# Make a proper Classic Klein Bottle in version 11.20 of Mathematica?

Posted 1 year ago
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 Everything works fine in version 10, but in Version 11.20 there is a slice taken out of the Klein Bottle image...It does this no matter what version of the code I use in Version 11.2. It also does it while making a stylized Klein Bottle described here... http://members.wolfram.com/jeffb/visualization/klein.shtmlHere is an example of code that makes a faulty output...Can someone come up with code that makes a proper Klein Bottle without a slice taken out out it in Version 11.20? klein[u_, v_] := Module[{ bx = 6 Cos[u] (1 + Sin[u]), by = 16 Sin[u], rad = 4 (1 - Cos[u]/2), X, Y, Z}, X = If[Pi < u <= 2 Pi, bx + rad Cos[v + Pi], bx + rad Cos[u] Cos[v]]; Y = If[Pi < u <= 2 Pi, by, by + rad Sin[u] Cos[v]]; Z = rad Sin[v]; {X, Y, Z} ] ParametricPlot3D[klein[u, v], {u, 0, 2 Pi}, {v, 0, 2 Pi}, Axes -> False, Boxed -> False, ViewPoint -> {1.4, -2.6, -1.7}]  Attachments:
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Posted 1 year ago
 For those interested, Wolfram tech support got back to me and gave the solution...In version 11 one must add... "Exclusions->None" to the ParemetricPlot3D command...Tech Support said..."Exclusions were re-worked internally in Version 11, and this seems to be a regression from doing so."
Posted 1 year ago
 This could make a nice 3D printing model: ParametricPlot3D[klein[u, v], {u, 0, 2 Pi}, {v, 0, Pi}, Axes -> False, Boxed -> False, ViewPoint -> {1.4, -2.6, -1.7}, Exclusions -> None, PlotTheme -> "ThickSurface"] 
 Support may have said it's a regression, but really, I believe it is an advance: The exclusions-processing capabilities now recognize the switch between formulas at u == Pi. (The next step in exclusion-processing will be, or at least could be, recognizing when such a switch is a true discontinuity or not. That's my opinion, by the way. There may be no intention at WRI to develop in that direction.)Another workaround is to hide the symbolic parametrization with _?NumericQ: klein[u_?NumericQ, v_?NumericQ] := Module[{bx = 6 Cos[u] (1 + Sin[u]), by = 16 Sin[u], rad = 4 (1 - Cos[u]/2), X, Y, Z}, X = If[Pi < u <= 2 Pi, bx + rad Cos[v + Pi], bx + rad Cos[u] Cos[v]]; Y = If[Pi < u <= 2 Pi, by, by + rad Sin[u] Cos[v]]; Z = rad Sin[v]; {X, Y, Z}] ParametricPlot3D[klein[u, v], {u, 0, 2 Pi}, {v, 0, 2 Pi}, Axes -> False, Boxed -> False, ViewPoint -> {1.4, -2.6, -1.7}] 
 Make a proper Classic Klein Bottle in version 11.20 of Mathematica?Surely a true Klein bottle would not have a surface blocking the "hole" as seen in the sectioned view below? ParametricPlot3D[klein[u, v], {u, Pi, 2 Pi}, {v, Pi, 2 Pi}, Axes -> False, Boxed -> False, ViewPoint -> {1.4, -2.6, -1.7}] Here is an image from the web that is accurate I believe:https://www.shapeways.com/product/MCBKAVKA4/half-klein-bottle