3D line approximation (spline)

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Hi everyone,

How can we use "spline" to approximate a sequence of points in three dimension rather than interpolate?

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Hongying LI 2011-2-21

I do look for a "approximation" method for a line in "3D".(I have done the interpolation)

Hongying LI 2011-2-22

% choose the number of pieces

pieces = 3;

s = cumsum([0;sqrt(diff(x(:)).^2 + diff(y(:)).^2 + diff(z(:)).^2)]);

pp1 = splinefit(s,xyz,pieces);

xyz1 = ppval(pp1,s);

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Answer 1

Bruno Luong 2011-2-21

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It's called spline fitting. Please take a look at File Exchange, such as

http://www.mathworks.com/matlabcentral/fileexchange/13812-splinefit

http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

http://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation

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Hongying LI 2011-2-21

Thanks Bruno,

This is my previous codes:

function newCurve = spline3dCurveInterpolation(curve, dt)

% interpote a 3d curve using spline

% path 3*x

% newPath 3*x

x = curve(1, :);

y = curve(2, :);

z = curve(3, :);

t = cumsum([0;sqrt(diff(x(:)).^2 + diff(y(:)).^2 + diff(z(:)).^2)]);

sx = spline(t,x);

sy = spline(t,y);

sz = spline(t,z);

tt = t(1):dt:t(end);

xp = ppval(sx, tt);

yp = ppval(sy, tt);

zp = ppval(sz, tt);

newCurve = [xp; yp; zp];

% end of function

Now, I'm thinking about the approximation and I don't want the line strictly pass the original points.(maybe I still don't understand your answer)

Bruno Luong 2011-2-21

Did you try the FEX file (try the first one) above? They are approximation (fitting) not interpolation, exactly as your request if I'm not mistaken.

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3D line approximation (spline)

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