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Supervision work is due by 4pm (16:00) on the day before the supervision. Partial work is perfectly fine as long as it's clear that you made an effort and it is visible from your work where you got stuck.
Feel free to attach any questions to your work.
Supervision questions based on the question set by the lecturer.
Supervision 1
Warmup questions
 Name four different ways to represent geometry
 What is a manifold and how does it differ from a manifold with boundaries ?
 What is the parametric representation of a circle in 2D?
 What is the implicit curve representation of a circle in 2D?
 How do you compute the surface normal n for a parametric surface?
 What data structure is used to represent triangle meshes? That is: how is the data that describes a triangle mesh stored? Which parts of this data structure pertain to the topology and which to the geometry of a surface?
Longer questions
 (Briefly) compare and contrast the different ways to represent geometry. Focus on the advantages and disadvantages of each approach. (This is not an essay question; a table/list or some equivalent works probably best).
 Which geometry representations work well with texture mapping?
 What geometric shape does the following planar curve describe?
 Below you find the parametrisation of a torus. Compute the surface normal n for

The following implicit equation describes an ellipsoid in
 Find a parametric equation that describes the same ellipsis. Hint: start off with the parametric equation of a sphere and then modify
 Prove that P = (2, 2, −11) lies on the ellipsoid’s surface.
 Determine the surface normal n at point P .
 If we define a curve in R ^{ 3 } with the implicit function f(x, y) = x ^{ 2 } y ^{ 2 } , what problem could there arise when computing the surface normal?


Compute the Laplacian of the given functions f(x) (assume that everything except for x is constant).


Supervision 2
Warmup questions
 What is rigging? Briefly describe what kind of structure and data are added to the geometry/surface model.
 What is the difference between active and passive optical scanning systems and what are the advantages of passive systems?
 Briefly describe the steps of the iterative closest point algorithm.

What is the advantage of representing rigid transformations with dual quaternions for
blending?
 Briefly explain one fundamental disadvantage of using quaternions based shortest path blending for rotations as compared to linear blend skinning (i.e. averaging rotation matrices).
 What is the BRDF?
 What is the rendering equation?
 How is path tracing an example of a Monte Carlo Algorithm?
Longer questions

 Simple 3D engines often approximate lighting as the superposition/combination of diffuse ambient light and direct illumination from point sources. This is a rather crude (yet efficient) approximation to the full rendering equation. What kind of effects are not captured by this simple approximation, i.e. what kind of visual effects cannot be rendered?
 If there is only diffuse ambient light, we can easily determine the radiosity of a point on the surface through ambient occlusion, i.e. by measuring how much of the ‘sky’ is visible from that specific point. Briefly describe how information about the curvature of a surface can help in this situation.


 https://www.cl.cam.ac.uk/teaching/exams/pastpapers/y2021p7q6.pdf

Run
https://www.shadertoy.com/view/MtfGR4
. Questions: how does the sample count affect the quality of the rendering, and how does it affect the performance?
Extension: if interested, then check out this page on denoising in ray tracing: https://developer.nvidia.com/blog/raytracingessentialspart7denoisingforraytracing/
_Revision questions