Graphics Reference
In-Depth Information
Figure 10.16.
An example of the
transformation defined by (10.79).
Y
V
slopes
m
3
m
3
m
2
m
2
m
1
m
1
X
U
V
Y
Y
V
X
U
X
U
(a)
(b)
Y
V
X
U
(c)
Figure 10.17.
Quadratic Transformations of Curves.
m
i
at those points. If the m
i
are distinct, then in effect we have separated the singu-
larity into distinct points that are now simple points (at least if the original tangent
lines had multiplicity 1). This process is referred to as
blowing up
or
resolving
the
singularity.
X
3
- X
2
+ Y
2
10.12.9. Example.
= 0
Equations (10.79) transform this into U - 1 + V
2
Result.
= 0. See Figure 10.17(a).
X
3
- Y
2
10.12.10. Example.
= 0
Equations (10.79) transform this into U - V
2
Result.
= 0. See Figure 10.17(b).
(Y - X
2
) (Y - 3X) = 0
10.12.11. Example.