Dose 2016

Ray Tracing: Siddon’s algorithm An individual distance d 1 , d 2 , ..d m .. d M

can be calculated as:

[

]

d d

2 geo

2 geo y x

=

− α−α⋅ m m

with

d

geo

1

=

+

m

geo

Finally, one obtains the radiological path as:

[

]

∑

d

d

=

µ⋅ α−α ⋅ i m m −

radiol

geo

m)(k,m)(,m)( 1

j

m

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

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