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What is Computer Graphics?

by Brian Wyvill

The University of Victoria Graphics Group

University of Victoria Graphics Lab. CSC 106 2011 page 2

University of Victoria Graphics Lab. CSC 106 2011 page 3

The Great Train Rubbery (1986/88)

University of Victoria Graphics Lab. CSC 106 2011 page 4

September-October 2006 First Place Winner Ghost Light by Bill Pragnell

Internet Ray Tracing Contest 2006

University of Victoria Graphics Lab. CSC 106 2011 page 5 Frozen Fire by Robert W. McGregor

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Frozen Fire Statistics: RENDER TIME: 37 hours @ 1280x1024 px HARDWARE USED: Dell PC, Pentium 4 (w/HT), 3 Ghz, 1 GB RAM

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Overview

Computer Graphics What Body of knowledge is studied? E.g. 305 course: • Graphics Fundamentals • Geometric Transformations + Maths • Graphics Data Structures and Algorithms • Modelling • Rendering • Animation

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Hardware and Fundamentals

Pixels Colour Tables OpenGl support Graphics Primitives (Scan Conversion) GPU

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Technology: Cathode Ray Tube (CRT) Plasma Panel Liquid Crystal Display (LCD)

Raster Displays

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CRT

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LCs (1888) do not emit light. Works by letting varying amounts of fixed intensity backlight through active filter, LEDs can be used for backlight. Liquid Crystal (organic compound) long molecules line up in with long axes parallel. Grooved surface causes them to line up parallel with the grooves. Sandwich LC between two finely grooved surfaces (perpendicular to each other) Light follows alignment of molecules and twisted through 90 degrees. When voltage applied causes molecules to realign allowing light to pass untwisted. Polarising filter wikipedia or http://www.pctechguide.com/07panels.htm

Liquid Crystal Displays

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Display Coordinate Systems

Depends on the API

X

Y

0,0

OpenGL nx-1,ny-1

X

Y

ny-1

0 Qt

0 nx-1

Pixel = Picture Element indexed by an ordered pair

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One Bit Display

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Look Up Table (LUT)

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Geometric Transformations

Homogeneus Coordinate Systems Transformations Properties 2D/3D Viewing Algorithms and Maths DAGS and DACS

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Translation

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Scaling

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Rotation

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Column Vector post multiplication notation.

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University of Victoria Graphics Lab. CSC 106 2011 page 21

University of Victoria Graphics Lab. CSC 106 2011 page 22

DAGS

Instancing – The Scene Graph

Mat

Obj

Obj

Transform Node next

Or Primitive

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DAGS - Instancing

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Model to be transformed

Model Node

Transform Node

Recursive Loops (DCGs)

University of Victoria Graphics Lab. CSC 106 2011 page 25

Multiple Recursion

tree

Cylinder

Mat

next Mat

next Mat

next

tree tree

Mat

next tree

Mat next

tree

University of Victoria Graphics Lab. CSC 106 2011 page 26

def h limit 12 a square scale 10 0.5 trans -5 -0.5 fill 1 col 0.3 0.2 0 a h scale 0.7 0.7 rotate 90 trans -5 0 a h scale 0.7 0.7 rotate -90 trans 5 0 endef

University of Victoria Graphics Lab. CSC 106 2011 page 27

traverse(model* x, matrix m) { if (x is primitive) draw(x, m); else { transform* t;

t=x->firstTransform; if (x->limit>0) { x->limit--; while (t != NULL) { if (t->mdl->limit==local)traverse(t->mdl, m*t->m); t=t->next; } x->limit++; }

} }

If Limit

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3

University of Victoria Graphics Lab. CSC 106 2011 page 29

def h limit 12 a square scale 10 0.5 trans -5 -0.5 fill 1 col 0.3 0.2 0 a h scale 0.7 0.7 rotate 90 trans -5 0 a h scale 0.7 0.7 rotate -90 trans 5 0 vlim 9 endef

1975

Shows: Mutual Recursion If limit Local Limit

Tree

Op Art?

Dragon Curve and variations

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University of Victoria Graphics Lab. CSC 106 2011 page 33

u v

-w

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Modelling

Parametric Curves and Surfaces Generalised Cylinders Subdivision Modelling Implicit Modelling

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CSG

Parametric Generalised Cylinders

Implicit Model Stanford Bunny (mesh)

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NURBS: The most important modeling technique in CAD

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B-Spline Basis for cubics

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DEMO

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Rendering

Lighting Z-Buffer BSP Trees Ray Tracing Antialiasing (A-Buffer) Texturing Global Illumination

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P201 Shirley

University of Victoria Graphics Lab. CSC 106 2011 page 47

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Refraction

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Reflections and Transparency

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Ray Traced Images Sphere with hard shadow point sampling source Sphere with soft shadow sampling wide light source

Ray Traced Shadows

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Shadows (hard edged)

Shadows (soft edged)

V

F1,2,3,4

Mesh Presentation: a common way

l  list of vertices l  list of faces storing pointers for its vertices l  efficient for many applications (well fit to Graphics pipeline)

l  “obj” format from Alias/wavefront (Maya) l  MD2 format (Games)

University of Victoria Graphics Lab. CSC 106 2011 page 54

One Step of Doo Subdivision v  One Step of Subdivision (F,V) (NF,NV)

v  Line Face Curve Surface

University of Victoria Graphics Lab. CSC 106 2011 page 55 3D Studio Max

Example of Doo Subdivision

University of Victoria Graphics Lab. CSC 106 2011 page 56 University of Victoria Graphics Lab. CSC 472/578c 2010 page 56

V -Clark Subdivision l  It is introduced in Computer Aided Design 1978. l  based on the tensor product of cubic B-spline l  at regular points and with the smooth tangent at extra-ordinary points

SIGGRAPH 98

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Example

v  Geri’s v Head v Hands v Clothing: Jacket, pants, shirt, tie and shoes

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The Geoff Function

Field Function

Proximity Blending: Add contributions from generating skeletal elements in the neighbourhood

Click Me

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Blending and The Soft Train

Polygonizer Info.

1986

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University of Victoria Graphics Lab. CSC 106 2011 page 61

The Great Train Rubbery (1986/88)

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Invert

Warping: Example Vector Warp

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Barr Operators

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University of Victoria Graphics Lab. CSC 106 2011 page 65

Ray Traced Canmore Coffee Grinder by Kees van Overveld and Brian Wyvill

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Model of 9ft. Steinway Concert Grand 1994

L-System Plant by Dr. Prusinkiwicz

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University of Victoria Graphics Lab. CSC 106 2011 page 68

American Type 4-4-0

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Controlled Blending and PCM

Controlled Blending with Precise Contact Modelling

Mari-Paule Cani

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Constructive Solid Geometry (CSG)

Primitives are combined using boolean set operations: Union, Intersection, Difference. Each primitive represents a half space, ie the set of points defining the half space E.g.

Boolean expression (u= union, d= difference, i= intersection) d( sphere, cylinder) u( sphere, i( i( cylinder, plane1), plane2) )

- - +

Sphere

- - +

Cylinder -

+

Plane

The cylinder is infinite in extent it is first intersected with two half space planes.

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CSG Tree

CSG Implementation

Boolean Expressions are usually represented as a binary tree.

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The BlobTree 1996 Andy Guy

+Eric Galin, Andy Guy

CSG + scene graph + blends + warps

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The Final Shell

Student: Callum Galbraith

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Global to Local – Inverse Modelling

Global Shape defined by set of functions Positional

Information

Colour change represents a new year Length of branches

Orientation of branch segments defined by interpolating between two functions for short and long branches

Loss of branches

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Sketch Based Modelling with the BlobTree

ShapeShop 2005 Ryan Schmidt

University of Victoria Graphics Lab. CSC 106 2011 page 78

l  Benefits Include: –  Solid (Volume) Modeling –  Shape composition is easy and

robust –  Scene Graph –  BlobTree is a full construction

history and can be animated

Interaction - ShapeShop U. Calgary Student : Ryan Schmidt see SBIM ’05 http://www.shapeshop3d.com/

University of Victoria Graphics Lab. CSC 106 2011 page 79

Examples

Demo

NPR : Pauline Jepp and Kevin Foster

University of Victoria Graphics Lab. CSC 106 2011 page 81

Animation - What You Should Know: Maths Programming Graphics Useful: Some Physics

Lagrange

0=!

!"

!

!

ii

LdtdL

## !)cos1(

21 2 !! ""="= mglmlUTL !

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Interpolation and Key-Framing

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Deforming and Morphing

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Camera and Path Control

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Flexible Objects

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Natural Phenomena

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Motion Synthesis

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Movie Production, Animation, Special Effects

Movie Production, Animation, Special Effects

University of Victoria Graphics Lab. CSC 106 2011 page 90

0sin

2

2

=+

=!"

#$%

&'

'

='

'

((

((

((

lg

mlLdtd

mlL

!!

!!!

!!

Same as Newton!!

Lagrange Looks more complicated than Newton but for more complex problems is simpler. E.g. Pendulum solve for theta.

Simple Pendulum

Lagrange

0=!

!"

!

!

ii

LdtdL

## ! !!

sinmglL "=#

#

)cos1(21 2 !! ""=

"=

mglmlL

UTL

!

θ

l

University of Victoria Graphics Lab. CSC 106 2011 page 91

Flocking l  AKA swarming or herding l  Relate to groups of characters

l  Craig W. Reynolds, “Flocks, herds and schools: A distributed behavioral model”, SIGGRAPH 87

l  Three simple rules (steering behavior):

–  Separation, Alignment, Cohesion

–  Together gives groups of autonomous agents (boids) a realistic form of group behavior similar to flocks of birds, schools of fish, or swarms of bees. ex1, ex2

–  The steering behavior determines how a character reacts to other characters in its local neighborhood.

Birds plus -oids

http://www.codepuppies.com/~steve/aqua.html

University of Victoria Graphics Lab. CSC 106 2011 page 92