Abstract In vivo imaging of cardiac 3D fibre architecture is still a practical and methodological challenge. However it potentially provides important clinical insights, for example leading to a better understanding of the pathophysiology and the follow up of ventricular remodelling after therapy. Recently, the acquisition of 2D multi-slice Diffusion Tensor Images (DTI) of the in vivo human heart has become feasible, yielding a limited number of slices with relatively poor signal-to-noise ratios. In this article, we present a method to analyse the fibre architecture of the left ventricle (LV) using shape-based transformation into a normalised Prolate Spheroidal coordinate frame. Secondly, a dense approximation scheme of the complete 3D cardiac fibre architecture of the \LV\ from a limited number of \DTI\ slices is proposed and validated using ex vivo data. Those two methods are applied in vivo to a group of healthy volunteers, on which 2D \DTI\ slices of the \LV\ were acquired using a free-breathing motion compensated protocol. Results demonstrate the advantages of using curvilinear coordinates both for the anaylsis and the interpolation of cardiac \DTI\ information. Resulting in vivo fibre architecture was found to agree with data from previous studies on ex vivo hearts.