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Midterm Exam with Solutions - Computer Graphics | SOCC 167, Exams of Introduction to Sociology

University of California - San DiegoIntroduction to Sociology

Material Type: Exam; Class: Science and War; Subject: Computer Science & Engineering; University: University of California - San Diego; Term: Winter 2003;

Typology: Exams

2009/2010

Uploaded on 03/28/2010

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Midterm Exam: Solutions
CSE 167, Winter 2003
Date: 2/14/2003
Questions:
1. Given the following code, find the current Modelview matrix as a set of
matrix multiplications. (You don’t have to actually multiply the matrices)
glMatrixMode(GL_MODEL_VIEW);
glLoadIdentity();
glTranslatei( 5, 2, 1 );
glRotatef( 1.0f, 0.0, 0.0, 1.0f );
−
1000
1100
20)180/cos()180/sin(
50)180/sin()180/cos(
ππ
ππ
pf3
pf4
pf5

Partial preview of the text

Download Midterm Exam with Solutions - Computer Graphics | SOCC 167 and more Exams Introduction to Sociology in PDF only on Docsity!

Midterm Exam: SolutionsCSE 167, Winter 2003

Date: 2/14/

Questions:

1. Given the following code, find the current Modelview matrix as a set of matrix multiplications. (You don’t have to actually multiply the matrices)

glMatrixMode(GL_MODEL_VIEW);glLoadIdentity();

glTranslatei( 5, 2, 1 );glRotatef( 1.0f, 0.0, 0.0, 1.0f );

cos(sin(ππ// 180180 )) cos(sin( ππ// 180180 )) 00 25

2. Suppose a triangle in object coordinates is represented by the following threepoints ( each point has the format: (x,y,z)):

P0: ( 1, 5 , 10 )P1: ( 3, 21, 10 )

P2: ( 5, -5, 10 )

Find a combination of transformations that will represent the triangle by thefollowing points in world coordinates:

P0’ : ( -1, 6, 13 )P1’: ( 3, 14, 13 )

P2’: ( 7, 1, 13 )

Write the transformation as a series of matrix multiplications in the correctorder. (You don’t have to actually do the multiplication)

Recognize that the problem is asking:Find the matrix such that the following is true

61 eai bfj kgc hdl and eai bfj kgc dhl and aei bfj kgc dh l

Step 1:The last transformation is a z-translation by 3. Remove z-translationby subtracting the constant difference between z-values from P0’,P1’,P2’

Now the problem is as follows.



 

 

 

− 

 

 

 

 

 

 

 

=^  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=^  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=^  

 

 

 

− (^101)

(^55) 00 00 01 13 0 0 0 1

01 10 00 00 (^131) 17 (^101) 213 00 00 01 13 0 0 0 1

01 10 00 00 (^131) 143 (^101) 51 00 00 01 13 0 0 0 1

01 10 00 00 (^131) 61 aie bfj kgc hdl and eai fbj kgc hdl and eai bfj kgc d lh or 

 

 

 

− 

 

 

 

=^  

 

 

 

 

 

 

 

 

 

 

 

=^  

 

 

 

 

 

 

 

 

 

 

 

=^  

 

 

 

− (^101)

(^55) (^1010001) 17 (^101) 213 (^1010001) 143 (^101) 51 (^1010001) 61 eai bfj kgc dlh and eai bfj kgc dlh and eai bfj kgc hd l

Step 2: Graph out the two triangles (after removing translation), note thatthis is now a 2-D problem because both triangles are on the same z-plane.

02.^050000

02.^050000

02.^050000

3. a. Orthogonal projection of PO:(-1,6,13), P1:(3,14,13), P2(7,1,13):

Use diagrams below, but need to first translate such that COP is at (0,0,-4), calculateb. Perspective projection w/ COP at (1,1,-4)

projected coordinates, and then translate back.Answers:

(x, z)

z

x

(xp, zp=-3)

z^ x /^ 1 = x^ p Y

(yp, zp=-3) z

z^ y /^ 1 = y^ p

(y, z)