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Accurate calculation of the catch efficiency β is of paramount importance for any ice accretion calculation since β is the most important factor in determining the mass of ice accretion. A new scheme has been proposed recently in [1] for accurately calculating β on a discretized two-dimensional geometry based on the results of a Lagrangian droplet trajectory integrator (start and impact conditions). This paper proposes an extension to the algorithm in Ref. [1], which is applicable to three-dimensional surfaces with arbitrary surface discretization. The 3D algorithm maintains the positive attributes of the original 2D algorithm, namely mass conservation of the impinging water, capability to deal with overlapping impingement regions and with crossing trajectories, computational efficiency of the algorithm, and low number of trajectories required to reach good accuracy in catch efficiency.