CS-184: Computer Graphics Lecture #7: BSP and AABB Trees Brandon - - PowerPoint PPT Presentation

CS-184: Computer Graphics

Lecture #7: BSP and AABB Trees

Brandon Wang and Prof. James O’Brien University of California, Berkeley

V2013-S-07-1.0

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BSP-Trees

• Binary Space Partition Trees
• Split space along planes
• Allows fast queries of some spatial relations
• Simple construction algorithm
• Select a plane as sub-tree root
• Everything on one side to one child
• Everything on the other side to other child
• Use random polygon for splitting plane

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a,b,c,d,e,f,g

BSP-Trees

a b c d e g f

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a b,c1,d c2,e,f,g

a b c1 d e g f c2

BSP-Trees

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a b c2,e,f,g c1 d

a b c1 d e g f c2

BSP-Trees

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a b c2 c1 d e1 ,f e2 ,g

a b c1 d g f c2 e1 e2

BSP-Trees

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a b c2 c1 d e1 e2 ,g f

a b c1 d g f c2 e1 e2

BSP-Trees

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a b c2 c1 d e1 e2 f g

a b c1 d g f c2 e1 e2

BSP-Trees

+

• +
• +
• +

+ + + + +

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BSP-Trees

• Visibility Traversal
• Variation of in-order-traversal
• Child one
• Sub-tree root
• Child two
• Select “child one” based on location of viewpoint
• Child one on same side of sub-tree root as viewpoint

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a b c2 c1 d e1 e2 f g

a b c1 d g f c2 e1 e2

BSP-Trees

c1:b:d:a:f:e1:c2:g:e2

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g:e2:c2:f:e1:a:c1:b:d

a b c2 c1 d e1 e2 f g

a b c1 d g f c2 e1 e2

BSP-Trees

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Your Ray Tracer

RayTrace(image)

For ray in camera image[pixel] = Trace(ray)

Trace(ray)

t_hit = infinity For object in scene t_hit = min(object.intersect(ray), t_hit) shade at t_hit possible calls to Trace(new_ray)

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Your Ray Tracer

RayTrace(image)

For ray in camera image[pixel] = Trace(ray)

Trace(ray)

t_hit = infinity For object in scene t_hit = min(object.intersect(ray), t_hit) shade at t_hit possible calls to Trace(new_ray)

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Your Ray Tracer

RayTrace(image)

For ray in camera image[pixel] = Trace(ray)

Trace(ray)

t_hit = infinity For object in scene t_hit = min(object.intersect(ray), t_hit) shade at t_hit possible calls to Trace(new_ray)

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Bounding Shapes

• Bounding shape completely encloses associated object
• Rays cannot hit object w/o intersecting bounding shape
• Two objects cannot collide if shapes don’t overlap
• Simplicity -vs- tightness

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Axis-Aligned Bounding Boxes

• Axis-aligned bounding box defined by min and max x,y,z

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Min x,y,z Max x,y,z

Axis-Aligned Bounding Boxes

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Transform box Not axis-aligned Min/max of new points Linear cost to compute

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Axis-Aligned Bounding Boxes

Min/max of transformed BB points Constant time Adds slop Cumulative slop if multiple transforms occur sequentially

Why would we do this?

Tightness

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Box Intersection

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Bounding Box of Bounding Boxes

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Overlapping Triangles

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Overlapping Triangles

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AABB Trees

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AABB Trees

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

Group node Geometry node Transformation stored at all nodes

One of many variations

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Head Shape B.Box Geometry Scale 2x Transformation XF B.Box

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AABB Trees

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R . L e g Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

One of many variations

Geometry node

XF B.Box Children Rot -25 Transformation Head Union B.Box XF B.Box

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AABB Trees

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R . L e g Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

One of many variations

Group node

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AABB Trees

One of many variations

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

Local Bounding Boxes

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

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AABB Trees

One of many variations

Transformed Bounding Boxes

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AABB Trees

One of many variations

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

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AABB Trees

One of many variations

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AABB Trees

One of many variations

Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape Robot L.Foot RFoot Head L.Arm R.Arm L.Leg R.Leg Torso Mouth L.Eye R.Eye Head Shape Leg Shape Leg Shape

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AABB Trees

One of many variations

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Ray Test Against Bound Tree

• RayHitSubTree(&ray,node)
• If RayHitsBB(ray,node.xfBB)
• ixfRay = Inverse(node.xf)*ray
• If RayHitsBB(ixfRay,node.BB)
• If node is group
• Foreach child in node.children
• RayHitSubTree(ixfRay,child)
• else // node not group
• RayHitGeometry(ixfRay,node.geom)
• ray.collisionInfo.update(ixfRay)

Building the tree

• Sort (or QuickSelect)

and split on one axis

• Repeat for the other

axis

• x,y,z

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Other Schemes

• Uniform Grid/Octrees
• Spatial Hierarchies
• Etc

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Voxels/Octree

• http://www.youtube.com/

watch?v=sciLNxmMTXM

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