How to add minimum radius of curvature limitation to 3D spline interpolation?
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I have 3D points data that a line should pass through these points. For this purpose I am using following code:
n = numel(xxx) ;
L = zeros(n,1) ;
for i=2:n
arc_length = sqrt((xxx(i)-xxx(i-1))^2+(yyy(i)-yyy(i-1))^2+(zzz(i)-zzz(i-1))^2);
L(i) = L(i-1) + arc_length;
end
% Normalize the arc lengths
L=L./L(n);
% do the spline
x_t = spline(L,xxx) ;
y_t = spline(L,yyy) ;
z_t = spline(L,zzz) ;
% for interpolation
tt = linspace(0,1,500) ;
xi = ppval(x_t,tt) ;
yi = ppval(y_t,tt) ;
zi = ppval(z_t,tt) ;
plot3(xi,yi,zi,'.b') ;
However, this line mimics seabed pipeline, therefore, there is a limitation for minimum radius of curvature. I need your opinions that how can I add that limitation to interpolation.
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