T spline Math

[jeffescott]

So i make skis as a hobby...

To form the shapes I use a select piece of maple curved around nails...then draw a line and i am good to go.

if I use five nails the cure is constrained to cubic equations.  I have model them in excel nicely.  this does not include the tip just the running surface sides and the profile of the ski.

My question is how to I constrain a t spline to a cubic curve..to force it too a "smooth" loft (as defined in boatbuiling.

Eventually I hope to have four curves that are formed in 3d to define the shape of the ski....firstly symetrical about the long axis and then assymetrical each side is moderatly different.

Any help is a godsend.

[TrippyLighting · Accepted solution]

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@jeffescott wrote:

..

To form the shapes I use a select piece of maple curved around nails...then draw a line and i am good to go.

if I use five nails the cure is constrained to cubic equations. 

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That depends on what kind of curve you use!

CAD software almost exclusively uses NURBS so non uniform rational B-splines.

A single span B-Spline is mathematically equivalent to a Bezier Spline.

A single span B-Spline with 5 points would be a 4-degree B-spline so one order higher than a cubic spline. 

There are 2 B-spline curves available in Fusion 360.

Control point splines , which allow you to define the number of control points and to a degree allow you control over the degree of the spline.

The functionality you describe would be a fit point spline as it defines a curve that passes through defined points on the curve. A fit-point spline in Fusion 360 is a 5-degree multi-span spline. 

I don't believe there is a direct mathematical equivalent that would address your requirements for a cubic spline with 5 fit points.  

T-Spline math is proprietary but like any other compound curved surface in Fusion 360. results in 3-degree NURBS surfaces.