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 Sep 27 comment Weighted Interpolation over Triangle Sorry it took me so long to approve. It took me a while to be able to test your algorithm. It seems to work very well; I will add some sample screenshots to the question so others can see that your approach works! Sep 11 comment General Formula for Volume of Spherical Triangle I scanned the paper again and caught the dot product formula written using this notation. $\vec{a}$ is a vector and $a$ is that vector's magnitude. Sep 11 comment General Formula for Volume of Spherical Triangle @achillehui I have now read that paper; it's over my head. If I understand their formula correctly, the numerator is the absolute value of the dot product of the first vector with the cross product of the other two, the letters without the vector bars are the great-circle arcs forming the triangle, and then I can use this $\Omega$ to calculate the volume I want by $\frac{\Omega}{3}(r^3-(r-1)^3)$? Jan 26 comment How do I calculate the unique k-dimensional hypersphere's center from k+1 points? Your answer helped me to figure out the equations on the original page I found. Are your equations the same as those on that page, or am I mistaken? Jan 26 comment How do I calculate the unique k-dimensional hypersphere's center from k+1 points? After some more research, I realized that the equations on that page are using Cramer's rule... those are the determinants of the matrices, not the matrices themselves.