Advanced Computer Graphics - SS 2022

This course will introduce students to advanced and more complex methods and techniques of computer graphics, as compared to the Bachelor's course "Computer Graphics"; also, some of those topics will be covered here in more depth. This approach will both broaden and deepen students' knowledge about the field of computer graphics.

This course is for you, if you want to acquire ...

There are no formal prerequisites, but some degree of the following skills are desirable:

  1. A little bit of experience with C/C++ ; note that you will need just "C with classes" during this course.
  2. Knowledge of the material of the Bachelor course "Computer Graphics" (if you didn't manage to attend that course, you can easily recap that material for yourself).
  3. Algorithmic thinking (and, hopefully, some pleasure when thinking about algorithms)

Some of the envisioned topics (these can change during the semester):

  1. Data structures and the theory of boundary representations (meshes);
  2. Advanced texturing methods;
  3. Generalized barycentric coordinates and parameterization of meshes;
  4. Advanced shader programming (special effects);
  5. Culling techniques (real-time rendering);
  6. Ray-tracing (photo-realistic images);
  7. Alternative object representations (modeling);
  8. Mesh processing


I encourage you to use this for discussions and Q&A amongst yourselves. (Rest assured that I don't have time to "listen" in to your chatting on discord ;-) )

Slides and Lecture Recordings

The following table contains the topics and the accompanying slides and videos (it will be filled step-by-step).
Note: the videos are encoded with H.265/HEVC, which should play fine with Safari and Edge, and with VP9/WEBM, which should play fine in all other browsers (but have twice the file size). You can also download the videos and watch them offline using your favorite video player on your laptop.

Ch. Topics Slides Video Assignments Frameworks
1. Organization;
Ray-tracing: principle, the rendering equation, Whitted-style ray-tracing, camera models, lighting model, reflected rays, refraction, Fresnel terms, attenuation, scattering, dispersion, intersection ray-polygon, intersection ray-triangle, intersection ray-box, ray-sphere intersection, ray-tracing height fields, numerical robustness, limitations of Whitted-style ray-tracing, distribution ray-tracing, stratified and Poisson disk sampling, grid-based construction algorithm, Poisson disk sampling on the sphere, distribution raytracing: anti-aliasing, soft shadows, glossy-matte reflection, depth-of-field, motion blur.
H265 VP9 Assignment 1 RayTracing Framework
2. Object representations: quadrics and superquadrics, implicit surfaces, sure-fire root finding methods (regula falsi, Illinois), metaballs, generalizations, polygonization of implicit surfaces using marching cubes, instancing, constructive solid geometry (definition, ray-tracing, polygonization), PDF 2 H265 VP9 Assignment 2 CSG Raytracing Framework
3. Acceleration data structures: taxonomy, light buffer, beam and cone tracing, bounding volumes, 3D grids and spatial hashing, traversal of grids, mailbox technique, optimal grid resolution, recursive & hierarchical grid, irregular grids (construction and ray traversal) proximity clouds (sphere tracing), octree, kd-trees, ray traversal using kd-trees, kd-tree construction, surface area heuristic (SAH), efficient storage of kd-trees, spatial v. object partitioning, bounding volume hierarchies (BVHs), BVH traversal using a p-queue, principles of construction of BVHs, median cut heuristic, plane sweep along principal axis with SAH. PDF 3 H265 VP9 Assignment 3 ADS RayTracing Framework
4. Collision Detection: requirements, collision detection pipeline, collision matrix, broad phase, narrow phase, 3D grid, sweep and prune, temporal coherence, broad phase algo for convex objs using separating planes, hierarchical collision detection, types of bounding volumes, k-DOPs, inner sphere trees, massively-parallel collision detection (kDet) PDF 4 H265 VP9
5. Advanced shader techniques: recap of the programmable pipeline and GLSL, procedural textures in the shader, value noise, gradient noise, spot noise, Worley noise, example: procedural textures with noise (brick texture), ambient occlusion, refractive objects, the geometry shader, simple examples, rendering furry objects with shells and fins, rendering silhouettes. PDF 5 H265 VP9
6. Physically-based lighting: radiometric quantities, solid angles and change of variables, properties of radiance, invariance of radiance, definition of BRDF, properties of BRDFs, reflectance equation, conservation of energy, constructing BRDFs, microfacet theory, the Fresnel equation, the normal distribution function, derivation of the NDF, the geometry function, the Disney BRDF. PDF Sorry, no video!
7. Advanced texturing methods: seams, texture atlas, cube maps, polycube maps, concept of environment mapping, cube environment mapping, spherical environment mapping, dynamic environment mapping, parallax mapping, view-dependent displacement mapping (VDM), VDM with self-shadowing. PDF H265 VP9 Assignment 4 Parallax Mapping Framework
8. Mesh Processing: calculating good vertex normals, Laplacian smoothing, extension to prevent shrinking, global Laplacian smoothing, subdivison surfaces (Catmull-Clark). PDF H265 VP9 Assignment 5 PBR Framework
9. Boundary Representations: definitions, orientability, 2-manifold, homeomorphism, indexed face set, OBJ file format, doubly-connected edge list (half-edge data structure), mesh traversals using a DCEL, limitations of DCEL, mesh matrices and example applications, Euler equation, complexity of polyhedra, Platonic solids, Euler characteristic, regular quad meshes. PDF H265 VP9
10. Procedural modeling: extrusion, fractal terrain modeling, L-systems: definition, turtle graphics, parametric L-systems, stochastic L-systems, procedural modeling using 3D L-systems and genetic algorithms.
Call for theses
PDF H265 VP9
11. Generalized Barycentric Coordinates: definition, interpolation property with proof, general construction scheme and properties, mean value coordinates, extension to non-convex polygons, applications: image warping, mesh morphing. PDF H265 VP9
12. Parameterization: general approach, condition for and proof of a unique solution, concrete parameterizations.
Striping/Stripification: concepts, NP-completeness, SGI algorithm, FTSG algorithm.
7. Culling and visibility: bottlenecks in the rendering pipeline, types of culling, detail culling. backface culling, normal masks, clustered backface culling, hierarchical clustered backface culling, view frustum culling, hierarchical view frustum culling, occlusion culling, batched occlusion queries, naive wait-and-draw algorithm, portal culling,
Lab meeting
PDF Assignment 2 CollisionDetection Framework
10. Tone mapping: HDR imaging, image histograms, histogram stretching, histogram equalization, tone reproduction using CLAHE, the Weber-Fechner law, Steven's power law, perceptually-based tone mapping, generating histograms on the GPU. PDF PDF View Frustum Culling Framework

If you are interested in doing a thesis with us, please check my Call for Theses. Also, be sure to check our research projects. If you are interested in any of these, just drop me a line (or anybody else in the CGVR group).

You can download some of the shaders that were discussed in class, plus some some very simple ones (discussed in the Bachelor course).

Video Recordings of the Lecture from SS 21

The videos are encoded with H.265/HEVC and should play fine with Safari and IE. With Chrome and Firefox, you might need to download the videos and play them with VLC, or install a browser plugin/extension.

Ray tracing, path tracing
Object representations
Acceleration data structures
Collision Detection
Culling and visibility computations
Advanced shader techniques, noise functions
H265 VP9
Mesh Processing
Boundary Representations
Striping, Stripification
Generalized Barycentric Coordinates
Procedural modeling


The following textbooks can help review the material covered in class:

Please note that the course is not based on one single textbook! Some topics might even not be covered in any current textbook! So, I'd suggest you first look at the books in the library before purchasing a copy.

If you plan on buying one of these books, you might want to consider buying a used copy -- they can often be purchased for a fraction of the price of a new one. Two good used book shops on the internet are Abebooks and BookButler.

Additional Literature and Demos for Deeper Insights

Other Interesting Bits and Pieces

Gabriel Zachmann
Last modified: Thu Aug 11 14:49:28 MDT 2022