Area inside a closed curve

I have generated a surface on a 3d plot and have created a 2d curve (closed loop) somewhere on the surface. How to identify the x-, y-coordinates (z-coordinates for all points lying on and inside the curve are same) lying inside the curve? This is somewhat similar to the 'Fill Color' command in MS Paint.

Edit: The curve is a plot of various discrete points.

[Amit]

Do you know the 2d curve? Is it a function or equation?

Answer 1

[Image Analyst]

Pass the planar coordinates into polyarea().

[Roger Stafford]

If the surface bounded by the closed curve is not planar, then "polyarea" will not be very accurate. It would be necessary to do a closely-spaced triangulation of this enclosed surface area and sum the area of the triangles as an approximation.

[Image Analyst]

Right - I thought of that. I wasn't sure how Amit was going to ensure that the curve on the 3D surface lies in a plane (constant z value) but I assume he has some way. Probably not a good assumption.

Answer 2

[Roger Stafford]

Sahil, if your surface is determined by some equation f(x,y,z) = 0, and if the boundary curve on this surface is determined by another function g(x,y,z) = c for some constant c, then it is likely that points on the surface which are inside the curve satisfy either g(x,y,z) < c or else g(x,y,z) > c. If so, this should furnish you the information you need for a closely-spaced set of points throughout the surface inside the curve to allow you to generate a triangulation of them so as to compute a good approximation for the surface area enclosed.

[Sahil]

Sorry, I forgot to mention in my description that the boundary curve is a plot of various discrete points. What should be the approach in this case?

[Image Analyst]

Are you saying that you can't use polyarea() for that case for some reason?