Lecture 5: 3D Rendering Pipeline (II)

Prof. Hsien-Hsin Sean LeeSchool of Electrical and Computer

EngineeringGeorgia Institute of Technology

2

Parallel Projection

Viewer’s position

View plane

• Project from 3D space to viewer’s 2D space

3

Perspective Projection

• The farther the object is, the smaller it appears• Some photo editing software allows you to

perform “Perspective Correction”

Viewer’s position

View plane

4

Perspective Projection

dzx

xsz

x

d

xs

dzz

zsdzs

xx

yy

zz

(x,y,z)

(xs,ys,d)

dxs

ys

x

y

z

dzy

ysz

y

d

ys

5

Perspective Projection

0000

1100

0010

0001

]1,,,[],,,[d

zyxwzyx

xx

yy

zz

(x,y,z)

(xs,ys,d)

dxs

ys

x

y

z

dzx

xsz

x

d

xs

dzz

zsdzs

dzy

ysz

y

d

ys

w

xxs

w

zzs

w

yys

6

Viewing Frustum

Far plane

Viewer’s position

Near plane

Think about looking through a window in a dark room

7

Viewing Frustum

Near plane

Far plane

Viewer’s position

8

Define Viewing Frustum(Projection Transformation)

Viewer’s position

+z

Parameters:Fov: Field of ViewAspect ratio = Width/HeightNear zFar z

fov/2

+y

Far z

Near z

Width

He

ight

9

Viewport Transformation

• The actual 2D projection to the viewer• Copy to your back buffer (frame buffer)• Can be programmed, scaled, ..

10

Other Geometry Optimizations• Backface Culling

• Clipping

• Hidden surface removal (Occlusion)

11

Backface Culling• Determine “facing direction”• Triangle order matters• How to compute a normal vector for 2 given vectors?

– Using Cross product Cross product of 2 given vectors

(c1, c2, c3) (b1, b2, b3)

(a1, a2, a3)

kji

kji

kji

)()()(21

2

1

122131132332

321

321

yxyxyxyxyxyxVV

yyyV

xxxV

Cross product

kji

kji

)33()22()11(2

)33()22()11(1

acacacV

abababV

2 Vectors

12

Compute the Surface Normal for a Triangle

(0, 0, 0) (4, 0, 0)

(3, 3, 0)

kji

kji

004v2

033v1

Compute Normals (Clockwise vectors)

v1

v2x

z

y

13

Compute the Surface Normal for a Triangle

(0, 0, 0) (4, 0, 0)

(3, 3, 0)

kji

kji

033v2

004v1

Compute Normals

v2

v1x

z

y

14

Backface Culling Method• Check if the normal is facing the camera• How to determine that?

– Use Dot ProductUse Dot Product

Surface vectors

Eye vector

15

Backface Culling Method (dot product)

A

B

cosBABA

22

0

BA

16

Backface Culling Method (dot product)

22

0

BA

17

When to Perform Backface Culling?

Clip

ping

Pers

pect

ive D

ivide

View

port

Tran

sfor

m

Rast

eriza

tion

Proj

ectio

n Tr

ansf

orm

Wor

ld T

rans

form

View

Tra

nsfo

rm

Ligh

ting

Back

face

Cul

ling

Clip

ping

Pers

pect

ive D

ivide

View

port

Tran

sfor

m

Rast

eriza

tion

Proj

ectio

n Tr

ansf

orm

Wor

ld T

rans

form

View

Tra

nsfo

rm

Ligh

ting

Back

face

Cul

ling

How?

Transform your camera to the world space first!

18

3D Clipping

• Test 6 planes if a triangle is inside, outside, or partially inside the view frustum

• Clipping creates new triangles (triangulation)– Interpolate new vertices info

19

How to Clip Against a Plane?• Test each vertex of a triangle

– Outside– Inside– Partially inside

• Incurred computation overhead• Save unnecessary computation (and

bandwidth) later• Need to know how to determine a plane• Need to know how to determine a

vertex is inside or outside a plane

20

What it Takes to Determine a Plane?

• You need two things to specify a plane– A point on the plane (p0, p1, p2)– A vector (normal) perpendicular to the plane (a, b, c)– Plane a*(x – p0) + b*(y – p1) + c*(z - p2) = 0

V=(5, 6, 7)

P=(1, 2, 3)K=(x, y, z)

Plane equation

5*(x-1)+6*(y-2)+7*(z-3)=0

21

Distance Calculation from a Plane

• Given a point R, calculate the distance– Distance > 0 inside the plane– Distance = 0 on the plane– Distance < 0 outside the plane

Normal R

d

d

)()(

|| cos|| dPR

PR

PRPRPR

P

22

Distance Calculation from a Plane

R

d

)(1

)(||1cos||1

)cos()180cos(|| )180cos(|| d

PR

PR

PRPRPR

PRPR

P

180-

23

Triangulation using Interpolation

(a2, b2, c2)

(a1, b1, c1)

(x, y, z)

d1d2

)12(1

)12(1

)12(121

1

ccscz

bbsby

aasaxdd

ds

24

Illumination Models

• It won’t look 3D without lighting• Part of geometry processing• Illumination Types

– Ambient– Diffuse– Specular– Emissive

25

Local vs. Global Illumination• Local Illumination

– Direct illumination: Light shines on all objects without blocking or reflection

– Used in most games

• Global Illumination– Indirect illumination: Light bounces from

one object to other objects– Add more realism (non real-time

rendering)– Computationally much more expensive– Ray tracing, radiosity

??

26

Common Light Sources

Directional Light(Infinitely far away)

Point Light(Emit in all directions)

Spot Light(Emit within a cone)

Inner

cone

outer

cone

27

Illumination: Ambient Lighting• Not created by any light source• A constant lighting from all directions• Contributed by scattered light in a surrounding

ambientambietambient LMC

RGB multiplies separatelyMaterial Color Light Color

28

Illumination: Diffuse Lighting• Light sources are given• Assume light bounces in all directions

Refelcted Light will reach the eyes no matter where the camera is!

Diffuse surface

29

Reflected Light Intensity Calculation• Reflectivity the entry angle • Use Lambert’s cosine Law

0

0.2

0.4

0.6

0.8

1

2

intensity

F()=cos()

2

Surface Normal

n

Surface Normal

n

Surface Normal

n

)()0,max( diffdiffdiff LMnLC

Dot product

ReflectionFull

None

Partial

L

30

Diffuse

Illumination: Diffuse Lighting

Material Color Light ColorAmbient +

Diffuse

)()0,max( diffdiffambientambientdiff LMnLLMC Ambient + Diffuse

31

Illumination: Specular Lighting• Create shining surface (surface perfectly reflects)• Viewpoint dependent

Ambient +Diffuse +SpecularMaterial Color Light Color

Specular

32

Jim Blinn’s Specular Model

• An improved version from Phong Specular model which uses Reflective vector R

• “SS” controls the bright region around surface

E

L

n

specspecS

spec LMHnC ))0,(max(

R

LE

LEH

Half-way vector

H

33

Brightness Effect (S)

cos here w

))0,(max(

HnHn

LMHnC specspecS

spec

L1

L2

n1

n2

H1

H2

More shining

E1

E2

34

Brightness Effect (S)

0

0.2

0.4

0.6

0.8

1intensity

cos

cos2

cos8

cos64

2 2

specspecS

spec LMHnC ))0,(max(

cos > cos

~0.65

~0.95

cos8 >>> cos8

~0.62

n1

n2

H1H2

S=1

n1

n2

H1H2

S=8

~0.05

radian

35

Specular Lighting Effect

• A larger S shows more concentration of the reflection

36

Illumination: Emissive Lighting

• Color is emitted by the material only

ssn

ddaaeall LMHnLMnLLMCC ))0,(max()()0,max(

Ambient +Diffuse +

Specular +Emissive

Material Emissive

Color

+

Ambient +Diffuse +Specular

37

Common Light Sources

Directional Light(Infinitely far away)

Point Light(Emit in all directions)

Spot Light(Emit within a cone)

Inner

cone

outer

cone

38

Light Source Properties• Position• Range

– Specifying the visibility

• Attenuation– The farther the light source, the dimmer the

color2

210 dadaaAtten

Atten

LMHnLMnLLMCC ss

ndd

aaeall

))0,(max()()0,max(

39

Falloff effect

Spotlight Effect

• Similar idea to specular lighting• Falloff factor determines the fading effect of a spotlight• “f” exponentially decreases the cos value

L d

allall

f

f

Cspot C

falloff

dLspot

spot

factor theis f where

))0,(max(

))0,(max(cos