Does the pattern of how we describe the sphere affect our sampling of the sphere? Describing the coordinates and derivative using this method are not spherically symmetric.

sungpark98

Is the calculation of dA coming from the fact that we're looking at a rectangle? So that each term is one side of the rectangle with the arc length r * dTheta, and the other side of r sin theta d Phi?

leonxu1

@WolfLink what do you mean by spherically symmetric? Your question sounds interesting but I don't fully understand it :/

@sungpark98 pretty sure that is what it's coming from, yeah. As dTheta, dPhi -> 0, the shape becomes arbitrarily close to a rectangle (or more precisely, the surface area becomes arbitrarily close to if it were a rectangle w/ the same width/height).

Does the pattern of how we describe the sphere affect our sampling of the sphere? Describing the coordinates and derivative using this method are not spherically symmetric.

Is the calculation of dA coming from the fact that we're looking at a rectangle? So that each term is one side of the rectangle with the arc length r * dTheta, and the other side of r sin theta d Phi?

@WolfLink what do you mean by spherically symmetric? Your question sounds interesting but I don't fully understand it :/

@sungpark98 pretty sure that is what it's coming from, yeah. As dTheta, dPhi -> 0, the shape becomes arbitrarily close to a rectangle (or more precisely, the surface area becomes arbitrarily close to if it were a rectangle w/ the same width/height).