CG ECSE-4750 Computer Graphics Final Exam, RPI, Tues 2018-12-18

W Randolph Franklin, RPI

2018-12-17 00:00

Name, RCSID:

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Rules:

You have 180 minutes.
You may bring in two 2-sided 8.5"x11" papers with notes.
You may not share material with each other during the exam.
No collaboration or communication (except with the staff) is allowed.
There are thirty six questions. Check that your copy of this test has all the pages.

Questions:

_____/2 Put these graphics pipeline components in the correct order:
1. fragment-shader
2. primitive-assembly
3. rasterizer
4. vertex-shader
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_____/2 Which of the following 3D rotation methods is vulnerable to gimbal lock?
1. Euler angles
2. matrix
3. quaternion
4. vector
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_____/2 In the OpenGL pipeline, the Primitive Assembler does what?
1. fits together pieces of ancient Sumerian pottery.
2. rotates vertices as their coordinate systems change.
3. creates lines and polygons from vertices.
4. finds the pixels for each polygon.
5. reports whether the keyboard and mouse are plugged in correctly.
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_____/2 When rotating an object, what can happen to an object?
1. Straight lines might turn into curves.
2. Straight lines stay straight, but angles might change.
3. Straight lines stay straight, and angles don't change, but distances may change, either longer or shorter.
4. Straight lines stay straight, and angles don't change, but distances might get longer.
5. Straight lines stay straight, and angles and distances don't change.
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_____/2 If i and j are quaternions, what is i+j?
1. -k.
2. 0.
3. 1.
4. i+j, there is no simpler representation.
5. k.
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_____/2 If i and j are quaternions, what is ij?
1. -k.
2. 0.
3. 1.
4. i+j, there is no simpler representation.
5. k.
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_____/2 The quaternion i represents what rotation?
1. 180 degrees about the x-axis.
2. 90 degrees about the x-axis.
3. 180 degrees about the y-axis.
4. 90 degrees about the y-axis.
5. no change, i.e., 0 degrees about anything.
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_____/2 The parametric equation of a line through the points (1,1) and (2,3) is:
1. P = (1,1) + t(1,0) + u(0,1)
2. P = (1,1) + t(1,1)
3. P = (1,1) + t(1,2)
4. P = (1,1) + t(2,3)
5. P = t(1,1) + u(2,3)
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_____/2 The normal vector of length one to the plane through the points (1,0,0), (0,1,0), (0,0,1) is
1. (1,0,0)
2. \(\left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)\)
3. (-1, 0, 0)
4. 3
5. (1/3, 1/3, 1/3)
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_____/2 You call gl.BufferSubData to do what?
1. to add or replace part of the buffer in the GPU.
2. to define a submarine object.
3. to subtract some data in the buffer.
4. to tell the GPU to look for a pattern and substitute any occurrences,
5. to tell the GPU to use a subroutine instead of the main program.
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_____/2 Translating the 2D homogeneous point by (1,2,3) by (in Cartesian terms) dx=1, dy=2 gives which new homogeneous point?
1. (1,2,3)
2. (1,2,3,4)
3. (2,4)
4. (2,4,3)
5. (4,8,3)
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_____/2 Rotating the 2D Cartesian point (0,1) by 90 degrees gives what:
1. (1,0)
2. (-1,0)
3. (0,1)
4. (0,-1)
5. (-.7,.7)
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_____/2 Give me a matrix M that has this property: for all vectors p, \(Mp = \begin{pmatrix}2&3&1\end{pmatrix} \times p\). The operator is the vector cross product.
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_____/2 In a fragment shader, a sampler2D does something more than a simple array lookup like you have in most programming languages. What?
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_____/4 Tell me about view normalization. What is it? What is good about it?
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_____/4 Compute the projection equations when the viewpoint is at (0,0,0) and the projection plane is 2x+y+z=4. Use Cartesian coordinates. You do not need to put the result into a matrix form, but simplify your result as much as possible.
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_____/2 Name the algorithm that was designed to rasterize a circle using only integer additions, subtractions, and shifts.
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_____/2 In a shader, what is the difference between a uniform variable and a varying variable?
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_____/2 Give 2 reasons why we usually use a sequence of low-degree curves instead of one high degree curve.
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_____/2 What does the word rational mean in NURBS?
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_____/2 What is the difference between Phong shading and Gouraud shading?
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_____/2 In the Phong lighting model, which computes the color or brightness of each pixel, how do you make a surface material more metallic or shiny?
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_____/2 Where is the 3D homogeneous point (1,0,0,0)?
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_____/2 Consider a 2D cubic Bezier curve with Cartesian control points (0,0), (1,1), (2,2), (3,3). What is the point at t=0.5?
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_____/2 Describe what the curve in the previous question looks like.
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_____/2 What is Constructive Solid Geometry?
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_____/2 What texture mapping problem does the mipmap solve?
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_____/2 Mathematically, the aliasing problem in CG
1. happens when high frequency signals are not sampled often enough.
2. happens when low frequency signals are sampled too often.
3. is a new problem that did not occur with the old displays.
4. can be reduced by subsampling and averaging
5. both (a) and (d).
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_____/2 About polygon clipping:
1. A polygon might gain vertices.
2. A polygon might gain area.
3. If a polygon's vertices are all outside the clip region, then it may be deleted.
4. Using a 6-stage pipeline keeps the latency the same.
5. Concave polygons become convex.
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_____/2 A small light source that is twice as far away is 1/4 as bright. That is, there is an inverse square fall off for brightness. However, when modeling light in graphics, we usually don't do that. Why?
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_____/2 What tool maps spectral colors into a human perceptual coordinate system? Your use it to determine the visual result of mixing colors.
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_____/2 With a B-spline, the joints are usually invisible because the two segments meet with C2 continuity. Sometimes a designer may want there to be a visible kink at a joint, i.e., wants only C0 continuity. How can that be achieved?
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_____/2 What's the hardest part of implementing the painters algorithm?
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_____/2 Consider a cube. It has both geometry and topology. What is the geometry and what is the topology?
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_____/2 Name the javascript WebGL function that sets the current buffer for future buffer operations.
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_____/2 Name the javascript WebGL function that declares that the current buffer contains 3 floats per vertex (or generally some number of some type per vertex).
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End of final exam. Total: 76 points.