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Advanced Scene Management System 1 Scene Management in Hierarchical Form A tree-based or graph-based representation is good for 3D data management Scene tree Scene graph 3D data management including : Transformations for each 3D object Hierarchical relationship Space coherence Data instancing Geometric computation Hit test Collision detection Terrain following Rendering management Visibility Alpha Sorting 2 An Object in the Scene (An Example from TheFly) Hierarchy Parent Object Parameters Etc Transformation Move Animation Motion Data Shape Geometric Data Clone 3 A Scene Tree (An Example) 1/2 A tree-based representation A simplified scene graph Root 4 A Scene Tree (An Example) 2/2 A tree-based representation A simplified scene graph Root 5 Bounding Volume Bounding sphere Bounding cylinder Axis-aligned bounding box (AABB) Oriented bounding box (OBB) Discrete oriented polytope (k-DOP) Bounding Sphere Bounding Cylinder AABB k-DOP OBB 6 Bounding Volume - Applications Collision detection Visibility culling Hit test Steering behavior In “Game AI” section 7 Application Example - Bounding Sphere B2 B1 D c2 c1 Bounding sphere B1(c1, r1), B2(c2, r2) If the distance between two bounding spheres is larger than the sum of radius of the spheres, than these two objects have no chance to collide. D > Sum(r1, r2) 8 Application Example - AABB Axis-aligned bounding box (AABB) Simplified calculation using axis-alignment feature But need run-timely to track the bounding box AABB 9 Application Example - OBB Oriented bounding box (OBB) Need intersection calculation using the transformed OBB geometric data 3D containment test Line intersection with plane For games, OBB 10 Advanced Scene Graphs This is a game-type-oriented issue. Bounding volume hierarchies (BVHs) Binary space partition trees (BSP Trees) “Quake” Octree & quadtree Possible Visible Set Culling Skills 11 Bounding Volume Hierarchies (BVHs) Bounding spheres or AABB in hierarchy Can be used for dynamic scene objects R B 12 BVH Construction - LBVH LBVH Linear BVH Tree construction using Morton Code 13 Morton Code (1/2) 2D example 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 binary 1-0-1- : 5 in binary xyxyxy 100011 : 35 Your interleaved Morton number 14 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. 15 BVH Construction – SAH Hierarchy Construction 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 volume KT & KI are constants nl : object number of left child node nr : object number of right child node Can be applied to BVH and KD Tree. 16 BSP Tree Two variants Axis-aligned KD tree Polygon-aligned The trees are created by using a plane to divide the space into two, and then sorting the geometry into two spaces. 17 Axis-aligned BSP Tree 0 plane plane 3 plane1 2 1 0 plane2 3 18 Polygon-aligned BSP Tree F A C G B A B C D E D E F G 19 Why BSP Tree ? Quickly to identify where you are BSP = Sorting Need a pre-processor to generate the PVS Visibility culling + occlusion culling PVS : Possible Visible Set Optimized for in-door game environment [Fuch80] Fuchs, H., On Visible Surface Generation by a Priori Tree Structures, Computer Graphics, 14, 124-33, (Proc. SIGGRAPH’80) 20 Octree & Quadtree Very similar to axis-aligned BSP tree. Except that a box is split simultaneously along all three axes. The split point should be the center of the box. This creates eight new boxes. Quadtree is the 2D version of octree. 21 Quadtree - Example 22 Octree – Some Discussion Data structure coherence Apply visibility culling from parents Split or not split ? Outdoor game scene ? 23 Culling (1/2) Culling means “remove from a flock” Visibility culling Remove the object not in view frustum A “must” feature within the game engine Backface culling Remove the polygons facing away from camera Hardware standard Occlusion culling Remove the objects hidden by the others A complicated issue for games 24 Culling (2/2) View frustum Occlusion culling eye Visibility culling Backface culling 25 BSP Implementation A Pre-processor Space partition the scene data from artist Generate the BSP data structure Generate the PVS BSP walk through Identify the room where you are Show/hide the rooms according to the PVS Perform terrain following & collision detection Or all interaction between the player’s character and the scene 26 BSP Preprocessor (1/2) Input A scene from artist Cutting planes (optional) Can be procedurally generated by algorithm Cutting policy Split or not split Ray casting resolution for PVS Output A BSP file BSP Tree PVS Geometry Data 27 BSP Preprocessor (2/2) Process Generate the BSP tree according to the cutting policy Split or sort the geometry into BSP room (leaves) For each “room”, ray cast all rooms to generate the possible visible room set 2D layers or 3D Time consuming 28 BSP Challenges Effectiveness of PVS Data set size The range Hard for dynamic scene objects Apply BSP to static scene objects Apply visibility culling and collision detection to dynamic scene objects Room size 29