I'm trying to give shapes in my physics engine roundness/ curvature.
I am aware of various methods for mathematically defining curves; such as bezier-cruves, ellipses, etc. However I am not sure which methods would be most appropriate for use in my physics engine, because speed, feasibility of construction, and flexibility of each method must be considered. I want a system in which a user can easily form fairly complex curves, but still make the intersection calculations simple and fast.
My physics engine is also purely continuous, which means I must be able to calculate the time in which curves will collide with other curves and lines based on a constant linear/angular velocity.
What techniques are there for mathematically defining a 2D curve?
What are the advantages/disatvantages of each in terms of speed, flexibility, and simplicity of construction?
Is the technique feasible for an engine where predictability of shape intersection is crucial?