3D Terrain Generation

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3D Terrain Generation

• Pablo Saldarriaga
• CSE4431

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Why virtual terrains?

• There are many applications for 3d terrains
• Just to name a few
• Virtual tourism and travel planning
• Education
• Civil engineering, urban planning
• Weather visualizations
• Real Estate
• Games
• Movies
• Placement of communication signal towers

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Background

• The defense industry created virtual terrains as
  early as the 1970s
• Their purpose were ballistics and training
  simulations
• TINs (Triangulated Irregular Networks) appeared
  in 1973, developed by Randolph Franklin at Simon
  Fraser University
• TIN vector based representation of the physical
  land surface or sea bottom
• In the 1980s procedural techniques are developed
  and they are used to generate artificial terrains
• This was the time Perlin created his noise
  functions
• It was only until the late 1980s that fractals
  and polygonal subdivision techniques started to
  become more widespread in artificial terrain
  generation

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Military simulation software SIMDIS
Triangulated Irregular Network(TIN)
Emil Multifractal terrain by Kenton Musgrave
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• A virtual terrain generated using Terragen 2 from
  
• Planetside software

Image created by Hannes Janetzko.
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How are virtual terrains generated?

• Heightfields
• Widespread approach for generating virtual
  terrain
• games and simulators use heightfields as a rough
  terrain model
• This lecture will be focused in this approach
• Voxels
• Volume based values in a 3D grid
• Meshes
• TINs, tesselation schemes such as ROAM (Realtime
  optimally adapting mesh) and other LOD(Level of
  Detail) techniques

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ROAM
Voxel Terrain
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Topics

• Glsl vertex displacement using height maps
• Fractal Terrain generation
• Midpoint displacement Alg.
• Diamond Square Alg.
• Fault Line Alg.
• Particle deposition

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• In Glsl, terrain can be generated relatively easy
  if
• a heightmap texture is available to the vertex
  shader
• the surface that is going to be displaced is
  tesselated fine enough to show the heightmap
  details
• If this is the case then add the following to the
  vertex shader
• //make sure your height value is in the desired
  range (for example from 0 to 1)
• float h texture(heightmap, st).r Scale Bias
• //ensures that the displacement happens in the
  direction of the normal of the current vertex
• vec3 newPos currentPos currentNormal h
• gl_Position uModelViewProjectionMatrix
  vec4(newPos,1.)

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• Very simple example

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Fractal Terrains

• first approach would be to generate a heightmap
  using fBm noise
• results look ok but not very realistic
• since fBm is homogeneous and isotropic

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• A better choice would be to use Multifractals
• These are fractals whose dimension/roughness
  varies with location
• So how do you generate a Multifractal?

Multifractal terrain by Kenton Musgrave. Texturing
and Modeling a Procedural Approach 3rd edition,
pg 490
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Multiplicative Multifractal
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• The above multifractal function is considered to
  be unstable
• It varies from highly heterogenous (at offset
  0) to flat (offset diverges to infinity)
• Its output usually needs to be rescaled

H controls the roughness of the fractal
Multifractal terrain patch with an offset of 0.8
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Other kinds of Multifractals

• Hybrid multifractals
• Called hybrid because they are both additive and
  multiplicative multifractals
• Ridged multifractals
• Similar to Perlins turbulence noise
• They calculate 1-abs(noise) so that the resulting
  canyons from abs(noise) become high ridges

Ridged multifractal terrains taken from
Texturing and Modeling A Procedural Approach pg
518 (left) pg 480(right)
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Midpoint displacement 1D version

• Type of polygon subdivision algorithm, also a
  fractal function
• Created to simulate tectonic uplift of mountain
  ranges
• One of its main input parameters is the roughness
  constant r

Step 0
Displace the midpoint of the line by some random
value between (-d, d)
Now reduce the range of your random
function depending on r by d pow( 2 , -r)
Step 1
Again displace the midpoint of all the line
segments and reduce your Random functions range
Step 2
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Keep iterating until you get the required detail
Always remembering to reduce d After every step
Step 3
How does r affect the outcome? If r 1 Your d
will half each iteration If r gt 1 d increases
faster generates smooth terrain If lt 1 d
increases slowly generates chaotic terrain
Nth step
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Diamond- Square

• Also called the cloud fractal , plasma fractal or
  random midpoint displacement
• The 2D version of the original Midpoint
  displacement algorithm
• Therefore it also has a roughness constant
• The diamond-square alg. works best if it is run
  on square grids of width 2n
• This ensures that the rectangle size will have an
  integer value at each iteration

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• the algorithm starts with a 2 x 2 grid
• The heights at the corners can be set to either
  zero, a random value or some predefined value

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• the first step involves calculating the midpoint
  of the grid based on its corners and then adding
  the maximum displacement for the current
  iteration
• This is called the Diamond step ,
• Because if you render this terrain you will see
  four diamond shapes

E (ABCD)/4 Rand(d)
Rand(d) can generate random values between -d
and d
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• Next is the Square step
• Calculate the midpoints of the edges between the
  corners
• Since the first iteration is complete, now d is
  reduced by
• d pow(2,-r) where r is the roughness
  constant

wrapping G (ABEE)/4 rand(d) H (BDEE)
/4 rand(d) I (DCEE)/4 rand(d) F
(ACEE)/4 rand(d)
Non-wrapping G (ABE)/3 rand(d) same for
H,I,F
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• Start the second iteration
• Again perform the diamond step

B
J (AGFE)/4 rand(d) K (GBEH)/4
rand(d) L (FEDI)/4 rand(d) M (EHIC)/4
rand(d)
Remember this d is smaller than the one in the
first iteration
C
D
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• Perform the square step
• Continue subdividing until you reach the desired
  level of detail

wrapping O (AGJJ)/4 rand(d) P
(JGKE)/4 rand(d) Q (JELF)/4 rand(d) N
(AFJJ)/4 rand(d)
Non-wrapping O (AGJ)/3 rand(d) N
(AFJ)/3 rand(d)
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• To summarize,
• Diamond - Square alg.
• While length of square sides gt 0
• Pass through the whole array and apply the
  diamond step for each square
• Pass through the whole array and apply the square
  step for each diamond
• Reduce the range of the random displacement

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Fault line algorithm

• Created to approximate real world terrain
  features such as escarpments, mesas, and seaside
  cliffs

First step in faulting process
Terrain generated after 400 iterations
Pictures from http//www.lighthouse3d.com/opengl/t
errain/index.php?fault
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• One way of generating fault lines in a height
  field grid
• randomly pick two grid points p1 p2
• calculate the line between them
• Go through all the points in the height field and
  add or subtract an offset value depending on what
  side of the line they are located
• Before the next fault is drawn, reduce the range
  of the offset by some amount

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• Height fields generated by this algorithm need to
  be filtered in order to look like realistic
  terrain
• A low pass filter is usually used

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• some variations to the fault line algorithm

Cosine
Sine
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Particle Deposition

• Simulates volcanic mountain ranges and island
  systems
• drop random particles in a blank grid
• Determine if the particles neighboring cells are
  of a lower height
• If this is the case increment the height of the
  lowest cell
• keep checking its surrounding cells for a set
  number of steps or until it is the lowest height
  among its surrounding cells
• If not increment the height of the current
• cell

Generated after 5 series of 1000 iterations
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Issues with using Height fields

• They cannot generate overhangs or caves
• Some solutions, for example
• mushrooming effects that involve the
  manipulation of vertex normals in order to render
  height field textures with overhangs
• the game Halo Wars implemented a new type of
  height field called a vector height field which
  stored a vector to displace a vertex instead of
  a height value

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Bibliography

• De Carpentier, Giliam J.P.. Interactively
  synthesizing and editing virtual outdoor
  terrain.MA thesis. Delft University of
  Technology, 2007. http//www.decarpentier.nl/downl
  oads/InteractivelySynthesizingAndEditingVirtualOut
  DoorTerrain_report.pdf
• DeLoura, Mark. Game Programming Gems. Charles
  River Media, 2002.
• Ebert, David S., Musgrave, F. Kenton, Peachey,
  Darwyn, Perlin, Ken and Worley, Steve.Texturing
  and Modeling A Procedural Approach, 3rd edition.
  USA. Morgan Kaufman Publishers, 2003.
• Martz, Paul. Generating Random Fractal Terrain.
  Game Programmer. Publisher Robert C.
• Pendleton, 1997. http//www.gameprogrammer.com/fra
  ctal.htmlmidpoint
• McAnlis, Colt. HALO WARS The Terrain of
  Next-Gen. GDC Vault, 2009. lthttp//www.gdcvault.c
  om/play/1277/HALO-WARS-The-Terrain-ofgt

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• Olsen, Jacob. Realtime Procedural Terrain
  Generation. Department of Mathematics and
  Computer Science, IMADA, University of Southern
  Denmark, 2004. lthttp//web.mit.edu/cesium/Public/t
  errain.pdfgt
• OpenGL. yaldex.com. http//www.yaldex.com/open-g
  l/ch20lev1sec2.html
• Polack, Trent. Focus on 3D Terrain Programming.
  Cengage Learning, 2002.
• Ramirez F., António. Terrain Tutorial. Open GL.
  Lighthouse 3D., 2012. lthttp//www.lighthouse3d.com
  /opengl/terrain/index.php3?introductiongt
• Tamshi. RE Heightmap, Voxel, Polygon (geometry)
  terrains. Game Development. StackExchange Inc.,
  2011. lthttp//gamedev.stackexchange.com/questions/
  15573/heightmap-voxel-polygon-geometry-terrainsgt
• Welcome to the Virtual Terrain Project.
  VTERRAIN.org, 2011. lthttp//vterrain.orggt