You want to perform an adaptive sampling of the boundary curve. Use de Casteljau algorithm recursively until the control points are approximately collinear. See for instance http://www.antigrain.com/research/adaptive_bezier/index.html.

You want to perform an adaptive sampling of the boundary curve.

For Bézier curves, use the de Casteljau algorithm recursively until the control points are approximately collinear. See for instance Adaptive Subdivision of Bezier Curves from the Anti-Grain Geometry project.

For general curves, see for instance Adaptive sampling of parametric curves, in Graphics Gems V, 1995.