Exam 2022.03.03 PDF

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Chair of Computer Graphics and Visualization Department of Informatics Technical University of MunichSPersonal stickerCompliance to the code of conduct I hereby assure that I solve and submit this exam myself under my own name by only using the allowed tools listed below.Signature or full name if no...

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Chair of Computer Graphics and Visualization Department of Informatics Technical University of Munich

Compliance to the code of conduct I hereby assure that I solve and submit this exam myself under my own name by only using the allowed tools listed below.

Personal sticker S0144

Signature or full name if no pen input available

Visual Data Analytics Exam: Examiner:

IN2026 / IN8019 / Endterm Prof. Dr. Westermann / Dr. Kehrer

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Date: Time:

Thursday 3rd March, 2022 14:15 – 15:30

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Working instructions • This exam consists of 10 pages with a total of 5 problems. Please make sure now that you received a complete copy of the exam. • The total amount of achievable credits in this exam is 78 credits. • Detaching pages from the exam is prohibited. • You need to sign the code of conduct on the first page of the exam, otherwise we will not grade it. • Allowed resources: – lecture scripts, books, dictionaries, own notes, exercise sheets (in digital or printed form) – a non-programmable calculator • This PDF contains text input forms that you can directly fill out using a keyboard. Therefore, it is not necessary to print out the exam or to fill it out by hand and scan it. • In your solution, only provide intermediate results when it is explicitly stated in the respective problem. Your answers need to be given in the format that is explained in the exercise text. We will not consider any additional information that is provided by you. • If there are multiple choice questions, only one answer/statement is correct per question (single choice). • If you think there is a mistake in an assignment, note this in your solution and answer the question accordingly. • Do not write outside of the text box since this information is lost when TUMexam processes the pages. • You are not allowed to have any contact or exchange with third parties during the examination, with the exception of the invigilator. • You are not allowed to communicate or discuss solutions, information, hints or assignments related to the examination during the examination period (including the upload time window). • Please note that sharing assignment sheets constitutes copyright infringement and legal action may be taken in such a case.

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Problem 1

Data Representation (4 credits)

For each of the following questions/statements, only one answer is correct. If any of the questions are unclear, you can state the assumptions you made in your solution here:

a) Visualization techniques can be classified according to their dependent and independent variables. Which of the following examples has a 1D domain (the independent variable) combined with 3D data values (the dependent variables) (1 credit)? A scalar volumetric data set (e.g., a computed tomography scan) A 3D vector field (e.g., atmospheric flow) A parametrized 3D curve ϕ: R → R3 b) Which type of data attribute are ISBN numbers (e.g., 978-1-4665-0891-0) (1 credit)? Nominal

Ordinal

Quantitative

c) Which type of data attribute are Starbucks drink sizes (e.g., venti, grande) (1 credit)? Nominal

Ordinal

Quantitative

d) Which statement on data grids is correct (1 credit)? A Cartesian grid must store the position of each vertex, but no neighborship information. A curvilinear grid must store both the position of each vertex and its neighborship information. An unstructured grid must store the position of each vertex, but no neighborship information. Rectilinear and curvilinear grids are both structured grids.

Problem 2 0 1 2 3

Interpolation (23 credits)

a) In each of the figures below, scalar values are given at the vertices of a triangle. Only one of the figures shows the filled iso-lines of a barycentric interpolation of the scalar values given at the vertices. Which one is it? Briefly explain your answer. Solutions without an explanation will not be graded.

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b) Given a triangle with vertices A = (0, 0), B = (3, 0), C = (3, 3) and corresponding scalar values f1 = 3, f2 = 6, f3 = 9. Compute the interpolated scalar values at pointsP = (2, 2) and Q = (2, 1.5) using a barycentric interpolation of the scalar values given at the triangle vertices. Use the functionf (X) = u · f1 + v · f2 + w · f3 to compute the interpolated scalar value at a point X . In your solution, specify the values of u, v, w together with the interpolated scalar value for the pointsA and B , respectively. No intermediate steps need to be provided.

c) In each of the figures below, scalar values are given at the vertices of a 2D Cartesian grid with3 × 3 cells. Only one of the figures shows the filled iso-lines of a cell-wise bi-linear interpolation of the scalar values given at the grid vertices. Which one is it? Briefly explain your answer. Solutions without an explanation will not be graded.

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d) Given a quadrilateral cell with vertices P1 = (0, 0), P2 = (2, 0), P3 = (0, 2), P4 = (2, 2) and corresponding scalar values f1 = 0, f2 = 1, f3 = 3, f4 = 2. Determine the coefficients a, b, c, d of the bi-linear interpolation function f (x, y) = a · x + b · y + c · x · y + d that interpolates the scalar values given at the vertices, where(x, y ) are Cartesian coordinates. In your solution, no intermediate steps need to be provided.

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e) For the quadrilateral cell given in Problem 2d, algebraically compute the gradient of the interpolated scalar field at point Q = (2, 2), i.e., do not use finite-difference approximations. Specify exactly how the gradient is computed.

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Problem 3

Volume Rendering (15 credits)

a) The figure below shows a viewing ray intersecting a volumetric data set during ray casting in direct volume rendering. The volume is sampled at three locations, and RGBα-colors are assigned by a transfer function as illustrated. The α-value (fourth component) represents the opacities, where0 = completely transparent and 1 = completely opaque. Determine the RGB-color and α-value seen along the viewing ray if alpha compositing and a front-to-back strategy are used. In your answer, state intermediate results for color Ci and αi after compositing the i -th sample point. Write your answer in the form: Sample 1: C1 = (R1, G1, B1), alpha1 = A1; Sample 2: . . .

b) Compute the color of the specular reflection at a surface point P = (1, 1, 0) using the Phong lighting model. The normal at the point is ~ n = (0, 1, 0). The position of a point light source is Lpos = (−1, 3, 1) and the viewer is located at Epos = (3, 2, 0). The specular reflection coefficient is ks = 1 and the specular exponent is n = 2. The color of both the light source and the object are white with RGB-values (1, 1, 1). Note that the specular reflection is based on the angle between two vectors. In your solution, name the two vectors and write each vector in the form V = (vx, vy, vz). Also, state the computed color of the specular reflection. No intermediate steps need to be provided in your solution.

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n = (0, 1, 0) that goes through the origin and only reflects diffusely. A point c) Given is a plane with normal vector ~ light source is positioned at Lpos = (1, 5, 2). The viewer is positioned at (4, 2, 4) and sees all points on the plane with 0 < x < 8 and 0 < z < 8. At which point on the plane does the viewer perceive the highest diffuse reflection?

Note that the diffuse reflection is based on the angle between two vectors. In your solution, name the two vectors and write each vector in the form V = (vx, vy, vz). Also, state the location of the highest diffuse reflection. No intermediate steps need to be provided in your solution.

Problem 4

Flow visualization (20 credits)

a) Two streak lines are seeded at fixed locations in a 2D vector field. Neither of the seed points belongs also to the other streak line. For which kind of flow can these streak lines(self-)intersector cross each other? Only one answer is correct (2 credits). only for time-varying but not steady flow

both for time-varying and steady flow

only for steady but not time-varying flow

neither for time-varying or steady flow

b) Two path lines are seeded at fixed locations in a 2D vector field. Neither of the seed points belongs also to the other path line. For which kind of flow can these path lines(self-)intersect or cross each other? Only one answer is correct (2 credits).

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only for time-varying but not steady flow

both for time-varying and steady flow

only for steady but not time-varying flow

neither for time-varying or steady flow

c) Calculate the Jacobian matrix, divergence, and curl for the 3D vector fieldv(x, y, z) = (2x − y, xz, x 2 − 1). In your solution, to specify a matrix that has multiple rows, separate the rows with semicolons, e.g.,   1

J = [1, 2, 3; 4, 5, 6; 7, 8, 9] = 4 7

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d) Line integral convolution (LIC) is a texture-based flow visualization technique based on convolution. What are the two functions/inputs which are convoluted in classical LIC? Where and how is the vector data considered?

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e) Compared to classical LIC, what must be changed in Oriented LIC (OLIC)?

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f) Given a steady 2D vector field v(x, y) =



y −x

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. Use the Midpoint integration method to compute the next two   2 points x1 and x2 of a stream line with a seed point x0 = and step size ∆t = 1. For each point of the streamline, 0

specify the vector ∆x resulting from the Euler step and the vectorvmid evaluated at the midpoint. Write your answer in the form: First point: delta_x = (ux, uy), v_mid = (vx, vx), x_1 = (wx, wy); Second point: . . .

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Problem 5

Visualization mapping (16 credits)

The following Parallel Sets vis. shows the proportion of survivors in the Titanic disaster with respect to passenger classes, crew, and gender. Annotations per horizontal bar show the percentages of the Total for different groups.

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a) Derive from the Parallel Sets visualization what percentage of Second Class passengers survived?

b) Only one of the following statements is correct and can be derived from the Parallel Sets visualization (3 credits). The Third Class was the largest group of people, larger even than the crew. Within the group of Third Class passengers, males and females had similar chances of surviving. While only 25% of Third Class passengers survived, about 60% of First Class passengers survived. Most female survivors belonged to the Second Class. c) Only one of the following statements is correct and can be derived from the Parallel Sets visualization (3 credits). Only 10% of the crew survived the disaster. Most female passengers (survivors and deceased) were in the Third Class. The largest group of people that survived were First Class passengers. None of the other statements is correct. d) Only one of the following statements is correct. Which one is it (1 credit)? Only 3-4 bins of categorical color are discriminable when the colored regions are small and scattered. Segmented rainbow colormaps are suitable for categorical data because they are highly saturated. The hue color channel in a rainbow colormap is perceptually ordered (e.g., the colors red vs. blue vs. green vs. purple have an intrinsic perceptual ordering). e) Only one of the following statements is correct. Which one is it (1 credit)? The human visual system is better at comparing 2D areas than lengths. Position and color hue are fully separable visual channels, but size and color are not. Shapes are a good choice to encode quantitative data. IN-VDA-3-20220303-E0144-08

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f) Only one of the following statements is correct. Which one is it (1 credit)? The human perceptual system is well suited for making relative judgements for the hue color channel and absolute judgements for the saturation and luminance channels. The color channels of luminance and hue have similar characteristics because they both convey magnitudes. Choropleth maps can be misleading when there is a lot of variability in region size. The following scatterplot matrix shows measurement data from penguins collected in the Antarctica. Properties such as culmen depth, flipper length, and body mass were collected per penguin. Points in the scatterplot matrix are labeled with random numbers.

In one of the scatterplots, points A, B, and C have been selected by a rectangular brush (gray background color). Which points in the other two scatterplots are consequently selected/highlighted when brushing and linking between the views is used? Only one answer is correct per question. g) Which points in the other two scatterplots are selected/highlighted because of point A (2 credits)? Only points 6 and 13

Only points 6, 9, and 13

Only points 6 and 9

Only points 6, 9, 13, and 18

h) Which points in the other two scatterplots are selected/highlighted because of point B (2 credits)? Only points 5 and 19

Only points 2 and 16

Only points 2, 5, 16, and 19

Only points 2, 5, 11, 16, and 19

i) Which points in the other two scatterplots are selected/highlighted because of point C (2 credits)? Only points 8 and 17

Only points 1, 8, 12, and 17

Only points 1 and 12

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Additional space for solutions–clearly mark the (sub)problem your answers are related to and strike out invalid solutions.

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