How to get the coordinates of intersection between vessel centerline and sequential MRI/CT slices in markup fiducials?

Dear Andras

I have divided into three steps of the solution that you proposed
Step #1: Get point coordinates of the centerline
Step #2: Get the slice plane position and orientation
Step #3: compute intersection

I can do step #1. Thanks a lot for your guidance. I can get points coordinates of the centerline by two methods:
Method A: Using command suggested by you.
The output I recevied is the following lines:

a = slicer.util.arrayFromModelPoints(slicer.util.getNode(‘CenterlineComputationModel’))
a
array([[ 145.84095764, 35.16293335, -164.67481995],
[ 145.79029846, 35.13619995, -164.64332581],
[ 145.7636261 , 35.12333679, -164.63772583],
[ 145.73847961, 35.11413574, -164.63140869],
[ 145.71414185, 35.10810852, -164.62069702],
[ 145.67230225, 35.09657669, -164.61920166],
[ 145.61857605, 35.08124542, -164.6227417 ],
[ 145.55818176, 35.0341835 , -164.62219238],
[ 145.47712708, 34.97132111, -164.60922241],
[ 145.36305237, 34.89616394, -164.60148621],
[ 145.14250183, 34.80304337, -164.60087585],

[ 136.29968262, 30.57961273, 119.75666809],
[ 136.34971619, 30.54818153, 122.34375 ],
[ 135.77685547, 31.20230293, 124.76610565]], dtype=float32)
Thanks a lot.

Method B: Saving the model of CenterlineComputationModel in vtk file format and open it with text editor. After opening it, I get the following lines inside it:
# vtk DataFile Version 4.1
vtk output SPACE=RAS
ASCII
DATASET POLYDATA
POINTS 154 float
145.841 35.1629 -164.675 145.79 35.1362 -164.643 145.764 35.1233 -164.638

LINES 1 155
154 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153

CELL_DATA 1
FIELD FieldData 1
Topology 2 1 vtkIdType
0 -1
POINT_DATA 154
FIELD FieldData 1
Radius 1 155 double
0 0.93539859067 0.98169177679 1.0529773639 1.1399722485 1.1279945604 1.1710665096 1.3120489148 1.4790625398
1.5613531004 1.5827807416 1.6833454452 1.7331424374 2.4758003289 2.6843646662 2.8318936472 3.0226237442 3.1406634818
3.2299563772 3.3291342158 3.4065516712 3.4812218855 3.558130136 3.6033167794 3.6237193518 3.6420448546 3.6487910235
3.646756415 3.5671632296 3.5345197373 3.6156178149 3.5892311481 3.5454585256 3.5587859741 3.5451988961 3.5659671104
3.5970395968 3.5993437286 3.5626123183 3.5145199888 3.5082920872 3.4765511836 3.3688799134 3.2587559158 3.3173820849
3.3570698617 3.3823053885 3.3323261841 3.3323714364 3.3222690597 3.3258639488 3.3141974444 3.3740845854 3.42227061
3.2932157077 3.1946814846 3.2159209807 3.1234082138 3.0537192217 3.0307876127 3.0736387129 3.1069941974 3.0766833051
3.0464739868 3.0470545098 3.0403655054 3.0116313169 2.9762177261 2.9530425806 2.9602956388 2.9723236359 2.9816882739
2.9728061364 3.0028494712 3.0220091921 3.0711024311 3.1281029641 3.1463048167 3.1366392897 3.1243575617 3.1142074113
3.091457596 3.1092488591 3.1247486255 3.148610963 3.1402409044 3.1902634973 3.2695987862 3.2484048694 3.2246822741
3.2381049868 3.2107577731 3.18916461 3.1834670934 3.192502973 3.2030683332 3.1314524702 3.0870774828 3.0907511031
3.1300404681 3.1447023816 3.1515719341 3.174958119 3.2599369918 3.2984029753 3.2512564972 3.2030528764 3.2006250886
3.1825085274 3.1688352282 3.1323133657 3.1304085566 3.1367795013 3.1228499729 3.1093491959 3.1121296408 3.0806374244
3.0769638698 3.1159708757 3.1032157933 3.0952879332 3.0613003183 3.0197624449 2.9648909979 2.9569908614 2.9897127257
3.0154655444 3.006690353 3.0511237927 3.0857934121 3.1663394771 3.2151247818 3.275425932 3.3145827323 3.3759095419
3.4072440224 3.3584509736 3.3152342845 3.3968093267 3.4845161645 3.541514986 3.4447521872 3.396156225 3.4341717148
3.4326186044 3.3588751135 3.3161116196 3.322315096 3.3851967338 3.3531960108 3.1299476549 2.8655719345 2.1236473996
1.4558911076 0

At now, I have some questions about these lines in CenterlineComputationModel.vtk file.
Question 1: I expected that I have the coordinates of the points (as mentioned above POINTS 154) that are equal to the number of MRI axial slices (173 slices, image dimensions: 512*512*173). Why not?

Question 2: In CenterlineComputationModel.vtk file, I see the following data:
Radius 1 155 double
0 0.93539859067 0.98169177679 1.0529773639 1.1399722485 1.1279945604 1.1710665096 1.3120489148 1.4790625398

What are these numbers?
Can these numbers be related to slice plane position and orientation?

In continue…
At now, I am in the second step.
You mentioned that I must use sliceNode.GetSliceToRAS() to get slice plane position and orientation. For doing it, I refer to reply you in 2D views and 3D model transformation. I enter the following commands:
liceViewName = slicer.app.layoutManager().sliceViewNames()[0]
sliceToRAS = slicer.app.layoutManager().sliceWidget(sliceViewName).sliceLogic().GetSliceNode().GetSliceToRAS()
print(sliceToRAS)

Unfortunately, I do not understand to use GetSliceToRAS method for getting the slice plane position and orientation.

Last question:
How can I save the output of the following command in Python Interactor in a csv file?

a = slicer.util.arrayFromModelPoints(slicer.util.getNode(‘CenterlineComputationModel’))

In other words, what command should I use to do it in Python Interactor?

Please guide me,
Thanks a lot.
Shahrokh