10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Last Time Terrain Dynamic LOD.

10/21/03 CS679 - Fall 2003 - Copyright Univ. of Wisconsin

Last Time

• Terrain Dynamic LOD


Today

• Terrain Generation– Most examples taken from Game Programming Gems


Terrain Generation Methods

• Paint the height field (artist generated)

• Various pseudo-random processes– Independent random height at each point

– Fault generation methods (based on random lines)

– Particle deposition

– Fractal terrain from meshes

• Triangulated point sample methods

• Plenty of commercial tools for terrain generation


Painting Terrain

• An artist paints a gray image– Light represents high points, dark is low

– The pixels directly give the function values on the grid

• The preferred method when good control is required and not too much terrain needs too be generated


Painted Terrain Example

Height

Color

Texture


Surface Attributes

• Rather than painting texture and color directly, paint attributes– E.g. Grass, Trees, Water, …

– Features can have game-play characteristics: speed of motion, impassable, …

• Then automatically generate colors/textures– Care must be taken at the boundaries of the regions

• Can also work for the terrain itself– E.g. Maps that have a finite number of possible heights, with ramps

between them


Random Processes

• The claim is that real terrain looks “random” over may scales

• Hence, random processes should generate realistic terrain– The catch is knowing which random processes

• Some advantages:– Lots of terrain with almost no effort– If the random values are repeatable, the terrain can be generated on

the fly, which saves on storage

• Some disadvantages:– Very poor control over the outcome– Non-intuitive parameter settings


Random Points

• Randomly choose a value for each grid point– Can make each point independent (don’t

consider neighbors)– Can make points dependent on previous

points - a spatial Markov process

• Generally must smooth the resulting terrain– Various smoothing filters could be used

• Advantage: Relatively easy to generate on the fly


Repeatable Random Values

• Most “random” number generators on computers are actually “pseudo-random”– Generated by functions that highly de-correlate their input

• Standard random number generators produce a sequence of values given some initial seed– Warning: Most implementations are poor, so find your own– Not good enough for on-the-fly terrain, because we don’t know

what order the terrain will be required• Hashing functions take a value and transform it into another

value with the appearance of randomness– Used in hash tables to transform keys to hash indexes– Great for terrain – Use (x,y) as the key, and hash it to the height


Fault Formation

• Claimed to model real fault lines, but not at all like real faults

• Process 1:– Generate a random line and lift everything on one side of the line by d

– Scale d and repeat

– What does the terrain typically look like?

• Process 2:– Generate a random line and lift the terrain adjacent to the line

– Repeat (maybe with a scale function)

– What does the terrain look like?

• Smoothing is very important


Fault Formation Example

Initial Smoothed


Fault Formation Example


Particle Deposition

• Supposed to model lava flow (or glacial drumlins!)

• Process:– Drop a particle onto the terrain

– Jiggle it around until it it is at most one unit higher than each of its neighbors

– Repeat

– Occasionally move the drop point around

• To do volcanoes, invert everything above a plane

• To do sinkholes, invert the hill

• To do rows of hills, move the drop point along a line


Particle Deposition Process

?

?In 3D, more scope for random choices on jiggling particles


Particle Deposition Image


Fractal Terrain

• Based on subdivision of a course polygon mesh

• Each subdivision adds detail to the mesh in a random way

• Algorithm (starting with a triangular mesh):– Split each edge, and shift the new vertex up or down by a random

amount

– Subdivide the triangles using the new vertices

– Repeat

• Also algorithms for quadrilateral meshes


Subdivision Method No 1

Note: Works on any triangular mesh - does not have to be regular or have equal sized trianglesSee my lecture notes from CS559 for implementation details



• Generates a triangle bintree from the top down

• Useful for LOD, as we have seen• Ideally, works for right-angled

isosceles triangles



• Note that the middle of each square is not on an edge, so what is its initial value?

• Answers vary


Fractal Terrain Details

• The original mesh vertices don’t move, so it defines the overall shape of the terrain (mountains, valleys, etc)

• There are options for choosing where to move the new vertices– Uniform random offset

– Normally distributed offset – small motions more likely

– Procedural rule – eg Perlin noise

• If desired, boundary vertices can be left unmoved, to maintain the boundary edge


Fractal Terrain Scaling

• Scaling the offset of new points according to the subdivision level is essential– For the subdivision to converge to a smooth surface, the

offset must be reduced for each level (to less than half its previous value)

– Why? (Intuitively)


Fractal Terrains

http://members.aol.com/maksoy/vistfrac/sunset.htm

This mesh probably doesn’t reduce the offset by much at each step.Very jagged terrain


Terrain, clouds generated using procedural textures and Perlin noisehttp://www.planetside.co.uk/ -- tool is called Terragen


Terrain, clouds generated using procedural textures and Perlin noisehttp://www.planetside.co.uk/ -- tool is called Terragen


Triangulated Point Sets

• Start with a set of points that define specific points on the terrain– Tops of mountains, and bottoms of valleys, for example

• Triangulate the point set, and then start doing fractal subdivision• What makes a good point set triangulation?


Delaunay Triangulation

• A triangulation with the circum-circle property:

• Several algorithms for computing it - look in any computational geometry book

For every triangle, a circle through its points does not contain any other point

DelaunayNot - points inside this circle


Populating Terrain

• Coloring terrain:– Paint texture maps

– Base color on height (with some randomness)

• Trees:– Paint densities, or randomly set density

– Then place trees randomly within regions according to density

• Rivers (and lakes):– Trace local minima, and estimate catchment areas


Terrain Generation Trade-Offs

• Control vs Automation:– Painting gives most control

– Fractal terrain next best control because you can always specify more points

– Random methods give little control - generate lots and choose the one you like

• Generate on-the-fly:– Random points and fractal terrain could be generated on the fly, but

fractal terrain generation is quite slow

– Tilings can also be generated on the fly


Todo

• By Monday, Nov 3, Stage 3 demo

• Thursday, Nov 6, Midterm– In class

– Material up to and including today’s lecture, but not beyond

10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Last Time Terrain Dynamic LOD.

Documents

terrain generation slide

real terrain

fly terrain

wisconsin painting terrain

wisconsin random points

wisconsin random processes

realistic terrain

height slide