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I am plotting a surface using ParametricPlot3D. Is there a way that only the region with negative Gaussian curvature is plotted?

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    $\begingroup$ Try RegionFunction! It would be very helpful if you provide a minimal example. $\endgroup$ Commented Aug 10, 2020 at 7:50
  • $\begingroup$ @UlrichNeumann Thank you for your reply. supposing that I am plotting a cyclide ParametricPlot3D[ ResourceFunction["Cyclide"][.3, 1.5, {u, v}], {u, -\[Pi], \[Pi]}, {v, -2 \[Pi], 2 \[Pi]}] and I only wanted to plot the regions with negative Gaussian curvature. I wasn't sure how to use RegionFunction. thank you for your reply! $\endgroup$ Commented Aug 10, 2020 at 8:01
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    $\begingroup$ If you know the curvature curv[u,v] try ParametricPlot3D[…,RegionFunction->Function[{u,v},curv[u,v]<0]] $\endgroup$ Commented Aug 10, 2020 at 8:13

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There is a ResourceFunction that can compute Gaussian curvature which allows you to incorporate the comment by Ulrich Neumann

Clear[surf, curv] surf[u_, v_] = ResourceFunction["Cyclide"][.3, 1.5, {u, v}]; curv[u_, v_] = ResourceFunction["GaussianCurvature"][#, {u, v}] &@surf[u, v]; ParametricPlot3D[ surf[u, v], {u, -\[Pi], \[Pi]}, {v, -2 \[Pi], 2 \[Pi]}, RegionFunction -> Function[{u, v}, curv[u, v] < 0]]

Regions of negative curvature of a cyclide

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  • $\begingroup$ In version 14.3, RegionGaussianCurvature became a system function. $\endgroup$ Commented Aug 11 at 14:21

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