plotting - Smoothing a cusp in plotted data

Here are my data points:

59.51 -59.3642
58.9944 -58.8079
58.4836 -58.2471
57.9778 -57.6819
57.4769 -57.1122
56.981 -56.5383
56.4901 -55.96
56.0043 -55.3775

55.5236 -54.7907
55.048 -54.1998
54.5777 -53.6048
54.1125 -53.0056
53.6525 -52.4025
53.1979 -51.7953
52.7486 -51.1842
52.3046 -50.5692
51.866 -49.9503
51.4328 -49.3277

51.0051 -48.7013
50.5828 -48.0712
50.4206 -47.8259
50.0013 -48.2641
49.5782 -48.6986
49.1514 -49.1294
48.7208 -49.5564
48.2865 -49.9797
47.8485 -50.3992
47.4069 -50.8148

46.9616 -51.2266
46.5128 -51.6344
46.0604 -52.0384
45.6046 -52.4383
45.1452 -52.8343
44.6824 -53.2263
44.2163 -53.6141
43.7467 -53.998
43.2738 -54.3777
42.7977 -54.7532

42.3182 -55.1246
41.8356 -55.4918
41.3497 -55.8548
40.8607 -56.2135
40.3686 -56.5679
39.8734 -56.918
39.3752 -57.2638
38.874 -57.6053
38.3698 -57.9423
37.8627 -58.2749

37.3528 -58.6031
36.8399 -58.9269
36.3243 -59.2461
35.8059 -59.5608
35.2848 -59.871
34.761 -60.1767
34.2345 -60.4777
33.7055 -60.7741
33.1738 -61.066
32.6397 -61.3531

32.103 -61.6356
31.5639 -61.9134
31.0224 -62.1865
30.4786 -62.4549
29.9324 -62.7185
29.384 -62.9773
28.8333 -63.2313
28.2804 -63.4805
27.7253 -63.7249
27.1682 -63.9644

26.609 -64.1991
26.0477 -64.4288
25.4845 -64.6537
24.9193 -64.8736
24.3522 -65.0886
23.7833 -65.2986
23.2126 -65.5037
22.6401 -65.7037
22.0658 -65.8988
21.4899 -66.0889

20.9124 -66.2739
20.3333 -66.4538
19.7526 -66.6288
19.1704 -66.7986
18.5867 -66.9633
18.0017 -67.123
17.4152 -67.2775
16.8275 -67.4269
16.2384 -67.5712
15.6481 -67.7103

15.0567 -67.8443
14.464 -67.9731
13.8703 -68.0968
13.2755 -68.2152
12.6798 -68.3285
12.083 -68.4365
11.4853 -68.5393
10.8868 -68.637
10.2874 -68.7294
9.68725 -68.8165

9.08635 -68.8984
8.48476 -68.9751

I plotted these point in Mathematica.

The plot shows a cusp. I would like to modify the plot to round off the cusp.

How can I do this in Mathematica?

Comments

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

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I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

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