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I have a listplot of data and I would like to collect all the data points within a specific boundary of a circle graphic that overlaps the listplot in Mathematica.

Is something like this possible?

The ellipse I have made is of the form 

{c, s, \[Theta]} = 1 /. ComponentMeasurements[f, {"Centroid", "SemiAxes", "Orientation"}] Show[Rasterize[p], Graphics[{Red, Rotate[Circle[c, s], \[Theta]]}]]

Can you help me fit your bottom-most solution into a form where I can input my ellipse with the Centroid, SemiAxes, and Orientation properties?

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1 Answer 1

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data = RandomReal[{0, 1}, {100, 2}] r = 1/5; center = {1/6, 1/4}; sd = Select[data, EuclideanDistance[#, center] < r &] Show[ListPlot@data, Graphics@Circle[center, r], Graphics[{Red, PointSize[Large], Point@sd}], AspectRatio -> 1]

Mathematica graphics

Edit

For an ellipse 

data = RandomReal[{0, 1}, {100, 2}] r = 1/5; f1 = {1/6, 1/4}; f2 = {1/3, 1/5}; sd = Select[data, EuclideanDistance[#, f1] + EuclideanDistance[#, f2] < r &] Show[ListPlot@data, RegionPlot[EuclideanDistance[{x, y},f1] + EuclideanDistance[{x, y},f2] <r, {x, 0, 1}, {y, 0, 1}], Graphics[{Red, PointSize[Large], Point@sd}], AspectRatio -> 1]

Mathematica graphics

Edit 2

Better code

data = RandomReal[{0, 1}, {100, 2}] r = 1/5; f1 = {1/6, 1/4}; f2 = {1/3, 1/5}; inside[{x_, y_}, {f1_, f2_}] := Sum[EuclideanDistance[{x, y}, i], {i, {f1, f2}}]; sd = Select[data, inside[#, {f1, f2}] < r &]; Show[ListPlot@data, RegionPlot[inside[{x, y}, {f1, f2}] < r, {x, 0, 1}, {y, 0, 1}], Graphics[{Red, PointSize[Large], Point@sd}], AspectRatio -> 1]

Edit 3

Here you have the whole thing translated to your ComponentMeasurements output

(*{c,s,t}=1/.ComponentMeasurements[f,{"Centroid","SemiAxes",\ "Orientation"}] *) c = {.3, .4} s = {.4, .2} t = Pi/8 {s1, s2} = s center = {cx, cy} = c f = Sqrt[s1 s1 - s2 s2] f1 = {f1x, f1y} = {cx + f Cos[t], cy - f Sin[t]} f2 = {f2x, f2y} = {cx - f Cos[t], cy + f Sin[t]} r = 2 Sqrt[f f + s2 s2] data = RandomReal[{0, 1}, {100, 2}]; sd = Select[data, EuclideanDistance[#, f1] + EuclideanDistance[#, f2] < r &]; Show[ ListPlot@data, RegionPlot[ EuclideanDistance[{x, y}, f1] + EuclideanDistance[{x, y}, f2] < r, {x, 0, 1}, {y, 0, 1}], Graphics[{Red, PointSize[Large], Point@sd}], AspectRatio -> 1]

Mathematica graphics

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4 Comments

Wow! Thank you so much belisarius. My Circle is actually an ellipse, but I think I can manage to translate your answer! This is perfect. Thank you!
@tquarton Please don't contact me by mail for further details, as that can't help others. If you need more help, post a comment here or update your question (the second option is better). Tnx!
Alright, I updated my question. My fault for not being very specific in the beginning. Thank you for all the help belisarius.
your solution worked perfectly, but I ran into another problem. I posted a related question here if you are interested in taking a look at it. I made it a separate question because its more related to image processing.

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