Recently it is relatively easy to produce digital point sampled 3D geometric models. In sight of the increasing capability of 3D scanning systems to produce models with millions of points, compression efficiency is of paramount importance. In this paper, we propose a novel competition-based predictive method for single-rate compression of 3D models represented as point cloud. In particular we aim at 3D scanning methods based on grid pattern. The proposed method takes advantage of the pattern characteristic made of vertical and horizontal lines, by assuming that the object surface is sampled in curve of points. We then designed and implemented a predictive coder driven by this curve-based point representation. Novel prediction techniques are specifically designed for a curve-based cloud of points, and been competing between them to achieve high quality 3D reconstruction. Experimental results demonstrate the effectiveness of the proposed method.