Orientation estimation is a fundamental task in 3D shape analysis which consists of estimating a shape's orientation axes: its side-, up-, and front-axes. Using this data, one can rotate a shape into canonical orientation, where its orientation axes are aligned with the coordinate axes. Developing an orientation algorithm that reliably estimates complete orientations of general shapes remains an open problem. We introduce a two-stage orientation pipeline that achieves state of the art performance on up-axis estimation and further demonstrate its efficacy on full-orientation estimation, where one seeks all three orientation axes. Unlike previous work, we train and evaluate our method on all of Shapenet rather than a subset of classes. We motivate our engineering contributions by theory describing fundamental obstacles to orientation estimation for rotationally-symmetric shapes, and show how our method avoids these obstacles.

3D Euler spirals are visually pleasing, due to their property of having their curvature and their torsion change linearly with arc-length. This paper presents a novel algorithm for fitting piecewise 3D Euler spirals to 3D curves with G2 continuity and torsion continuity. The algorithm can also handle sharp corners. Our piecewise representation is invariant to similarity transformations and it is close to the input curves up to an error tolerance.