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課程名稱︰ 計算機圖形
課程性質︰ 選修
課程教師︰ 歐陽明
開課學院： 電資學院
開課系所︰ 資工所
考試日期（年月日）︰ 2010/12/6
考試時限（分鐘）： 180
是否需發放獎勵金： 是
（如未明確表示，則不予發放）
試題 :
1. (15%) Surface Normal
(a) (3%) What is the normal vector? (in geometry)
(b) (4%) What relationship do the normal and tangent vector have?
(c) (8%) If we apply a transform matrix M on an object, can M be used to
transform the object's normal vectors? If not, how to tackle this problem
2. (10%) Curves and Surfaces
(a) (7%) If we have four control points for the Bezier curve, P1(1, 2, 5),
P2(5, 8, 3), P3(7, 6 5), and P4(9, 2, 3). In order to draw the curve, we
split it by half. What are the new control points of the two split curves?
(Please give exact numbers).
(b) (3%) Make a brief comparison between Bezier curve and B-spline.
3. (10%) In your homework 2, you realize pixel-based Phong shading utilizing
vertex and fragment shaders. However, Phong shading can still be realized
without shaders. Please describe what should be done in the OpenGL
implementation. (For example, how to find pixels and their normals which will
be rendered on the screen? In your homework 2, those are covered by the
fragment shader.)
4. (10%) Illumination Model
(a) (5%) The Blinn-Phong lighting model uses the half-vector
h = (v + l) / |v + l| and the expression (n ˙ h)^k in its specular term.
Describe the motivation behind the use if the half-vector in this lighting
model.
(b) (5%) Using the rendering equation, can you explain what's wrong with in
Phong shading model for a scene with many objects.
5. (15%) Visible Surface Determination
In general polygon rendering, the Z-buffer technique is used for visible
surface determination. Some modified techniques can be applided to reduce the
rendering time in implementation.
(i) Using depth sort + Z-buffer (always display the nearest polygon first)
(ii) Only using Z-buffer
(a) (10%) Let the screen width = W, height = H, and there are N polygons in
the building model. Based on yours experience, using the teapot model and
CSIE department building model, how will you describe the improvement
(speedup) using (i) over (ii)?
(b) (5%) Compare the computational complexity of the two methods above, in
terms of worst case and average case.
6. (10%) Shadow Generation
(a) (5%) How can shadows be generated in the ray tracing algorithm?
(b) (5%) Besides ray tracing, could you provide another way to simulate shadow
in an OpenGL implementation? (describe the ideas first, then OpenGL
implementation)
7. (10%) Microsoft XBox 369 just announced its KINECT depth camera (each pixel
has a depth from 1 to 10000, at 30 FPS), and has gained more popularity than
its competitor such as Sony Playstation 3. Please give your explanations on
this fact. Why?
8. (15%) BSP Tree
(a) (10%) Construct the binary space partitioning tree of the model in Figure 1
(use polygon 1 as the root, and always use the smaller polygon as the next
node)
(b) (5%) From the BSP tree in (a), derive the correct display sequence in terms
of the viewing position (eye).
2
╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴
︳ ↓ ↖ eye ︳
︳ ⊙ ︳
︳ 4 ↑ ︳
3 ︳ ╴╴╴╴╴╴╴╴╴╴ ︳1
︳ ︳
︳ ︳ ︳
︳→ ︳ ︳
︳ ← ︳5 ← ︳
︳ ↑ ︳ ︳
︳ ╴╴╴╴╴╴╴╴╴╴╴╴ ︳ Figure 1
6
9. (5%) What is your term project for this semester? What are the technical
difficulties involved in the project? (You can refer to the project list).
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