8.5.3 Edge setup linear case
8.5.3.1
Mathematical background
To setup a linear edge you can look at the line equation in the classical form:
b
x
a
y
~
~
+
=
If you rewrite this you can write it as:
c
y
b
x
a
b
y
x
a
y
x
f
+
⋅
+
⋅
=
+
−
⋅
=
=
~
~
)
,
(
0
with
b
c
b
a
a
~
,
1
,
~
=
−
=
=
This is a more general form. Lets look at a vector form with
c
n
p
c
y
b
x
a
y
x
f
b
a
n
y
x
p
+
⋅
=
+
⋅
+
⋅
=
⇒
=
=
)
,
(
,
If a point
0
p
is on the line then
n
p
c
c
n
p
y
x
f
⋅
−
=
⇒
+
⋅
=
=
0
0
)
,
(
0
If you rewrite the constant the equation looks like this:
(
)
n
p
p
y
x
f
n
p
c
⋅
−
=
⇒
⋅
−
=
0
0
)
,
(
The vector
n
is called the normal vector and it is perpendicular to the line. The
setup can be seen in the next image.
n
O
p
0
p
0
p
p
−
d
Drawing Engine
Chapter 8
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