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I mapped a 3D triangle to an arbitrary position in an arbitrary 2D plane using the lengths of 3 sides. So now the two triangles are exactly same but on different planes.

For a point inside the 2D triangle, I want to know its corresponding 3D point inside the 3D triangle, which I think is unique.

How do I achieve this? Is barycentric interpolation of the 2D-to-3D mapping precise? If yes, why?

Thank you in advance.

1 Answers 1

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Yes, every isometry $\mathbb{R}^2 \to \mathbb{R}^3$ preserves barycentric coordinates, because every isometry is an affine transformation, and every affine transformation preserved barycentric coordinates.

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    What book do you recommend for the basic 3D geometry for knowledge on this kind of stuff? – 2017-02-26