the first vertex $R_1^1(x)$. The rest of the vertices of the spiral are ordered inductively. The direction is chosen by moving clockwise or counterclockwise, while the choice of the first vertex, the *reference point*, is based on the underlying geometry of the shape to ensure the robustness of the method. In particular, we fix a reference vertex $x_0$ on a template shape and choose the initial point for each spiral to be in the direction of the shortest geodesic path to $x_0$, . $$R_1^1(x) = \operatorname*{arg\,min}\limits_{y \in R^1(x)}{d_\mathcal{M}(x_0,y)},$$ where $d_{\mathcal{M}}$ is the geodesic distance between two vertices on the mesh $\mathcal{M}$. In order to allow for fixed-sized spirals, we choose a fixed length $L$ as a hyper-parameter and then either truncate or zero-pad each spiral depending on its size.

**Comparison to Lim [@spirals]**: The authors choose the starting point of each spiral at random, for every mesh sample, every vertex, and every epoch during training. This choice prevents us from explicitly encoding the fixed connectivity, since corresponding vertices in different meshes will not undergo the same transformation (as in image convolutions). Moreover, single vertices also undergo different transformations every time a new spiral is sampled. Thus, in order for the 