The study of fundamental mathematical, algorithmic and representational issues in computer graphics. The topics include an overview of graphics pipeline, projective geometry, homogeneous coordinates, projective transformations, quadrics and tensors, line-drawing, surface modeling and object modeling, reflectance models and rendering, texture mapping, polyhedral representations, colour perception, and other selected topics according to available time (see the tentative schedule below).

There will be four assignments during the term, totaling 50% of the course mark. Assignmetns will be equal weight but not equal effort, and may have opportunities for bonus marks. Assignmetns will be in C++ and use OpenGL (4.1 core profile to make it likely that those with Mac to use their own machines). Links to assignments will be posted to MyCourses during the term. Instructions for assignment setup are on github and can be discussed on MyCourses.

Late assignments will be graded with a 10% penalty and will be accepted up to 3 days from the original due date (i.e., if you are not going to make the deadline, get some sleep and find the time to finish your submission properly with only a 10% penalty for all 3 days). Given that we are still undergoing an unpredictable transition from emergency online teaching to a normal classroom, the lowest mark of the four assignmetns will dropped as additional accomodations. The idea is that students can handle any unforseen circumstance that arises in the term with the combination of a minmal late penalty and the possibility of dropping one assignemnt mark. All students are strongly advised to complete all assignments as doing the work will be the best way to learn the material necessary for the exams. Assignment solutions will not be provided, but important parts of the assignemtn solutions may be discussed in class.

There will be two exams, worth a total of 50% of the final grade. The first will be a midterm exam which will take place in mid to late October. It is worth 20% of your grade. There will be a makeup midterm for anyone who misses the midterm. The second exam will take place during the Final Exam Period and is worth 30% of the final grade. Practice problems, old midterms and final exams, and in some cases solutions will be posted to MyCourses during the term.

There is no required text for the course, but the following course textbooks is recommended and is available online for free in the McGill library.

• Fundamentals of Computer Graphics , 3rd or 4th Edition, Shirley and Marschner

Throughout the term I will also make references to material within another excellent text. You may consider consulting this book too.

• Computer Graphics Principles and Practice, 3rd Edition, Hughes et al.

I refer to these books with abbreviations FCG and CGPP. Th CGPP book is a recent update of a classic textbook, and is possibly the most complete reference available (covering many additional topics that we will not have time for in the course). That said, I will also provide other reference material on other topics in class.

The other very useful reference for working on OpenGL assignments is the OpenGL programming guide.

• OpenGL Programming Guide: The official guide to learning OpenGL (4.0 or higher), find an appropriate version in the McGill library or search online

Note that we will be using OpenGL 4.1 core profile in this course.

There are also many alternative and online resources that you may find helpful for much of the material, including these listed below.

• The Graphics Codex (mostly focuses on rendering, but has an important overlap with many fundamentla topics, and shows how material across several popular texts is related)

Additional resources will be provided in MyCourses throughout the term.

Graduate students interested in this course, who have not already taken a graphics course, will likely have taken courses equivalent to the prerequisites listed below. For undergraduate students, there are three official prerequisites for the course:

• COMP 206 Introduction to Software Systems -- we build on familiarity with c and the unix make utility as we are using cmake and c++ and various libraries for programming assignmetns in this course. Debugging and testing of code is likewise an important part of the course.
• MATH 222 Calculus 3 -- Graphics involves parametric representations, partial derivatives and integrals and some vector calculus. This prerequisite will ensure you are prepared, and it or its equivalent is required for all CS Majors.
• MATH 223 Linear Algebra -- This course will build upon your basic understanding of vectors and matrices. You should have at least a B grade in your linear algebra course, or be prepared for a serious review.
• COMP 250 Introduction to Computer Science -- This prerequisite is to ensure that students have a sufficiently high level of computer science and mathematical maturity.

The following list is a tentative schedule of topics. MyCourses course content will have the official list of topics as the term progresses. That is, adjustments will be made to synchronize with assignments and to better match material in the textbook and other sources. Topics will be added and removed depending on interest and time permitting.

Introduction Sets as Geometry 2D Transformations Vector spaces Affine spaces Homogeneous coordinates Rotation Transformations Hierarchies Viewing transformation Perspective projection Projection taxonomy Normalized device coordinates Mesh terminology Euler characteristic Half edge data structure introduction Half Edge data structure examples Level of Detail introduction Edge collapse and vertex split Point plane distance Quadric error metric introduction Mesh simplification Quadric error metric Subdivision curves Corner cutting Limit point analysis Subdivision surface introduction Curves introduction Bezier, Interpolation, and Hermite curves Bezier properties Change of basis Tensor product patches Decaslejau algorithm Rational curves B-spline introduction and intuition Surfaces of revolution, Swept surfaces, Frenet frame, Parallel transport Clipping Pipeline rasterization and operations Painter's and Warnock algorithm Binary space partitions Depth Buffer Midterm Exam (in class) Ray tracing Ray transformation Shadow rays Ray triangle intersection Ray quadric intersection Barycentric coordinates Barycentric interpolation Bilinear interpolation Quadric transformations Quadric normals Constructive solid geometry Illumination (ambient, diffuse, specular, attenuation) Light and reflectance models (Lambertian, Blinn-Phong) Shading models (Phong, Gouraud) Texture mapping Magnification and Minification Mip maps Bilinear interpolation Shadow maps Stencil shadow volumes The rendering equation Radiosity Compositing Transparency Blending Colour Colour matching experiment CIE XYZ Chromaticity diagram Colour conversion between different displays Colour purity and saturation Complementary colours Just noticable differences Gamuts and gamma Review for final