What method of interpolation should I apply to this 3D path data?

For my project, I take x, y, and z coordinates of a tracer particle ever 10 seconds. When I plot these points, they form a 3D curve which I would like to trace. So far, I have used spline(), pchip(), and interp(). However, to my understanding, these interpolation methods only take one axis at a time and performs the interpolations separately. I have looked at cscvn(), from the Curve Fitting Toolbox, but since it is a natural spline, I feel it is also only doing the interpolations in one dimension as well.

My biggest issue with interpolating each dimension separately is with alteration of correlation between the axes.

Are there any methods which utilize all three dimensions at the same time? Maybe a method that considers the points as vectors and performs a vector interpolation? Either way, I would be very appreciative if I was pointed to a method of interpolation which can be performed on all three axes at once rather than one at a time. Thank you very much!