Using BSP for CD

Ref:BSP in deBerg et al’s book (url)

Fall 2010 2

Introduction

BSP: binary space partitionCD: collision detectionEspecially useful for indoor scenes

Fall 2010 3

Kd-Tree and BSP tree

kd-tree is a special kind of bsp tree

+–

Fall 2010 4

BSP Tree Construction

Fall 2010 5

Equation at a Node

Defines the hyperplane, : ax+by+cz+d=0Subtree polygons are classified according to the coefficients stored at (internal) nodesCoefficients are often “normalized” for distance computation between point and plane 222

000),,,(cba

dczbyaxzyxd

Fall 2010 6

Elements of BSP Construction

Choosing the partition plane Auto-partition: choose the partition plane

from the input set of polygons It is desirable to have a balanced tree,

where each leaf contains roughly the same number of polygons. However, there is some cost in achieving this.

Partitioning polygons If a polygon happens to span the partition

plane, it will be split into two or more pieces. A poor choice of the partition plane can result in many such splits, and a marked increase in the number of polygons.

Fall 2010 7

Elements of BSP Construction (cont)

The decision to terminate tree construction can be: when the number of polygons in a leaf node is

below a maximum value. until every polygon is placed in an internal node. maximum tree depth.

Fall 2010 8

S3S3S2S2

S2

S2S3

S3

S1

S1

SIZE=3

Different ordering generates different trees

Different ordering generates different trees

Fall 2010 9

S3

S2

S2b

S2a

S2

S3

S3a

S3bS1

S2b S3b S2a S3a

S1

S2b S3b S2a S3aS2b S2a

S3b S3aS3b S3aS3b S3a

SIZE=5

Fall 2010 10

Painter’s Algorithm

What do we mean “sort in z”? That is for a triangle, what is its representative z value? Minimum z Maximum z Polygon’s centroid

Work cost = sort + drawAn object space visibility algorithm

Fall 2010 11

Painter’s Algorithm (cont)

Pros: No extra memory Relatively fast Easy to

understand and implement

Cons: Precision issues

(and additional work to handle them)

Sort stage Intersecting

objects

Fall 2010 12

Painter’s Algorithm (BSP Version)

S(v) need not be drawn!

Fall 2010 13

Example Scene

Fall 2010 14

A

B

E

C

F

D

G

Fall 2010 15

A

E

C1

F

D

G

C2B2

B1

D

A B1 C1 B2 C2 EFG

+–

Fall 2010 16

A

E

C1

F

D

G

C2B2

B1

D

C1F

A B1 C2 B2 EG

Fall 2010 17

A

E

C1

F

D

G

C2B2

B1

D

C1F

B1 C2 E

G B2 A

Tree completed!Tree completed!

Fall 2010 18

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

Rendering BSP [b-to-f]

Fall 2010 19

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

hv-

hv+

Fall 2010 20

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

C1

hv-

hv+

Fall 2010 21

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1

hv-

hv+

Fall 2010 22

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1A

Fall 2010 23

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AD

hv-

hv+

Fall 2010 24

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AD

hv- hv

+

Fall 2010 25

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AD

hv-hv

+

Fall 2010 26

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1ADB2

Fall 2010 27

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AB2 E D

hv-hv

+

Fall 2010 28

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AB2 E D

G

Fall 2010 29

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AB2 E DFG

hv- hv

+

Fall 2010 30

A

E

C1

F

D

G

C2

B2

B1

D

C1F

B1 C2 E

G B2 Aeye

V

B1 C1AB2 E DFG

hv- hv

+

C2

Line Equation

P1(x1,y1)

P2(x2,y2)

L = 0L > 0 (left side)

P(x,y)

(1,0)

(0,1)

01

01,11,1

00,110),01(

yx

yxyx

yx

Check: origin on + (left) side !

Left side correspond to positive side

0

0,,

0:)(0:

90cos90sin

90sin90cos90,

1211211212

111212

11

12

12

12

1221

xxyyyxyxxxyy

yyxxxxyy

PPnsideleftPPnline

xx

yy

yy

xxPProtn

n

Fall 2010 32

BSP in Games (ref)

•To account for character size, use offset planes in BSP•Problems when angles between planes are large

Character-environment collision detection

Fall 2010 33

Collision Resolution

Better to solve a collision by deflecting the motion rather than stopping at the impact pointStepping and climbing

Fall 2010 34

Example

L1 L2

L3

L1

L2

L3(0,4)

(6,0)

(6,4)

L1: (0,4)(6,0)L2: (6,0)(6,4)L3: (6,4)(0,4)

+–

solid

free

free

free

Fall 2010 35

Point-Scene Test

Fall 2010 36

Example

L1 L2

L3

L1

L2

L3

0<0

d0 d-r

r

Fall 2010 37

Example

L1 L2

L3

L1

L2

L3

0<0

d-r

r

d-r

Fall 2010 38

Example

L1 L2

L3

L1

L2

L3

0<0

d-r

d-r

d-r

solid

free

free

free

Fall 2010 39

Example

L1 L2

L3

L4

L5

L6

L1

L2

L5

L4

L3

L6

+–

solid

solid

free

free

free

free

free

Fall 2010 40

Ex: Tree Building1/4 L1

+–

L1

L2

L3

L7

L5

L6

L4

L2,L3,L4,L5,L6L5,L6,L7

Fall 2010 41

Tree Building2/4 L1

+–

L1

L2

L3

L7

L5

L6

L4

L2,L3,L4,L5,L6L5,L6,L7

L4

L2,L3L5,L6

L7

L5,L6

Fall 2010 42

Tree Building3/4 L1

+–

L1

L2

L3

L7

L5

L6

L4

L4

L2,L3L5,L6

L7

L6

L5

L2

L3

L5

L6

Fall 2010 43

Tree Building4/4 L1

+–

L1

L2

L3

L7

L5

L6

L4

L4L7

L6

L5

L2

L3

L5

L6

solidsolidsolid

Fall 2010 44

Dynamic Scenes

Moving camera: no problemMoving objects: Fuchs et. al. was to specify a bounding

polygon around the area that of the scene that would be changing.

Doom: use z-buffer for for dynamic objects (missiles and bullets)

Adding objects: no problemDeleting objects: BIG problem (ref)

Fall 2010 45

[BSP & Ray Tracing]

Speed up ray tracing by:Reaching leaf nodesDetermine face through which ray exits

Find region-binding faces: collect all parental halfplanes

Compute exit pointsExtending ray into next region

… until the ray shoots into infinity

reference