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1.1 SI31_2001 SI31 Advanced Computer Graphics AGR Ken Brodlie kwb@comp.leeds.ac.uk Lecture 1 - Overview

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1.2 SI31_2001 Objectives n To understand how 3D scenes can be modelled - in terms of geometry, appearance and behaviour - and rendered on a display n To understand how to deliver interactive animated 3D graphics over the Internet n To be able to create interactive 3D graphics applications using industry standard software (OpenGL, VRML and POVRAY)

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1.3 SI31_2001 Lecture Outline - The Basics n MODELLING – representing objects in 3D – transforming objects and composing scenes n VIEWING – projecting 3D scenes onto a 2D display surface n RENDERING – illumination – shading – adding realism via textures, shadows

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1.4 SI31_2001 Basic Modelling x y z objects represented as set of faces - ie polygons- and faces as a set of points scenes composed by scaling, rotating, translating objects to create a 3D world

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1.5 SI31_2001 Viewing n Clipping – selects a volume of interest n Projection – 3D scene is projected onto a 2D plane camera

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1.6 SI31_2001 Rendering ?? shading: how do we use our knowledge of illumination to shade surfaces in our world? illumination: how is light reflected from surfaces?

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1.7 SI31_2001 Rendering n texture n shadows

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1.8 SI31_2001 Lecture Outline - Internet n VRML – ISO standard for 3D graphics over the Web – allows modelling of geometry, appearance and behaviour

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1.9 SI31_2001 Lecture Outline - Advanced n ADVANCED RENDERING – direct versus global illumination methods – ray tracing and radiosity n OTHER ADVANCED FEATURES – curve and surface modelling – image based rendering – non-photorealistic rendering

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1.10 SI31_2001 Lecture Outline - Advanced n Advanced Rendering - global illumination – ray tracing – radiosity based on physics of radiative heat transfer between surfaces light eye screen objects

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1.11 SI31_2001 Ray Tracing

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1.12 SI31_2001 Ray Tracing n POVRAY - freely available ray tracing software http://www.povray.org

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1.13 SI31_2001 Radiosity from www.lightscape.com

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1.14 SI31_2001 Practical Outline n Basic graphics programming – creation of interactive 3D worlds using OpenGL n Web graphics – creating interactive, animated 3D virtual worlds on the Web using VRML n Advanced rendering – using POVRAY n Practical work will use the Linux and NT machines

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1.15 SI31_2001 AGR n Mastersclasses – additional seminars / study groups on more advanced topics in computer graphics and virtual environments… such as simulation of soft objects n Additional practical project

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1.16 SI31_2001 Course Info n Lectures – Monday 2.00 - 3.00 (LT19) – Tuesday 1.00 - 2.00 (LT25) n Practicals n Web site – http://www.comp.leeds.ac.uk/kwb/si31 n Newsgroups – local.modules.si31local.modules.agr – local.modules.si31.talklocal.modules.agr.talk

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1.17 SI31_2001 Books n Computer Graphics (second edition) – Hearn and Baker, Prentice Hall n 3D Computer Graphics (third edition) – Alan Watt, Addison Wesley n OpenGL Manual

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1.18 SI31_2001 Books n Introduction to Computer Graphics – Foley, van Dam, Feiner and Hughes, Addison-Wesley n Interactive Computer Graphics (top- down approach using OpenGL) – Angel, Addison Wesley n The VRML 2.0 Handbook – Hartman and Wernecke, Addison-Wesley n 3D Games – Alan Watt and Fabio Policarpo

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1.19 SI31_2001 Assessment ModuleExaminationCoursework SI3167%33% AGR60%40%

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1.20 SI31_2001 Applications - Computer Games

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1.21 SI31_2001 Applications - Computer- Aided Design n This is Hubble Space Telescope modeled using the BRL-CAD system n Uses CSG modeling and ray tracing for rendering http://ftp.arl.mil/brlcad

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1.22 SI31_2001 Applications - Virtual Reality n Virtual oceanarium built for EXPO in Lisbon n Example taken from Fraunhofer Institute site http://www.igd.fhg.de

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1.23 SI31_2001 Applications - Cartography and GIS n Ordnance Survey http://www.ordsvy.gov.uk n GIS-3D also from Fraunhofer Institute

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1.24 SI31_2001 Applications - Computer Art n This example can be found on the SIGGRAPH Web Site n Important computer graphics resource http:www.siggraph.org

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1.25 SI31_2001 Applications - Scientific Visualization n Turning scientific data into pictures – with applications to medicine and computer simulations

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1.26 SI31_2001 Before we begin...mathematics! n 3D Co-ordinate Systems LEFT RIGHT x y z x y z z points awayz 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.

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1.27 SI31_2001 Points and Vectors n We shall write points as column vectors xyzxyz P = Difference of two points gives a direction vector: D = P 2 - P 1 x y z P2P2 P1P1 x y z P Note: If P 1 and P 2 are on a plane, then D lies in the plane

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1.28 SI31_2001 Magnitude of a Vector n The magnitude of a vector V = (v 1,v 2,v 3 ) T is given by: |V| = sqrt(v 1 *v 1 + v 2 *v 2 + v 3 *v 3 ) eg (1,2,3) T has magnitude sqrt(14) n A unit vector has magnitude 1 n A unit vector in the direction of V is V / |V|

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1.29 SI31_2001 Scalar or Dot Product n The scalar product, or dot product, of two vectors U and V is defined as: U.V = u 1 *v 1 + u 2 *v 2 + u 3 *v 3 n It is important in computer graphics because we can show that also: U.V = |U|*|V|*cos where is the angle between U and V This lets us calculate angle as cos = (u 1 *v 1 + u 2 *v 2 + u 3 *v 3 ) / (|U|*|V|)

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1.30 SI31_2001 Diffuse Lighting n 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 lets us calculate cos

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1.31 SI31_2001 Vector or Cross Product n The vector or cross product is defined as: UxV = (u 2 v 3 - u 3 v 2, u 3 v 1 - u 1 v 3, u 1 v 2 - u 2 v 1 ) n 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 n This allows us to find the normal to a plane – cross-product of two directions lying in plane, eg (P 3 -P 2 ), (P 2 -P 1 ), where P 1, P 2, P 3 are three points in the plane

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1.32 SI31_2001 Exercises n Convince yourself that the x-axis is represented by the vector (1,0,0) n What is the unit normal in the direction (2,3,4)? n What is the angle between the vectors (1,1,0) and (1,0,0)? n Which vector is orthogonal to the vectors (1,0,0) and (0,1,0)? n What is the normal to the plane through the points (1,2,3), (3,4,5) and (0,0,0)?

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