Sampling

Triangles

Spatial Transformations

3D Rotations

Complex Transformations

Perspective Projection

Texture Mapping

Occlusion

Geometry

Meshes and Manifolds

Digital Geometry Processing

Geometric Queries

Spatial Data Structures

Color

Radiometry

Rendering Equation

Numerical Integration

Monte Carlo Rendering

Variance Reduction

Animation

Dynamics and Time Integration

Optimization in Graphics

Physically-Based Animation

Partial Differential Equations (PDEs)

15-462/662 Computer Graphics Carnegie Mellon University Fall 2020 This is an intensive course on computer graphics, covering a variety of topics such as rendering, animation, and imaging. It requires previous knowledge in vector calculus, linear algebra, and C/C++ programming. Concepts include ray tracing, radiometry, and geometric optics, among others. This course provides a comprehensive introduction to computer graphics. It focuses on fundamental concepts and techniques, and their cross-cutting relationship to multiple problem domains in graphics (rendering, animation, geometry, imaging). Topics include: sampling, aliasing, interpolation, rasterization, geometric transformations, parameterization, visibility, compositing, filtering, convolution, curves & surfaces, geometric data structures, subdivision, meshing, spatial hierarchies, ray tracing, radiometry, reflectance, light fields, geometric optics, Monte Carlo rendering, importance sampling, camera models, high-performance ray tracing, differential equations, time integration, numerical differentiation, physically-based animation, optimization, numerical linear algebra, inverse kinematics, Fourier methods, data fitting, example-based synthesis.  Course prerequisites are (15-213, 21-259, and 21-240) or (15-213, 21-259, and 21-241) or (18-213 and 18-202). Basic vector calculus and linear algebra will be an important component of this course. Previous exposure to basic programming in C/C++ or similar languages is very helpful as course programming assignments will involve significant implementation effort. There is no required textbook for 15-462, though a variety of books may provide good supplementary material:

Pete Shirley and Steve Marschner with Michael Ashikhmin, Michael Gleicher, Naty Hoffman, Garrett Johnson, Tamara Munzner, Erik Reinhard, Kelvin Sung, William B. Thompson, Peter Willemsen, and Bryan Wyvill
**Fundamentals of Computer Graphics**. A K Peters, 2009
[[ On Amazon ]](http://www.amazon.com/Fundamentals-Computer-Graphics-Peter-Shirley/dp/1568814690)

John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley
**Computer Graphics: Principles and Practice**
[[ On Amazon ]](http://www.amazon.com/Computer-Graphics-Principles-Practice-3rd/dp/0321399528/ref=sr_1_2?s=books&ie=UTF8&qid=1440872554&sr=1-2&keywords=foundations+of+3d+computer+graphics)

Matt Pharr and Greg Humphreys
**Physically Based Rendering: From Theory to Implementation**
[[ On Amazon ]](http://www.amazon.com/gp/product/0123750792?ie=UTF8&tag=pharr-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0123750792)

This book (PBRT) is the book for learning about modern ray tracing techniques. It has a [great website](http://www.pbrt.org/) with full source code online for an advanced physically-based ray tracer. It even won an [oscar](https://www.youtube.com/watch?v=7d9juPsv1QU) for its impact on the film industry!

15-462/662 Computer Graphics

Computer Graphics

Histograms

Pivots

Models

P-Value

Confidence Intervals

Sample Means

Least Squares

Privacy

Bayes' theorem

Data type

Iteration 

Census

Function (computer programming)

Joins

Chance

Comparing Distributions

A/B Testing

Center and Spread

Correlation

Residuals

Classification

Conditional probability

Tables

Charts

Groups

Conditional (computer programming)

Decisions

Causality

Normal distribution

Linear regression

Regression Inference

Classifiers

Data 8: The Foundations of Data Science UC Berkeley Fall 2022 UC Berkeley's course blends inferential thinking, computational thinking, and real-world relevance, offering students hands-on analysis of real-world datasets. It covers critical concepts in computer programming, statistical inference, privacy, and study design. Foundations of Data Science combines three perspectives: inferential thinking, computational thinking, and real-world relevance. Given data arising from some real-world phenomenon, how does one analyze that data so as to understand that phenomenon? The course teaches critical concepts and skills in computer programming and statistical inference, in conjunction with hands-on analysis of real-world datasets, including economic data, document collections, geographical data, and social networks. It also delves into social issues surrounding data analysis such as privacy and study design.  This course does not have any prerequisites beyond high-school algebra. The curriculum and format is designed specifically for students who have not previously taken statistics or computer science courses. Students with some prior experience in either statistics or computing are welcome to enroll and will find much of interest due to the innovative nature of the course. Students who have taken several statistics or computer science courses should instead take a more advanced course. Our primary text is an online book called [Computational and Inferential Thinking: The Foundations of Data Science](http://inferentialthinking.com/). This text was written for the course by the course instructors. A complete PDF of the textbook can be found in the Student Materials Google Drive.

The computing platform for the course is hosted at [data8.datahub.berkeley.edu](file:///Users/jweichert/Desktop/Data%208/data-8.github.io/fa22/data8.datahub.berkeley.edu). Students find it convenient to use their own computer for the course. If you do not have adequate access to a personal computer, we can help you borrow a machine; please contact data8@berkeley.edu.

Data 8: The Foundations of Data Science

Data Science

Ray Tracing

Recursive Ray Tracing

Optics

Shading

Global Illumination

Advanced Rendering

Photon Mapping

Geometric Modeling

CS 148 Introduction to Computer Graphics and Imaging Stanford University Fall 2022 This course is an introductory one in computer graphics, focusing on synthetic computer-generated images creation. It starts with basic concepts and moves to more complex subjects like BRDF and ray tracing technology. A final project involves building a ray tracer.  This is the introductory prerequisite course in the computer graphics sequence which introduces students to the technical concepts behind creating synthetic computer generated images. The beginning of the course focuses on using Blender to create visual imagery, as well as an understanding of the underlying mathematical concepts including triangles, normals, interpolation, texture mapping, bump mapping, etc. Then we move on to a more fundamental understanding of light and color, as well as how it impacts computer displays and printers. From this we discuss more thoroughly how light interacts with the environment, and we construct engineering models such as the BRDF and discuss various simplifications into more basic lighting and shading models. Finally, we discuss ray tracing technology for creating virtual images, while drawing parallels between ray tracers and real world cameras in order to illustrate various concepts. Anti-aliasing and acceleration structures are also discussed. The final class project consists of building out a ray tracer to create a visually compelling image. Starter codes and code bits will be provided here and there to aid in development, but this class focuses on what you can do with the code as opposed to what the code itself looks like. Therefore grading is weighted towards in person "demos" of the code in action - creativity and the production of impressive visual imagery are highly encouraged. Prerequisites: CS 107, MATH 51.

This is the first course in the computer graphics sequence at Stanford. The second course is CS248 and requires this course, CS 148, as a prerequisite. Topics include: Scanline Rendering; Triangles; Rasterization; Transformations; Shading; Triangle Meshes; Subdivision; Marching Cubes; Textures; Light; Color; Cameras; Displays; Tone Mapping; BRDF; Lighting Equation; Global Illumination; Radiosity; Ray Tracing; Acceleration Structures; Sampling; Antialiasing; Reflection; Transmission; Depth of Field; Motion Blur; Monte Carlo; Bidirectional Ray Tracing; Light Maps.  - CS 107, MATH 51
- Must be fluent in Python.
- We will assume knowledge of the following mathematical topics
    - Vectors, vector operations, and vector spaces
    - Matrices
    - Basic linear algebra, such as solving a system of linear equations 

CS 148 Introduction to Computer Graphics and Imaging

Digital Drawing

Aliasing

Antialiasing

Transforms

Rasterization Pipeline

Bezier Curves

Splines

Mesh Representations & Geometry Processing

Radiometry & Photometry

Monte Carlo Integration

Material Modeling

Camera & Lenses

Animation / Kinematics

Color Science

Image Sensors

Digital Image Processing

Light Fields

Virtual Reality

Neural Radiance Fields

CS 184/284a: Computer Graphics and Imaging UC Berkeley Spring 2022 This course provides a broad introduction to computer graphics, covering modeling, rendering, animation, and imaging. It emphasizes the mathematical and geometric aspects of graphics and requires a data structures course and programming ability. Covered concepts range from 2D and 3D transformations to image processing. This course provides a broad introduction to the fundamentals of computer graphics. The main areas covered are modeling, rendering, animation and imaging. Topics include 2D and 3D transformations, drawing to raster displays, sampling, texturing, antialiasing, geometric modeling, ray tracing and global illumination, animation, cameras, image processing and computational imaging. There will be an emphasis on mathematical and geometric aspects of graphics, and the ability to write complete 3D graphics programs.  A data structures course (e.g. CS 61B), C/C++ programming ability, fluency with development environment and debugging programs, knowledge of vectors, matrices basic linear algebra, calculus and trigonometry. Helpful: exposure to statistics, signal processing, and the Fourier transform. The primary source for the course will be the website, lectures, and section. Suggested supplementary reading and resources will be posted on the course readings page. The following textbooks are recommended, but optional, resources for you in this course and beyond:

### *Physically Based Rendering: From Theory to Implementation (Third Edition):*

Authors: Matt Pharr and Greg Humphreys

- This book (PBRT) is the book for learning about modern ray tracing techniques. It has a [great website](http://www.pbrt.org/) with full source code online for an advanced physically-based ray tracer. It even won an [Oscar](https://www.youtube.com/watch?v=7d9juPsv1QU) for its impact on the film industry!
- PBRT is available free online for you through Berkeley login: ([Second edition](http://www.sciencedirect.com/science/book/9780123750792), [Third edition](http://www.sciencedirect.com/science/book/9780128006450))
- Also available on [Amazon](https://smile.amazon.com/gp/product/0128006455/)

### *Fundamentals of Computer Graphics*

Authors: Pete Shirley and Steve Marschner with Michael Ashikhmin, Michael Gleicher, Naty Hoffman, Garrett Johnson, Tamara Munzner, Erik Reinhard, Kelvin Sung, William B. Thompson, Peter Willemsen, and Bryan Wyvill

- Available on [Amazon](http://www.amazon.com/Fundamentals-Computer-Graphics-Peter-Shirley/dp/1568814690)

### *Computer Graphics: Principles and Practice*

Authors: John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley

- Available on [Amazon](http://www.amazon.com/Computer-Graphics-Principles-Practice-3rd/dp/0321399528/ref=sr_1_2?s=books&ie=UTF8&qid=1440872554&sr=1-2&keywords=foundations+of+3d+computer+graphics)

CS 184/284a: Computer Graphics and Imaging

Bayesian network

Message Passing

Parameter Learning

Variational Inference

Undirected Models

Bayesian Learning

Probability theory

Exact Inference

Structured prediction

Exponential family

Learning Bayes Nets

MAP Inference

Structure Learning

CS 228 - Probabilistic Graphical Models Stanford University Winter 2023 An in-depth study of probabilistic graphical models, combining graph and probability theory. Equips students with the skills to design, implement, and apply these models to solve real-world problems. Discusses Bayesian networks, exact and approximate inference methods, etc. Probabilistic graphical models are a powerful framework for representing complex domains using probability distributions, with numerous applications in machine learning, computer vision, natural language processing and computational biology. Graphical models bring together graph theory and probability theory, and provide a flexible framework for modeling large collections of random variables with complex interactions. This course will provide a comprehensive survey of the topic, introducing the key formalisms and main techniques used to construct them, make predictions, and support decision-making under uncertainty.

The aim of this course is to develop the knowledge and skills necessary to design, implement and apply these models to solve real problems. The course will cover: (1) Bayesian networks, undirected graphical models and their temporal extensions; (2) exact and approximate inference methods; (3) estimation of the parameters and the structure of graphical models.  Students are expected to have background in basic probability theory, statistics, programming, algorithm design and analysis. If you are able to comfortably able to complete homework 1 then you likely have all the relevant background knowledge. ## Recommended Readings

**Corresponding Textbook**: (“PGM”) *Probabilistic Graphical Models: Principles and Techniques* by Daphne Koller and Nir Friedman. MIT Press.

**Course Notes**: Available [here](https://ermongroup.github.io/cs228-notes/). Student contributions welcome!

**Lecture Videos**: [here](https://canvas.stanford.edu/courses/166637/external_tools/3367)

**Further Readings**:

- (“GEV”) *Graphical models, exponential families, and variational inference* by Martin J. Wainwright and Michael I. Jordan. Available [online](https://www.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf).
- *Modeling and Reasoning with Bayesian Networks* by Adnan Darwiche. Available [online](http://ebookcentral.proquest.com/lib/stanford-ebooks/detail.action?docID=424583) (through Stanford).
- *Pattern Recognition and Machine Learning* by Chris Bishop. Available [online](https://www.microsoft.com/en-us/research/people/cmbishop/#!prml-book).
- *Machine Learning: A Probabilistic Perspective* by Kevin P. Murphy. Available [online](http://ebookcentral.proquest.com/lib/stanford-ebooks/detail.action?docID=3339490) (through Stanford).
- *Information Theory, Inference, and Learning Algorithms* by David J. C. Mackay. Available [online](http://www.inference.org.uk/mackay/itila/book.html).
- *Bayesian Reasoning and Machine Learning* by David Barber. Available [online](http://www.cs.ucl.ac.uk/staff/d.barber/brml/).

CS 228 - Probabilistic Graphical Models

Machine Learning

Big-O notation

Integer multiplication

Master theorem

Median finding

Coefficient/value representation

Roots of unity

Topological sorting

Paths in graphs

Greedy Algorithm

Kruskal's Algorithm

Linear Programming

Simplex Algorithm

Bipartite Matching

Zero Sum Games

Search problem

Reductions

Streaming

Fast Fourier transform

Arithmetic

Recurrence relation

Matrix Multiplication

Polynomial multiplication

Complex numbers

Fourier Transform

Depth-first search (DFS)

Strongly connected components

Single Source Shortest Paths

Dynamic programming

Algorithms to Linear Programming

Duality

Multiplicative Updates

NP-completeness

Sketching

Minimum Spanning Tree (MST)

Network flow problem

CS 170: Efficient Algorithms and Intractable Problems UC Berkeley Spring 2020 This is an introductory course to computer science theory, exploring the design and analysis of various algorithms, number theory, and complexity. The prerequisites include familiarity with mathematical induction, big-O notation, basic data structures, and programming in a standard language. CS 170 is Berkeley’s introduction to the theory of computer science. In CS 170, we will study the design and analysis of graph algorithms, greedy algorithms, dynamic programming, linear programming, fast matrix multiplication, Fourier transforms, number theory, complexity, and NP-completeness.  The prerequisites for CS 170 are CS 61B and CS70. You will need to be comfortable with mathematical induction, big-O notation, basic data structures, and programming in a standard imperative language (e.g., Java/C/Python). Another “prerequisite” for doing well in the course is [mathematical maturity](https://en.wikipedia.org/wiki/Mathematical_maturity), or the ability to think about and work with proof-based math (which CS70 can help build). The required textbook is [Algorithms](http://cseweb.ucsd.edu/~dasgupta/book/index.html) by Dasgupta, Papadimitriou, and Vazirani, also known as DPV. Most readings will be from the textbook, and the relevant textbook chapters will be linked for each lecture. Any readings not from the textbook will be freely available as notes.

CS 170: Efficient Algorithms and Intractable Problems

Data Structures and Algorithms

Theoretical Computer Science

Complex Representations

Depth

Transparency

Geometry Processing

Monte Carlo Ray Tracing

Pathtracer

15-462/662 Computer Graphics Carnegie Mellon University Spring 2022 Similar to Course ID 29, this course provides a comprehensive introduction to computer graphics. It also demands a strong mathematical and programming background. The topics covered include rasterization, geometric transformations, and Monte Carlo ray tracing.  This course provides a comprehensive introduction to computer graphics. It focuses on fundamental concepts and techniques, and their cross-cutting relationship to multiple problem domains in graphics (rendering, animation, geometry, imaging). Topics include: sampling, aliasing, interpolation, rasterization, geometric transformations, parameterization, visibility, compositing, filtering, convolution, curves & surfaces, geometric data structures, subdivision, meshing, spatial hierarchies, ray tracing, radiometry, reflectance, light fields, geometric optics, Monte Carlo rendering, importance sampling, camera models, high-performance ray tracing, differential equations, time integration, numerical differentiation, physically-based animation, optimization, numerical linear algebra, inverse kinematics, Fourier methods, data fitting, example-based synthesis  Course prerequisites are (15-213, 21-259, and 21-240) or (15-213, 21-259, and 21-241) or (18-213 and 18-202). Basic vector calculus and linear algebra will be an important component of this course. Previous exposure to basic C/C++ programming is very helpful as course programming assignments will involve significant implementation effort. There is no required textbook for 15-462, though a variety of books may provide good supplementary material:

Steve Marschner and Pete Shirley
Fundamentals of Computer Graphics. A K Peters, 2021
[ On Amazon ](https://www.amazon.com/Fundamentals-Computer-Graphics-Steve-Marschner-dp-0367505037/dp/0367505037/ref=dp_ob_title_bk)

John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley
Computer Graphics: Principles and Practice
[ On Amazon ](http://www.amazon.com/Computer-Graphics-Principles-Practice-3rd/dp/0321399528/ref=sr_1_2?s=books&ie=UTF8&qid=1440872554&sr=1-2&keywords=foundations+of+3d+computer+graphics)

Matt Pharr and Greg Humphreys
Physically Based Rendering: From Theory to Implementation
[ On Amazon ](https://www.amazon.com/Physically-Based-Rendering-Theory-Implementation/dp/0128006455/ref=dp_ob_title_bk)

This book (PBRT) is the book for learning about modern ray tracing techniques. It has a [great website](http://www.pbrt.org/) with full source code online for an advanced physically-based ray tracer. The [textbook](http://www.pbr-book.org/) is online as well. It even won an [oscar](https://www.youtube.com/watch?v=7d9juPsv1QU) for its impact on the film industry!

Sampling (statistics)

Sampling

7 courses cover this concept

15-462/662 Computer Graphics

Data 8: The Foundations of Data Science

CS 148 Introduction to Computer Graphics and Imaging

CS 184/284a: Computer Graphics and Imaging

CS 228 - Probabilistic Graphical Models

CS 170: Efficient Algorithms and Intractable Problems

15-462/662 Computer Graphics