16.837Introduction to Computer GraphicsOverview 2Luxo Jr• Pixar Animation Studios, 1986• Director: John LasseterOverview 3Plan• Introduction• Overview of the semester• Administrivia• Iterated Function Systems (fractals)Overview 4Team• Lecturers– Frédo Durand– Barb Cutler•TAs– Rob Jagnow– Patrick Nichols• Course secretary– Bryt Bradley• Staff email lists:– TAs only: [email protected]– Staff: [email protected] 5Why Computer Graphics?• Movies•Games•CAD-CAM• Simulation• Virtual reality• Visualization• Medical imagingOverview 6Movies2Overview 7Digression• George Borshukov, vfx technology supervisor , ESC entertainment (The Matrix)Will give a talk at MIT Nov 12Overview 8GamesOverview 9SimulationOverview 10CAD-CAM & designOverview 11ArchitectureOverview 12Virtual reality3Overview 13VisualizationOverview 14Medical imagingOverview 15What you will learn in 6.837• Fundamentals of computer graphics algorithms• Able to implement most applications just shown• Understand how graphics APIs and the graphics hardware workOverview 16What you will NOT learn• Software packages– CAD-CAM– Photoshop and other painting tools• Artistic skills•Game design• Graphics API– Although you will be exposed to OpenGLOverview 17Questions?Overview 18Plan• Introduction• Overview of the semester• Administrivia• Iterated Function Systems (fractals)4Overview 19Overview of the semester• Ray Tracing– Quiz 1• Animation, modeling, IBMR– Choice of final project• Rendering pipeline– Quiz 2• Advanced topicsOverview 20Ray Casting• For every pixel construct a ray from the eye – For every object in the scene• Find intersection with the ray • Keep if closestOverview 21Ray Casting• For every pixel construct a ray from the eye – For every object in the scene• Find intersection with the ray • Keep if closestOverview 22Ray Tracing• Shade (interaction of light and material)• Secondary rays (shadows, reflection, refractionOverview 23Ray Tracing• Original Ray-traced image by Whitted• Image computed using the Dali ray tracer by Henrik Wann Jensen• Environment map by Paul DebevecOverview 24Overview of the semester• Ray Tracing– Quiz 1• Animation, modeling, IBMR– Choice of final project• Rendering pipeline– Quiz 2• Advanced topics5Overview 25Animation: KeyframingACM © 1987 “Principles of traditional animation applied to 3D computer animation”Overview 26Particle system (PDE)• Animation– Keyframing and interpolation– SimulationOverview 27Rigid body dynamics• Simulate all external forces and torques()tx()tv()1btp()3btp()2btp()2tf()3tf()1tfOverview 28Modeling• Curved surfaces• Subdivision surfacesOverview 29Image-based Rendering• Use images as inputs and representation• E.g. Image-based modeling and photo editingBoh, Chen, Dorsey and Durand 2001Input image New viewpoint RelightingOverview 30Overview of the semester• Ray Tracing– Quiz 1• Animation, modeling, IBMR– Choice of final project• Rendering pipeline– Quiz 2• Advanced topics6Overview 31The Rendering PipelineRay Casting• For each pixel– For each objectSend pixels to the sceneRendering Pipeline• For each triangle– For each projected pixelProject scene to the pixelsOverview 32The Rendering Pipeline• Transformations• Clipping• Rasterization• VisibilityOverview 33Overview of the semester• Ray Tracing– Quiz 1• Animation, modeling, IBMR– Choice of final project• Rendering pipeline– Quiz 2• Advanced topicsOverview 34Textures and shading For more info on the computer artwork of Jeremy Birnsee http://www.3drender.com/jbirn/productions.htmlOverview 35shadowsOverview 36Traditional Ray Tracing7Overview 37Ray Tracing+soft shadowsOverview 38Ray Tracing+causticsOverview 39Global IlluminationOverview 40ColorOverview 41AntialiasingOverview 42Questions?8Overview 43Plan• Introduction• Overview of the semester• Administrivia• Iterated Function Systems (fractals)Overview 44Administrivia• Web: http://graphics.csail.mit.edu/classes/6.837/F03/• Lectures– Slides will be online• Office hours– Posted on the web• Review sessions– C++, linear algebraOverview 45Prerequisites• Not enforced• 18.06 Linear Algebra– Simple linear algebra, vectors, matrices, basis, solving systems of equations, inversion• 6.046J Algorithms– Orders of growth, bounds, sorting, trees•C++– All assignments are in C++– Review/introductory session Monday Overview 46Grading policy• Assignments: 40%– Must be completed individually– No late policy. Stamped by stellar.• 2 Quizzes: 20%– 1 hour in class• Final project: 40%– Groups of 3, single grade for the group– Initial proposal: 3-5 pages– Steady weekly progress– Final report & presentation– Overall technical meritOverview 47Assignments• Turn in code AND executable• We will watch code style• Platform– Windows– Linux• Collaboration policy:– You can chat, but code on your own• No late policyOverview 48Project• Groups of 3• Brainstorming– Middle of the semester• Proposal • Weekly meeting with TAs• Report & presentation9Overview 49Non-Photorealistic Rendering•Eric Ho • Philip Lee• Vivienne LeeOverview 50Simulating a Starship Battle• Christopher Taylor• Benji Sterling• Jon WolkOverview 51Bubble Trouble bobble 3D Challenge 3000 • Roger Hanna• Ryan Williams• Chris Elledge• Paul Elliott Overview 52Selective Ray Recast For Optimized Rendering of Animation• Bradley Lassey• Ying Li• Patrick Menard Overview 53QuestionsOverview 54Plan• Introduction• Overview of the semester• Administrivia• Iterated Function Systems (fractals)10Overview 55IFS: self-similar fractals• Described by a set of n transformations fi– Capture the self-similarity– Affine transformations– Contractions (reduce distances)• An attractor is a fixed pointImage from http://spanky.triumf.ca/www/fractal-info/ifs-type.htmU)(AfAi=Overview 56Example: Sierpinsky triangle• 3 transforms• Translation and scale by 0.5Overview 57Rendering• Probabilistic application of one transformationFor a number of random input points (x0, y0)For j=0 to big numberPick transformation i(xk+1, yk+1) = fi(xk, yk)Display (xk, yk)Overview 58Example: Sierpinsky triangleFor a number of random input points (x0, y0)For j=0 to big numberPick transformation i(xk+1, yk+1) = fi(xk,
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