# Thread: Splines in 3D space

1. ## Splines in 3D space

Hello, I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanation on how to use splines to achieve this. Are splines a subset of other types of curves such as Bezier curve or the Hermite curve?

2. ## Re: Splines in 3D space

How did you find cubic splines in 2 dimensions? Extension to three dimensions should be straightforward.

3. ## Re: Splines in 3D space

Hi,
Natural cubic spline interpolation is done separately in each dimension. So as soon as you can do it in one dimension, you can do it anywhere. This web page has all the relevant information for one dimensional interpolation -- Cubic Spline -- from Wolfram MathWorld. Just repeat in each coordinate. The reference cited (Bartels et al) is 25 years old, but the math is still good. I have implemented the algorithm to good effect; it's pretty straight forward.

4. ## Re: Splines in 3D space

Originally Posted by johng
Hi,
Natural cubic spline interpolation is done separately in each dimension. So as soon as you can do it in one dimension, you can do it anywhere. This web page has all the relevant information for one dimensional interpolation -- Cubic Spline -- from Wolfram MathWorld. Just repeat in each coordinate. The reference cited (Bartels et al) is 25 years old, but the math is still good. I have implemented the algorithm to good effect; it's pretty straight forward.
Thank you for your reply. It is a great source, however I can't understand how the author arrived to the equation 18? Could you explain briefly?

What is Di? Is it the first differential of Y(t)?

Hi,