Computer Graphics

Computer Graphics

Computer Science & Information Technology Co p te Sc e ce & o at o Tec o ogy Yung-Yu Chuang

2009/03/2 2009/03/27

Introduction

• Instructor: Yung-Yu Chuang (莊永裕)

E il i d

• E-mail: cyy@csie.ntu.edu.tw

• Office: CSIE 527

• Grading: exam on the final exam week

What is computer graphics ?

• Definition

h i i l

h i

objects from their computer-based models

OUTPUT

descriptions images

descriptions Computer Graphics

NPUT

images Computer Vision Image Processing

IN

Computer graphics

• Create a 2D image/animation of a 3D world

Applications

• Movies

I i i

• Interactive entertainment

• Industrial design

• Architecture

• Culture heritage

• Culture heritage

Computer graphics

modeling rendering

animation

Modeling

A simple example

# vertices 0 0 0 0 0 0

(0,0) (1.5,0)

0.0, 0.0, 0.0 1.5, 0.0, 0.0 0 0 1 5 0 0 0.0, 1.5, 0.0 1.5, 1.5, 0.0

# triangles 0 2 1 0, 2, 1 1, 2, 3

(0,1.5) (1.5,1.5)

x z

y

The power of triangles

• Every thing can be represented by triangles to a degree of precision

degree of precision.

20 triangles 80 triangles 320 triangles

More complex examples

a real buddha 4K mesh rendered 2.4M mesh

Modeling

• The position of the model can be acquired by 3D scanner or made by artists using modeling 3D scanner or made by artists using modeling tools.

Th th f ti

• There are other ways for representing geometric objects, but triangles have many

d t

advantages.

Triangle meshes

{f

{f } {} { }}

{f

{f₁₁} : { v} : { v₁₁, v, v₂₂ , v, v₃₃}}

{f

{f₂₂} : { v} : { v₃₃, v, v₂₂ , v, v₄₄}} connectivityconnectivity

…

…

geometry geometry {v

{v₁₁} : (x,y,z)} : (x,y,z) {v

{v₂₂} : (x,y,z)} : (x,y,z)

…

…

face attributes face attributes {f

{f₁₁} : } : “skin material”“skin material”

{f

{f } :} : “brown hair”“brown hair”

{v

{v ff } : (n} : (n nn nn ) (u v)) (u v) {f

{f₂₂} : } : brown hairbrown hair

…

… {v

{v₂₂,f,f₁₁} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v) {v

{v₂₂,f,f₂₂} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v)

…

…

corner attributes corner attributes

Copyright©1998, Microsoft

Composition of a scene

z x yy

x z

x y

Graphics pipeline

Transformations

Representation

Representation 2D transformations

Identity Scaling

Scaling Reflection

Shearing Rotation

Limitations of a 2X2 matrix

• Scaling

R i

• Rotation

• Reflection

• Shearing

• What do we miss?

Homogeneous coordinate

Translation 3D scaling

3D translation 3D rotation

3D shearing Graphics pipeline

Projections

Imaging with the synthetic camera

Specifying a viewer Projections

Parallel and perspective projections

orthographic perspective

Orthographic transformation

Perspective projection Perspective transform

Graphics pipeline review

Triangle meshes

{f

{f } {} { }}

{f

{f₁₁} : { v} : { v₁₁, v, v₂₂ , v, v₃₃}}

{f

{f₂₂} : { v} : { v₃₃, v, v₂₂ , v, v₄₄}} connectivityconnectivity

…

…

geometry geometry {v

{v₁₁} : (x,y,z)} : (x,y,z) {v

{v₂₂} : (x,y,z)} : (x,y,z)

…

…

face attributes face attributes {f

{f₁₁} : } : “skin material”“skin material”

{f

{f } :} : “brown hair”“brown hair”

{v

{v ff } : (n} : (n nn nn ) (u v)) (u v) {f

{f₂₂} : } : brown hairbrown hair

…

… {v

{v₂₂,f,f₁₁} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v) {v

{v₂₂,f,f₂₂} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v)

…

…

corner attributes corner attributes

Copyright©1998, Microsoft

Review of graphics pipeline

Transformation

Review of graphics pipeline

Projection & clipping

Review of graphics pipeline

• Rasterization Vi ibili

• Visibility

Visibility (Hidden surface removal)

Hidden surface removal

• Determining what to render at each pixel.

A i i i ibl if h i di li f

• A point is visible if there exists a direct line-of- sight to it, unobstructed by another other

bj t ( i ibl f

d t i ti )

• Moreover, some objects may be invisible because there are behind the camera, outside of the field-of-view, too far away (clipping) or back faced (backface culling).

Hidden surfaces: why care?

• Occlusion: Closer (opaque) objects along same viewing ray obscure more distant ones

viewing ray obscure more distant ones

• Reasons for removal

Effi i A ith – Efficiency: As with

clipping, avoid wasting work on invisible work on invisible objects

– Correctness: The image Correctness: The image will look wrong if we don’t model occlusion properly

Hidden surface removal algorithms

• Painter’s algorithm

• Binary space partitioning

• Z-buffer

• Ray casting

• And many others

• And many others

Painter’s algorithm

Draw primitives from back to from back to front to avoid need for depth comparisons

from Shirley

Painter’s algorithm

• Idea: Sort primitives by minimum depth, then rasterize from furthest to nearest

rasterize from furthest to nearest

• When there are depth overlaps, do more tests

f b di ll

of bounding areas, etc. to see one actually occludes the other

• Cyclical overlaps are a problemy p p

Z-buffer algorithm

• Resolve depths at the pixel level

Idea: add Z to frame buffer when a pixel is

• Idea: add Z to frame buffer, when a pixel is drawn, check whether it is closer than what’s already in the framebuffer

already in the framebuffer

• Proposed by Ed Catmull in 1975, widely used today especially in hardware

today, especially in hardware.

• Z-buffer texture subdivsion

• Z-buffer, texture, subdivsion surface, RenderMan

• Co-founder of PixarCo founder of Pixar

• 3 Oscars (1993, 1996, 2001),

SIGGRAPH Steven Coons Award (1993)( )

Z-buffer algorithm Z-buffer algorithm

The z-Buffer Algorithm

+ =

+ =

Z-buffer: example

color buffer depth bufferp

Z-Buffer

• Benefits

E t i l t

– Easy to implement

– Works for any geometric primitive

P ll l ti i h d (i d d t f

– Parallel operation in hardware (independent of order of polygon drawn)

Li it ti

• Limitations

– Memory required for depth buffer – Quantization and aliasing artifacts – Overfill

– Transparency does not work well

Clipping (view frustum culling)

Review of graphics pipeline

• Rasterization Vi ibili

• Visibility

Review of graphics pipeline

• Shading

Shading

Z-buffer algorithm

What is normal? Normal for a triangle

plane n ·(p - v₀) = 0 n v₂

plane n (p v₀) 0 n = (v₂- v₀) ×(v₁- v₀)

v₁ ( _{2 0} ) ( _{1 0} )

normalize n ← n/ |n|

p v₀

normalize n ← n/ |n|

N t th t i ht h d l d t i t d f Note that right-hand rule determines outward face

Using average normals

N ^{( i ) l}

N = true (geometric) normal

Using average normals

N N N N ² N 1

Using average normals

N N ^{N = 1} ( _{N N}

⁺

) N N ²

N (

)

2 N N

N 1

Using average normals

( N

N

N

N

)

N

+ + +

1 2 3 4

N

N

N

N

N

M ll

N

∑

More generally,

N

N

∑

=

N

N

^{N N}

υ

∑

=

N

N

N

N

=

i 1

N

It l b ight d It can also be area-weighted.

Definitions of Triangle Meshes

{f

{f } {} { }}

{f

{f₁₁} : { v} : { v₁₁ , v, v₂₂, v, v₃₃ }}

{f

{f₂₂} : { v} : { v₃₃ , v, v₂₂, v, v₄₄ }} connectivityconnectivity

…

…

geometry geometry {v

{v₁₁} : (x,y,z)} : (x,y,z) {v

{v₂₂} : (x,y,z)} : (x,y,z)

…

…

face attributes face attributes {f

{f₁₁} : } : “skin material”“skin material”

{f

{f } :} : “brown hair”“brown hair”

{v

{v ff } : (n} : (n nn nn ) (u v)) (u v) {f

{f₂₂} : } : brown hairbrown hair

…

… {v

{v₂₂,f,f₁₁} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v) {v

{v₂₂,f,f₂₂} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v)

…

…

corner attributes corner attributes

Copyright©1998, Microsoft

Illumination (shading) models

• Interaction between light sources and objects in scene that results in perception of intensity in scene that results in perception of intensity and color at eye

• Local

• Local

– Local: perception of a particular primitive only depends on light sources directly affecting that one p g y g primitive

• Geometry

Material properties

• Material properties

• Shadows cast (global?)

– Global: also take into account indirect effects on light of other objects in the scene

• Light reflected/refracted I di t li hti

• Indirect lighting

Local vs. global models

Direct lighting

Direct lighting Indirect lighting Indirect lighting Direct lighting

Direct lighting Indirect lighting Indirect lighting

Setup

v

v

• Point P on a surface through a pixel p

• Normal N at P

• Lighting directionLighting direction

v

• Viewing direction

• Compute color L for pixel p

v

v

• Compute color L for pixel p

Surface types

• The smoother a surface, the more reflected light is concentrated in the direction a perfect mirror would concentrated in the direction a perfect mirror would reflected the light

• A very rough surface scatters light in all directionsy g g

smooth surface rough surface

smooth surface g

Basics of local shading

• Diffuse reflection

li ht h l d b bj t l

– light goes everywhere; colored by object color

• Specular reflection

– happens only near mirror configuration; usually white

• Ambient reflection

– constant accounted for other source of illumination

Ambient shading

• add constant color to account for disregarded illumination and fill in black shadows; a cheap illumination and fill in black shadows; a cheap hack.

ambient lightg

Diffuse shading

• Assume light reflects equally in all directions

Th f f l k l f ll i

– Therefore surface looks same color from all views;

“view independent”

Diffuse shading

• Illumination on an oblique surface is less than on a normal one (Lambertian cosine law)

on a normal one (Lambertian cosine law)

– Generally, illumination falls off as cosθ

Diffuse shading (Gouraud 1971)

• Applies to diffuse, Lambertian or matte surfaces

surfaces

(albedo)

( )

Diffuse shading

0.4 0.55 0.7 0.85 1.0

diffuse-reflection model with different k_d

0.0 0.15 0.3 0.45 0.6

ambient and diffuse-reflection model with differentk_a

and I_a =I_p =1.0,k_d =0.4

Diffuse shading

For color objects, apply the formula for each color channel separately

color channel separately

Specular shading

• Some surfaces have highlights, mirror like reflection; view direction dependent;

reflection; view direction dependent;

especially for smooth shinny surfaces

Specular shading (Phong 1975)

• Also known as glossy, rough specular and

directional diffuse reflection

directional diffuse reflection

Specular shading

• Fall off gradually from the perfect reflection direction

direction

Specular shading

• Increasing n narrows the lobe

σ cos

n=1 n=2 n=2 n=3

°

0 90 °

° 90

n=10

°

0 90 °

°

− 90

Specular shading

ks

1 . 0

25 . 0

5 . 0

0 .

=3

n n=5.0 n=10.0 n=27.0 n=200.0

Specular shading

diffuse diffuse + specular diffuse diffuse + specular

Put it all together

• Include ambient, diffuse and specular

• Sum over many lights

• Sum over many lights

Choosing the parameters

Computing lighting at each pixel

• Most accurate approach: Compute component illumination at each pixel with individual illumination at each pixel with individual positions, light directions, and viewing directions

directions

• But this could be expensive...

y y₁

y_s I_p

Scan line y₂

y₃

Shading models for polygons

• Flat Shading

F t d Sh di – Faceted Shading – Constant Shading

d h d

• Gouraud Shading

– Intensity Interpolation Shading – Color Interpolation Shading

• Phong Shadingg g

– Normal-Vector Interpolation Shading

Flat Shading

• Compute constant shading function, over each polygon, p yg

• Same normal and light vector across whole polygonp yg

• Constant shading for polygon

I1

y s

I I

I2

I

s

I3

Ip

Intensity Interpolation (Gouraud)

1 2 2 1

y I y

y I y

I

=

− + −

2 1 2 2 1

1

y y y y

a

− −

I a

Ib I1

3 1 1 3 3 1

3

1

y y

y I y

y y

y I y

I

− + −

−

= − ^a

I

y s

3 1 3

1

y y y

y

a p p

b

x x x

x

I

s

a b

a p b a b

p b a

p

I x x

x I x

I

= − I2

I3

Ip

Normal Interpolation (Phong)

1

2

y y

y N N y

N

− −

2 1 1 2 2 1

2

1

y y

y N y

y y

y N y

N

+ −

= −

N a

Nb

1

y s

3 1 1 3 3 1

3

1

y y

y N y

y y

y N y

N

− + −

−

= −

N2

s

3 N

1 3

1 2

N3

Np

Normal Interpolation (Phong)

⎥ ⎤

⎢ ⎡ −

⎥ ⎤

⎢ ⎡ − x

x

N

x

x

N N

~

⎥ ⎦

⎢ ⎣ −

⎥ +

⎢ ⎦

= ⎣ −

a b

a p b

b a

b p b a

p a

x N x

N x

N x N N

⎦

⎣

⎦

⎣ N

~

N p p

N N

=

Normalizing makes

thi it t

Np

this a unit vector

Gouraud v.s. Phong Shading

Gouraud Phong Gouraud Phong

Flat shading

Gouraud shading Phong shading

Graphics Pipeline

Triangle meshes

{f

{f } {} { }}

{f

{f₁₁} : { v} : { v₁₁, v, v₂₂ , v, v₃₃}}

{f

{f₂₂} : { v} : { v₃₃, v, v₂₂ , v, v₄₄}} connectivityconnectivity

…

…

geometry geometry {v

{v₁₁} : (x,y,z)} : (x,y,z) {v

{v₂₂} : (x,y,z)} : (x,y,z)

…

…

face attributes face attributes {f

{f₁₁} : } : “skin material”“skin material”

{f

{f } :} : “brown hair”“brown hair”

{v

{v ff } : (n} : (n nn nn ) (u v)) (u v) {f

{f₂₂} : } : brown hairbrown hair

…

… {v

{v₂₂,f,f₁₁} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v) {v

{v₂₂,f,f₂₂} : (n} : (n_xx,n,n_yy,n,n_zz) (u,v)) (u,v)

…

…

corner attributes corner attributes

Copyright©1998, Microsoft

Review of graphics pipeline

Transformation

Review of graphics pipeline

Projection & clipping

Review of graphics pipeline

• Rasterization Vi ibili

• Visibility

Review of graphics pipeline

• Shading

Animation

Hierarchical modeling: a robot arm

Hierarchical modeling Animator demos

Videos

•

TigerWang R i

•

Racing

Advanced topics

Global illumination Complex materials

Realistic motion Graphics hardware

Nvidia GT200 GPU 200 cores

Animation production

Animation production pipeline

t t t t t t t b d

story text treatment storyboard

voice storyreal look and feel

Animation production pipeline

l t animation

d li / ti l ti layout animation

modeling/articulation

shading/lighting rendering final touch

What’s next?

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