tinyspline | ANSI C library for NURBS , B-Splines , and Bézier curves | Development Tools library

I am wondering how you would model arbitrarily complex Bézier curves. I am not quite understanding the underlying abstraction yet of what a bezier curve is fundamentally composed of, as there are too many equations. I would like to have a generic struct that defines a bezier curve. The SVG path gives many examples of the types of curves you can create. They include linear, cubic, and quadratic bezier curves.

If a B-spline is a better generic model, then that would be fine to use too. I am not familiar with those yet tho. Difference between bezier segment and b-spline. I guess "a B-spline curve is a curve that consists of Bezier curves as segments", so that is what I am looking for.

SVG docs say:

Cubic Béziers take in two control points for each point.

Several Bézier curves can be stringed together to create extended, smooth shapes. Often, the control point on one side of a point will be a reflection of the control point used on the other side to keep the slope constant. In this case, a shortcut version of the cubic Bézier can be used, designated by the command S (or s).

The other type of Bézier curve, the quadratic curve called with Q, is actually a simpler curve than the cubic one. It requires one control point which determines the slope of the curve at both the start point and the end point. It takes two parameters: the control point and the end point of the curve.

Arcs and NURBS (non-uniform rational B-splines) are more complex than just plain bezier curves, but it would be nice if the model could be generalized enough to include these as well. Basically I would like a generic model of bezier curves/b-splines/nurbs to use in a drawing/graphics framework, and not sure what that would be.

• Must each bezier class be implemented separately, or can they be combined into one generic class?
• If separate, are they each basically just an array of control points?

So basically I start to think: