Welcome to COMP 770 (236) Introduction. Prerequisites. Prerequisites

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1 Welcome to COMP 770 (236) Introduction Computer Graphics COMP 770 (236) Spring 2007 Instructor: Brandon Lloyd Instructor: Brandon Lloyd Office: SN349 Office hours: MW 1:00 2:00 (or by appt.) Webpage: 1/10/07 1 1/10/07 2 Prerequisites COMP 665(235) Displays and 2D Graphics Pixels, lines, images Foundations of 3D Graphics Points, vectors, matrices, transformations Foundations of Image Analysis Sampling, reconstruction, aliasing Foundations of Vision Eye, color, perception Prerequisites Know a programming language in the C family (C / C++ / C# / Java / Python) Be familiar with event driven application programming 1/10/07 3 1/10/07 4

2 Overview Topics Modelling Simulation & Rendering Image Mathematical tools 3D models and interaction Hidden surface removal Rasterization Lighting and shading Shadows Texture mapping Ray tracing Global illumination Curves and surfaces Simplification and levels of detail Graphics hardware Image-based rendering Computer vision inverts the process 1/10/07 5 1/10/07 6 Mathematical tools 3D models and interaction homogeneous coordinates vectors planes frames transformations Loading and view models Picking and selection Modeling a trackball VR is all about interaction COMP 872 b v a v axis 1/10/07 7 1/10/07 8

3 Hidden surface removal Rasterization Classic problem BSP trees Ray casting Depth buffering Clipping Scan conversion Images courtesy of Cornell University 1/10/07 9 1/10/07 10 Lighting and shading Shadows Flat, gouraud, and phong shading Empirical and physicallybased illumination models BRDFs Shadow volumes Shadow maps Soft shadows Images courtesy of Stamminger and Drettakis 02 Umbra Penumbra 1/10/ /10/07 12

4 Texture mapping Surface parameterization Mipmaps and filtering Reflection and environment mapping Ray tracing Object intersection Reflection and refraction Depth-of-field, motion blur, glossy reflections, soft shadows Images courtesy of Jeremy Birn ( 1/10/ /10/07 14 Global illumination Rendering equation Path tracing, photon mapping, radiosity COMP 870 Advanced rendering Curves and surfaces Bezier curves and B-splines NURBS and subdivision surfaces Parametric solids COMP 767 Geometric and solid modeling Images courtesy of Caligari ( 1/10/ levels 1-level 2-levels 3-levels 4-levels 5-levels 1/10/07 16

5 Simplification and LOD Graphics hardware Levels of detail Progressive meshes History Architecture Shading languages Future 82 million triangles 1/10/ /10/07 18 Image based rendering Animation Lightfields and lumigraphs Reconstruction Keyframing Parameteric splines Motion capture Simulation COMP 768 1/10/ /10/07 20

6 Textbook Textbook No official textbook. Here are some possible references: No official textbook. Here are some possible references: 1/10/ /10/07 22 Textbook Assignments No official textbook. Here are some possible references: Viewing and manipulating 3D models with OpenGL Rasterization and clipping Texture mapping and lighting Raytracing Final Project 1/10/ /10/07 24

7 Grading Honor Code Assignments: 40% Final project: 30% 2 Tests: 30% Late policy: Assignments will lose 5% each day late (M-F) Graduate students are here for the learning not the grade. Collaboration encouraged, but assignments must be your own work. Cite any other s work if you use their code. 1/10/ /10/07 26 About your instructor My work - Shadows From Draper, Utah B.S. CS Brigham Young University, th year Ph.D. student at UNC 1/10/ /10/07 28

8 About you Your new world Name Where are you from (school, state)? What are you studying? Previous graphics experience A 2D square ranging from (-1, -1) to (1, 1) You can draw in the box with just a few lines of code 1/10/ /10/07 30 Code example Another code example OpenGL Code: glcolor3d(0.0, 0.8, 1.0) glbegin(gl_polygon) glvertex2d(-0.5, -0.5) glvertex2d( 0.5, -0.5) glvertex2d( 0.5, 0.5) glvertex2d(-0.5, 0.5) glend() glflush() OpenGL Code: glcolor3d(0.0, 0.8, 1.0) glbegin(gl_polygon) glvertex2d(-0.5, -0.5) glvertex2d( 0.5, -0.5) glvertex2d( 0.5, 0.5) glend() glflush() 1/10/ /10/07 32

9 Yet another code example Cool toys OpenGL Code: glcolor3d(0.8, 0.6, 0.8) glbegin(gl_line_loop) for ang in range(0, 360, 2): x = cos(ang*pi/180) y = sin(ang*pi/180) glvertex2d(x, y) glend() glflush() 1/10/ /10/07 34 Thinking mathematically Programming graphically router rinner roffset An outer circle with radius router An inner circle with radius rinner A hole for the pen at roffset The inner and outer circle rotate through the same arc lengths 1/10/ /10/07 36

10 And some code Next time... OpenGL Code: router = 1.0 rinner = 0.63 roffset = 0.59 revs = 100; theta = 0.0 glcolor3d(1.0, 0.0, 0.0) for i in range(int(360*revs)): glpushmatrix() glrotated(theta, 0, 0, 1.0) gltranslated(router-rinner, 0, 0) thetap = -theta*router/rinner glrotated(thetap,0,0,1) glbegin(gl_points) glvertex2d(roffset, 0) glend() glpopmatrix() theta += 1.0 GLUT Let s see some pixels! Screen space the final frontier 1/10/ /10/07 38

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