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Creating and Navigating Virtual Worlds

Creating and Navigating Virtual Worlds. David Mould. Overview. Creating scenery in virtual worlds Navigating through virtual worlds Helping game players to understand virtual worlds. [World of Warcraft, 2004-2008]. [Oblivion, 2006]. Ontogenetic Modeling.

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Creating and Navigating Virtual Worlds

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  1. Creating and Navigating Virtual Worlds David Mould

  2. Overview • Creating scenery in virtual worlds • Navigating through virtual worlds • Helping game players to understand virtual worlds

  3. [World of Warcraft, 2004-2008]

  4. [Oblivion, 2006]

  5. Ontogenetic Modeling • Ontogenetic modeling: approach appearance of model without regard for underlying process • Seek lightweight means of mimicking appearance of dendritic objects • Path planning: • irregular curves • paths from root never cross

  6. Path Planning Problem • Given a weighted graph, a start node S, and a destination D, find the path from S to D that has the lowest cost. • a path is a sequence of edges. • the cost of a path is the sum of all the edge weights along the path.

  7. Path planned dendrites

  8. Basic Idea • Shortest paths in a weighted graph • Automated process • Offers user control: • weights in graph influence path shape • endpoint choice affects dendrite’s appearance • generator shape, likewise

  9. Implementation • Dijkstra’s algorithm used to get costs from root to all other nodes in graph • O(N) to cover graph • O(n) for path from arbitrary endpoint to root • endpoints placed by hand or procedurally

  10. Fractal Dendrites • Real objects often exhibit fractal (multiscale) detail • Explicitly introduce hierarchical detail: • Create low-frequency detail • Add structure at higher frequency • Repeat previous step

  11. real DLA imitated DLA

  12. [Xu and Mould 2007 – GRAPP 2007 Best Paper]

  13. “Rocks” • Multi-source path planning partitions space – can be used to produce irregular 3D objects

  14. Constructive Path Planning • Path planning for procedural structure • Simple implementation • Rich control handles • Wide variety of phenomena • Trees, rocks, coral, lightning

  15. [Mould 2005]

  16. Navigating Virtual Worlds • Virtual worlds are full of obstacles and hazards, and getting from point A to point B is not trivial • Both computer-controlled and player-controlled agents need automatic navigation • Formal framework: least-cost path through a weighted graph

  17. [Total Annihilation, 1997] [Heroes of Might and Magic V, 2007]

  18. Weighted Graphs 3 2 7 1 1 4 3 4 3 8 2 2 5 2 1

  19. Weighted Graphs 3 1 - Weights represent difficulty - distance - time - hazard

  20. Heuristic Search: A* • If the heuristic is perfect, we always search exactly in the right direction, and only look at nodes on the path • If the heuristic is admissible, the final path is guaranteed to be optimal

  21. Bad heuristics • If the heuristic is poor (doesn’t give much information about where to search) then A* does no better than breadth-first search • It's very difficult to devise general heuristics • In computer games, level designers try to invent maps which defeat simple heuristics

  22. Giving up • But, is there much need for optimal paths? • People don’t usually use the optimal path, and they seem to get around fine • A path can be “good enough” without being optimal • [Aside: non-admissible heuristics can work OK, but can result in extremely high costs fixing the errors in tricky maps]

  23. Hierarchical search

  24. Hierarchical Search

  25. Hierarchical Search • Create a second graph which is an abstraction of the first (maybe repeat) • Use the hierarchy to give the paths • waypoints • Use the hierarchy to give estimates • Use the hierarchy to constrain the search • HTAP’s pyramid

  26. HTAP • HTAP: Hierarchical Terrain Representation for Approximately Shortest Paths [Mould and Horsch 2004; Mould and Horsch 2005] • Offline construction of hierarchy • Online linear-time pathfinding • Search space constrained by hierarchy

  27. Creating the Hierarchy • Choose “representatives” – nodes estimated to be on many paths • Associate nodes with representatives • Insight: according to path cost in original graph • Place edges between representatives • again, based on original-graph path cost • New graph obtained; repeat if still too big

  28. Using the Hierarchy • Find representatives of endpoints in coarsest graph, and search for path there • Next level down: • find representatives of endpoints in current level (just a lookup) • find path, searching only in regions whose representatives one level up were on the path • Repeat until bottom level reached

  29. Search space comparison

  30. Results computational cost (number of vertices opened) A* - quadratic HTAP - linear path cost

  31. Results computational cost (number of vertices opened) path cost

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