Figure 1
From: Computational analyses decipher the primordial folding coding the 3D structure of the beetle horn
Methods for analyzing furrows and transformations. In Matsuda et al.7 reconstructed a three-dimensional mesh of horn primordia that can transform into the pupal horn shape through computer simulation of applying pressure to the 3D mesh from the inside. In this work, we developed three methods to study the relationship between folding patterns and transformation, using the unfolding simulation together with smoothing methods. The first one is the correspondence analysis (red broken lines), in which the position in the folded primordia corresponding to a given position in the unfolded primordia can be easily identified. The second one is furrow visualization (blue dotted lines). The first step of the operation was smoothing the mesh, and then, by comparing the original mesh and the smoothed mesh, the ridges and valleys were colorized. We used the HC-modified Laplacian smoothing algorithm as a smoothing filter. The third method is the furrow removal analysis (yellow solid lines). The first step of the analysis also consisted of smoothing the mesh. Then, the smoothed mesh was expanded in the computer simulation. Because smoothing algorithms can make the furrows at a particular position shallower, the contribution of specific furrows to transformation can be understood by comparing the original mesh with the smoothed mesh after unfolding (red double-headed arrow). The details of each algorithm are provided in the supplementary material.
