Emerging Technologies for Games Spatial Partitioning 2

1
Emerging Technologies for GamesSpatial
Partitioning 2

• CO3303
• Week 11-12

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Contents

• Introduction
• Binary Space Partitioning
• Quad-Trees / Oct-Trees
• Other Partitioning Schemes
• Rabin p456 onwards

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Introduction / Recap

• Dividing a game world into partitions has many
  uses
• Have looked at PVS portal systems
• To cull unseen partitions
• Such visibility techniques also useful for AI
  entities
• Here we introduce a range of tree-based
  partitions
• BSP / Quad / Oct trees

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Binary Space Partitioning

• A Binary Space Partition (BSP) is a hierarchical
  division of space
• A tree structure that represents the entire space
• Partitions separated by
• Lines in 2D
• Planes in 3D
• Recursively divide each partition into two
  smaller ones with a line / plane
• Creates a binary tree

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Creating a BSP

• Repeatedly divide space in two
• Stop when
• Maximum of X elements in each partition (X 1
  here)
• Partitions are small enough
• Tree reaches certain depth
• Choice depends on application

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Locating a Point in a BSP

• Given a point, easy to find which partition it is
  in
• Start at root of tree
• Find which side of the dividing line/plane the
  point is on
• Follow appropriate edge
• Repeat until find leaf partition
• Example here
• Check P against X
• Not in A, follow other edge
• Check P against Y
• Not in B, follow other edge, etc.

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Recap Which Side of a Plane?

• A plane is defined by
• A vertex on the plane P
• A vector / normal N at right angles to the plane
• To find which side of the plane a vertex A is on
• d N PA N PA cos a
• A will be on the side pointed at by the vector N
  if
• N PA is a simple operation
• Dont need to calculate a

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BSP for Solid/Hollow Spaces

• Can use the polygons in the scene as the division
  planes
• Choose a polygon as a plane
• All other polygons placed on one or other side of
  plane

• Polygons crossing the planes are split
• BSP splits space into hollow / solid volumes
• All polygons / entities placed in hollow ones

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BSP / Brush Modelling

• This kind of BSP is often used for FPS games
• First appeared in Doom (original version)
• Often used in conjunction with a PVS
• Can also be used to render partitions in a strict
  back to front order
• Lends itself to a unique form of 3D modelling
  called brush modelling Rabin p690
• Start with a entirely solid world
• Cut out primitives (boxes, cylinders etc.)
• Entities placed in hollowed out areas
• Like "digging out" the level
• See Counter-Strike, Unreal, Quake III editors

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BSP Pros / Cons

• BSP trees are well established technique
• Used for rendering / collision / ray-tracing
• Can be generated automatically
• Fully classify space
• Easy to find which partition a point is in
• Need good algorithm to choose dividing planes
• Try to balance tree
• Hollow/solid BSP generates extra polygons due to
  splitting

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Quadtrees / Octrees

• Quadtrees and Octrees can be seen as specific
  kinds of BSP tree
• A hierarchy / tree
• Classifies all of space
• Formed by recursive subdivision
• Unlike a BSP the division scheme is very specific
• Quadtrees are in 2D, octrees are in 3D
• Otherwise the same

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Creating a Quadtree

• Root node is entire space
• Usually square
• Divide into four equal quadrants
• These are the children nodes
• Repeat with each quadrant
• Until some condition is met
• Maximum depth
• An empty node
• Only one entity contained
• Etc. - application dependent

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Location in a Quadtree

• Simple to find which node a point is in
• Start at root node
• Find the quadrant the point is in
• Just two comparisons
• Repeat process on this quadrant
• Can be optimised
• Have world space as square
• Power of 2 in size (e.g. 2048)
• Centred on origin
• Can use bitwise integer math
• See Rabin

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Quadtrees for Visibility Culling

• Use for frustum culling
• Traverse quadtree from root
• Cull entire nodes outside frustum
• Along with all entities and all child nodes in
  them
• Reject many entities at once
• Nodes are AABB
• Viewing frustum is 6 planes
• To test if a node is visible
• Six AABB lt-gt plane tests
• Several approaches, see

www.lighthouse3d.com/opengl/viewfrustum/index.php
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Quadtree Problem

• Problem
• Entities arent points
• May overlap a node boundary
• In this case the entity needs to be in a larger
  parent node
• E.g. Entity overlaps origin
• Can fit in any node except root
• Even a tiny entity
• Lose possibility to cull
• Hot-spots like this around the boundaries of
  larger nodes

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Loose Quadtrees

• Solution Loose Quadtrees
• Have nodes overlap
• Entities will then fit in original node area
• Potentially with their bounding sphere
  overlapping adjacent nodes
• Few changes to algorithms
• Just increase node size
• When inserting entities
• When doing frustum culling
• Removes hot-spot problem
• At the expense of larger nodes at the same level

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Quadtrees for Collision Detection

• We saw intersection of viewing frustum with
  quadtree
• Fairly easy to find intersection of other
  primitives
• Spheres, cuboids, rays, capsules
• Find the set of nodes intersected
• And hence the set of entities that are candidates
  for collision
• Basis for collision detection / ray casting /
  physics systems
• Helps to add adjacency info to the tree