Electron spin precession in nonuniform Rashba-Dresselhaus two-dimensional electron systems along arbitrary continuous paths is investigated. We derive an analytical formula to describe the spin vectors (expectation values of the injected spin) in such conditions using a contour-integral method. The obtained formalism is capable of dealing with the nonuniformity of the Rashba spin-orbit field due to the inherent random distribution of the ionized dopants, and can be applied to curved one-dimensional quantum wires. Interesting examples are given, and the modification to the spin precession pattern in a Rashba-Dresselhaus channel when taking the random Rashba field into account is shown.