I recently finished some work involving constrained bezier curves for use in my browser-based digital audio workstation. Specifically, I used them in its envelope generator, which looks like this:
The circles are draggable handles that allow the user to create whatever shape they desire for the envelope. The green handles define the start and end point of each curve segment and the blue circles control its shape/steepness.

Casey Primozic

A deep dive into implementing constrained cubic Bezier curves for a browser-based DAW envelope generator. The author explains why x^n curves were insufficient (numerical instability, asymmetry), then derives a method using coincident control points to prevent degenerate curve shapes. The key insight is that setting both control points to the same position ensures monotonically increasing X values. A clean algebraic solution is derived to compute the shared control point from a single draggable handle at t=0.5 (curve midpoint), resulting in an intuitive UI where the handle position maps directly to curve shape.

Creating Constrained Bezier Curves for an Envelope Generator