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Ray Tracing: Siddon’s algorithm (illustrated in 2D)
………… as being intersections p
i
with the equally spaced
vertical and horizontal lines (by a) in blue
X
X coordinates of the
intersection points (green):
X
geo
geo
1
42
x
x
x
i,x
,
i
⋅
α+ =
=
(
)
x/ x x
− = α
and green
26
p
1
p
2
p
3
p
4
p
5
p
6
Y
geo
1
6531
y
y
y
i,y
, , , i
⋅
α+ =
=
y
geo
geo
1
i
i,x
(
)
geo
1
y/ y y
i
i,y
− = α
a
Y coordinates of the
intersection points (blue):
The
α
x,i
and
α
y,i
can be merged into a
common series of
increasing values
:
{ }
[
]
{
}
{
}
6
1
α α α
α α
=α
..., ,
...., ,
,
merge
m
i,y i,x