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Math Help - Comparison between cylinder volume and extruded circular spline volume equal dia

  1. #1
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    Comparison between cylinder volume and extruded circular spline volume equal dia

    Hi, I am trying to approximate the length of a spline. I have circular cross section extruded perpendicular to the spline though the whole length.

    My 3d cad software will not give me the spline length. I have used the volume / area of extruded circle is approximately equal to spline length. Of course this is really the cylinder formula to find the height of a cylinder.

    Does anyone have an approximation ratio that I could multiply to reduce the cylinder volume formula to get the spline length closer? My one test shows 98%.

    I don't have any way of analyzing the spline in terms of aspect ratio or curliness. Does anyone know of a way?

    Thanks Cozmo
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  2. #2
    Junior Member mathbyte's Avatar
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    Re: Comparison between cylinder volume and extruded circular spline volume equal dia

    I'm a bit confused and don't follow your description. It's not exactly a math problem, but still... The issue with a spline is that there is no mathematical formula to give its properties like length, width, etc.



    Is the spline 3D? Can you trace a polyline or linestring over it and have the software measure that instead? It's a graphical as opposed to mathematical solution and can be time consuming, but it gets you there in the end.
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  3. #3
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    Re: Comparison between cylinder volume and extruded circular spline volume equal dia

    Hi mathbyte,
    The splines could be 3d or 2d but my 1 experiment was a 3d spline.

    maybe it helps to look at the problem backwards?
    If I have the length of a 2d or 3d extruded right circle spline, what is the volume?

    If the spline is very straight it will reach the limit of a right cylinder (pi*r^2*L).
    OR if the spline gets circular it will approximate a ring torus, with you get the same (pi*r^2*L) where L is the circumference of the torus path.

    In my test as you make the spline, the volume will decrease but not by much.

    It is not a huge issue for me, I was just curious if there was any research on it. The approximation pi*r^2*L is close enough.

    Thanks cozmo
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