1. Geometry Synthesis Mathias Ricken Rice Undergraduate Scholar Program November 11, 2003

2. 2 Overview  Computer-Generated Geometry  Uses  Creation  Previous Work  Landscapes  Mazes  Problems  Geometry Synthesis  Parametric synthesis  Synthesis by analogy

3. 3 Computer-Generated Geometry 1

4. 4 Creating Geometry  Hand-Crafted  Computer games 1 Man-Year for 40 hours of game play 2 2  Automation  Lower costs  Better training  Higher replay value

5. 5 Landscapes 3

6. 6  Filters  Smoothen or roughen landscape  Add rivers and lakes  Height Map  Matrix of numbers  e.g. one per square foot  Numbers  Elevation

7. 7 Mazes

8. 8  Recursive Backtracking  Regular grid  2-Dimensional  Creates perfect mazes  All cells connected in exactly one way  No loops algorithm explained in extra slides

9. 9 Problems  Landscapes  Large scale, but low detail  Only natural, not artificial  Mazes  2-dimensional  Small scale  Not reminiscent of human architecture

10. 10 Proposed Project  Create meaningful geometry  Similar to human architecture  3-dimensional  High detail  Algorithms  Parametric synthesis  Synthesis by analogy

11. 11 Parametric Synthesis  Create a network of rooms and corridors  Generalization of DungeonMaker algorithm 4 4  Tunnelers, agents (“robots”)  Randomly  Probabilities controlled by parameters  change direction  create rooms  create branches

12. 12 4 Parametric Synthesis

13. 13  Generalize  3D, not 2D  Not grid-based  Examples of Parameters  Frequencies  Dimensions  Angles  Alignment 4 Parametric Synthesis

14. 14 Synthesis by Analogy  Automatically enhance bare geometry created by parametric synthesis  Use design templates  Add colors, patterns, details 5

15. 15 Texture Synthesis by Analogy  Given small texture, create arbitrarily large similar texture  Few visual flaws  Similar to a jigsaw puzzle  Look at the surrounding pieces (neighborhood) and pick best match  Does not have to be perfect fit  Pieces can be used more than once or not at all

16. 16 Texture Synthesis by Analogy TemplateSynthesis Target 1.Randomly pick first color 2.Move left to right, top to bottom 3.Pick neighborhood that matches best

17. 17 Texture Synthesis by Analogy TemplateSynthesis Target 1.Randomly pick first color 2.Move left to right, top to bottom 3.Pick neighborhood that matches best

18. 18 Texture Synthesis by Analogy  Large features require large neighborhood Source5 x 57 x 79 x 9 6

19. 19 Geometry Synthesis by Analogy  Geometry can be represented by matrix  Distance to next surface  Implicit representation  Positive  inside  Negative  outside  Zero  surface  Convert geometry into matrix  Apply synthesis by analogy to it 7

20. 20 Geometry Synthesis by Analogy  Previous research in two dimensions  Generalize from 2D to 3D  Improve speed 8

21. 21 Editor  Build application  Graphical user interface  3D display  Support all synthesis steps 9

22. 22 Notes [1]Lord of the Rings. New Line Cinema. Beasts. Comp 460, Rice University. Midfield Terminal Complex. Southwest Florida International Airport. Dynamic Flight Simulator. Naval Warfare Center, Westminster, Penn. United States Navy. [2]Rollings, A., and Morris, D. Game Architecture and Design. [3]Terragen. Planetside Software. http://www.planetside.co.uk/terragen/ [4]DungeonMaker. Dr. P. Henningsen. http://dungeonmaker.sourceforge.net/

23. 23 Notes [5]Illustration. Hive Assault. Comp 460, Rice University. [6]Wei, Li-Yi. Texture Synthesis by Fixed Neighborhood Searching. Ph.D. thesis. [7]Implicit Modeling Editor. Scott Schaefer, Rice University. [8]Actual synthesis result. Geometry Synthesis by Analogy. Mathias Ricken, Rice University (unpublished). [9]Illustration.

24. 24 Extra Slides  Recursive Backtracking Recursive Backtracking

25. 25 Recursive Backtracking  Square grid  Start in one cell  Pick a neighboring cell that has never been reached before and tear down the wall to it  Remember previous cell  If no unvisited neighboring cell, backtrack No more unvisited neighbors, backtrack! Unvisited neighbor to the north. Tear down wall!