Extracting points for sharp curvature from signed distance function array

Question

Geoffrey Rivers 2023-4-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1949168-extracting-points-for-sharp-curvature-from-signed-distance-function-array

回答： Supraja 2023-5-5

I have a signed distance array, extracted from a black-and-white bitmap. The shape described by the bitmap is arbitrary, and could contain concave or convex curvature of varying scales. I am interested in extracting the position of corners that are sharper than a certain amount. I'm frankly not sure how to define that sharpness here; what I care about is 'shoving' a circle of a defined radius into that corner, and for the corner in total to be larger than that circle (in other words, I don't want it reporting every single rasterisation of the bitmap):

identifying if any convex curvatures' radius is less a code-defined radius of curvature limit
calculating what coordinate in the bitmap represents the centrepoint of the code-defined radius of curvature limit for that corner, and then
to list any and all found sets of centerpoint coordinates in an array of format T= [x1, y1; x2, y2; .... xn, yn].

I'm obtaining my distance array and interpolation function as follows.

    X = imread("MeshTest01.bmp"); %load logical (1 or 0) bitmap
    A = imrotate(X,-90);
    E=edge(A);  % Edge finding of bitmap
    DistE = bwdist(E, "euclidean"); % signed distance function from edge 
    DistA = bwdist(A, "euclidean"); % signed distance function from whitespace
    D = DistE-2*DistA % Pixel-enumerative distance for signed distance function from material (outside is positive)
    D = double(D); %make array forced to Double so interpolation works correctly
    
    Fi = griddedInterpolant(D,'linear')
    
    fd=@(p) Fi(p);  %defining the interpolation function call

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Answer 1

Supraja 2023-5-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1949168-extracting-points-for-sharp-curvature-from-signed-distance-function-array#answer_1229609

在 MATLAB Online 中打开

You can use ‘ischange()’ function which detects abrupt changes in data.

The detailed documentation link for the same is given here: https://www.mathworks.com/help/matlab/ref/ischange.html?searchHighlight=ischange%20function&s_tid=srchtitle_ischange%20function_1

The sample code to use this function is as shown below:

f = @(x) 1-(x./sqrt(1+x.^2)); % Create Function

x = linspace(-10, 10);

y = f(x);

changes = ischange(y, 'linear', 'SamplePoints', x);

plot(x, y, '-', x(changes), y(changes), 'gp')

grid on

axis('equal')

xlim([-2.5 2.5])