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

Questions
,
1

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?

2

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]

745001.jpg
745001.jpg360Ă—288 4.29 KB

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

663302.jpg

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]

279803.jpg
279803.jpg280Ă—432 4.93 KB

3

Thanks. I think The ugly way is the only way

4

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?

5

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.

6

Thank you.