Smooth the Boundary of a Region

Use a Koch curve of order 4 to generate a snowflake:

In[1]:=

Region[KochCurve[4]]

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Use translations and rotations of the curve to generate the 2D region:

In[2]:=

range={{-0.1,1.1},{-0.1,1.1}};region=RegionTranslationTransform0,3-

3

6[Polygon[Join@@Map[With[{tr=RotationTransform@@#},Map[tr,First@KochCurve[4]]]&,{{π,{1/2,0}},{π/3,{0,0}},{-π/3,{1,0}}}]]],PlotRangerange

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Convert the region into an image:

In[3]:=

flake=RegionImage[region,range]

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Smooth the contour via a curvature flow filter:

In[4]:=

corn=CurvatureFlowFilter[flake,24]

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Convert the resulting image back into a region using

:

In[5]:=

region2=ImageMesh[corn,DataRangerange,ImageSizeMedium]

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Highlight the difference between the original and the smoothed snowflake:

In[6]:=

Show[region,Region[RegionDifference[region,region2],BaseStyleRed]]

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Related Symbols