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1 CS171 Computer Graphics Time: 3pm-3:55pm MW(F) - Location: Annenberg Text: Mostly Self-Contained on course Web pages Instructor: - Al Barr TAs: - Kevin (Kevli) Li - - Nailen Matschke - Parker Won - Kevin Yuh - Andrew Zhao

2 Today s Topics Introduction, Definition of Computer Graphics Course Syllabus, Structure of Assignments Examples - Geometric Modeling - Physically-based Modeling - Rendering - Human-Computer Interaction

3 What is Computer Graphics? Using computers to construct models and turn them into images Images Models Computational and Mathematical Model Representations Computer(s)

4 Main Areas in Computer Graphics Modeling making mathematical representations of objects - e.g., Geometric models - Physical/Newtonian models, Collision models, etc. - Scientific simulation methods (molecular biology, weather, etc.) Rendering making images from these representations - Vector images (the oldest CG days, line drawings on paper, pen-plots, or in analog displays on a radar screen CRT) - Raster images (color images made out of PIXELS) - Stereo images, etc. (one image per eye, etc.) Interaction - human /computer, gestural, verbal, comunication methods from humans to computers and back, also human-to-human with computer intermediary, etc.

5 Computer Graphics Computer graphics: Modeling (representations of things) Rendering, (images of things) - Simulation, - Scientific visualization, and human/computer interaction. Uses mathematical principles, eg differential geometry, constrained optimization, integral equations; Physical principles, eg, mechanics of solids, physics of light. Emphasizes correct underlying mathematics and on careful realization in efficient, provably robust algorithms

6 Examples of Rendered Models Fur Texels for light ray probability distributions Dynamic constraints to hold chain links together and do physics

7 Tentative Course Topics Introduction and 3D Geometry. Rotation. 4x4 transforms, etc. Intro to Surface Representations (Polygonal, Parametric, Implicit) OpenGL and Event Programming Intro to Visibility, Rasterization Shading, Lighting calculations Ray Tracing Texture Mapping methods Anti-Aliasing, Linear Filtering Theory Quaternions, Dual Quaternions Intro. Animation, Inverse Kinematics GPU Digital filtering

8 Structure of Assignments Nine (or so) Assignments, generally due Wed 3pm - See web site, - click on Assignments (assignments and policies still being updated) Assignment 0: relatively straightforward mini-assignment - Setting up the OpenGL development environment, Getting familiar with using parsers and the C++ Matrix Library Eigen, Outputting images in the Portable Pixel Map (PPM) format Assignment 1: 3D Wireframe Renderer - Covers 4x4 Geometric Transformations (Translation, Rotation, and Scaling), World and Camera Coordinate Spaces, Perspective Projection and Normalized Device Coordinates (NDC), Line Rasterization using Bresenham's Line Drawing Algorithm

9 Assignment 2: 3D Shaded Surface Renderer, - builds on Assignment 1 to render 3D shaded surfaces based on file input. Covers Triangle Rasterization and Interpolation using Barycentric Coordinates, Surface Normals, Ambient, Diffuse, and Specular Reflections, Lighting Attenuation, Phong Reflection Model (also known as the standard Lighting Model), Depth Buffering, Backface Culling, Gouraud and Flat Shading Algorithms Assignment 3: Intro to OpenGL - You recreate the 3D shaded surface renderer program from Assignment 2 using OpenGL; add arcball mouse interface. - Covers OpenGL Syntax and Functionality, Arcball Mouse User Interface

10 Assignment 4: Animation (To be out) - Two animation programs: one using physics and one using keyframe interpolation. Covers Time Integrators, Symplecticity, part of Lagrangian Mechanics, The Discrete Lagrangian Integrator, Keyframes, Cubic Splines, Cardinal and Catmull-Rom Splines,Quaternions, Spherical Linear Interpolation (Slerp) Assignment 5: Meshing and Texturing (To be out) - Render bump mapped textured meshes. Covers Half-Edge Mesh Data Structure, Texture Mapping and Mipmapping, Surface Normal Computations for Meshes, Bump Mapping Assignment 6: Ray Tracing (To be out) - Geometric Optics, Shadowing, Reflection, Refraction, alg speedups.

11 Ray Tracing, HW 6,7 Pinhole Camera algorithm to trace computational light rays in reverse time shadows, reflections, refractions in one method Images by Al Barr, 1981, Ray Tracing Superquadrics

12 Ray Tracing, continued HW 7 Image (2014) by David Warrick

13 3D Geometry and Physics Need reliable ways to represent and run the model Geometry, movement and configuration of modeled items, cameras, etc. Everything that s needed for object color, texture, camera motion, etc. Physical interaction properties if objects are supposed to be physical like billiards Requires a powerful computational approach to scoped Language tools for time dependent shape representation, interaction, etc., also needs very robust mathematical methods. Many parts of computer graphics involve efforts using Parsers in line with the need for Languages

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15 Inspired by common foundation for Mechanical, Biological simulation A source of motivation, long term goal for some of the research: the creation of tools for simulation and behavioral prediction of mechanical and biophysical structures

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17 Implicit Fairing of Surface Meshes Mathieu Desbrun et al, Siggraph 99 Improved set of parameterization independent Curvature flow and Laplacian smoothing operators Original Previous New

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19 Original Smoothed

20 Interactive-speed Physical Simulations Real-time flexible sheets w/ collision and contact constraints implemented on Responsive Workbench Developing methods for combining sheets and real-time deformable volumes with real-time articulated rigid bodies, with body-body contact constraints. (See Billiards demo, also Flexible demo)

21 Real-time Flexible sheets Mathieu Desbrun et al, CGI 99, uses inverse Euler and angular momentum correction see demo on Responsive Workbench

22 Finding Global contact points Old New Old New

23 Level Set methods for Computer Graphics Representing surface shapes with implicit functions f(x) = 0 3D level-set morphing method that allows topology changes Research for using volumes as first-rate modeling primitives.

24 Long Term Goals for Physically Based Modeling Develop robust mathematical methods and a PBM language ; imitate success of 2D languages used for printing, but for 3D mechanics. Enable nonexpert people to reliably specify, design, control and build computational models of physical systems of rigid, flexible, and fluid objects. Make PBM and rapid simulation a key enabling technology for Virtual Engineering, Biological Simulation, Mechanical Simulation, Manufacturing New methods to create, modify, and represent increasingly complex and/or realistic models. Modeling research augments research in rendering, interaction, visualization and performance

25 Example: PBM Language enables Model Extraction Pipeline

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34 OpenGL OpenGL is a low-level graphics API (C/C++ library) -API= Application Program Interface: routines, protocols, and tools for building software applications. - A good API makes it easier to develop a program by providing all the needed building blocks. Window system independent, but Has no facility for window events/user input. Use other libraries for interaction (eg. GLUT) Vertex driven Geometric Primitives assembled from vertices ***OpenGL creates/runs a state machine***

35 OpenGL Overview Commands or display list per vertex operations & primitive assembly Rasterization per pixel operations Frame Buffer

36 Clearing the Buffers Clears the buffers using the specified values glclearcolor(glclampf red, GLclampf green, GLclampf blue, GLclampf alpha) glclear(glbitfield mask) Masks: GL_COLOR_BUFFER_BIT, GL_DEPTH_BUFFER_BIT, GL_ACCUM_BUFFER_BIT, GL_STENCIL_BUFFER_BIT

37 Drawing Primitives Begin/End drawing a primitive glbegin(glenum mode) glend() Modes: GL_POINTS, GL_LINES, GL_TRIANGLES, GL_TRIANGLE_STRIP, GL_QUADS, GL_POLYGON

38 Basic Mathematical Types Scalars: s (a real number) Column Vectors: Rep of 3D Points: Column Vectors: Rep of 3D Directions: x y z x y z

39 Math Types, continued Matrices (3x3 rotation, 4x4 transformation) We will be using Eigen see HW 0 to set up environment. Higher order Tensors - Tensors can be defined as the abstract geometric mathematical objects that are Linear - 0 th order tensors are scalars, 1 st order are vectors, 2 nd order are matrices, etc - 3-D tensors of order N are represented with 3 n components

40 Summary Covered intro to Computer Graphics - Modeling, Rendering and Interaction - Need reliable mathematics and algorithms to implement these Touched on several course topics Gave several examples

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