1GR2-00

GR2Advanced Computer

GraphicsAGR

GR2Advanced Computer

GraphicsAGR

Ken Brodliekwb@scs.leeds.ac.uk

Lecture 1 - Overview

2GR2-00

ObjectivesObjectives

To understand how 3D scenes can be modelled - in terms of geometry, appearance and behaviour - and rendered on a display

To understand how to deliver interactive animated 3D graphics over the Internet

To be able to create interactive 3D graphics applications using industry standard software (OpenGL and VRML)

3GR2-00

Lecture Outline - The Basics

Lecture Outline - The Basics

MODELLING– representing objects in 3D– transforming objects and composing scenes

VIEWING– projecting 3D scenes onto a 2D display

surface RENDERING

– illumination– shading– adding realism via textures, shadows

4GR2-00

Basic ModellingBasic Modelling

x

y

z

objects representedas set of faces - iepolygons- and facesas a set of points

scenes composedby scaling, rotating,translating objects tocreate a 3D world

5GR2-00

ViewingViewing

Clipping– selects a volume of interest (cf 2D

clipping in GR1) Projection

– 3D scene is projected onto a 2D plane

camera

6GR2-00

RenderingRendering

??

shading:how do we use ourknowledge of illuminationto shade surfaces in ourworld?

illumination:how is light reflectedfrom surfaces?

7GR2-00

RenderingRendering

texture

shadows

8GR2-00

Lecture Outline - InternetLecture Outline - Internet

VRML– ISO standard for 3D graphics over

the Web– allows modelling of geometry,

appearance and behaviour

9GR2-00

Lecture Outline - Advanced

Lecture Outline - Advanced

ADVANCED RENDERING– direct versus global illumination

methods– ray tracing and radiosity

OTHER ADVANCED FEATURES– curve and surface modelling– image based rendering– non-photorealistic rendering

10GR2-00

Lecture Outline - Advanced

Lecture Outline - Advanced

Advanced Rendering - global illumination– ray tracing

– radiositybased on physics of radiative heat

transfer between surfaces

light

eye

screen

objects

11GR2-00

Ray TracingRay Tracing

12GR2-00

RadiosityRadiosity

13GR2-00

Practical OutlinePractical Outline

Basic graphics programming– creation of interactive 3D worlds

using OpenGL Web graphics

– creating interactive, animated 3D virtual worlds on the Web using VRML

Practical work will use the Silicon Graphics O2 laboratory, and the linux machines

14GR2-00

AGR AGR

Virtual Environments– study group looking at the

advanced requirements for VR .. or interactive simulation

Practical work using Open Inventor

15GR2-00

Course InfoCourse Info

Lectures– Monday 2.00 - 3.00 (LT25)– Tuesday 1.00 - 2.00 (LT25)

Practicals Web site

– http://www.scs.leeds.ac.uk/kwb/GR2 Newsgroups

– local.modules.gr2 local.modules.agr– local.modules.gr2.talk

local.modules.agr.talk

16GR2-00

BooksBooks

Computer Graphics (second edition)– Hearn and Baker, Prentice Hall

3D Computer Graphics (third edition)– Alan Watt, Addison Wesley

Introduction to Computer Graphics– Foley, van Dam, Feiner and Hughes,

Addison-Wesley

17GR2-00

BooksBooks

Interactive Computer Graphics (top-down approach using OpenGL)– Angel, Addison Wesley

The VRML 2.0 Handbook– Hartman and Wernecke, Addison-

Wesley

OpenGL Manual

18GR2-00

AssessmentAssessment

Module Examination Coursework

GR2 75% 25%

AGR 60% 40%

19GR2-00

Before we begin...mathematics!

Before we begin...mathematics!

3D Co-ordinate Systems

LEFT RIGHT

x

yz

x

y

z

z points away z points toward

Align thumb with x, first finger with y, then second fingerof appropriate hand gives z direction. Common now touse a RIGHT HANDED system.

20GR2-00

Points and VectorsPoints and Vectors

We shall write points as column vectors

xyz

P =

Difference of two points gives a direction vector:D = P2 - P1

x

y

z

P2

P1

x

y

z

P

Note: If P1 and P2are on a plane, thenD lies in the plane

21GR2-00

Magnitude of a VectorMagnitude of a Vector

The magnitude of a vector V = (v1,v2,v3)T is given by:

|V| = sqrt(v1*v1 + v2*v2 + v3*v3)

eg (1,2,3)T has magnitude sqrt(14) A unit vector has magnitude 1 A unit vector in the direction of

V is V / |V|

22GR2-00

Scalar or Dot ProductScalar or Dot Product

The scalar product, or dot product, of two vectors U and V is defined as:

U.V = u1*v1 + u2*v2 + u3*v3

It is important in computer graphics because we can show that also:

U.V = |U|*|V|*coswhere is the angle between U and V

This lets us calculate angle ascos = (u1*v1 + u2*v2 + u3*v3) / (|U|*|V|)

23GR2-00

Diffuse LightingDiffuse Lighting

Diffuse reflection depends on angle between light direction and surface normal:reflected intensity = light intensity *

cosine of angle between light direction and surface normal

light normal

scalar product letsus calculate cos

24GR2-00

Vector or Cross ProductVector or Cross Product

The vector or cross product is defined as:UxV = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1)

We can also show that:UxV = N |U||V| sin where N is unit vector orthogonal to U and V

(forming a right handed system) and is angle between U and V

This allows us to find the normal to a plane– cross-product of two directions lying in plane ,

eg (P3-P2), (P2-P1), where P1, P2, P3 are three points in the plane