The Rendering Pipeline CS 445/645 Introduction to Computer Graphics David Luebke, Spring 2003.

The Rendering Pipeline

CS 445/645Introduction to Computer Graphics

David Luebke, Spring 2003

David Luebke 2 04/20/23

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● Call roll● Assignment 0: questions?


Framebuffers

● So far we’ve talked about the physical display device● How does the interface between the device and the

computer’s notion of an image look?● Framebuffer: A memory array in which the computer

stores an image■ On most computers, separate memory bank from main

memory (why?)■ Many different variations, motivated by cost of memory


Framebuffers: True-Color

● A true-color (aka 24-bit or 32-bit) framebuffer stores one byte each for red, green, and blue

● Each pixel can thus be one of 224 colors● Pay attention to

Endian-ness● How can 24-bit

and 32-bit mean the same thing here?


Framebuffers: Indexed-Color

● An indexed-color (8-bit or PseudoColor) framebuffer stores one byte per pixel (also: GIF image format)

● This byte indexes into a color map: ● How many colors

can a pixel be?● Still common on

low-end displays (cell phones, PDAs,GameBoys)

● Cute trick: color-map animation


Framebuffers: Hi-Color

● Hi-Color is/was a popular PC SVGA standard● Packs pixels into 16 bits:

■ 5 Red, 6 Green, 5 Blue (why would green get more?)■ Sometimes just 5,5,5

● Each pixel can be one of 216 colors● Hi-color images can exhibit worse quantization

artifacts than a well-mapped 8-bit image


Recap: Matrices

● By convention, matrix element Mrc is located at row r and column c:

● By (OpenGL) convention, vectors are columns:

mnm2m1

2n2221

1n1211

MMM

MMM

MMM

M

3

2

v

v

v

v

1


Recap: Matrices

● Matrix-vector multiplication applies a linear transformation to a vector:

● Recall how to do matrix multiplication

z

y

x

v

v

v

MMM

MMM

MMM

vM

333231

232221

131211


Recap: Matrix Transformations

● A sequence or composition of linear transformations corresponds to the product of the corresponding matrices

■ Note: the matrices to the right affect vector first, e.g:

rotation about x, then translation along y, then rotation about z

■ Note: order of matrices matters!

● The identity matrix I has no effect in multiplication

● Some (not all) matrices have an inverse:

vvMM 1

' z y xp pR T R

x xPQ QP

x xI


Vectors and Matrices

● Vector algebra operations can be expressed in this matrix form■ Dot product:

■ Cross product:○ Note: use

right-handrule!

z

y

x

zyx

b

b

b

aaaba

0

0

0

z y x x

z x y y

y x z z

a a b c

a a b c

a a b c

a b c

a c 0

b c 0


The Rendering Pipeline: A Whirlwind Tour

Transform

Illuminate

Transform

Clip

Project

Rasterize

Model & CameraModel & CameraParametersParameters Rendering PipelineRendering Pipeline FramebufferFramebuffer DisplayDisplay


The Display You Know

Transform

Illuminate

Transform

Clip

Project

Rasterize



The Framebuffer You Know

Transform

Illuminate

Transform

Clip

Project

Rasterize



The Rendering Pipeline

Transform

Illuminate

Transform

Clip

Project

Rasterize



2-D Rendering: Rasterization(Coming Soon)

Transform

Illuminate

Transform

Clip

Project

Rasterize



The Rendering Pipeline: 3-D

Transform

Illuminate

Transform

Clip

Project

Rasterize




ModelingTransforms

Scene graphObject geometry

LightingCalculations

ViewingTransform

Clipping

ProjectionTransform

Result:Result:

• All vertices of scene in shared 3-D “world” coordinate All vertices of scene in shared 3-D “world” coordinate systemsystem

• Vertices shaded according to lighting modelVertices shaded according to lighting model

• Scene vertices in 3-D “view” or “camera” coordinate Scene vertices in 3-D “view” or “camera” coordinate systemsystem

• Exactly those vertices & portions of polygons in view Exactly those vertices & portions of polygons in view frustumfrustum

• 2-D screen coordinates of clipped vertices2-D screen coordinates of clipped vertices



Scene graphObject geometry

LightingCalculations

Clipping

Result:Result:

• All vertices of scene in shared 3-D “world” coordinate All vertices of scene in shared 3-D “world” coordinate systemsystem

• Vertices shaded according to lighting modelVertices shaded according to lighting model

• Scene vertices in 3-D “view” or “camera” coordinate Scene vertices in 3-D “view” or “camera” coordinate systemsystem

• Exactly those vertices & portions of polygons in view Exactly those vertices & portions of polygons in view frustumfrustum

• 2-D screen coordinates of clipped vertices2-D screen coordinates of clipped vertices

ModelingTransforms

ViewingTransform

ProjectionTransform


Rendering: Transformations

● So far, discussion has been in screen space● But model is stored in model space

(a.k.a. object space or world space)● Three sets of geometric transformations:

■ Modeling transforms■ Viewing transforms■ Projection transforms



● Modeling transforms■ Size, place, scale, and rotate objects parts of the model

w.r.t. each other■ Object coordinates world coordinates

Z

X

Y

X

Z

Y



● Viewing transform■ Rotate & translate the world to lie directly in front of the

camera○ Typically place camera at origin○ Typically looking down -Z axis

■ World coordinates view coordinates



● Projection transform■ Apply perspective foreshortening

○ Distant = small: the pinhole camera model

■ View coordinates screen coordinates



● All these transformations involve shifting coordinate systems (i.e., basis sets)

● That’s what matrices do…● Represent coordinates as vectors, transforms as

matrices

● Multiply matrices = concatenate transforms!

Y

X

Y

X

cossin

sincos

The Rendering Pipeline CS 445/645 Introduction to Computer Graphics David Luebke, Spring 2003.

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