I am trying to get a normal of a triangle on a sphere, however the normal equations (straight line) give the wrong answer.
For the points:
$$(-986.786743, -93.348259, -132.439041)\\ (210.731644, -534.785583, -818.290039)\\ (637.734985, -449.826904, -553.501648)$$
on a radius $1000$ sphere, the average point (straight line) is $(-0.074536, -0.580873, -0.810574) * 1000$, which is visibly incorrect on a sphere.
The triangle's normal normalized to distance $1000$ gives: $(0.086455, 0.899604, -0.428062) * 1000$ which is different from the average value above (which would have also given a normal) and also far off from the spherical triangle.
Edit: I was trying to unwrap a mesh into a globe to map it to a texture. I needed to know if triangles were upside down using normals.