3 D Terrain Generation Pablo Saldarriaga CSE 4431
3 D Terrain Generation Pablo Saldarriaga CSE 4431
Why virtual terrains? There are many applications for 3 d 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
Background The defense industry created virtual terrains as early as the 1970’s 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 1980’s procedural techniques are developed and they are used to generate artificial terrains Their purpose were ballistics and training simulations This was the time Perlin created his noise functions It was only until the late 1980’s that fractals and polygonal subdivision techniques started to become more widespread in artificial terrain generation
Military simulation software SIMDIS Triangulated Irregular Network(TIN) Emil Multifractal terrain by Kenton Musgrave
A virtual terrain generated using Terragen 2 from Planetside software Image created by Hannes Janetzko. http: //www. planetside. co. uk/gallery/f/tg 2/Hannes-Another+jungle+flyover. jpg. html
How are virtual terrains generated? Heightfields games and simulators use heightfields as a rough terrain model This lecture will be focused in this approach Voxels Widespread approach for generating virtual terrain Volume based values in a 3 D grid Meshes TIN’s, tesselation schemes such as ROAM (Realtime optimally adapting mesh) and other LOD(Level of Detail) techniques
ROAM Voxel Terrain ROAM : Inventor Projects 2006, http: //merlin. fit. vutbr. cz/wiki/index. php/Inventor_Projects_2006 Voxel Terrain: Generating Complex Procedural Terrains Using the GPU, http: //http. developer. nvidia. com/GPUGems 3/gpugems 3_ch 01. html
Topics Glsl vertex displacement using height maps Fractal Terrain generation Midpoint displacement Alg. Diamond – Square Alg. Fault Line Alg. Particle deposition
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 vec 3 new. Pos = current. Pos + current. Normal * h; gl_Position = u. Model. View. Projection. Matrix * vec 4(new. Pos, 1. );
Very simple example
Fractal Terrains first approach would be to generate a heightmap using f. Bm noise results look ok but not very realistic since f. Bm is homogeneous and isotropic
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 3 rd edition, pg 490
“Multiplicative Multifractal”
H controls the roughness of the fractal Multifractal terrain patch with an offset of 0. 8 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
Other kinds of Multifractals Hybrid multifractals Called hybrid because they are both additive and multiplicative multifractals Ridged multifractals Similar to Perlin’s 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)
Midpoint displacement 1 D 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) Step 1 Step 2 Now reduce the range of your random function depending on r by d* = pow( 2 , -r) Again displace the midpoint of all the line segments and reduce your Random function’s range
Keep iterating until you get the required detail Step 3 Always remembering to reduce d After every step How does r affect the outcome? If r = 1 Your d will half each iteration If r > 1 d increases faster generates smooth terrain Nth step If < 1 d increases slowly generates chaotic terrain
Diamond- Square Also called the cloud fractal , plasma fractal or random midpoint displacement The 2 D 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 2^n This ensures that the rectangle size will have an integer value at each iteration
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
the first step involves calculating the midpoint of the grid based on its corners and then adding the maximum displacement for the current iteration E = (A+B+C+D)/4 + Rand(d) can generate random values between -d and +d This is called the Diamond step , Because if you render this terrain you will see four diamond shapes
Next is the Square step Calculate the midpoints of the edges between the corners wrapping G = (A+B+E+E)/4 + rand(d) H = (B+D+E+E) /4 + rand(d) I = (D+C+E+E)/4 + rand(d) F = (A+C+E+E)/4 + rand(d) Non-wrapping G = (A+B+E)/3 +rand(d) same for H, I, F Since the first iteration is complete, now d is reduced by d *= pow(2, -r) where r is the roughness constant
Start the second iteration Again perform the diamond step B J = (A+G+F+E)/4 + rand(d) K = (G+B+E+H)/4 + rand(d) L = (F+E+D+I)/4 + rand(d) M = (E+H+I+C)/4 + rand(d) Remember this d is smaller than the one in the first iteration D C
Perform the square step wrapping O = (A+G+J+J)/4 + rand(d) P = (J+G+K+E)/4 + rand(d) Q = (J+E+L+F)/4 + rand(d) N = (A+F+J+J)/4 +rand(d) Non-wrapping O = (A+G+J)/3 + rand(d) N = (A+F+J)/3 + rand(d) Continue subdividing until you reach the desired level of detail
To summarize, Diamond - Square alg. While length of square sides > 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
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. lighthouse 3 d. com/opengl/terrain/index. php? fault
One way of generating fault lines in a height field grid randomly pick two grid points p 1 p 2 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
Height fields generated by this algorithm need to be filtered in order to look like realistic terrain A low pass filter is usually used
some variations to the fault line algorithm Cosine Sine
Particle Deposition Simulates volcanic mountain ranges and island systems drop random particles in a blank grid Determine if the particle’s 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
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
Bibliography De Carpentier, Giliam J. P. . Interactively synthesizing and editing virtual outdoor terrain. MA thesis. Delft University of Technology, 2007. http: //www. decarpentier. nl/downloads/Interactively. Synthesizing. And. Editing. Vir tual. Out. Door. Terrain_report. pdf De. Loura, 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, 3 rd edition. USA. Morgan Kaufman Publishers, 2003. Martz, Paul. “Generating Random Fractal Terrain. ” Game Programmer. Publisher Robert C. Pendleton, 1997. http: //www. gameprogrammer. com/fractal. html#midpoint Mc. Anlis, Colt. “HALO WARS: The Terrain of Next-Gen. ” GDC Vault, 2009. <http: //www. gdcvault. com/play/1277/HALO-WARS-The-Terrain-of>
Olsen, Jacob. Realtime Procedural Terrain Generation. Department of Mathematics and Computer Science, IMADA, University of Southern Denmark, 2004. <http: //web. mit. edu/cesium/Public/terrain. pdf> “Open. GL”. yaldex. com. http: //www. yaldex. com/open-gl/ch 20 lev 1 sec 2. html Polack, Trent. Focus on 3 D Terrain Programming. Cengage Learning, 2002. Ramirez F. , António. “Terrain Tutorial. ” Open GL. Lighthouse 3 D. , 2012. <http: //www. lighthouse 3 d. com/opengl/terrain/index. php 3? introduction> Tamshi. “RE: Heightmap, Voxel, Polygon (geometry) terrains. ” Game Development. Stack. Exchange Inc. , 2011. <http: //gamedev. stackexchange. com/questions/15573/heightmap-voxelpolygon-geometry-terrains> “Welcome to the Virtual Terrain Project. ” VTERRAIN. org, 2011. <http: //vterrain. org>
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