Fit Point vs Control Point Curves

[janos.adelsberger]

I've recently found a beautiful video explaining the math behind Bezier Curves (https://youtu.be/aVwxzDHniEw?t=187). What confuses the heck out of me is that she explains it using a control polygon just like Control Point Curves. Usually when talking about Bezier Curves I have tangency handles in mind, basically a Fit Point Curve or paths in Illustrator. What I found out so far is that splines in general refer to multiple polynomials which are curvature continuous at their intersection. So are Fit Point Curves and Control Point Curves the same thing under the hood just using different interfaces or is there a difference? 

[TrippyLighting · Accepted solution]

I've seen that video last year and it is indeed outstanding.

The mathematical concepts of these splines are the same.

One thing to be aware of is that the purpose of splines in a 2D vector graphics application such as Adobe Illustrator is different from the spline found in CAD software. In Illustrator you don't create  surfaces from Splines, however, that is the main purpose of splines in a CAD application.

The spline type used in CAD application is NURBS (Non Uniform Rational B-Spline).

The Autodesk Alias Theory Builders have an excellent explanation of their use in CAD.

The "cleanest" splines to create surfaces with are single-single span control point splines. Examples of  single span splines are 3-degree control point spline with 4 points or a 5-degree control point splines with 6 points.   

Fit point splines in Fusion 360 are 5-degree multi span splines. Their exact implementation is application specific. A fit point spline in another CAD software will unlikely create the same curve.

Control point splines translate across applications.

I am sure I've added to the confusion.

[janos.adelsberger]

Actually you didn't 🙂 Perfectly answers my question – Thanks!