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Ray Tracing: Siddon’s algorithm
An individual distance d
1 ,
d
2 ,
..d
m
.. d
M
can be calculated as:
with
[
]
1
geo
−
α−α⋅
=
m m
m
d d
2
geo
2
geo
geo
y x
d
+
=
Finally, one obtains the radiological path as:
[
]
∑
µ⋅
α−α ⋅
=
−
j
i
m m
d
d
m)(k,m)(,m)( 1
geo
radiol
27
This approach does not scale with the number of
voxels
N
i
x N
j
x N
k
but with number of
planes
(N
i
+1)+(N
j
+1)+(N
k
+1).
For instance in the same voxel array:
Instead of 256 x 256 x 64 = 4 million iterations we need
only (256+1)+(256+1)+(64+1) = 579 iterations
m