We have previously developed methods for quickly estimating the object-shape-dependent scatter response function (SRF) in uniformly attenuating objects for single photon emission computed tomography (SPECT). These methods are based on parameterization of the SRF for line sources in slab phantoms. Previously this parameterization was determined from tedious measurements or lengthy Monte Carlo (MC) simulations with line sources at various depths in slab phantoms. In this paper we present a simple method for determining this parameterization based on a single measurement of a line source in a triangular phantom. A rule of thumb has been formulated for the minimum vertex angle of the triangular phantom. The method has been evaluated by a MC simulation study in which the triangular phantom SRFs are compared with the `true' SRFs simulated using slab phantoms. The SRFs are computed for 99mTc. We have observed good agreement between the shapes of the SRFs from the slab and triangular phantoms. The parameterization of the slab phantom SRF, determined using this single measurement, can be combined with knowledge of the geometric detector response and the object-shape dependent SRF model to compute the full response function for sources in a large class of convex shaped objects. Fits of an object shape dependent scatter model are close to data obtained by the triangular phantom. This model can serve as the basis for accurate scatter compensation in SPECT.