Extract border points from surface points (compatible with autogeneration in C)

Hello everyone! I am working in MatLab r2017a and I am doing some geometrical computations. I got all the points of a surface with which I am working in x and y coordinates. I am trying to extract only the points of the border of this surface, but I can't use MatLab functions that are not compatible with autogeneration in C and I also have to use only fixed-size variables. I already tried to extract them using a local search for extremes in x and y but it doesn't work properly. Can you help me finding a way to implement this?

This is an example of the kind of surface points I get. There are some regions with denser points because this is the result of the projection of a 3D surface in a 2D plane that should represents my FOV.

I hope someone will help me find a solution! Thanks a lot in advance!

Answer 1

[Image Analyst]

Try alphaShape

help alphaShape

 alphaShape - Polygons and polyhedra from points in 2-D and 3-D
    An alphaShape creates a bounding area or volume that envelops a set of
    2-D or 3-D points.

    Creation
      Syntax
        shp = alphaShape(x,y)
        shp = alphaShape(x,y,z)
        shp = alphaShape(P)
        shp = alphaShape(___,a)
        shp = alphaShape(___,Name,Value)

      Input Arguments
        x - x-coordinates
          column vector
        y - y-coordinates
          column vector
        z - z-coordinates
          column vector
        P - Point coordinates
          matrix with two columns | matrix with three columns
        a - Alpha radius
          nonnegative scalar

      Name-Value Arguments
        HoleThreshold - Maximum interior holes
          0 (default) | finite, nonnegative scalar
        RegionThreshold - Maximum regions
          0 (default) | finite, nonnegative scalar

    Properties
      Points - Coordinates of points
        matrix
      Alpha - Alpha radius
        nonnegative scalar
      HoleThreshold - Maximum interior holes
        0 (default) | finite nonnegative scalar
      RegionThreshold - Maximum regions
        0 (default) | finite nonnegative scalar

    Object Functions
      numRegions         - Number of regions in alpha shape
      area               - Area of 2-D alpha shape
      perimeter          - Perimeter of 2-D alpha shape
      surfaceArea        - Surface area of 3-D alpha shape
      volume             - Volume of 3-D alpha shape
      boundaryFacets     - Boundary facets of alpha shape
      alphaTriangulation - Triangulation that fills alpha shape
      inShape            - Determine if point is inside alpha shape
      alphaSpectrum      - Alpha values giving distinct alpha shapes
      criticalAlpha      - Alpha radius defining critical transition in shape
      nearestNeighbor    - Determine nearest alpha shape boundary point
      plot               - Plot alpha shape

    Examples
      openExample('matlab/AlphaShapeFrom2DPointCloudExample')
      openExample('matlab/AlphaShapeFrom3DPointCloudExample')
      openExample('matlab/FillHolesIn2DAlphaShapeExample')
      openExample('matlab/DiscardSmallRegionsOf3DAlphaShapeExample')
      openExample('matlab/ModifyPointsOf2DAlphaShapeExample')

    See also convhull, boundary, delaunayTriangulation, triangulation,
      trisurf, criticalAlpha

    Introduced in MATLAB in R2014b
    Documentation for alphaShape
       doc alphaShape

th = (pi/12:pi/12:2*pi)';
x1 = [reshape(cos(th)*(1:5), numel(cos(th)*(1:5)),1); 0];
y1 = [reshape(sin(th)*(1:5), numel(sin(th)*(1:5)),1); 0];
x = [x1; x1+15];
y = [y1; y1];
plot(x,y,'.')
axis equal

shp = alphaShape(x,y);
plot(shp)

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[Alessio]

Ouch, sorry if I didn't follow the rules for writing questions. I haven't attached my data and code because it consists only of a surface generation and projection in the new reference frame in the present state.

Thanks a lot for the answer, it would work normally but unluckily alphaShape is not compatible with autogeneration in C.

I will keep looking for alternative solutions!