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Math Help - Splines in 3D space

  1. #1
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    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?

    I have successfully found cubic splines in 2 dimensions, but I'm not sure how to extend it into 3 dimensions and why there is no explanation about this. Please help.
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  2. #2
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    Re: Splines in 3D space

    How did you find cubic splines in 2 dimensions? Extension to three dimensions should be straightforward.
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  3. #3
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    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.
    Thanks from emakarov
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  4. #4
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    Re: Splines in 3D space

    Quote Originally Posted by johng View Post
    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)?
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  5. #5
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    Re: Splines in 3D space

    Hi,
    I hope the two attachments answer all your questions.

    Splines in 3D space-mhfsplinecurves1a.png

    Splines in 3D space-mhfsplinecurves1b.png
    Thanks from LoneWolf
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