Computer Graphics

Introduction

Prof. Dr. Ulrich Schwanecke

RheinMain University of Applied Sciences

🚀 by Decker

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Acknowledgments

Many thanks to Mario Botsch!

images/botsch_mario_custom.png — Prof. Mario Botsch,
TU Dortmund

About Computer Graphics

Computer Graphics vs. Computer Vision

Computer Graphics & Geometry Processing

Computer Graphics & Geometry Processing

Representation of Objects

Objects can be represented mathematically in different forms
- Explict: $y=\pm\sqrt{r^2-x^2}$
- Implicit: $x^2+y^2-r^2=0$
- Parametric: $\left(r\cdot\cos(t), r \cdot\sin(t)\right)^\top, t\in [0,2\pi)$

Triangle Meshes

Triangle meshes can represent arbitrary surfaces

Triangle Meshes

Triangle meshes can represent arbitrary surfaces
Approximation error inversely proportional to #triangles

Triangle Meshes

Triangle meshes can represent arbitrary surfaces
Approximation error inversely proportional to #triangles
Adaptive tessellation can adapt to surface curvature

images/adaptive-sampling-1.png adaptive meshing images/adaptive-sampling-2.png curvature visualization

Triangle Meshes

Triangle meshes can represent arbitrary surfaces
Approximation error inversely proportional to #triangles
Adaptive tessellation can adapt to surface curvature
Simple primitives can efficiently be processed by CPU/GPU

Computer Graphics & Geometry Processing

Realistic Lighting Computations

images/spheres-0.png color only images/spheres-1.png +diffuse images/spheres-2.png +specular

images/spheres-3.png +shadows images/spheres-4.png +reflections

Realistic Lighting Computations

$shadows + reflection + refraction$ shadows + reflection + refraction images/cbox-1.png +soft shadows

images/cbox-2.png +caustics images/cbox-3.png +indirect lighting

Realistic Rendering for Movie Industry

images/gollum.png Lord of the Rings images/alita.jpg Alita Battle Angel

Realtime Rendering for Computer Games

images/farcry.png Far Cry images/tombraider.jpg Tomb Raider

Scientific Visualization

Visualization in Medical Imaging (Volume Rendering)

Computer Graphics & Geometry Processing

(Laser) Scanning

images/max-0.png Get a nice model… images/scanner.gif …buy a laser scanner images/max-1.png …perform some scans images/max-2.png …and reconstruct a virtual model!

Cultural Heritage

images/david.png David
1G sample points images/saint-matthew.png St. Matthew
4G sample points

Automotive Industry

images/bmw-0.png Real model images/bmw-1.png Scanner point cloud images/bmw-2.png Reconstructed surface
images/bmw-3.png Flow simulation

Avatar Generation

Computer Graphics & Geometry Processing

Motion Capturing & Character Animation

Real-Time Motion Capturing

Face Animation

Facial Animation by Linear Delta-Blendshapes

Facial expressions by blending example poses \[ \vec{x}_i \;=\; \vec{x}_i^{(0)} + \sum_{k=1}^n w_k \left( \vec{x}_i^{(k)} - \vec{x}_i^{(0)} \right) \]
- Examples (blendshapes) have identical triangulation
- Linear interpolation per vertex $\vec{x}_i$
- Weights $w_k$ typically are in $[0,1]$.
  (see what happens at 200% on Youtube)

Face Scanner at HSRM

images/Scanner/Scanner1_crop.png images/Scanner/Scanner3_crop.png images/Scanner/Scanner4_crop.png

16 synchronized 12MP, 30fps cameras

Expressions

Face Animation

Cloth Simulation

Collisions

Elastic Deformations

Plasticity & Fracture

Cutting Simulation

About this course

Course Goal and Content

Goal
- Gain an understanding of the theoretical and practical concepts of computer graphics
After attending the course, you should be able to
- understand the basic principles of image generation using local and global illumination
- implement a rendering system based on real-time OpenGL or offline ray-tracing
- know the pros/cons of the main geometry representations for 3D models or scenes

(Planned) Content (12 Lectures)
1. Introduction, Organization
2. Primitives, Transformations
3. Raytracing
4. Colors
5. Lighting
6. Rendering Equation
7. Meshes
8. 3D Transformations
9. Projections
10. Rasterization
11. OpenGL
12. Textures and Shadows

Organization

SWS 2V + 2Ü, 6 ECTS, Total Workload: 180h
Lecture
- Thursday D14, 10:00-11:30
Exercise Sessions
- Thursday D12, Group B: 11:45-13:15, Group A: 14:15-15:45
- Friday D12, Group C: 14:15-15:45
- Exercises are mandatory
- Three evaluated assignments
Exam
- Content: lectures and exercises
- Very likely written (date and time will be announced)

Course Materials

Books (Graphics in General, Global Illumination and a little bit about Matrices)
- A. Watt, 3D Computer Graphics, Addison-Wesley Longman, 1999
- J. D. Foley, A. van Dam, S. K. Feiner, Computer Graphics: Principles and Practice, Addison Wesley, 2012
- T. Akenine-Möller, E. Haines, N. Hoffman, Real-time Rendering, A K Peters/CRC Press, 2018
  http://www.realtimerendering.com/
- A. S. Glassner, An Introduction to Ray Tracing, Academic Press, 1989. http://www.realtimerendering.com/raytracing/An-Introduction-to-Ray-Tracing-The-Morgan-Kaufmann-Series-in-Computer-Graphics-.pdf
- M. Pharr, W. Jakob, g. Humphreys, Physically Based Rendering, 2016.
  http://www.pbr-book.org/

Course Materials

Books (OpenGL)
- J. Kessenich, G. Sellers, D. Shreiner, OpenGL Programming Guide, 9th edition, Addison-Wesley, 2016
  http://www.opengl-redbook.com
- R. J. Rost, OpenGL Shading Language, 3rd edition, Addison-Wesley, 2009
- R. S. Wright, N. Haemel, G. Sellers, B. Lipchak, OpenGL SuperBible: Comprehensive Tutorial and Reference, Addison Wesley, 2015
- E. Angel, D. Shreiner, Interactive Computer Graphics with WebGL, Addison Wesley, 2015
Books (Curves and Surfaces)
- G. Farin, Curves and Surfaces for CAGD: A Practical Guide, 5th edition, Morgan Kaufmann, 2002
Books (Matrices)
- K. B. Petersen, M. S. Pedersen, The Matrix Cookbook
  http://www.cs.toronto.edu/~bonner/courses/2012s/csc338/matrix_cookbook.pdf

Course Materials

Tutorials
- The Python Tutorial: https://docs.python.org/3/tutorial
- Numpy Quickstart: https://numpy.org/devdocs/user/quickstart.html
Frameworks, IDEs
- Visual Studio Code: https://code.visualstudio.com/

Prerequisites

Basic math skills
- Linear Algebra
  - Vectors: $\mathbf{x}, \mathbf{y} \in \mathbb{R}^n$
  - Matrices: $\mathbf{A}, \mathbf{B} \in \mathbb{R}^{m\times n}$
  - Operations:
    - $\mathbf{x}^\top\mathbf{y}, \mathbf{x}\times\mathbf{y}$, $\mathbf{A}\mathbf{x}$
    - $\mathbf{A}^\top, \mathbf{A}^{-1}, \text{trace}(\mathbf{A}), \text{det}(\mathbf{A}), \mathbf{A}+\mathbf{B}, \mathbf{AB}$
  - Norms: $||\mathbf{x}||_1, ||\mathbf{x}||_2, ||\mathbf{x}||_\infty, ||\mathbf{A}||_F$
  - Eigenvalues, Eigenvectors, SVD: $\mathbf{A}=\mathbf{UDV}^\top$
- Calculus
  - (Multivariate) functions: $f:\mathbb{R}^{n}\rightarrow \mathbb{R}$
  - (Partial) derivatives: $\frac{\partial f}{\partial x_i}, i=1,\ldots, n$, Gradient
  - Integrals: $\int f(x)dx$

Basis computer science skills
- Variables
- Functions
- Loops
- Classes
- Algorithms
Basic Python coding skills
- https://docs.python.org/3/turorial/

Time Management

Activity	Times	Total
Attending (watching) the lecture	2h / week	24h
Self-study of lecture materials	2h / week	24h
Participation in exercise	2h / week	24h
Solving the assignments	6h / week	72h
Preparation for the final exam	36h	36h
Total workload		180h