Computer Graphics (CMU 15-462/662)

This page contains lecture slides, videos, and recommended readings.

(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)

(basic math of spatial transformations and coordinate spaces)

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

Supplementary material:

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

(occlusion via the depth buffer, alpha composition, the graphics pipeline and modern GPUs)