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3D

Image

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Vector graphics

Raster / Vector

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Aplicação Vector

Transformações

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Aplicação 3D

Display Object

DB Graphics Pipeline

.obj .dxf .iv .dwg .wrl .flt

.3ds .blend

Simulator

Eye, Lookat

Graphics Pipeline

Screen

Model Transformation

Culling

Ilumination

Projection

Oclusion

Shading

Viewport Transformation

Screen Transformation

Objects

3D, Object Space 3D, World Space

2D, Fragments

pixels

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Transformações 3D

Escalamento

Translação

z

y

x

vzz

vyy

vxx

'

'

'

zsz

ysy

xsx

z

y

x

'

'

'

1000

100

010

001

z

y

x

v

v

v

vT

1000

000

000

000

,,

z

y

x

szsysx

s

s

s

S

zyxPjObzyxPObj ii ,,,,

PP vT

PP szsysx ,,S

Rotação 3D

Rotação

Rotação

Rotação

1000

0cos0sen

0010

0sen0cos

,

yR

zz

yxy

yxx

'

cossen'

sencos'

cossen'

sencos'

'

zyz

zyy

xx

cossen'

'

sencos'

zxz

yy

zxx

1000

0cossen0

0sencos0

0001

,

xR

1000

0100

00cossen

00sencos

,

zR

PP zR ,

PP xR ,

PP yR ,

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Modelação

Sala

CadeiraTampoPerna 4Perna 3Perna 2Perna 1

Perna

Cadeira 2 Cadeira 3SofáMesa ArmárioCadeira 1

Sala{ Mesa; Sofá; Cadeira 1; Cadeira 2; Cadeira 3; Armário}

Mesa{ Perna 1; Perna 2; Perna 3; Perna 4; Tampo;}

Perna{ Box(10,100,10);}

Perna 1{ Transformação(p1); Perna;}

Perna 2{ Transformação(p2); Perna;}

Perna 3{ Transformação(p3); Perna;}

Perna 4{ Transformação(p4); Perna;}

Cadeira 1{ Transformação(c1); Cadeira;}

Cadeira 2{ Transformação(c2); Cadeira;}

Cadeira 3{ Transformação(c3); Cadeira;}

Cadeira{ … …}

Orientação HPR

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View Frustum Culling

Hirarchical Culling

-> Todos os sub-objetos são rejeitados

-> Todos os sub-objetos são mantidos

-> Todos os sub-objetos são analisados

• Objetos são organizados hierarquicamente. • Volume envolvente definido para cada nó.

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Projection

Projecção

PMP

z

zyy

z

zxx

per

'

0

0

0100

000

000

000

d

d

d

M per

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Projecção perspectiva P

z0

P’

O

x

z

P

yp

yp’

zpz0

P’

z

y

P

xp

xp’

zpz0

P’

z

x

0100

000

000

000

'

0

0

d

d

d

M

PMP

z

zyy

z

zxx

per

per

Visibilidade

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Z-Buffer

AD

Z

Z

WR RD

Reg

VRAM

Controlo

Comparador

R

R

G

G

B

B

Z_Buffer[max_x, max_y]; Put_Pixel_Z(x, y, z) { if( z<Z_Buffer[x,y] ) { Put_Pixel(x,y); Z_Buffer[x,y] = z; } } Clear_Window_Z() { Clear_Window(); for x:=1 to max_x for y:=1 to max_y Z_Buffer[x,y] = max_z; }

Z-Buffer

dmin dmax

z=Zmax

dd

z=0

O

minmax

minmax

dd

ddZz

Bits por pixel no Z-Buffer ( ):Zbits 12 Zbits

maxZ

NCNLZbitsZbuffer Tamanho do Z-Buffer:

Zbits

minmax

max

minmax

res

dd

Z

ddZ

21

Resolução em :z

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Iluminação ambiente

I0

Ia

ka

aa kII 0

Ka = Coefieciente de reflexão ambiente

Reflexão Difusa

NL

IL

Id

)(cos NL dLdLd kIkII

Coeficiente de reflexão difusa

kd

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Iluminação difusa + ambiente

ka

kd

Reflexão especular

N

IL

Ir

Is

n

sL

n

sLs KIKII )()(cos)( VR

n

sLs kII )( VR

Simplificando:

Coeficiente de reflexão especular

Brilho (Shininess)

NIL

Ir NIL

Ir

n pequeno: n grande:

n

ks

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Iluminação Global

IL

IL’|L|

n

sdLasda kkIkIIIII )()(0 VRNL

n

sdL

a kkk

IkII )()(0 VRNL

L

Para considerar a atenuação da luz em função da distância:

Para considerar os efeitos devidos à existência de fontes de luz:NL

NL

i

i

s

i

da IIII0

Normais de Polígonos

• Normal - Vetor perpendicular à superfície a representar.

• O cálculo de iluminação requer a definição de normais.

• As normais podem ser:

– obtidas implicitamente, a partir das das coordenadas dos vértices. -> Regra da mão direita.

– especificadas explicitamente.

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Constant Shading ou flat shading

Uma única intensidade luminosa é utilizada para colorir todo o polígono.

Um único cálculo de iluminação por polígono.

Interpolated Shading

R

F P

T

G

S

São determinados os valores da intensidade luminosa em cada um dos vértices de um triângulo. O triângulo é colorido pela interpolação linear dos valores obtidos para os seus vértices.

),,()1(),,(),,( FFFGGGPPP BGRdBGRdBGRFG

FPd

),,()1(),,(),,( SSSTTTGGG BGRdBGRdBGRST

SGd

Independentemente de se utilizar constant shading, interpolated shading ou shading por píxel, quando os polígonos são coloridos de forma independente, os objectos aparecem facetados. Diferentes orientações dos polígonos provocam iluminações distintas. Solução: Agrupar os polígonos em malhas que partilham vértices e normais!

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Iluminação por Vértice

Fonte de Luz

Desejado Obtido

Gouraud Shading

As superfícies curvas são aproximadas por uma malha de polígonos. Este método requer a especificação de uma normal para cada vértice da malha poligonal. As intensidades luminosas nos vértices são determinadas utilizando as normais especificadas para cada vértice. Os polígonos são coloridos por interpolação linear.

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Normais por vértice

Normais por vértice

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Phong Shading

É realizada uma interpolação da normal em vez da interpolação da intensidade luminosa.

IS&T Tutorial: Graphics Prog - OpenGL and OSG

Texture map

+

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Texturas

Coordenadas de Textura

Imagem de Textura tem coordenada (u,v ) [0, 1]

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Texture Mapping

v0

v1

v2

t2 t0

t1

(1,1)

(0,0) x

y

Texture Space Triangle (in any space)

Vértice em OpenGL

void Draw() { glColor3f(Color.x, Color.y, Color.z); glNormal3f(Normal.x, Normal.y, Normal.z); glTexCoord2f(TexCoord.x, TexCoord.y); glVertex3f(Position.x, Position.y, Position.z);

// This has to be last

}

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Wavefront obj format

# example obj file v -1.63 -3.04 -8.81 v -4.62 -2.47 -4.55 v -7.34 -5.84 -9.22 vn 0.03 0.40 0.01 vt 0.22 0.97 vt 0.98 0.97 vt 0.98 0.14 f 1/3/1 3/2/1 2/1/1 (index to v/t/n)

Tiling / Clamping

x

y

Tiling

(0,0)

(1,1)

A imagem de textura existe entre as coordenadas (0,0) e (1,1). É possível especificar coordenadas fora desta zona.

(0,0)

(1,1)

Clamping

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Bump mapping

Simulação de rugosidade

Photorealism

Co

rnel

l PC

G

Real Synthetic

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Photorealism?

Shadows motivation

Shadows help to:

• improve the realism in rendered images

• illustrate spatial relations between objects

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Shadows

with shadows without shadows

Shadow support

• shadow algorithms are not standard functionality of the rasterization-based rendering pipeline

• rendering pipeline

– generates 2D images from 3D scenes (camera, light, objects)

– evaluates lighting models using local information

– spatial relations among objects are not considered

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Shadow maps

• see shadow casting as a visibility problem

• scene points are

– visible from the light source (illuminated)

– invisible from the light source (in shadow)

• resolving visibility is standard functionality in the rendering pipeline (z-buffer algorithm)

Visualizing the Shadow

• The scene from the light’s point-of-view

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Shadow map Algorithm

• Shadow map generation – render scene from the light source

– store all distances to visible (illuminated) scene points in a shadow map

• Scene Rendering – render scene from the camera

– compare the distance of rendered scene points to the light with stored values in the shadow map

– if both distances are equal, the rendered scene point is illuminated

Shadow map generation

Scene is rendered from the light source

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Shadow map

• The depth buffer from the light’s point-of-view

Visualizing the Shadow

• Projecting light’s planar distance onto eye’s view

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Shadow map: Scene Rendering

Shadow map: Summary

• use two depth buffers – the “usual” depth buffer for the view point

– a second depth buffer for the light position (shadow map)

• render the scene from the light position into the shadow map

• render the scene from the view position into the depth buffer

• transform depth values to shadow values

• compare transformed depth values and shadow map values to decide whether a fragment is shadowed or not

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Shadow map offset

• discretized representation of depth values can cause an erroneous classification of scene points

• offset of shadow map values reduces artifacts

No offset Correct offset

Blocky Shadow Edge

Light position out

here pointing

towards the viewer.

Blocky shadow

edge artifacts.

Shadow

edge is well

defined in

the distance.

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Hardware Shadow Map Filtering

GL_NEAREST: blocky GL_LINEAR: antialiased edges

Low shadow map resolution

used to heightens filtering artifacts

Backward Ray-Tracing

Os raios são enviados do olho para a fonte de luz !

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Ray-Tracing

R1

N1

N2S11

S12S21

S22

Obj1

L1

L2

Obj2Obj3

R2

T2

R3

Ray-Tracing

• Qualidades do Ray-Tracing

– Reflexões especulares exatas.

– Sombras detalhadas.

• Deficiências do Ray-Tracing

– Deficientes inter-reflexões difusas.

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Radiosity

Basic Ideas:

• Divide surfaces into discrete patches

– Object space algorithm

• Model light transfer between patches as system of linear equations

• Solve matrix equation for radiosity of each patch

– Do it for R,G,B

• Render patches as colored polygons

Simplifying assumptions

• All surfaces are perfectly diffuse

– Does not matter which way light enters or leaves a surface

• Radiosity is constant over a patch

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Radiosity Equation

• Bi is radiosity of patch i – energy per unit area leaving a surface patch per unit time – rate energy emitted + rate energy reflected

• Ei is the rate of energy emitted. (non-zero for emitters) • Ri is reflectivity of the patch

– Wavelength dependent

• Fij is the form factor – how much light patch j contributes to patch i – Depends on geometric relationship – distance and relative

orientation

Radiosity solution

• Finding form factors – Hemicube method

– Ray casting

– …

• Solving set of linear equations to get radiosity for each patch

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Progressive radiosity

What is a GPU?

• It is a processor optimized for 2D/3D graphics, video, visual computing, and display.

• It is highly parallel, highly multithreaded multiprocessor optimized for visual computing.

• It provide real-time visual interaction with computed objects via graphics images, and video.

• It serves as both a programmable graphics processor and a scalable parallel computing platform.

• Heterogeneous Systems: combine a GPU with a CPU

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GPU Evolution

1980’s: No GPU. PC used VGA controller

1990’s: Add more function into VGA controller

1997: 3D acceleration functions: Hardware for triangle setup and rasterization

Texture mapping

Shading

2000: A single chip graphics processor (beginning of GPU term)

2005: Massively parallel programmable processors

2007: CUDA (Compute Unified Device Architecture)

Why Program the GPU ?

http://ixbtlabs.com/articles3/video/cuda-1-p1.html

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Modern GPU Architecture Size

• NV40 (Geforce 6)

– 225 million xtors

– 450mhz

• Pentium 4 EE chip

– 175 million xtors

– 3.2 Ghz

From ‘Stream Programming Environments’ – Hanrahan, 2004:

Results:

Matrix Dimension GPU CPU GPU/CPU

64x64 0.417465 ms 18.0876 ms

128x128 0.41691 ms 18.3007 ms

256x256 2.146367 ms 145.6302 ms

512x512 8.093004 ms 1494.7275 ms

768x768 25.97624 ms 4866.3246 ms

1024x1024 52.42811 ms 66097.1688 ms

2048x2048 407.648 ms Didn’t finish

4096x4096 3.1 seconds Didn’t finish

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The (Old) Graphics Pipeline

Vertex Shader

Light

Transform

Project

Triangle Setup

Combine vertices into triangle, convert to fragments

Frame- buffer

GPU CPU

Fragment Blender

Z-cull

Alpha Blend

Fragment Shader

Texture Maps

Texture map fragments

3dfx Voodoo (’96), Nvidia RIVA TNT (‘98)

More Programable Graphics Pipeline

Vertex Shader

Triangle Setup

Fragment Blender

Light

Transform

Project

Combine vertices into triangle, convert to fragments

Texture map fragments

Z-cull

Alpha Blend

Frame- buffer

GPU

Fragment Shader

Texture Maps

Geforce, ATI 3D Rage II (’97)

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Texture map fragments

Light

Programable Graphics Pipeline

Vertex Shader

Triangle Setup

Fragment Blender

Light

Transform

Project

Combine vertices into triangle, convert to fragments

Z-cull

Alpha Blend

Frame- buffer

GPU

Fragment Shader

Texture Maps

Geforce2-4, Xbox, Radeon 7000-8000, DX8

The Modern Graphics Pipeline

Vertex Shader

Triangle Setup

Fragment Shader

Fragment Blender

Transform

Project

Combine vertices into triangle, convert to fragments

Texture map fragments

Light

GPU

Texture Maps

Z-cull

Alpha Blend

Frame- Buffer(s)

Radeon 9000,X---, GeforceFX-6, DX9

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Basic Unified GPU Architecture

Logical pipeline mapped to physical processors.

Vertex Shader

Geometry

Shader

Pixel Shader

Input

Assembler

Rasterizer Output Merger

Unified Processor Array

Basic unified GPU architecture

Copyright © 2009 Elsevier, Inc

GPU with 112 streaming processor (SP) cores organized in 14 streaming multiprocessors (SMs); Each SM has eight SP cores, two special function units (SFUs), instruction and constant caches, a multithreaded instruction unit, and a shared memory.

Nvidia GeForce 8800