Graphics Reference
In-Depth Information
Section 3.6.1
3.6.1.1.
Find the projective transformation (like in Example 3.6.1.2) that transforms the conic
2
xy
+-++=
2
y
x
y
3
0
into the unit circle.
3.6.1.2.
Find the tangent line to the conic in Exercise 3.6.1.1 at the point (0,1).
3
3.6.1.3.
Find the equation of the conic through the points
p
1
= (1,1),
p
2
= (2,1+(3/2)
),
3
p
3
= (5,1),
p
4
= (4,1-(3/2)
) and that has tangent line x - 1 = 0 at the point
p
1
.
3.6.1.4.
Find the equation of the conic through the points
p
1
= (1,2),
p
2
= (-3,2), and
p
3
= (-1,1) and which has tangent lines y - x - 1 = 0 and x + y + 1 = 0 at the point
p
1
and
p
2
, respectively.
3.6.1.5.
Find the equation of the conic through the points
p
1
= (2,-1) and
p
2
= (4,-2) that has
tangent lines y =-1 and x + y - 2 = 0 at those points, respectively, and is also tangent
to the line 2x - y - 1 = 0.
3.6.1.6.
Solve conic design problem 4.
3.6.1.7.
Solve conic design problem 5.
Section 3.7
3.7.1.
Consider the following quadric surface
2
2
2
22
xy z y
++ - -
2 220
x
-
y
-=.
(a) Determine its type.
(b) Find its tangent plane at the point (0,0,1).
Section 3.10
3.10.1.
Show that the inverse
-
1
n
n
{}
p
n
:
RSe
Æ
n
+
1
of the stereographic projection is defined by
1
(
)
-
1
2
n
()
=
p
y
22
y
,
y
,...,
2
y
,
y
-
1
,
y
Œ
R
.
n
12
n
2
y
+
1
