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AdvancedAdvancedScene ManagementScene ManagementSystemSystem

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A tree-based or graph-based representation is good for 3D data A tree-based or graph-based representation is good for 3D data managementmanagement Scene treeScene tree Scene graphScene graph

3D data management including :3D data management including : Transformations for each 3D objectTransformations for each 3D object

Hierarchical relationshipHierarchical relationship Space coherenceSpace coherence Data instancingData instancing Geometric computationGeometric computation

Hit testHit test Collision detectionCollision detection Terrain followingTerrain following

Rendering managementRendering management VisibilityVisibility Alpha SortingAlpha Sorting

Scene Management in Hierarchical FormScene Management in Hierarchical Form

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EtcEtc

ParametersParameters

Geometric DataGeometric Data

ShapeShape

TransformationTransformation MoveMove

Parent ObjectParent ObjectHierarchyHierarchy

Motion DataMotion Data

AnimationAnimation

CloneClone

An Object in the Scene (An Example from An Object in the Scene (An Example from TheFly)TheFly)

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A tree-based representation A simplified scene graph

RootRoot

A Scene Tree (An Example) 1/2A Scene Tree (An Example) 1/2

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A tree-based representation A simplified scene graph

A Scene Tree (An Example) 2/2A Scene Tree (An Example) 2/2

RootRoot

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Bounding sphereBounding sphere

Bounding SphereBounding Sphere AABBAABB

OBBOBB

k-DOPk-DOP

Bounding VolumeBounding Volume

Bounding CylinderBounding Cylinder

Bounding cylinderBounding cylinder Axis-aligned bounding box (AABB)Axis-aligned bounding box (AABB) Oriented bounding box (OBB) Oriented bounding box (OBB)

Discrete oriented polytope (k-DOP)Discrete oriented polytope (k-DOP)

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Collision detectionCollision detection VVisibility cullingisibility culling HHit testit test SSteering behaviorteering behavior

IIn “Game AI” sectionn “Game AI” section

Bounding Volume - ApplicationsBounding Volume - Applications

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Bounding sphere BBounding sphere B11(c(c11, r, r11), B), B22(c(c22, r, r22))

If the distance between two bounding spheres isIf the distance between two bounding spheres islarger than the sum of radius of the spheres, thanlarger than the sum of radius of the spheres, thanthese two objects have no chance to collide.these two objects have no chance to collide.

D > Sum(rD > Sum(r11, r, r22))

DD

BB11

BB22

cc11

cc22

Application Example - Bounding SphereApplication Example - Bounding Sphere

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Axis-aligned bounding box (AABB)Axis-aligned bounding box (AABB) SSimplified calculation using axis-alignment featureimplified calculation using axis-alignment feature BBut need run-timely to track the bounding boxut need run-timely to track the bounding box

AABBAABB

Application Example - AABBApplication Example - AABB

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Oriented bounding box (OBB)Oriented bounding box (OBB) Need intersection calculation using the transformed Need intersection calculation using the transformed

OBB geometric dataOBB geometric data 3D containment test3D containment test Line intersection with planeLine intersection with plane

FFor games, or games,

OBBOBB

Application Example - OBBApplication Example - OBB

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This is a game-type-oriented issue.This is a game-type-oriented issue. Bounding volume hierarchies (BVHs)Bounding volume hierarchies (BVHs) Binary space partition trees (BSP Trees)Binary space partition trees (BSP Trees)

““Quake”Quake” Octree & quadtreeOctree & quadtree Possible Visible SetPossible Visible Set Culling SkillsCulling Skills

Advanced Scene GraphsAdvanced Scene Graphs

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Bounding spheres or AABB in hierarchy Can be used for dynamic scene objects

R

B

Bounding Volume Hierarchies (BVHs)Bounding Volume Hierarchies (BVHs)

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LBVH Linear BVH Tree construction using Morton Code

BVH Construction - LBVHBVH Construction - LBVH

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2D example

Morton Code (1/2)Morton Code (1/2)

Generate the Morton Code Convert the x and y coordinate numbers into binary Then “interleave” the bits to get the Morton number

-0-0-1 : 1 in binary1-0-1- : 5 in binaryxyxyxy100011 : 35 Your interleaved Morton number

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Morton Code (2/2)Morton Code (2/2)

By constructing a 2kx2kx2k lattice within the AABB of the whole scene, we can quantize each of the 3 coordinates of the center of the bounding volume of the scene object.

The 3-bit Morton Code of the object is constructed by interleaving the successive bits of these coordinates.

Sorting the objects in increasing order along the Morton curve. We construct the 1st level split by examining the most

significant bit of all codes, placing those with 0 and 1 bits in the 1st and 2nd child, respectively, of the root.

Applying the bucketing procedures recursively in each child, looking at the 2nd most significant bit.

In each recursive step, we look at the next bit in the Morton code until all bits are consumed.

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BVH Construction – SAH Hierarchy BVH Construction – SAH Hierarchy ConstructionConstruction SAH

Surface Area Heuristic method Calculate the cost to bin the tree node into two children

SAH cost function

SA(N) the surface area of the node’s bounding volumeKT & KI are constantsnl : object number of left child nodenr : object number of right child node

Can be applied to BVH and KD Tree.

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Two variantsTwo variants Axis-alignedAxis-aligned

KD treeKD tree Polygon-alignedPolygon-aligned

The trees are created by using a plane to divide the space into The trees are created by using a plane to divide the space into two, and then sorting the geometry into two spaces.two, and then sorting the geometry into two spaces.

BSP TreeBSP Tree

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plane1plane1

plane

plane

00

plane2plane2

plane

plane

33

00

11 22

33

Axis-aligned BSP TreeAxis-aligned BSP Tree

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AABB

CC

DD

EE

FF

GG

AA

BB CC

DD EE FF GG

Polygon-aligned BSP TreePolygon-aligned BSP Tree

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Quickly to identify where you areQuickly to identify where you are BSP = SortingBSP = Sorting

Need a pre-processor to generate the PVSNeed a pre-processor to generate the PVS Visibility culling + occlusion cullingVisibility culling + occlusion culling PVS : Possible Visible SetPVS : Possible Visible Set

Optimized for in-door game environmentOptimized for in-door game environment [Fuch80][Fuch80]

Fuchs, H.,Fuchs, H., On Visible Surface Generation by a Priori Tree StructuresOn Visible Surface Generation by a Priori Tree Structures, , Computer GraphicsComputer Graphics, , 1414, 124-33, (Proc. SIGGRAPH’80) , 124-33, (Proc. SIGGRAPH’80)

Why BSP Tree ?Why BSP Tree ?

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Very similar to axis-aligned BSP tree.Very similar to axis-aligned BSP tree. Except that a box is split simultaneously along all three axes.Except that a box is split simultaneously along all three axes. The split point should be the center of the box.The split point should be the center of the box. This creates eight new boxes.This creates eight new boxes. Quadtree is the 2D version of octree.Quadtree is the 2D version of octree.

Octree & QuadtreeOctree & Quadtree

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Quadtree - ExampleQuadtree - Example

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Data structure coherenceData structure coherence Apply visibility culling from parentsApply visibility culling from parents Split or not split ?Split or not split ? Outdoor game scene ?Outdoor game scene ?

Octree – Some DiscussionOctree – Some Discussion

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Culling means “remove from a flock”Culling means “remove from a flock” Visibility cullingVisibility culling

Remove the object not in view frustumRemove the object not in view frustum A A “must”“must” feature within the game engine feature within the game engine

Backface cullingBackface culling Remove the polygons facing away from cameraRemove the polygons facing away from camera Hardware standardHardware standard

Occlusion cullingOcclusion culling Remove the objects hidden by the othersRemove the objects hidden by the others A complicated issue for gamesA complicated issue for games

Culling (1/2)Culling (1/2)

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eyeeye

View frustumView frustum

VisibilityVisibilitycullingculling

BackfaceBackfacecullingculling

OcclusionOcclusioncullingculling

Culling (2/2)Culling (2/2)

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A Pre-processorA Pre-processor Space partition the scene data from artistSpace partition the scene data from artist Generate the BSP data structureGenerate the BSP data structure Generate the PVSGenerate the PVS

BSP walk throughBSP walk through Identify the room where you areIdentify the room where you are Show/hide the rooms according to the PVSShow/hide the rooms according to the PVS Perform terrain following & collision detectionPerform terrain following & collision detection

Or all interaction between the player’s character and the Or all interaction between the player’s character and the scenescene

BSP ImplementationBSP Implementation

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InputInput A scene from artistA scene from artist Cutting planes (optional)Cutting planes (optional)

Can be procedurally generated by algorithmCan be procedurally generated by algorithm Cutting policyCutting policy

Split or not splitSplit or not split Ray casting resolution for PVSRay casting resolution for PVS

OutputOutput A BSP fileA BSP file

BSP TreeBSP Tree PVSPVS Geometry DataGeometry Data

BSP Preprocessor (1/2)BSP Preprocessor (1/2)

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ProcessProcess Generate the BSP tree according to the cutting policyGenerate the BSP tree according to the cutting policy Split or sort the geometry into BSP room (leaves)Split or sort the geometry into BSP room (leaves) For each “room”, ray cast all rooms to generate the possible For each “room”, ray cast all rooms to generate the possible

visible room setvisible room set 2D layers or 3D2D layers or 3D Time consumingTime consuming

BSP Preprocessor (2/2)BSP Preprocessor (2/2)

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Effectiveness of PVSEffectiveness of PVS Data set sizeData set size The rangeThe range

Hard for dynamic scene objectsHard for dynamic scene objects Apply BSP to static scene objectsApply BSP to static scene objects Apply visibility culling and collision detection to dynamic Apply visibility culling and collision detection to dynamic

scene objectsscene objects Room sizeRoom size

BSP ChallengesBSP Challenges