3D line approximation (spline)

Hi everyone,

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

[Hongying LI]

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

[Hongying LI]

% 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);

Answer 1

[Bruno Luong]

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

[Hongying LI]

Maybe you mean that I should learn from these and write one myself ? (as I think that these files can not be used directly to approximate a 3D line)

[Bruno Luong]

No. I do not mean that. A 3D line are simply three independent functions parametrized by an independent variables (called t for example).

All you need is interpolate (xi,yi,zi) by

xi = f(ti)

yi = g(ti)

zi = h(ti)

I recommend select {ti} as the cumulative sum of the euclidian distance of the data.

[Hongying LI]

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]

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.