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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︰資工系
考試日期（年月日）︰2008.11.24
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 :
Interactive Computer Graphics Midterm Exam 11/24, 2008
1.Shadow generation:(10%)
(a)(5%)Why there will be shadows in a scene with Ray Tracing Algorithm?
(b)(5%)Please describe briefly any method as to how to add fake shadows?
(Hint: Visible-surface algorithm with some modifications is one possible
solution. Maybe you can draw some pictures to show the ideas.)
2.Shading(10%)
(a)(5%)Please describe the Gouraud Shading and Phong shading. Draw a triangle
and state how the colors of interior pixels are interpolated.
(b)(5%)What are the visual differences between Gouraud Shading and Phong
Shading? Also, discuss the cffect on simple models and complex models.
3.(5%)What is your term project for this semester? What are the technical
difficulties involved in the project?(You can refer to the project listing.)
4.The Rendering Equation(20%)
(a)(10%)What is "The Rendering Equation", please draw pictures and show the
equations with short explanations.
(b)(10%)Using the above equation to explain the weakness of Phong shading and
ray tracing.
5.(15%)In two dimensions, we can specify a line by the equation y = mx + b.
(a)(10%)Find an affine transformation to reflect two-dimensional points about
this line.
(b)(5%)Extend your results to reflection about a plane in three dimensions.
6.(10%)In 2D, please consider if a rotation transformation by angle A can be
specified as a series of shear transformation matrices. Give these matrices,
or it can't be done, prove it.
7.Illumination Models(20%)
A popular illumination model is called Phong model, which is developed in 1975.
The formula of this model for each color channel is(please refer to textbook):
_ _ _ _
I = IakaOd + fattIp[kdOd(N‧L) + ks(R‧V)^n].
where L is light direction, V is viewing direction.
(a)(6%)Could you give two examples of materials that definitely can not be
approximated by the Phong model? And simply explain why.
(b)(8%)A general depiction of illumination model is called bidirectional
reflectance distribution function (BRDF) (bidirectional reflectivity):
I = fBRDF(L,V).
The idea of this function is that given a viewing and lighting(single light
source) direction, the BRDF function returns its reflectance (or precisely,
the retio between the incident flux and reflected intensity).
Please design a platform to capture BRDF of materials. You will have the
following equipments:
1.Spheres of different materials
2.A digital camera
3.A light source with a 1DOF rotational arm that allows you to move the
light direction horizontally.
(c)(6%)The function I, if stored as a database, can be quite big(much larger
than 1.0 Giga bytes). This can be a problem for ordinary PC graphics card in
real-time graphics. Can you think of a way to compress the data of function I?
(Assume viewing and lighting direction is in division of one degree, say in
spherical coordinate system, per sample in theta and phi direction.).
8.BSPtree(10%)
i.(5%)Construct the Binary Space Partitioning(BSP) tree of the model in Fig 1.
Please use the right part of node 3 as the root.
Split any line segment as you wish, and mark them as a, b, c, d etc.
ii.(5%)From the BSP tree in (a), derive the display sequence in terms of the
viewing position "the eye".
2
-----------------------------
│ ↓ │
│6 │
│→ │
│ ←│1
│eye ↑3 │
│ ------------ │
5│ │ │
│ ↑ │→
-------------│ Figure 1.
│
│4
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