1. Interactive Terrain Synthesis
Image Synthesis
Interactive Terrain Synthesis

2. Fractal Terrain Synthesis
Goals:
Generation of fractal terrain
Non-repetitive, infinite extent
Interactive frame rates
Real-time editable
Methods
Rescale & Add on GPU

3. 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

4. Rescale-and-Add Noise synthesis by point evaluation
Summation of scaled and dilated noise functions

5. Rescale-and-Add Add weighted noise octaves to simulate 1/f-noise
1/f noise: as frequency increases, amplitude decreases

6. Rescale-and-Add Another method to simulate 1/f-noise =
Generate noisy copies on-the-fly from a base random texture 20 21 22 =
• • • 23 24

7. Rescale-and-Add H(x,y): synthesized height field
F(x,y): basis function
n: number of octaves

8. 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

9. Rescale And Add - Parameters
Roughness r

10. Rescale And Add - Parameters
Lacunarity l

11. Rescale And Add - Parameters
Octaves o

12. 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 like  breaks up repetitions

13. 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 roughness
Emphasize or de-emphasize high roughness
Avoid sine / cosine computations
Rotation expressed via unit vector (no explicit angle) Entries are treated as cos(),sin()

14. Rotations & Translations

15. Domain Warping

16. GPU Implementation Tileable textures Basis functions
Weights for multifractal
Low frequency basis height field
Final height field

17. Demo

18. Conclusion Terrain visualization: Terrain Synthesis:
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