In the context of autonomous rendezvous and space debris removal, visual model-based tracking can be particularly suited. Some classical methods achieve the tracking by relying on the alignment of projected lines of the 3D model with edges detected in the image. However, processing complete 3D models of complex objects, of any shape, presents several limitations, and is not always suitable for real-time applications. This paper proposes an approach to avoid these shortcomings. It takes advantage of GPU acceleration and 3D rendering. From the rendered model, visible edges are extracted, from both depth and texture discontinuities. Correspondences with image edges are found thanks to a 1D search along the edge normals. Our approach addresses the pose estimation task as the full scale nonlinear minimization of a distance to a line. A multiple hypothesis solution is also proposed, improving tracking robustness. Our methods has been evaluated on both synthetic images (provided with ground truth) and real images.