Dynamics and Time Integration

Triangles

Spatial Transformations

Sampling

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

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

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!

Dynamics and Time Integration

2 courses cover this concept

15-462/662 Computer Graphics

15-462/662 Computer Graphics