# Fast methods for adding the basepoint to an elliptic curve point?

Are there any clever (fast) methods for adding the basepoint (generator) to an arbitrary point on elliptic curve, finally ending in affine coordinates? I.e. if G is the generator for a group on the curve (e.g. 25519) and P is an arbitrary point, is there a faster-than-naive way to find P + G in affine coordinates?

I'm interested in quickly enumerating the points on a curve, starting with G, then 2G, 3G, etc, with final values in affine coordinates.

My current solution starts with G and P in Edwards coordinates and then converts G + P to affine coordinates (which is slow). But I figure there might be some magic that 1) takes advantage of G being known or 2) uses the work previously done when computing the sequence G, 2G, 3G, etc.

Thank you!

EDIT: To be clear, I'm not interested in scalar multiplication of an elliptic curve point by a number (I don't want to compute nG for arbitrary n). Instead I want to "increment" a point P by adding it with the generator G.