Quiz

This lists some questions, without answer, with which you can test how much you know.

• What is the difference between subdivision and refinement?
• What does isotropic and anisotropic mean?
• What is the difference between topology and geometry?
• Is radiosity possible for specular surfaces? (hint: http://portal.acm.org/citation.cfm?id=37438&coll=portal&dl=ACM , http://www.cs.huji.ac.il/labs/cglab/papers/clustering/ )
• What is linear precision? In respect of {splines|parameterisation|smoothing}?
• What is anisotropic filtering?
• What is the difference between the Aitken Neville Scheme and the de Boor recursion?
• How can we express a {uniform|nonuniform} Spline in terms of a box-spline?

# Questionnaire

You can find a very meticulous quiz about the four subjects under http://www.malte-weiss.de/cgquiz

I am sorry but the quiz is written in German. Feedback is always welcome.

# Exam questions

This part contains questions that have been asked in a similar form in the oral examination. These can also be found with some answers in the link section.

## CG 1

• What have we done in CG1?
• What steps does the rendering-pipeline contain?
• Which 3D-transformations do you know?
• How do you rotate around an arbitrary axis?
• Write down a {rotation|translation|scale|shear} matrix!
• Which projective mappings have been discussed?
• How do you rasterise lines? Without using float computations? Why are we using decision variables for that?
• What volume-rendering methods do you know?
• Discuss the difference between Ray-Casting and Splatting!
• Explain extended coordinates!
• Explain homogeneous coordinates!
• {Compare|enumerate|explain} the {line|polygon} clipping algorithms!
• Translation and rotation matrices combined into one, what is the order of applications of T and R?
• What is the formula for diffuse reflection? How can it be justified?
• Explain direct-illumination techniques for shadow computation!
• Which method is the best to simulate a room with a single candle?
• Can shadow volumes be calculated on the GPU?
• How does volume ray casting work? How can you compute the accumulated color value?
• Explain raytracing!
• Explain the Phong model!
• How can the cosine term in the diffuse and specular components be explained?
• What does the attenuation term model?
• Which one is the best shadow method? (trick question)
• Explain the {standard|general} projection matrix!
• How do we transform normals?
• How can we realize a spotlight?
• Describe the flaws of Shadow-Mapping!
• Explain classic multi-point perspective constructions!
• What is a vanishing point?
• What is a Spurgerade? (What is it, anyway? ;-)
• What is perspective division?
• How do we rasterize triangles? What problems can occur, and how can they be solved?
• How does anti-aliasing work?
• How does dithering work?

## CG 2

• How do you convert a point cloud to a mesh?
• What is a Voronoi Diagram?
• What is Voronoi Filtering?
• How do we process 3D laser scan data? Explain direct/indirect methods!
• How is registration performed?
• What methods of global illumination do you know?
• How can you accelerate radiosity?
• Explain hierarchical radiosity! What is its complexity?
• What is image based rendering?
• What is a visual hull?
• What is a light field?
• What is a lumi graph?
• What is the difference between both?
• Show and explain the rendering equation of Kajiya? How is he spelled correctly?
• Explain the BRDF!
• Explain Monte Carlo methods!
• Explain Photon Mapping!
• Explain the light particle path notation!
• How can an implicit function be raytraced?
• Describe some error measures you know!
• How can one interpret the 4D function of the light fields?
• How does the algorithm of Touma/Gotsman work? Explain Alliez extensions to it! How many add/split/merge operations can happen?
• How can we compress a mesh?
• How can we smooth a mesh?
• Explain the umbrella operator!
• Explain the lambda-mu smoothing!
• What can we choose as the weights for the umbrella operator on a mesh?
• What is the problem with cotangent weights?
• What is a shape preserving weight?
• How does ICP work? How can the rotation be computed?
• Smoothing shrinks the surface, what can we do against it?
• Explain monte carlo path tracing!
• What is the advantage of MCPT compared to ray tracing?
• Explain the idea of solid angles/form factors! "one can compute \cos\teta with the cos distribution function as shown in the lecture. Whats up with the rest of the term"
• Explain valence encoding!
• What is a limit to the compression efficiency?
• Explain entropy coding!
• How does a 3D laser scanner work?
• Explain how quaterion rotation works!
• Explain the idea behind marching cubes!
• How can we reduce the complexity of a extracted mesh?
• What class of algorithms does incremental decimation belong to? (greedy)
• How does {gathering|shooting} work? How do they compare?
• What is Push-Pull variant of Radiosity?

## GM1

• What is a spline?
• What is a B-Spline?
• What is the Mansfield-Cox-de-Boor recursion?
• What is a blossom?
• What is the de-Boor algorithm?
• What is the relationship between blossoms and de-Boor?
• What are the divided differences?
• Explain multiple knots! Relation to de-Boor?
• What is a Bezier curve?
• What is the relationship between Bezier curves and Splines?
• What is $B^n_i$?
• Can any polynomial be described in the Bezier Basis?
• How many Bezier functions do you need for an $n$ dimensional basis?
• How can we evaluate a Bezier curve?
• What can you see in the de Casteljau algorithm?
• What is the blossom of $ax^2+bx+c$?
• Can blossoms be used on B-Splines?
• How does knot-insertion work?
• What happens between the blossoms $F(a,b,b)$ and $F(b,b,a)$?
• How is the spline space defined?
• How can Spline basis functions be derived? (truncated power, convolution, recursion)
• Enumerate the polynomial bases you know!
• What are the properties of blossoms?

## GM2

• How is a Bezier patch defined?
• What are the properties of a Bezier patch?
• What is the C1 condition of Bezier patches?
• What is a Tensor-Product-Patch?
• What is the C1 condition of TP-Patches? Do the vectors have to be of equal size?
• What is a box spline?
• What are the properties of box splines?
• What is the degree of a box spline?
• Construct a Box-Spline of degree X with smoothness Y!
• How does Subdivision of box-splines work?
• How is such a subdivision scheme constructed?
• What is a simplex spline?
• Explain multiple knots wrt. to Box Splines!
• How can we evaluate a {TP-Patch|Bezier-Patch}? How can the derivate be read from this?
• How can we evaluate the derivatives of a {TP-Patch|Bezier-Patch}?
• Why do TP-patches have two parameters, Bezier-Patches 3?
• What is the continuity, degree, support of a box-spline?
• How does a boxspline of degree two and $C^2$ look like?
• Draw the case of projecting a 3D box on a line! How should the box be oriented to minimize the continuity?
• How do you join two Bezier patches in a C^{0,1} fashion?
• How can you join cubic patches?
• How does the bivariate case of the Bezier curve look like? (Bezier Patch)
• How does the de Casteljau work on Bezier Patches (graphically)?
• How do you compute directional derivatives of Bezier Patches?
• There is a very well known box-spline, which one is it? (hint: loop)

CG1:
- Homogenous Coordinates
- Rotationmatrix/Translationmatrix
- Projection matrix with on an arbitrary plane through center
- Vanishing points of the aforementioned (small problems here)

CG2:
- Laser range scanning
- Registration (ICP)
- Integration (mainly Levoy's paper)
- Mesh smoothing in all its glory
- What are the frequencies in mesh smoothing? (answer: the eigenvectors!)
- Fourier Transformation
- Monte Carlo integration (expected value)
- MCPT in all depth, russian roulette
- rendering equation

GMI:
- Spline space
- B-Splines in all its glory
- De Boor

GM2:
- Box-Splines in all its glory
- B-Splines as Box-Splines

CG1:
- Homogenous Coordinates
- Vanishing points
- Vanishing points from matrices (4th column)
- Bresenham Midpoint Algorithm
- Implicit functions, representation of data (explicit vs implicit), whats better for which task
- boolean operations on implicit functions
- Euler formula, proof idea

CG2:
- Voronoi diagrams (how does a cell look like, how many edges does a vornoi cell have in average)
- Delaunay triangulation
- mesh smoothing, 3d case, umbrella operator, weights, low pass filter, frequencies, mathematical interpretation of umbrella, cosine, sine (eigenfunctions)
- Mesh compression: Valence Coding + Entropy Encoding + what compression ratios can be achieved
- rendering equation, lambertian term
- MCPT: how to solve integrals, algorithmus, russian roulette

CG1:
- Homogenous Coordinates
- Vanishing points
- Vanishing points from matrices (4th column)
- Bresenham Midpoint Algorithm
- Euler formula, proof idea
- Implicit functions, representation of data (explicit vs implicit), whats better for which task -> CSG

CG2:
- Voronoi diagrams (how does a cell look like, how many edges does a vornoi cell have in average)
- Delaunay triangulation
- mesh smoothing, 3d case, umbrella operator, weights, low pass filter, frequencies, mathematical interpretation of umbrella, cosine, sine (eigenfunctions)
- Mesh compression: Valence Coding + Entropy Encoding + what compression ratios can be achieved
- rendering equation, lambertian term

CG1:
- Voronoi Diagram (how many edges, formula for voronoi cell)
- Bresenham (explain in 3 sentences why it is good and how it works… decision variable, no multiplications, how?)
- Polygon rasterization (Scanline-conversion, how does it work? Special cases/stability: half open right/top)
- Projection (Write projection matrix of own choice, where is viewer etc. How many vanishing points? What is a vanishing point?)
- Multipoint perspectives (how many vanishing points? why?)
- Affine transformations (Rotation matrix, translation)

CG2:
- Delaunay Triangulation (shortly mention some properties)
- Sweepline algorithm (explain how works? complexity)
- Rendering equation (write one of the two formulas)

GM1:
- Spline space (why is it a space? how many DoFs?)
- BSplines (Why a basis? What support? (minimal) Explain all terms in Truncated Power spline definition (Partition of unity, positivity, (minimal) support, and one more thing)
- Evaluation of Spline curves (explain deBoor, what indices for control points?)

GM2:
- Box Splines (some definition, which one is best for proving properties? Name some properties: poly. degree, contin….)
- What is subdivision? (Given some vectors how does support look? what do the subdiv. rules look like? Use 2-scale relation to obtain/create some rules. Apply rules to a mesh)

CG2:
- detailed explanation of contangent and shape preserving weights.
- laserscanner: what problems (angle too small/too large).
- incremental decimation: one million triangles -> how much memory do you need for the error quadrics?

GM1:
- Spline basis: why is the function value outside of the support 0?
- why is the dimension of the splinespace m? explain the dimension. depends on the knots.

CG1:
- Volume Representations? (meshes, implicit, parametric)
- Implicit functions, intersections
- Prove Euler, Valence=?
- Compression Methods?
- Huffman Encoding? Haar Wavelets?
CG2:
- Parametrization: the works!

page revision: 19, last edited: 18 Dec 2008 19:46