Graphic Design and Mathematical Concepts (CSC219)
Computer Science - COS
Semester: Resit
Level: 300
Year: 2015
1
SCHOOL: H.T.T.T.C DEPARTEMENT: CS LECTURER: Dr. DADA Jean-Pierre
COURSE CODE: CS222 COURSE TITLE: Graphic design mathematical concepts
OPTION: FCS DATE: September, 2015 HALL: TIME: 1:30 NATURE: Resit
Instructions:…… NA…………..
Exercise 1: Demonstrate that for a scaling, the homogenous matrix 0(0,0,0) as the center could be written in the
form:
=
1 0 0 0
0k 0 0
0 0k 0
0 0 0 k
H
where k is the ratio.
Exercise 2: Demonstrate that for a scaling, the homogenous matrix 0(a,b,c) as the center could be written in the
form:
=
1 0 0 0
k)-c(1k 0 0
k)-b(1 0k 0
k)-a(1 0 0 k
H
where k is the ratio.
Exercise 3: Demonstrate that for a rotation around OX axis, the homogenous matrix could be written in the
form:
=
1 0 0 0
0 cos sin 0
0 sin- cos 0
0 0 0 1
ox
R
where
is the rotation angle.
Exercise 4: Let us consider Hermitian curves define with two points
1
P
et
2
P
and the tangents at those points
/
1
P
et
/
2
P
. By taking a degree 3 Hermitian curve, demonstrate that the coordinates of a point M can be written
on the form:
( )
=
/
2
/
1
2
1
123
0 0 0 1
0 1 0 0
1- 2- 3 3-
1 1 2- 2
1 ),,(
P
P
P
P
tttzyx
And give the expression of Hermitian polynomials
)(tH
i
(i=1,2,3,4).
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