In vivo imaging of the cardiac 3D fibre architecture is still a challenge, but it would have many clinical applications, for instance to better understand pathologies and to follow up remodelling after therapy. Recently, cardiac MRI enabled the acquisition of Diffusion Tensor images (DTI) of 2D slices. We propose a method for the complete 3D reconstruction of cardiac fibre architecture in the left ventricular myocardium from sparse in vivo DTI slices. This is achieved in two steps. First we map non-linearly the left ventricular geometry to a truncated ellipsoid. Second, we express coordinates and tensor components in Prolate Spheroidal System, where an anisotropic Gaussian kernel regression interpolation is performed. The framework is initially applied to a statistical cardiac DTI atlas in order to estimate the optimal anisotropic bandwidths. Then, it is applied to in vivo beating heart DTI data sparsely acquired on a healthy subject. Resulting in vivo tensor field shows good correlation with literature, especially the elevation (helix) angle transmural variation. To our knowledge, this is the first reconstruction of in vivo human 3D cardiac fibre structure. Such approach opens up possibilities in terms of analysis of the fibre architecture in patients.