This is to some extent equivalent to Lambert's problem. Namely, if you pick any point along the two orbits you can draw transfer orbits between. This can be constrained to one orbit if you for example also specify the true anomaly when departing or arriving (if the two points and the celestial body do lie on one line). You could also specify the transfer time, but this can yield multiple solutions. The ∆v can be calculated by adding the difference in norm of the difference in velocity at the two points.
It can be noted that this only considers transfers with only two (instantaneous) velocity changes. Therefore, this method as described can not obtain things like the bi-elliptic transfer or mid-transfer plane change. You could of course expand the method and add an additional velocity change, for example by picking a additional point in space where you would perform another burn. This would add four additional degrees of freedom (three for the point and one for true anomaly/travel time between points).
Lambert's problem is also used to generate pock chop plots. Though, that problem has only two degrees of freedom, since the arriving point is a function of the departure point and travel time
In general there not an analytical solution for the transfer that minimizes the total ∆v, even not for the pock chop plot case. I think that such problem is not convex in which case there is also no guarantee that numerical methods can approximate the optimal transfer.