We present a registration method relying on geometric constraints extracted from parametric primitives contained in 3D parametric models. Our method solves the registration in closed-form from three line-to-line, line-to-plane or plane-to-plane correspondences. The approach either works with semantically segmented RGBD scans of the scene or with the output of plane detection in common frameworks like ARKit and ARCore. Based on the primitives detected in the scene, we build a list of descriptors using the normals and centroids of all the found primitives, and match them against the pre-computed list of descriptors from the model in order to find the scene-to-model primitive correspondences. Finally, we use our closed-form solver to estimate the 6DOF transformation from three lines and one point, which we obtain from the parametric representations of the model and scene parametric primitives. Quantitative and qualitative experiments on synthetic and real-world data sets demonstrate the performance and robustness of our method. We show that it can be used to create compact world anchors for indoor localization in AR applications on mobile devices leveraging commercial SLAM capabilities.