1.1SI31_2001

SI31Advanced Computer

GraphicsAGR

SI31Advanced Computer

GraphicsAGR

Ken Brodliekwb@comp.leeds.ac.uk

Lecture 1 - Overview

1.2SI31_2001

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, VRML and POVRAY)

1.3SI31_2001

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

1.4SI31_2001

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

1.5SI31_2001

ViewingViewing

Clipping– selects a volume of interest

Projection– 3D scene is projected onto a 2D

plane

camera

1.6SI31_2001

RenderingRendering

??

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

illumination:how is light reflectedfrom surfaces?

1.7SI31_2001

RenderingRendering

texture

shadows

1.8SI31_2001

Lecture Outline - InternetLecture Outline - Internet

VRML– ISO standard for 3D graphics over

the Web– allows modelling of geometry,

appearance and behaviour

1.9SI31_2001

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

1.10SI31_2001

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

1.11SI31_2001

Ray TracingRay Tracing

1.12SI31_2001

Ray TracingRay Tracing

POVRAY - freely available ray tracing software

http://www.povray.org

1.13SI31_2001

RadiosityRadiosity

from www.lightscape.com

1.14SI31_2001

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

Advanced rendering– using POVRAY

Practical work will use the Linux and NT machines

1.15SI31_2001

AGR AGR

Mastersclasses– additional seminars / study groups

on more advanced topics in computer graphics and virtual environments… such as simulation of soft objects

Additional practical project

1.16SI31_2001

Course InfoCourse Info

Lectures– Monday 2.00 - 3.00 (LT19)– Tuesday 1.00 - 2.00 (LT25)

Practicals Web site

– http://www.comp.leeds.ac.uk/kwb/si31 Newsgroups

– local.modules.si31 local.modules.agr– local.modules.si31.talk

local.modules.agr.talk

1.17SI31_2001

BooksBooks

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

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

OpenGL Manual

1.18SI31_2001

BooksBooks

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

Addison-Wesley Interactive Computer Graphics (top-

down approach using OpenGL)– Angel, Addison Wesley

The VRML 2.0 Handbook– Hartman and Wernecke, Addison-Wesley

3D Games– Alan Watt and Fabio Policarpo

1.19SI31_2001

AssessmentAssessment

Module Examination Coursework

SI31 67% 33%

AGR 60% 40%

1.20SI31_2001

Applications - Computer Games

Applications - Computer Games

1.21SI31_2001

Applications - Computer-Aided Design

Applications - Computer-Aided Design

This is Hubble Space Telescope modeled using the BRL-CAD system

Uses CSG modeling and ray tracing for rendering

http://ftp.arl.mil/brlcad

1.22SI31_2001

Applications - Virtual Reality

Applications - Virtual Reality

Virtual oceanarium built for EXPO in Lisbon

Example taken from Fraunhofer Institute site

http://www.igd.fhg.de

1.23SI31_2001

Applications - Cartography and GIS

Applications - Cartography and GIS

Ordnance Survey

http://www.ordsvy.gov.uk

GIS-3D also from Fraunhofer Institute

1.24SI31_2001

Applications - Computer Art

Applications - Computer Art

This example can be found on the SIGGRAPH Web Site

Important computer graphics resource

http:www.siggraph.org

1.25SI31_2001

Applications - Scientific Visualization

Applications - Scientific Visualization

Turning scientific data into pictures

– with applications to medicine and computer simulations

1.26SI31_2001

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.

1.27SI31_2001

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 P2

are on a plane, thenD lies in the plane

1.28SI31_2001

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|

1.29SI31_2001

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|)

1.30SI31_2001

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

1.31SI31_2001

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

1.32SI31_2001

ExercisesExercises

Convince yourself that the x-axis is represented by the vector (1,0,0)

What is the unit normal in the direction (2,3,4)?

What is the angle between the vectors (1,1,0) and (1,0,0)?

Which vector is orthogonal to the vectors (1,0,0) and (0,1,0)?

What is the normal to the plane through the points (1,2,3), (3,4,5) and (0,0,0)?