CS148: Introduction to Computer Graphics Final Review Session.

CS148: Introduction to Computer Graphics

Final Review Session

CS148 Final Review Winter 2008

Outline

Final Info

Review of TopicsMattes and CompositingSampling and FilteringCompressionProgrammable ShadingCamerasRenderingModeling


Final Exam Info

Time: Thursday March 20, 12:15Location: Meyer Forum 112Duration: 3 hours

Closed book

Consists of a few (4 or 5) multi-part questions

Emphasis on the second half of the course, but don’t forget the first half


Mattes and Compositing

α = Coverage= Area= Opacity= 1 – Transparency

Standard Compositing EquationC = α * CF + (1 – α) * CB

Premultiplied α: C’ = αC = (αr, αg, αb, α)

α


Porter-Duff Compositing Algebra

BBAA CFCFc


Green Screen Matte Extraction

Given:C – Observed colorCB – Backing color

Compute:CF = (αFRF, αFGF, αFBF, αF)

Compositing Equation:C = CF + (1 – αF)CB

3 Equations, 4 Unknowns – must make some assumptions


The Horrors of Poor Sampling


The Horrors of Poor Sampling

Retort sequence by Don Mitchell


Nyquist Frequency

Nyquist Frequency – ½ the sampling frequency

A periodic signal with a frequency above the Nyquist frequency cannot be distinguished from a periodic signal below the Nyquist frequency

These indistinguishable signals are called aliases


Fourier Transform

You can express any (periodic) signal as a sum of sinusoids


Fourier Transform

Spatial Domainf(x,y)

Frequency DomainF(ωx, ωy)

Fourier Transform

InverseFourier

Transform

Convolution Multiplication

Multiplication Convolution

Sinc Box


Convolution

Convolution – integration/summation of translated filter with signal

n

nmgnfmgf )()())(*(


Fourier Transform


Low Pass Filter


High Pass Filter


Band Pass Filter


Sampling – Spatial Domain


Sampling – Frequency Domain


Reconstruction – Frequency Domain


Reconstruction – Spatial Domain


Undersampling – Frequency Domain


Compression

Kolmogorov Complexity – smallest program to generate data

Lossless CodingRun length coding – exploit obvious redundancyHuffman Coding – variable length code, highly probable characters -> shorter codes

Transform Coding – perform invertible transform on data to make it more amenable to compression (applies to lossless and lossy!)


Lossy Image Compression (JPEG)

Image

DiscreteCosine

TransformTransformed

Image

Quantization

(Lossy Step)

Reorder+

Coding CompressedData Stream

JPEG2000 is similar but uses the wavelet transform.Exploit human perception – quantize high frequencies more heavily since we are less sensitive to them.


Wavelet Transform

Just another invertible transform (expresses signal in different basis)

Generated in steps by calculating smoothed (approximate) values and detail (corrective) values

Resulting basis functions have compact support – they are only non-zero over a limited range – error in coefficient causes localized error


Wavelet Transform

6 8 5 9 5 5 6 6

6.25 0 -1 -2 0 0

Full Transform

High Resolution DetailsMedium Resolution DetailsLow Resolution DetailsAverage Value

-.5.75


Rendering Pipeline

Vertex Data

Primitive Data

Tessellation

Vertex Processin

g

Geometry Processin

g

Pixel Processin

g

Texture Sampler

Textured Surface

Pixel Rendering


Example Vertex Shader

Vertex Shader


Example Pixel Shader

Pixel Shader


GPGPU

CPU

Thread synchronization

Bandwidth limitations

Scheduling overhead

Small number of cores

GPU

All threads independent

Message passing is not allowed

Resource allocation is done by GPU

Many cores available (12 to 48 typical)


GPGPU Applications

Beyond triangle rendering

Collision detection

Fluid simulation

Physics

Raytracing

Video compression

Beyond graphics

Folding@Home

Speech Recognition

Partial differential equation solvers

Fourier transform


Pinhole Camera

film

f

x’

(x,z)

pinhole

Field of view


Pinhole Camera

z

fxx '

film

f

x’

(x,z)

pinhole

Field of view

f

xfov ')

2tan(


Homogeneous Coordinates


Perspective Transform


Orthographic Projection


Field of View and Focal Length


Depth of Field


Circle of Confusion


Types of Reflection

Mirror

Ideal reflection

Reflection law

Diffuse

Matte

Lambert’s Law

Specular

Highlights and gloss

Microfacet model


Lambert’s Law


Ideal Reflection


Microfacets


Modeling

RepresentationsDense Polygonal MeshesBicubic surfacesSubdivision Surfaces

OperationsInstancingTransformation – linear and non-linearCompression, simplificationDeform, skin, morph, animateSmoothSet operations


Bezier Curve


Subdivision Surfaces

Loop subdivision algorithmExtraordinary points

CS148: Introduction to Computer Graphics Final Review Session.

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