Average point on sphere between 3 other points (spherical triangle) 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.
If i read you right, you have a triangular patch which is on the surface of a sphere - so the triangle isn't really a true triangle in that it isn't flat, but instead is just made up of 3 points on a sphere connected by lines across the spheres surface.

Also if I understand you correctly, you have a point on this triangle that you want to get the normal at.

If all that is right, the way to get the normal is to subject subtract the origin from your point on the triangle (since it is also a point on the sphere) and normalize it.

The normal at any point on a sphere is parallel to the point from the center of the sphere to that point on the surface.