point in convex hull?

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Noe alvarado 2012-3-23

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https://ww2.mathworks.cn/matlabcentral/answers/33194-point-in-convex-hull

采纳的回答： Friedrich

how compute if a point point is inside the convex hull ?

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Answer 1

Friedrich 2012-3-23

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Hi,

I would use convhull and inpolygon:

xx = -1:.05:1; yy = abs(sqrt(xx));
[x,y] = pol2cart(xx,yy);
k = convhull(x,y);
hold on
plot(x(k),y(k),'r-',x,y,'b+')
x_test = rand(10,1);
y_test = rand(10,1);
IN = inpolygon(x_test,y_test,x(k),y(k))
plot(x_test(IN),y_test(IN),'g*',x_test(~IN),y_test(~IN),'y*')
hold off

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Noe alvarado 2012-3-23

thanks for your answer, but it can work in high dimension?

I'm vorking with points in high dimension (4,5,6..)

Friedrich 2012-3-23

This wont work in higher dimensions. You have to do some smart geometry stuff to get the information you like. you can use convhulln to get the facets of your convex hull and also the corners (x_i, i = 1..m). After that try to get coefficients a_i > 0 so that

sum_i x_i*a_i = v where sum_i a_i = 1 (basically that's the definition of the convex hull). (v is the vector you like to know if its inside or outside of the convex hull). Finding one solution for the system of equations is easy, but the condition that the sum over the coefficients gives 1 is pretty tricky. I don't know if there is an easy way to get solve this.

Seems more like a mathematical question rather than a MATLAB question for me.

If you know an algorithm come back and ask how to implement/use this in MATLAB. But first you need to know how to check this in theory before doing it in MATLAB.

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