ray tracing, indices and path length registration
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Albert
am 2 Okt. 2017
Kommentiert: Albert
am 27 Jun. 2018
Dear all
Thank you for reading my following question and I greatly appreciate any of your help.
Problem: Given a grid (N*N) and a non-straight ray with known discrete coordinates, how to register the indices and path length in the pixels crossed by the ray? This is on a plane, what if it is in 3d space? Are there any existing MATLAB script to carry out this function?
Thank you very much.
Sincerely
Albert
6 Kommentare
Alexander Jones
am 26 Jun. 2018
Hello, I am trying to do some microwave tomography, and am in need of a very similar thing - I was wondering if you found a solution to the problem of finding path length, and if so if you could please point me in the right direction.
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Anton Semechko
am 26 Jun. 2018
Bearbeitet: Anton Semechko
am 26 Jun. 2018
For 2D reconstruction, the problem can be approached follows:
1) Let's say you have a set of K rays {Rk}, where Rk is k-th ray parameterized by the equation Rk(t)=Xk+t*Dk, where Xk is the point of origin and Dk is the direction of travel.
2) Given a M-by-M grid (G) sampled on a plane passing through point P with unit normal N, find points of intersection between G and all of the rays {Rk}.
3) Find transformation that aligns N with the z-axis, and horizonal and vertical grid lines of G with the x- and y-axes, respectively.
4) Apply the transformation from (3) to the points of intersection in (2).
5) Bin data from (4) to get the intensity image corresponding to the number of hits in a given bin (i.e., grid cell/pixel).
This process can be easily generalized to get a volumetric image using a 3D grid. This is because 3D grid is just a stack of 2D grids.
2 Kommentare
Anton Semechko
am 27 Jun. 2018
Yeah, I missed the part where you said that the rays aren't straight. In that case, rays can be (i) approximated as piecewise linear curves composed of several straight line segments, (ii) points intersection can be approximated by finding line segments that intersect with the plane containing the grid, (iii) if the rays have analytical representation, points of intersection can be refined using a root-finding algorithm.
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