1. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Last Time Terrain Dynamic LOD

2. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Today Terrain Generation –Most examples taken from Game Programming Gems

3. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

4. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

5. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Painted Terrain Example Height Color Texture

6. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

7. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

8. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

9. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

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

11. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Fault Formation Example Initial Smoothed

12. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Fault Formation Example

13. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

14. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Particle Deposition Process ? ? In 3D, more scope for random choices on jiggling particles

15. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Particle Deposition Image

16. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

17. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Subdivision Method No 1 Note: Works on any triangular mesh - does not have to be regular or have equal sized triangles See my lecture notes from CS559 for implementation details

18. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Subdivision Method No 2 Generates a triangle bintree from the top down Useful for LOD, as we have seen Ideally, works for right-angled isosceles triangles

19. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Subdivision Method No 3 Note that the middle of each square is not on an edge, so what is its initial value? Answers vary

20. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

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

22. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

23. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Terrain, clouds generated using procedural textures and Perlin noise http://www.planetside.co.uk/ -- tool is called Terragen

24. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin Terrain, clouds generated using procedural textures and Perlin noise http://www.planetside.co.uk/ -- tool is called Terragen

25. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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?

26. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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 Delaunay Not - points inside this circle

27. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

28. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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

29. 10/21/03CS679 - Fall 2003 - Copyright Univ. of Wisconsin 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