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[✓] Place a point out of a region using GeometricScene?

Posted 3 months ago
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In a GeometricScene, I want a point to be out of a region. Say a triangle and a point B out of it. How can I do it?

5 Replies

Vasileios, I hope this might help.

[Element] works well. However, [NotElement] doesn't work. I will expect for WL to support it.

gs = GeometricScene[{"B", "X", "Y", "Z"},
   {t = Triangle[{"X", "Y", "Z"}],
     "B" \[Element] t}
   ];
RandomInstance[gs]

enter image description here

gs = GeometricScene[{"B", "X", "Y", "Z"},
   {t = Triangle[{"X", "Y", "Z"}],
     "B" \[NotElement] t}
   ];
RandomInstance[gs]

enter image description here

But there is the following ugly way.

gs = GeometricScene[{"B", "X", "Y", "Z"},
   {p = Polygon[{"B", "X", "Y", "Z"}],
    GeometricAssertion[p, "Convex"],
    Triangle[{"X", "Y", "Z"}]}
   ];
RandomInstance[gs]

enter image description here

Thanks. I think The ugly way is the only way

In fact, inspired by your Publish "computable famous theorems of geometry", I was trying to construct a right triangle and three squares with sides at triangle sides, trying the Pythagorean theorem. Any ideas?

This should work for specifying that a point is not in a polygon, for instance:

gs = GeometricScene[{"B", "X", "Y", "Z"}, {
    t == Triangle[{"X", "Y", "Z"}],
    SignedRegionDistance[t, "B"] > 0
    }];
RandomInstance[gs]

As for the Pythagorean theorem, see here.

Thank you.

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