blank space in alpha shape

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yonatan s 2017-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/338057-blank-space-in-alpha-shape

评论： John D'Errico 2017-4-30

crater from above.jpg

在 MATLAB Online 中打开

using the alphavol function i wrote the following code:

%create crater alpha shape. 
clear;clc;
ddr=0.12; %depth diameter ratio
a=1/ddr/2; %semi major axis. horizontal axes are equal 
n=31; %number of points for x y vectors. 
x = linspace(-a,a,n);
y = linspace(-a,a,n);
[X,Y] = meshgrid(x,y);
Z =real(sqrt(1-(X.^2)/a^2-(Y.^2)/a^2))*-1+1; % the plus for Z>0
[V,S] = alphavol([X(:),Y(:),Z(:)],1,1);
trisurf(S.bnd,X,Y,Z,'FaceColor','blue','FaceAlpha',1)
xlabel('x');ylabel('y');zlabel('z'); 
___

as the picture shows, i get blank space in the bottom of the shape. i know i can resolve this by assigning greater values to n, but it is still only an approximation. also, i dont want to set up R=inf, because this will give a surface on the X-Y plane(where z=1).

thank you for your help

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Image Analyst 2017-4-30

Do you want to fill in the hole? If so try regionfill().

John D'Errico 2017-4-30

Of course, if you fill in the hole, then what is the purpose of the alpha shape?

As for something being an approximation, ANYTHING you do on a computer is an approximation. The skill of working on a computer, in any discipline, be it applied mathematics, statistics, image processing, any engineering discipline, any physical science, etc., is in knowing what approximations are viable to use, and which ones will kill you.

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