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

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Feb 02, 2023 123 likes •271 views

CS-184: Computer Graphics Lecture #7: BSP and AABB Trees Prof. James OBrien University of California, Berkeley V2011-F-07-1.0 Announcements Assignment 4: due October 10 by 11pm 2 BSP-Trees Binary Space Partition Trees Split space

SLIDE 1

CS-184: Computer Graphics

Lecture #7: BSP and AABB Trees

Prof. James O’Brien

University of California, Berkeley

V2011-F-07-1.0

Announcements

Assignment 4: due October 10 by 11pm

SLIDE 2

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

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

BSP-Trees

a b c d e g f

SLIDE 3

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

a b c1 d e g f c2

BSP-Trees

a b c2,e,f,g c1 d

a b c1 d e g f c2

BSP-Trees

SLIDE 4

a b c2 c1 d e1 ,f e2 ,g

a b c1 d g f c2 e1 e2

BSP-Trees

a b c2 c1 d e1 e2 ,g f

a b c1 d g f c2 e1 e2

BSP-Trees

SLIDE 5

a b c2 c1 d e1 e2 f g

a b c1 d g f c2 e1 e2

BSP-Trees

+ + + + +

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

SLIDE 6

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

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

SLIDE 7

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

Axis-Aligned Bounding Boxes

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

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

SLIDE 8

Axis-Aligned Bounding Boxes

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

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?

SLIDE 9

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

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

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

One of many variations

Geometry node

SLIDE 10

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

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

One of many variations