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Mapping a 3D Point to a 2D Triangle

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Given a point in 3D, the numbers

[more]

,

,

satisfy the triangle inequality and so can be the lengths of the sides of a 2D triangle.

The reverse is also true, but with more complicated formulas, as shown in the Details.

[less]

Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

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Details

Let

,

,

,

,

.

Then the triangle with sides , , corresponds to the 3D point with

,

,

.

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