Piecewise-smooth curve
A curve made of finitely many smooth pieces joined end to end, with at most finitely many corners.
A curve is piecewise-smooth if it can be cut into finitely many pieces, each with a continuously turning, nonzero tangent direction (a smooth parametrization with nonvanishing derivative), joined end to end so the curve itself never actually breaks. The only irregularities allowed are a finite number of corners -- points where the tangent direction jumps abruptly from one piece to the next -- and a contour is exactly a piecewise-smooth curve equipped with a direction of travel.
Examples
A rectangle's boundary is piecewise-smooth: four smooth straight edges, with a corner at each vertex.
A circle is piecewise-smooth with zero corners, since a single smooth parametrization covers the whole curve.
See also