Geometry terminology: concrete vs. continuous polygons?

Question

I am trying to find the proper terminologies for 2 kinds of shapes:

• The first type of shape I'm calling "concrete polygons". They have a finite number of straight sides (connecting at vertices) and do not have any round/squiggly sides.
• The second type of shape I'm calling "continous polygons". They have 1+ curved, rounded or "squiggly" sides, which technically, each consist of infinite sides (since they're "continuous").

Examples:

• Rectangle = concrete
• Circle = continuous
• Line = concrete
• Bezier curve = continuous

What are the 2 proper geometric terminologies for these 2 kinds of shapes? Thanks in advance!

Answer 1

I think the common term is curvilinear polygon.

In this context, an ordinary polygon could be called a linear polygon or a straight polygon.

Answer 2

You can call your 'continuous polygons' topological polygons.

Edit: As for your 'concrete polygons', I would call them simply 'polygons'.

Answer 3

I would say that these things are all "curves". Some are closed (like rectangles and circles), and some are not.

The property that interests you, I think, is "smoothness". More precisely, you are interested in the presence or absence of "corners" where the (unit) tangent vector is discontinuous. So, circles and lines and Bezier curves are "smooth" (they lack corners), whereas rectangles and polylines are not "smooth".

Answer 4

I would call your "continuous polygons" $1$-dimensional manifolds.

http://en.wikipedia.org/wiki/Manifold