With the increasing demands for highly detailed 3D data, dynamic scanning systems are capable of producing 3D+t (a.k.a. 4D) spatio-temporal models with millions of points recently. As a consequence, effective 4D geometry compression schemes are required to face the need to store/transmit the huge amount of data, in addition to classical static 3D data. In this paper, we propose a 4D spatio-temporal point cloud encoder via a curve-based representation of the point cloud, particularly well-suited for dynamic structured-light-based scanning systems, wherein a grid pattern is projected onto the surface object. The object surface is then naturally sampled in a series of curves, due to the grid pattern. This motivates our choice to leverage a curve-based representation to remove the spatial and temporal correlation of the sampled point along the scanning directions through a competitive-based predictive encoder that includes different spatio-temporal prediction modes. Experimental results show the significant gain obtained with the proposed method.