Computer Graphics (CMU 15-462/662)

This page contains lecture slides and optional readings for the Fall 2018 offering of 15-462/662.

(Overview of graphics + making a line drawing of a cube!)

(Vectors, vector spaces, linear maps, inner product, norm, L2 inner product, span, basis, orthonormal basis, Gram-Schmidt, frequency decomposition, systems of linear equations, bilinear and quadratic forms, matrices)

(Euclidean inner product, cross product, matrix representations, determinant, triple product formulas, differential operators, directional derivative, gradient, differentiating matrices, differentiating functions, divergence, curl, Laplacian, Hessian, (multivariable) Taylor series)

(coverage testing as sampling a 2D signals, challenges of aliasing, performing point-in-triangle tests)

Further Reading:

- A Pixel is Not A Little Square, Alvy Ray Smith, 1995
- A Nice Video Illustration of Temporal Aliasing. by Valvano and Yerraballi
- The Fourier Transform and It's Applications (Ch. 5) by B. Osgood (this is an outstanding reference)
- Stanford CS348B's Notes on Sampling. by Pat Hanrahan (also see Chapter 7.1 in the Physically Based Rendering book)

(basic math of spatial transformations and coordinate spaces)

Further Reading:

- Real Time Rendering -- Chapter 4. by T. Akenine Moller, E. Haines, N. Hoffman
- 3D Rotations (exerpt from Ch. 15 of Advanced Animation and Rendering Techniques. by A. Watt, M. Watt)

(3D rotations, commutativity of rotations, 2D rotation matrix, Euler angles, rotation from axis/angle, complex numbers, quaternions, quaternion rotation)

(understanding perspective projection, texture mapping using the mip-map)

Further Reading:

- Pyramidal Parametrics. by L. Williams (the original mipmapping paper from 1983!)