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circlefit3d - fit circle to three points in 3d space

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circlefit3d - fit circle to three points in 3d space

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26 Jan 2012 (Updated )

Calculate center, radius and plane of circle that passes through three given points

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Description

[center,rad,v1,v2] = circlefit3d(p1,p2,p3)

This function computes centers and radii of circles, that interpolate some given triples of points in 3d space.

The function accepts the input of matrices of trial points also, returning a matrix of corresponding centroids and a vector of corresponding radii. Corresponding points are assumed to be located in the same row in each matrix p1, p2 and p3.

Several error checks are done (collinearity, size of inputs) and return different error codes in return argument rad.

The function uses vector algebra only, is fully vectorized and should run quite fast.

Additional outputs are basis vectors v1 and v2 to describe the plane of the resulting circle.

Check:

p1=rand(4,3);p2=rand(4,3);p3=rand(4,3);
[center,rad,v1,v2] = circlefit3d(p1,p2,p3);
plot3(p1(:,1),p1(:,2),p1(:,3),'bo');hold on;plot3(p2(:,1),p2(:,2),p2(:,3),'bo');plot3(p3(:,1),p3(:,2),p3(:,3),'bo');
for i=1:361,
 a = i/180*pi;
 x = center(:,1)+sin(a)*rad.*v1(:,1)+cos(a)*rad.*v2(:,1);
 y = center(:,2)+sin(a)*rad.*v1(:,2)+cos(a)*rad.*v2(:,2);
 z = center(:,3)+sin(a)*rad.*v1(:,3)+cos(a)*rad.*v2(:,3);
 plot3(x,y,z,'r.');
end
axis equal;grid on;rotate3d on;

Required Products MATLAB
MATLAB release MATLAB 7.11 (R2010b)
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Comments and Ratings (2)
21 Mar 2014 Fernando

Thanks!!! very helpful

02 Aug 2012 Job

Thanks for sharing!

Updates
27 Jan 2012

minor bugfixes

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