Optimization in Graphics

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

Dynamics and Time Integration

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!

Monte Carlo Integration

Uniform Hemisphere Sampling

Bidirectional reflectance distribution function (BRDF)

Refraction

Tone Mapping

Advanced Materials

Polygon mesh

Subdivision surface

Remeshing

Geometry Representations

Continuum Mechanics

ARAP (As-Rigid-As-Possible surface modeling)

Path tracing

Russian Roulette

Ideal Specular Reflection

Direct Lighting

Advanced Sampling

Light Transport Algorithms

Mesh Simplification

Image Filtering

Physically based animation (simulation)

Finite Element Method (FEM)

Linear Solvers

CSCI 2240: Advanced Computer Graphics Brown University Spring 2023 CSCI 2240 is a comprehensive exploration of 3D graphics, diving into rendering, geometry processing, simulation, and optimization. Expect a mathematically intensive approach to topics such as light transport physics, 3D triangle mesh algorithms, and 3D shape optimization. Culminating in an open-ended project, students will be equipped to undertake graphics research and delve into recent research papers.  CSCI 2240 is an advanced computer graphics course. It assumes prior experience with the fundamentals of computer graphics, typically by having completed an introductory computer graphics course. The course explores several key areas of 3D graphics---rendering, geometry processing, simulation, and optimization---taking a mathematically-sophisticated approach to each. We will study computational approximations to the physics of light transport and the motion of deformable objects, algorithms for processing 3D triangle meshes, and optimization-based techniques for manipulating 3D shapes. The course culminates with an open-ended, group final project in which students choose a recent research paper of interest and implement the techniques it describes.

[Past Projects](https://cs2240.graphics/past_projects.html) Students who complete this course will:

- Understand the physics of light transport and be able to implement approximate solutions to the rendering equation.
- Understand the strengths and weakness of different geometry representations and be able to build efficient algorithms for processing and manipulating meshes.
- Know how to pose graphics problems as quadratic optimization problems and solve the resulting sparse linear systems.
- Understand the continuum mechanics governing the motion of solid objects and be able to simulate them through finite element approximations.
- Build depth of knowledge in one area of computer graphics by completing an open-ended final project.
- Be able to read technical papers in the graphics literature and implement the algorithms they describe.

More holistically: completing this course will take you from "I know the fundamentals of computer graphics" to "I can read and implement graphics research papers and contribute to new graphics research." Students who complete this course will be well-prepared to begin an academic research career in computer graphics or to join an industrial research and development lab.

Accordingly, this course is challenging. On your journey to becoming an independent graphics researcher/practitioner, expect to be pushed out of your comfort zone. It is totally normal to struggle with some assignments in this course (to which the TAs can attest). If you feel stuck, remember: we're here for you! Take advantage of office hours and ask for help from your fellow students on Slack.  The following skills will be necessary for this course:

- **Computer Graphics:** This course assumes familiarity with the fundamentals of computer graphics, such as 3D transformations, viewing and projection, basic illumination models, raytracing, and OpenGL. Brown's introductory computer graphics course, [CSCI 1230](https://cs.brown.edu/courses/info/csci1230), is a prerequisite for this course. Similar courses from other institutions may also be acceptable.
- **Software Engineering:** The assignments in this course, and particularly the final project, require you to design, develop, and debug large pieces of software. The project work required for CSCI 1230 should be sufficient preparation. If you took an introductory graphics course elsewhere that did not emphasize large software projects, you should have experience with building such projects from other courses.
- **Math:** The techniques we will explore in this course are based on physics concepts, involve geometric calculations in three-space, and/or require solving large systems of equations. Familiarity with linear algebra and vector calculus are important for successfully understanding and applying these techniques.
 
 If you are not sure whether you can/should take the course, we encourage you to show up to the first class and talk to the instructor.  There is no required textbook this semester. Readings relevant to each course assignment will be posted on this website. Optionally, you might consider purchasing [The Graphics Codex](http://graphicscodex.com/), which costs only $10 and provides reference materials which can be useful for the first part of the course (on rendering).

CSCI 2240: Advanced Computer Graphics

Optimization in Graphics

3 courses cover this concept

15-462/662 Computer Graphics

15-462/662 Computer Graphics

CSCI 2240: Advanced Computer Graphics