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Advancements in Computer-Generated Geometry: Synthesis Techniques and Applications

This overview presents innovative methods for generating computer-generated geometry, focusing on parametric synthesis and synthesis by analogy. Techniques for creating landscapes and mazes are discussed, including the use of height maps and recursive backtracking algorithms. Challenges in generating meaningful, high-detail geometry, reminiscent of human architecture, are outlined. Proposed projects aim to enhance geometry generation through the application of design templates, adding textures and details automatically. The synthesis process is illustrated with applications in gaming, architectural design, and more.

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Advancements in Computer-Generated Geometry: Synthesis Techniques and Applications

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  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!

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