Geometry Synthesis

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

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

3. Computer-Generated Geometry 1

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

5. Landscapes 3

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

7. Mazes

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

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

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

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

12. Parametric Synthesis 4

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

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

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. Texture Synthesis by Analogy Template Synthesis Target • Randomly pick first color • Move left to right, top to bottom • Pick neighborhood that matches best

17. Texture Synthesis by Analogy Template Synthesis Target • Randomly pick first color • Move left to right, top to bottom • Pick neighborhood that matches best

18. Texture Synthesis by Analogy • Large features require large neighborhood Source 5 x 5 7 x 7 9 x 9 6

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

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

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. 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. Extra Slides • Recursive Backtracking

25. Recursive Backtracking Unvisited neighbor to the north. Tear down wall! • 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!