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SI31 Advanced Computer Graphics AGR Ken Brodlie [email protected] Lecture 1 - Overview Objectives To understand how 3D scenes can be modelled - in terms of geometry, appearance and behaviour - and rendered on a display

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objectives
Objectives
  • 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)
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
basic modelling
Basic Modelling

y

objects represented

as set of faces - ie

polygons- and faces

as a set of points

x

z

scenes composed

by scaling, rotating,

translating objects to

create a 3D world

viewing
cameraViewing
  • Clipping
    • selects a volume of interest
  • Projection
    • 3D scene is projected onto a 2D plane
rendering
Rendering

illumination:

how is light reflected

from surfaces?

??

shading:

how do we use our

knowledge of illumination

to shade surfaces in our

world?

rendering7
Rendering
  • texture
  • shadows
lecture outline internet
Lecture Outline - Internet
  • VRML
    • ISO standard for 3D graphics over the Web
    • allows modelling of geometry, appearance and behaviour
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
lecture outline advanced10
eye

screen

Lecture Outline - Advanced
  • Advanced Rendering - global illumination
    • ray tracing
    • radiosity

based on physics of radiative heat transfer between surfaces

objects

light

radiosity
Radiosity

from

www.lightscape.com

practical outline
Practical 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
slide15
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
course info
Course 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
books
Books
  • Computer Graphics (second edition)
    • Hearn and Baker, Prentice Hall
  • 3D Computer Graphics (third edition)
    • Alan Watt, Addison Wesley
  • OpenGL Manual
books18
Books
  • 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
assessment
Module

Examination

Coursework

SI31

67%

33%

AGR

60%

40%

Assessment
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

Applications - Computer-Aided Design
applications virtual reality
Virtual oceanarium built for EXPO in Lisbon

Example taken from Fraunhofer Institute site

http://www.igd.fhg.de

Applications - Virtual Reality
applications cartography and gis
Ordnance Survey

http://www.ordsvy.gov.uk

GIS-3D also from Fraunhofer Institute

Applications - Cartography and GIS
applications computer art
This example can be found on the SIGGRAPH Web Site

Important computer graphics resource

http:www.siggraph.org

Applications - Computer Art
applications scientific visualization
Turning scientific data into pictures

with applications to medicine and computer simulations

Applications - Scientific Visualization
before we begin mathematics
Before we begin...mathematics!
  • 3D Co-ordinate Systems

y

y

z

x

x

z

LEFT

RIGHT

z points away

z points toward

Align thumb with x, first finger with y, then second finger

of appropriate hand gives z direction. Common now to

use a RIGHT HANDED system.

points and vectors
Points and Vectors
  • We shall write points as column vectors

y

P

P =

x

y

z

x

z

Difference of two points gives a direction vector:

D = P2 - P1

y

P2

Note: If P1 and P2

are on a plane, then

D lies in the plane

x

z

P1

magnitude of a vector
Magnitude 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|

scalar or dot product
Scalar 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|*cosq

where q is the angle between U and V

  • This lets us calculate angle q as

cos q = (u1*v1 + u2*v2 + u3*v3) / (|U|*|V|)

diffuse lighting
Diffuse 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

normal

light

scalar product lets

us calculate cosq

q

vector or cross product
Vector 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 q 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
exercises
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)?

Exercises
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