Computation of the diffraction field from a given set of arbitrarily distributed data points in space is an important signal processing problem arising in digital holographic 3D displays. The field arising from such distributed data points has to be solved simultaneously by considering all mutual couplings to get correct results. In our approach, the discrete form of the plane wave decomposition is used to calculate the diffraction field. Two approaches, based on matrix inversion and on projections on to convex sets (POCS), are studied. Both approaches are able to obtain the desired field when the number of given data points is larger than the number of data points on a transverse cross-section of the space. The POCS-based algorithm outperforms the matrix-inversion-based algorithm when the number of known data points is large. (C) 2006 Elsevier B.V. All rights reserved.