8.5.4 Edge setup quadratic case
8.5.4.1
Mathematical background
It is also possible to setup the limiters to incrementally calculate the following
equation:
f
dy
cx
by
ax
y
x
f
+
+
+
+
=
2
2
)
,
(
At the origin the value is like this:
f
f
=
)
0
,
0
(
The step in x direction is like this:
1
2
)
(
)
,
1
(
)
(
1
2
)
,
(
1
2
)
1
(
)
1
(
)
,
1
(
2
2
2
2
+
+
=
−
+
=
+
+
+
=
+
+
+
+
+
+
+
=
+
+
+
+
+
+
=
+
c
ax
x
f
y
x
f
x
dx
c
ax
y
x
f
f
dy
c
cx
by
ax
ax
f
dy
x
c
by
x
a
y
x
f
The step in y direction is like this:
1
2
)
(
)
,
1
(
)
(
1
2
)
,
(
1
2
)
1
(
)
1
(
)
1
,
(
2
2
2
2
+
+
=
−
+
=
+
+
=
+
+
+
+
+
+
+
=
+
+
+
+
+
+
=
+
d
by
x
f
y
x
f
y
dy
bx
y
x
f
f
d
dy
cx
by
by
ax
f
y
d
cx
y
b
ax
y
x
f
In the quadratic case the increments
dx
,
dy
depend on x and y and are not
constant. They can be calculated incrementally:
a
c
ax
c
x
a
x
dx
x
dx
x
d
2
)
1
2
(
1
)
1
(
2
)
(
)
1
(
2
=
+
+
−
+
+
+
=
−
+
=
b
d
by
d
y
b
y
dy
y
dy
y
d
2
)
1
2
(
1
)
1
(
2
)
(
)
1
(
2
=
+
+
−
+
+
+
=
−
+
=
At the Origin the increments are like this:
1
)
0
(
+
=
c
dx
and
1
)
0
(
+
=
d
dy
With incrementing the value by
dx
,
dy
for every step in x and y direction and
incrementing
dx
,
dy
by
x
d
2
,
y
d
2
for every step in x and y direction the quadratic
equation can be easily calculated for the whole bounding box.
Drawing Engine
Chapter 8
Preliminary User's Manual S19203EE1V3UM00
231
Содержание uPD72257
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