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Graphics-1 Gentle Introduction to Computer Graphics Based on: –David Brogan’s “Introduction to Computer Graphics” Course Slides, University of Virginia –Jack van Wijk’s “Computer Graphics” Course Slides, University of Eindhoven.
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Graphics-2 Outline Graphics Applications What is Computer Graphics Representations in Graphics Supporting Disciplines Introduction to 2d Modeling Transformations Matrix Representations Linear Transformations
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Graphics-3 Graphics Applications Entertainment: Cinema Pixar: Monster’s Inc. A Bug’s Life (Pixar)
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Graphics-4 Graphics Applications Medical Visualization MIT: Image-Guided Surgery Project The Visible Human Project
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Graphics-5 Graphics Applications Everyday use
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Graphics-6 Graphics Applications Scientific Visualization
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Graphics-7 Graphics Applications Computer Aided Design (CAD)
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Graphics-8 Graphics Applications Training Designing Effective Step-By-Step Assembly Instructions (Maneesh Agrawala et. al)
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Graphics-9 Graphics Applications Games GT Racer 3 Polyphony Digital: Gran Turismo 3, A Spec
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Graphics-10 Graphics Applications Games Circus Atari (Atari)
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Graphics-11 What is Computer Graphics? Computer graphics: generating 2D images of a 3D world represented in a computer. Main tasks: –modeling: (shape) creating and representing the geometry of objects in the 3D world –rendering: (light, perspective) generating 2D images of the objects –animation: (movement) describing how objects change in time
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Graphics-12 What is Computer Graphics? ImageMath. Model Image Analysis (pattern recognition) Image Synthesis (Rendering) ModelingImage processing
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Graphics-13 Representations in graphics Vector Graphics Image is represented by continuous geometric objects: lines, curves, etc. Raster Graphics Image is represented as a rectangular grid of colored pixels
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Graphics-14 Vector graphics Graphics objects: geometry + color Relatively low processing time – in terms of the number of graphic objects Geometric transformation possible without loss of information (zoom, rotate, …) Examples: PowerPoint, CorelDraw,...
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Graphics-15 Raster graphics Generic Image processing techniques Geometric Transformation: loss of information Relatively high processing time – in terms of the number of pixels Realistic images, textures,... Examples: Paint, PhotoShop,...
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Graphics-16 Supporting Disciplines Computer science (algorithms, data structures, software engineering, …) Mathematics (geometry, numerical, …) Physics (Optics, mechanics, …) Psychology (Colour, perception) Art and design
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Graphics-17 Introduction to Modeling Transformations Specify transformations for objects –Allows definitions of objects in own coordinate systems –Allows use of object definition multiple times in a scene
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Graphics-18 2D Modeling Transformations Scale Rotate Translate Scale Translate x y World Coordinates Modeling Coordinates
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Graphics-19 Scaling Scaling a coordinate means multiplying each of its components by a scalar Uniform scaling means this scalar is the same for all components: 2 2
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Graphics-20 Non-uniform scaling: different scalars per component: How can we represent this in matrix form? Scaling X 2, Y 0.5
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Graphics-21 Scaling Scaling operation: Or, in matrix form: scaling matrix
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Graphics-22 2-D Rotation (x, y) (x’, y’) x’ = x cos( ) - y sin( ) y’ = x sin( ) + y cos( )
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Graphics-23 2-D Rotation This is easy to capture in matrix form: Even though sin( ) and cos( ) are nonlinear functions of , –x’ is a linear combination of x and y –y’ is a linear combination of x and y
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Graphics-24 2-D Translation (x, y) (x’, y’) x’ = x + tx y’ = y + ty tx ty
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