Last Time Terrain Dynamic LOD 102103 CS 679

Last Time • Terrain Dynamic LOD 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Today • Terrain Generation – Most examples taken from Game Programming Gems 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Painted Terrain Example Texture Height Color 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Fault Formation Example Initial 10/21/03 Smoothed CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Fault Formation Example 10/21/03 CS 679 - 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 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Particle Deposition Process ? ? In 3 D, more scope for random choices on jiggling particles 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Particle Deposition Image 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 CS 559 for implementation details 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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) 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Fractal Terrains This mesh probably doesn’t reduce the offset by much at each step. Very jagged terrain http: //members. aol. com/maksoy/vistfrac/sunset. htm 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Terrain, clouds generated using procedural textures and Perlin noise http: //www. planetside. co. uk/ -- tool is called Terragen 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Terrain, clouds generated using procedural textures and Perlin noise http: //www. planetside. co. uk/ -- tool is called Terragen 10/21/03 CS 679 - 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? 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin

Delaunay Triangulation • A triangulation with the circum-circle property: For every triangle, a circle through its points does not contain any other point • Several algorithms for computing it - look in any computational geometry book Not - points inside this circle 10/21/03 Delaunay CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - 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 10/21/03 CS 679 - Fall 2003 - Copyright Univ. of Wisconsin