This study proposes a quantitative, non-destructive and semi-automatic method to quantify the geometry of the mollusc shell through its ontogeny. The proposed approach consists to acquire digital 3-D data of a gastropod shell by micro-computed tomography. The resulting series of grey-scaled 2-D images is then processed to obtain a model of the shell both as a grid of voxels and as a triangular mesh. Next, a centreline of the shell is extracted and serves as a guide to slice the shell throughout ontogeny and extract the successive outlines of the whorl sections. The series of outlines are then quantified by means of elliptic Fourier analysis. The resulting coefficients of the harmonics, coupled with the displacement vector of the successive cross-sectioning planes, constitute an n-dimensional morphometric space, in which ontogenetic trajectories of different individuals and species can be compared. This approach adds a novel set of continuous and quantitative characters on the geometry of the mollusc shell. The approach proposed in this study produces a relatively detailed, accurate and realistic representation of the shell of gastropods. It makes very few assumptions about the shell characteristics by assuming only that the shell is basically conic, coiled and characterized by an accretionary growth. This method also does not assume any coiling axis, which makes it possible to apply to irregularly coiled mollusc shells compared to existing methods. It thus provides a quantitative basis for the analysis of growth patterns and ontogeny within and across species. The analysis of a complete family of snails to illustrate this point will be dealt with in another forthcoming paper.