# Region plot with predicate [duplicate]

How can I plot the "cartesian sum" of two disks in the plane? In other words, how can I plot the set of points that are the sum of a point from one disk and a point from another disk?

An example: if I have two discs $x^2 + y^2 \le 1$ and $(x-2)^2 + (y-1)^2 \le 2$, how can I plot the region defined by

$$\{(x+u, y+v) | x^2+y^2\le1 \text{ and } (u-2)^2 + (v-1)^2 \le 2\}?$$

I've taken a look at ContourPlot and RegionPlot, but I don't see yet how to do this.

• I don't understand your notation in between the curly brackets. Google turns up much less on "Cartesian sum" than it does on "Cartesian product." You'll have to be more specific if you want an answer here. I suspect that some use of RegionPlot will be more than sufficient once you can figure out how to express your constraints. – djphd Dec 11 '15 at 5:05
• The notation inside the brackets is set-builder notation. I put "cartesian sum" in quotes because I don't know what it's actual name is -- I don't even know if it has a name. I use the name "cartesian sum" because that is a reasonable way to think about what I'm asking. Also, I'm asking the question here because I don't know how to express my constraints; I'm hoping someone here can help with that! – feralin Dec 11 '15 at 5:59
• Can you talk about the context in which this problem came up? – J. M.'s technical difficulties Dec 11 '15 at 6:33
• Sure! I'm considering the question of boundary-limits of sequences: a closed ball (with a given center and radius) that contains all points in a sequence, once you skip at most a finite number of terms. I'm trying to determine what the "sum" of two boundary-limits might conceivably even mean. I mean, with the normal definition of a sequence limit, we have $lim_{n -> \inf} (x_n + y_n) = lim_{n -> \inf} x_n + lim_{n -> \inf} y_n$. With boundary-limits it's not that simple, since if a sequence has terms bounded only by a closed hypersphere, the "sum" of two sequences will be bounded by an even – feralin Dec 11 '15 at 6:39
• stranger shape. With my original question I'm just trying to figure out how to plot that "stranger" shape for a simple case - boundary limits in the 2-d plane. – feralin Dec 11 '15 at 6:39