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Modeliranje kompleksnih modelov

Modeliranje kompleksnih modelov. Hierahična, drevesna struktura modela. Polygonal Meshes. Used to model solid objects Objects are defined by: List of vertices List of normals Face list. 3. 2. 7. 6. 0. 1. 4. 5. Vertex List. 4. 3. 0. 1. 2. 5. Normal list. 0: Rear Face

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Modeliranje kompleksnih modelov

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  1. Modeliranje kompleksnih modelov Hierahična, drevesna struktura modela

  2. Polygonal Meshes • Used to model solid objects • Objects are defined by: • List of vertices • List of normals • Face list

  3. 3 2 7 6 0 1 4 5 Vertex List

  4. 4 3 0 1 2 5 Normal list 0: Rear Face 1: Right Face 2: Front Face 3: Left Face 4: Top Face 5: Bottom Face

  5. 3 2 7 6 0 1 4 5 Face List 0: Rear Face 1: Right Face 2: Front Face 3: Left Face 4: Top Face 5: Bottom Face

  6. # Vertices # Normals # Faces Vertices Normals Faces Data File • 8 6 6 • 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 • 1 0 1 1 1 1 0 1 1 • 0 0 -1 1 0 0 0 0 1 1 0 0 0 1 0 • 0 -1 0 • 4 0 3 2 1 • 4 1 2 6 5 • 4 4 5 6 7 • 4 0 4 7 3 • 4 2 3 7 6 • 4 0 1 5 4

  7. Spatial Data Structures • Used to organize geometry in n-dimensional space (2 and 3D are of this course’s interest) • For accelerating queries – culling, ray tracing intersection tests, collision detection • They are mostly hierarchy by nature • Topics: • Bounding Volume Hierarchies (BVH) • Binary Space Partitioning Trees (BSP trees) • Octrees

  8. Anwendungen für Objekthierarchien • Culling • Raytracing • Radiosity • Navigation

  9. Binary Space Partitioning (BSP) Trees • Main purpose – depth sorting • Consisting of a dividing plane, and a BSP tree on each side of the dividing plane (note the recursive definition) • The back to front traversal order can be decided right away according to where the eye is back to front: A->P->B P BSP A BSP B back to front: A->P->B

  10. BSP Trees (cont’d) • Two possible implementations: Axis-Aligned BSP Polygon-Aligned BSP Intersecting?

  11. 0 1a 1b B A C 2 D E Axis-Aligned BSP Trees • Starting with an AABB • Recursively subdivide into small boxes • One possible strategy: cycle through the axes (also called k-d trees) D E B 2 1b 1a A C 0 Q: objects intersect the boundaries?

  12. A B C D E F Polygon-Aligned BSP Trees • The original BSP idea • Choose one divider at a time – any polygon intersect with the plane has to be split • Done recursively until all polygons are in the BSP trees • The back to front traversal can be done exact • The dividers need to be chosen carefully so that a balanced BSP tree is created F B C A D E result of split

  13. Octrees • Similar to Axis-Aligned BSP trees • Each node has eight children • A parent has 8 (2x2x2) children • Subdivide the space until the • number of primitives within • each leaf node is less than a • threshold • Objects are stored in the leaf • nodes

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