The creation of conic section curves

I’d like to know if a conic curve tool is something that is possible. I use Shapr3D for general aircraft design as a hobbyist; having the ability to create conic curves would save a lot of time trying to fair my loft lines instead of using splines. I can’t ever seem to completely smooth my curves using splines.

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Are you not able to use a plane to intersect a cone at the appropriate angle to produce the conic curve you want?

Yeah they can be created that way, but that would be even more steps to do that for every curve. I believe the current sketch geometry in Shapr3D could easily accommodate a conic curve defined by two endpoints, a vertex, and a rho value. A conic tool would also use a lot less math to solve than splines and guarantee a completely smooth transition in curves. They use x-squared and y-squared terms mathematically so the curvature can vary but convexity does not change. With splines it takes forever to smooth out the wrinkles and dimples using splines.

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I’m elaborating on what @welshsteve suggested. While not having the tools you’d like to see in Shapr3D, it’s not difficult to make such curves. Yes, you would have to plan out the dimensions and angles beforehand to achieve what you’d like to do. Good luck.


A bit of trial and error should get the desired curves (or a quick study of the geometry of angularly truncated cones).

…is ‘angularly truncated’ a word?

Technically speaking, it’s two words! :crazy_face:


Thank you for your responses. I’ve been attempting to use planar slices of cones but still haven’t had an easy time when I’m trying to accurately reproduce curvature for reverse engineered drawings. This is the most simple example I could find

especially when I find the correct curvature then try to keep it dimensionally accurate and apply tangent constraints to keep every needed conic curve. I found a work around through fusion 360’s conic tool so I can just import the needed curves from fusion 360. Would just love to see a future sketch tool in shapr3d

You’re not wrong :laughing:

Out of the 4 different conic section curves (circle, ellipse, parabola and hyperbola) only the last two are of interest here :grinning:

If you have a drawing of the target curve, it is quite fast to get a decent spline curve that fits the conic section curves.

Considering that conic curves are totally defined by 5 points, it makes sense to draw them with 5 points splines (or the equivalent of 5 points).

  • for parabola, I place 3 particular points of a control spline, as it creates perfect parabola.
  • for hyperbola or parabola, I use 5 points fit spline, with symmetrical control points and do not adjust the tangent controls of the spline but adjust the middle points to fit the curve.

Videos show it all.