The tradeoff between recovering fibre populations crossing in the cerebral white matter and resolving it with a reduced number of Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) images presents an interesting problem. In this work, we combine the Delaunay triangulation and an interpolation method to estimate the DW images in non-measured Diffusion Gradients (DG) directions. The overarching aim of this work is to perform a comparison among interpolation methods. The experimentation is performed on simulated data in order to compare the methods as a function of the number of directions and crossing angle. Moreover, we investigate the robustness under various noise levels. Finally, we compare the methods using the data of five healthy volunteers from Human Connectome Project (HCP). Experimental results on synthetic and in-vivo data show that the linear interpolation methods and distance-based interpolation methods give equivalent results in terms of both the number and orientation of fibre compartments in each voxel, for all noise levels. Statistical results obtained from a one-way analysis of variance (ANOVA) confirm the simulations results. As a conclusion, Planar Linear Interpolation (PLI) method provides a way to avoid the complicated interpolation procedure while preserving the accuracy with a relatively small number of DW images.