Estruturas de Dados Espaciais

1
Estruturas de Dados Espaciais

• MC-930
• MO-603

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Speeding Up Ray Tracing
3
Estruturas de Dados Espaciais
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Bounding Volumes
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Hierarquical Bounding Volume
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Grids

• Data structure a 3-D array of cells (voxels)
  that tile space
• Each cell points to list of all surfaces
  intersecting that cell

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Mais sobre Grids

• Be Careful! The fact that a ray passes through a
  cell and hits na object doesnt mean the ray hit
  that object in that cell
• Optimization cache intersection point and ray id
  in mailbox associated with each object
• Grids are a poor choice when the world is
  nonhomogeneous (clumpy)
• e.g. a teapot in a stadium many polygons
  clustered in a small space
• How many cells to use?
• too few Þ many objects per cell Þ slow
• too many Þ many empty cells to step through Þ
  slow
• Grids work well when you can arrange that each
  cell lists a few (ten, say) objects
• Better strategy for some scenes nested grids

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Octrees
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Which Structure is Best for Ray Tracing?
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K-d Trees and BSP Trees
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Building a BSP Tree
d
1
2
c
a
3
1
2
b
a
b
c
d
3
the subdivision of space it implies
a BSP tree using 2 as root
viewpoint
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Building the Tree 2
Using line 3 for the root requires a split
3
1
2a
2a
2b
3
2b
1
viewpoint
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Building a Good Tree - the tricky part
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Uses for Binary Space Partitioning (BSP) Trees
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Painters Algorithm with BSP trees
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Drawing a BSP Tree
front_to_back(tree, viewpt) if
(tree null) return if
(positive_side_of(root(tree), viewpt))
front_to_back(positive_branch(tree, viewpt)
display_polygon(root(tree))
front_to_back(negative_branch(tree, viewpt)
else draw negative branch
first
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Drawing Back to Front
Hidden surface removal
3
1
2a
2a
2b
3
2b
1
viewpoint
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Clipping BSP Trees
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Clipping BSP Trees
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Clipping Using Spatial Data Structures