If I have a sphere $x^2+y^2+z^2=R^2$, how can I parametrize a curve in the radial direction of this sphere?
Imagine I want to parametrize the segment $r$ between origin and the point $P(x,y,z)$ in this picture.
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2026-03-30 14:41:19.1774881679
How to parametrize the radial direction of a sphere?
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You need to give more information on the nature of the curve. If it is a line segment, then you can use the parametrization: $$ tP, \quad t\in [0,1]: $$ when $t=0$, you are clearly at the origin, and when $t=1$, you are precisely at point $P$. For intermediate values of $t$, you are on the line segment between the origin and $P$.