WOLFRAM NOTEBOOK

Graphics Metric Graphs

From Parametric Region

In[]:=

parametricRegion=ParametricRegion[{x,y,2Exp[-(x^2+y^2)]},{{x,-4,4},{y,-4,4}}];

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parametricPoints=RandomPoint[parametricRegion,100000];

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Graphics3D[Point[RandomSample[parametricPoints,10000]]]

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parametricGraph=NearestNeighborGraph[parametricPoints,{All,0.05}];

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parametricEmbedding=GraphEmbedding[parametricGraph,"SpringElectricalEmbedding",3];

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Graphics3D[Point[RandomSample[parametricEmbedding,10000]]]

Out[]=

Deimos

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deimos=ExampleData[{"Geometry3D","Deimos"}];

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deimosPolygon=Polygon[deimos〚1,2,2,1,1〛/.p_Integerdeimos〚1,2,1,p〛];

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Graphics3D[deimosPolygon]

Out[]=

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deimosPoints=RandomPoint[deimosPolygon,20000];

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deimosGraph=NearestNeighborGraph[deimosPoints,{All,0.3}];

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deimosEmbedding=GraphEmbedding[deimosGraph,"SpringElectricalEmbedding",3];

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Graphics3D[Point[deimosEmbedding]]

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Cow

In[]:=

cow=ExampleData[{"Geometry3D","Cow"}];

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cowPolygon=Polygon[cow〚1,2,2,1,1〛/.p_Integercow〚1,2,1,p〛];

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Graphics3D[cowPolygon]

Out[]=

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cowPoints=RandomPoint[cowPolygon,20000];

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cowGraph=NearestNeighborGraph[cowPoints,{All,0.01}];

Ellipsoid

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