(Simple drawing of lines and triangles (in 2D or 3D), drawing via point sampling, point-in-triangle testing, how different representations are preferable for different tasks involving these primitives. How rasterization and ray tracing algorithms are two ways to perform the same task.)

(Point sampling, interpolation, aliasing/anti-aliasing, upsampling/downsampling, Fourier interpretation of aliasing, a bit on neural anti-aliasing)

(Definition of linear transforms, basic geometric transforms, homogeneous coordinates, transform hierarchies, perspective projection)

(Properties of surfaces (manifold, normal, curvature), implicit vs. explicit representations, representations such as triangle meshes, voxel grids, signed-distance fields, 3D Gaussian splats, neural representations like NeuralSDFs, converting between representations)

(How acceleration structures such as bounding volume hierarchies (BVHs), K-D trees, uniform grids, and sparse grids accelerate operations like ray tracing on complex scenes, two-level acceleration structures)

(Texture coordinate spaces, how aliasing arises during texture sampling, pre-filtering (rather than supersampling) as an anti-aliasing technique)

(End-to-end 3D rasterization pipeline as implemented by modern GPUs, Z-buffer algorithm, alpha compositing)

(Definition of radiometric quantities, the light field, BRDFs (reflection models), light transport via reflection, integrating energy reflecting from surfaces, the basics of extending to volumes)

(Recovering scene parameters from images using optimization methods like gradient descent, how to compute the gradients of rendering functions, why some scene geometry representations are much more amenable to computing gradients than others, discussion of NeRF, plenoxels, and 3D gaussians)

(More advanced reflection models (specular reflection, transmittance), numerical estimation of direct illumination using Monte Carlo integration, variance reduction using importance sampling)

(Estimating direct lighting due to various types of light sources using Monte Carlo integration)

(Brute force path tracing, Russian roulette, challenges of variance, a more vigorous description of volume volume rendering than we had earlier in the class)