Exam 2 //cs378/GraphicsExam2.pdf · · 2010-12-07For each of the following objects or effects, ... efficiency and visual artifacts of the texture-mapping process. ... D. they are

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Exam 2

Part 1 of 5 - Modern Graphics Pipeline

Question 1 of 27 2.0 Points

Match each stage in the graphics pipeline with a description of the operations generally performed therein.

A. generate new vertices and primitives, subdivide surface dynamically

B. matrix transformations (projection, camera, object), flat or smooth shading, clipping

C. z-buffer algorithm, interpolating normal vectors, viewport transform

D. creation of base geometry, definition of lighting properties, animation

E. compositing, per-pixel shading, texture mapping

select 1. vertex

select 2. fragment

select 3. rasterizer

select 4. geometry

select 5. application

Mark for Review What's This?


Which of the stages from the prior question are programmable in the modern pipeline?

A. all of them

B. only the application stage

C. vertex, rasterizer, and fragment

D. all except the rasterizer

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Gouraud smooth shading is performed at the stage of the pipeline, while Phong shading is done at the

stage.



Exam 2 https://ilearn.marist.edu/xsl-portal/tool/d4e4fd3a-a3...

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Consider the image above. Following the Cohen-Sutherland algorithm, the outcodes for endpoints a and b are

and , respectively.



Can we trivially accept/reject the line segment in the prior question? Explain your answer.

(Maximum number of characters: 60000)


Part 2 of 5 - Lighting & Shading


Match each type of reflection with the appropriate heuristic formula. Use accompanying diagram to jog you memory.


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A. k * I

B. k * I * max(0, n · l)

C. k * I * max(0, r · v)p

select 1. diffuse reflection

select 2. specular reflection

select 3. ambient reflection



Derive a complete reflection model for multiple lights incorporating each of the formulæ from the prior question.




What do the k, I, and p scalars represent, respectively, in the above formulæ?




Smooth shading differs from flat shading in that:

A. colors are blended across the surface using a texture map

B. it requires programmable geometry shaders

C. the underlying surface geometry is subdivided to yield finer detail

D. lighting is computing multiple times per primitive using vertex normals

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For Phong shading, the lighting equation must be evaluated once for each of the rasterized primitive.

Gouraud shading is more efficient because the lighting equation must be evaluated once per .



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If, upon rendering, one object (but not the whole scene) appears completely black and featureless, which of the following is the most common,plausible explanation?

A. there are no active lights in the scene

B. the alpha color component is accidentally set to zero

C. it is obscured by another, closer object

D. the surface normal vectors are inverted (pointing inward)

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Briefly explain the "infinite light" and "infinite viewer" optimizations.



Part 3 of 5 - Texture Mapping


For each of the following objects or effects, indicate whether it would be best modeled using image-based (I) textures, or procedural (P) textures.

decal or logo

stone

clouds

surface of Earth

fabric

wood



Briefly discuss the relative advantages and disadvantages using of procedural versus image-based textures. Address issues such as time/memoryefficiency and visual artifacts of the texture-mapping process.



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Bump mapping is a technique used to simulate small-scale surface features without the need for detailed geometric models. The effect is achievedby:

A. changing the color at each point based on the nearest texel in the texture image

B. moving the position of each vertex by some random small amount

C. recalculating the lighting for each point using a slightly different position for the light source

D. perturbing the normal vector at each point based on the associated texel value

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A tell-tale artifact of the bump mapping technique is that the object's will appear unchanged. A more

expensive approach that does affect the actual shape of the object is called mapping.



Consider the texture image above. For each possible mapping to a quad face shown below, specify the normalized UV texture coordinates of thelower right-hand vertex. Assume that texture coordinates (0,0) and (0,1) map to the upper and lower left-hand corners of the image, respectively.Furthermore, the texture function wraps horizontally and vertically, so that (2,0) maps to the same color as (1,0).


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(

, )

1.

(

, )

2.


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(

, )

3.


Part 4 of 5 - Graphics Data Structures


Consider the following description of a (possibly animated) 3D scene. Then draw a plausible scene graph for this scene, being sure to considerhow various elements may be positioned or animated. Note: You may create your scene graph in an editor, save the file and then upload;alternatively, you can simply sketch the graph by hand on paper and submit the hard-copy at the conclusion of the exam.

"A small cottage has a two windows that each may open by sliding up/down, a hinged front door that can swing open. On the door is a knob thatcan turn in the usual way."

File: Browse...

Upload



Scene graphs offer many opportunities for optimization. One method discussed in class, known as instancing, involves taking advantage ofsimilar/identical geometry in order to reduce memory requirements. Explain how using this method would change the scene graph you sketched forthe previous question; or, if you accounted for this technique in your graph, explain where.




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Briefly explain how animation is achieved when using a scene graph. (Hint: Recall the various types of graph traversal used by OSG.)




Shared-vertex representations such as triangle strips or fans can be useful for some applications, but not so much for others. Select the explanationbelow that best characterizes why.

A. they require too much memory for certain mesh topologies

B. they are useful in C-programs but are difficult to implement in an object-oriented design

C. they are extremely slow to traverse for large meshes

D. they are storage efficient but are not conducive to editing

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Explain what data we store in a Half-Edge data structure and why this is a more time-efficient representation, for traversal, than the traditionalWinged-Edge. You may refer to the diagram of a Winged-Edge below to jog your memory.




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Complete the following pseudo-code for the EdgesOfVertex routine.

EdgesOfVertex (v)

let e = .edge

do

if (v == e. )

e = e.leftNext else

e = e.

while ( != v.e)



Complete the tables below, given the above diagram of a triangle mesh. Note that uppercase letters indicate Vertices, lowercase letters indicateEdges, and digits indicate Faces.

WingedEdge Table

EdgeHeadVertex

TailVertex

LeftFace

RightFace

LeftPrev

LeftNext

a A B 2 0 f c

b A

c D A 2 1 a f

d B C 3 0 h g

e D

f B

g E B 3 5 d h

h C

i D E 4 5 h e

Vertex Table

Vertex Edge

A b


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B

C e

D i

E

Face Table

Face Edge

0 a

1 c

2

3 g

4

5 i


Part 5 of 5 - Antialiasing & Compositing


Complete the formula for basic alpha compositing. Type cf to indicate the foreground color, and cb to indicate the background color.

c = α * + ( - α) *



Briefly explain how resampling is used to implement antialiasing in each of the following algorithms: rasterization, ray-tracing, and texture-mapping. Specifically, describe differences in what we are sampling.




Which of the following describes what mipmaps are?

A. a subtree within a scene graph hierarchy

B. images used to make a surface appear bumpy

C. a function used to match 3D world coordinates to 2D texture coordinates

D. smaller resolution versions of an image used for blending or LOD

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Exam 2 //cs378/GraphicsExam2.pdf · · 2010-12-07For each of the following objects or effects, ... efficiency and visual artifacts of the texture-mapping process. ... D. they are