Doug's MATLAB Video Tutorials

May 5th, 2010

By Doug Hull

Doug first used MATLAB in 1994, could not figure it out until he got some help in 1995. He is now dedicated to making sure that no one else wastes a year of their life not knowing MATLAB like he did.

20:40 UTC | Posted in Format: Video, Level: Basic, Topic: Practical example | Permalink | 3 Comments »

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3 Responses to “Set up: Finding closest point on a surface”

1. Matt Whitaker replied on May 6th, 2010 at 15:25 UTC :
   

   Hi Doug,
   This calculation is a very common one in medical physics for radiation therapy quality assurance. We have an expected dose distribution in [X,Y,Dose] space from a treatment planning system and a measured dose distribution in the same space. There is a ‘gamma’ metric that is derived from calculating the minimum distance from all the points(in practice pixels) on one surface to the other surface. The distance is normalized to dose difference and distance to agreement tolerances but the basic calculation is as you describe. There have been a number of numerical solutions in the fields similar to what you describe in your video.

   For an elegant computational geometry solution see:
   Geometric interpretation of the gamma dose distribution comparison technique: Interpolation-free calculation
   Med. Phys. Volume 35, Issue 3, pp. 879-887 (March 2008)
   http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=MPHYA6000035000003000879000001&idtype=cvips&gifs=yes&ref=no

   This has a really nice recursive algorithm that solves minimum distance to a 3 point ‘simplex’ whether that point falls in the surface , on the edges, or at the vertices.

   Anyways thanks for the video on a subject that is relevant to my daily work.

   Matt W.

2. dhull replied on May 6th, 2010 at 15:40 UTC :
   

   @Matt,

   Thanks for the kind words and the link. The next installment will show the actual code used. I think for this problem, the implementation was much easier than figuring out what to implement.

3. Joao replied on May 8th, 2010 at 18:11 UTC :
   

   I believe an elegant and precise solution for this problem that is easily done in MATLAB would be to use a Linear Programming model to minimize the distance from the external point to the affine space of all the vertices (v_{1} … v_{j}) of the 3D shape (only works for a convex space). Using the linearized 1-norm, a model would be:

   min{a} Z = sum_{i} (z_{i})
   s.t.: sum (a_{j}) = 1 ; a_{j} >=0
   z_{i} >= [sum_{i,j}(a_{j}*v_{j,i}) - P_{i}]
   z_{i} >= -[sum_{i,j}(a_{j}*v_{j,i}) - P_{i}]

   where 1<= j <= no of vertices; 1<=i<=3

   It has the disadvantage (advantage?) that it will find the closest point to the affine space of the surface. Thus if the point is inside the space enclosed by the surface, it will be the solution.

   Non-convex spaces would have to be broken into convex subspaces before applying the algorithm.

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<pre class="code">
a = magic(3);
sum(a)
</pre>

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