COMSATS Institute of Information Technology Lahore | Department of Computer Science | Program Name: BS(CS) 2012-Fall | Course Title: Computer Graphics | Assignment #: 1 | Assignment out: 12-09-2012 | Topic: Math. for CG | Last date of submission: 19-09-2012 |
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Name: Hassaan Javaid Roll # 23
Evaluation: Through quiz
Credit: 10
Instructions:
1. Submit your assignment in hard form in class as per format given in course hand book. It must include a. Start page(s): print of this sheet b. Plagiarism policy with your signature. Assignments without it, will not be checked. Download it from http://zulfiqar.8m.com. 2. Late submission policy: deduction @ of 10% of total marks per day.

Problem Statements:
1. Vectors
Given vertices P1 = (1, 1, 0), P2 = (1, 0, 2), and P3 = (3, 2, 0) of a triangle T, counter clock wise around the normal. a. Find vector u from P1 to P2 b. Find vector v from P1 to P3 c. (u+v).(u-v) d. (u+v)×(u-v) e. the length of u f. the vector 3 times longer than u g. the unit vector of u h. the angle between u & v i. the length of projection of u on v j. compute the normal to T k. compute the area of T

2. Matrices
Let A = 123404212, B= 213114330 a. Compute C = AB b. Does AB = BA? c. Given the vector u from previous question, find Au d. Given the vector v from previous question, find vTA

3. Frames
Express point P in each of the given coordinate frames.P i o
F1
i j o
F2
j i o
F3
j i o
F4
j i o
F5
j
P
i o F1 i j o F2 j i o F3 j i o F4 j i o F5 j 4. Segments & Lines
Given P1(1, 2, 3) and P2(5, 5, 5). a. Find a line in parametric form using parameter t starting from P1 and ending at P2 b. Compute a point on the line at t = 1/3

Vectors
a) Find vector u from P1 to P2
U = P2-P1
U = (1,0,2)-(1,1,0)
U= (0,-1,2)

b) Find vector v from P1 to P3
V = P3-P1
V=(3,2,0)-(1,1,0)
V = (2, 1, 0)
c) (u+v).(u-v)

(u+v) = (2,1,0) +(0,-1,2)
(u+v) = (2,0,2)

(u-v) = (0,-1,2)-(2,1,0)
(u-v) =(-2,-2,2)
(u+v).(u-v) =(2,0,2) ∙ (-2,-2,2)
(u+v).(u-v) = 0

d) (u+v)×(u-v)
= (2,0,2) x (-2,-2,2)
= (4 ,-8 , -4)

e) the length of U
U=4+1
U =5

f) the vector 3 times longer than u
= 3U
= (0, -3, 6)
g) the unit vector of u
= (0, 3 /√5 , 6 / √5 )

h) the angle between u & v cosθ = -1√5×√5 θ=101.53 i) the length of projection of u on v
= U ∙ VV
=( 0, -1 , 2 )∙( 2 / √5 , 1/ √5, 0 )
= - 1√5

j) Compute the normal to T
= U x V
= 2i + 4j + 2k

k) Compute the area of T
= U×V
= 4+16+4
=26
Area of triangle = 6

2. Matrices
Let A = 123404212, B= 213114330

A) Compute C = AB

C = 13121120161211910,
b) Does AB = BA?
No because BA = 127161361615621

c) Given the vector u from previous question, find Au
Not possible

d) Given the vector v from previous question, find vTA
Not possible

3. Frames
a) Express point P in each of the given coordinate frames
F1 (-2,-2), F2 (-0.5, 2), F3 (2.5, 1), F4 (2, 1), F5 (2, 3)

4. Segments & Lines
Given P1 (1, 2, 3) and P2 (5, 5, 5).
a) Find a line in parametric form using parameter t starting from P1 and ending at P2
P1P2 = (4, 3, 2)
X=1+4t
Y=2+3t
Z =3+2t

b) Compute a point on the line at t = 1/3
= (73,3,113)

Plagiarism Policy
Plagiarism involves the unacknowledged use of someone else’s work, usually in coursework, and passing
It offs as if it were one’s own. Many students who submit apparently plagiarized work probably do so inadvertently without realizing it because of poorly developed study skills, including note taking, referencing and citations; this is poor academic practice rather than malpractice. Some students, particularly those from different cultures and educational systems, find UK academic referencing/acknowledgement systems and conventions awkward, and proof-reading is not always easy for dyslexic students and some visually-impaired students. Study skills education within programmes of study should minimize the number of students submitting poorly referenced work. However, some students plagiarize deliberately, with the intent to deceive. This intentional malpractice is a conscious, pre-mediated form of cheating and is regarded as a particularly serious breach of the core values of academic integrity. The Dual Degree Prorgamme has zero tolerance for intentional plagiarism.
Plagiarism can include the following:
1. Collusion, where a piece of work prepared by a group is represented as if it were the student’s own;
2. Commission or use of work by the student which is not his/her own and representing it as if it were, e.g. :a. purchase of a paper from a commercial service, including internet sites, whether prewritten or specially prepared for the student concerned
b. submission of a paper written by another person, either by a fellow student or a person who is not a member of the university;
3. Duplication (of one’s own work) of the same or almost identical work for more than one module;
4. The act of copying or paraphrasing a paper from a source text, whether in manuscript, printed or electronic form, without appropriate acknowledgement (this includes quoting directly from another source with a reference but without quotation marks);
5. Submission of another student’s work, whether with or without that student’s knowledge or consent;
6. Directly quoting from model solutions/answers made available in previous years;
7. Cheating in class tests, e.g. a. when a candidate communicates, or attempts to communicate, with a fellow candidate or individual who is neither an invigilator nor member of staff
b. copies, or attempts to copy from a fellow candidate
c. attempts to introduce or consult during the examination any unauthorized printed or written material, or electronic calculating, information storage device, mobile phones or other communication device
D. personates or allows himself or herself to be impersonated.
8. Fabrication of results occurs when a student claims to have carried out tests, experiments or observations that have not taken place or presents results not supported by the evidence with the object of obtaining an unfair advantage.
These definitions apply to work in whatever format it is presented, including written work, online submissions, group work and oral presentations.
I ______________________________ Roll #__________________have read the plagiarism policy.
Signature: _______________________ Date: _______________