1. 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.

2. Graphics-2 Outline Graphics Applications What is Computer Graphics Representations in Graphics Supporting Disciplines Introduction to 2d Modeling Transformations Matrix Representations Linear Transformations

3. Graphics-3 Graphics Applications Entertainment: Cinema Pixar: Monster’s Inc. A Bug’s Life (Pixar)

4. Graphics-4 Graphics Applications Medical Visualization MIT: Image-Guided Surgery Project The Visible Human Project

5. Graphics-5 Graphics Applications Everyday use

6. Graphics-6 Graphics Applications Scientific Visualization

7. Graphics-7 Graphics Applications Computer Aided Design (CAD)

8. Graphics-8 Graphics Applications Training Designing Effective Step-By-Step Assembly Instructions (Maneesh Agrawala et. al)

9. Graphics-9 Graphics Applications Games GT Racer 3 Polyphony Digital: Gran Turismo 3, A Spec

10. Graphics-10 Graphics Applications Games Circus Atari (Atari)

11. 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

12. Graphics-12 What is Computer Graphics? ImageMath. Model Image Analysis (pattern recognition) Image Synthesis (Rendering) ModelingImage processing

13. 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

14. 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,...

15. 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,...

16. Graphics-16 Supporting Disciplines Computer science (algorithms, data structures, software engineering, …) Mathematics (geometry, numerical, …) Physics (Optics, mechanics, …) Psychology (Colour, perception) Art and design

17. 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

18. Graphics-18 2D Modeling Transformations Scale Rotate Translate Scale Translate x y World Coordinates Modeling Coordinates

19. 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

20. Graphics-20 Non-uniform scaling: different scalars per component: How can we represent this in matrix form? Scaling X  2, Y  0.5

21. Graphics-21 Scaling Scaling operation: Or, in matrix form: scaling matrix

22. Graphics-22 2-D Rotation  (x, y) (x’, y’) x’ = x cos(  ) - y sin(  ) y’ = x sin(  ) + y cos(  )

23. 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

24. Graphics-24 2-D Translation (x, y) (x’, y’) x’ = x + tx y’ = y + ty tx ty