness like2.173482... breaks up repetitions

),(),(),( yxFyxyxFi ii

yxyxi i ,1),( ii 0



Rotations & Translations• Warp domain with pseudo-random rotations:– Substitutes height field H(x,y) H( Rot(x,y)+T(x,y) )

• Some basic math involved. Key ideas:– Rotation and Translation depend on octave

Levels are warped against each other

– Rotation and Translation depend on roughnessEmphasize or de-emphasize high roughness

– Avoid sine / cosine computationsRotation expressed via unit vector (no explicit angle)

Entries are treated as cos(),sin()



Rotations & Translations



Domain Warping



GPU Implementation• Tileable textures– Basis functions– Weights for multifractal– Low frequency basis height field– Final height field



Demo



Conclusion• Terrain visualization:

– Major challenge: data volume– GPU-friendly compression beyond S3TC needed– GPU-friendly geometry compression needed– In research…

• Terrain Synthesis:– So far, can achieve ~30fps– Faster soon due to improved vertex texture fetches– Powerful, interactive WYSIWYG editing tools

• Editing of basis functions makes sense, now– Future direction: fractal geotypical texture synthesis– Anti-aliasing for some cases still hard

Computer graphics & visualization Interactive Terrain Synthesis.

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