SignificanceIron limits the growth of photosynthetic organisms, especially in marine environments. Understanding the response of photosynthetic organisms to changing iron concentrations is therefore important for agriculture and biotechnology. We have identified a protein that is essential for the correct response to changing iron concentrations in photosynthetic bacteria (cyanobacteria). This protein was previously annotated as an electron transfer component of photosynthesis, called Fed2, and contains an iron−sulfur cluster. We tested Fed2, and found that it cannot act in photosynthetic electron transport. The corresponding gene is essential, and is highly conserved between cyanobacteria, algae, and higher plants. By specifically perturbing its function, we could show that it is essential for the low-iron response at the posttranscriptional level.

The so‐called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2‐manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi‐structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three‐dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher‐dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T‐spline construction.

Developments in the field of parametrization-based quad mesh generation on surfaces have been impactful over the past decade. In this context, an important advance has been the replacement of error-prone rounding in the generation of integer-grid maps, by robust quantization methods. In parallel, parametrization-based hex mesh generation for volumes has been advanced. In this volumetric context, however, the state-of-the-art still relies on fragile rounding, not rarely producing defective meshes, especially when targeting a coarse mesh resolution. We present a method to robustly quantize volume parametrizations, i.e., to determine guaranteed valid choices of integers for 3D integer-grid maps. Inspired by the 2D case, we base our construction on a non-conforming cell decomposition of the volume, a 3D analogue of a T-mesh. In particular, we leverage the motorcycle complex, a recent generalization of the motorcycle graph, for this purpose. Integer values are expressed in a differential manner on the edges of this complex, enabling the efficient formulation of the conditions required to strictly prevent forcing the map into degeneration. Applying our method in the context of hexahedral meshing, we demonstrate that hexahedral meshes can be generated with significantly improved flexibility.

Base Complex 1352 blocksMotorcycle Complex 79 blocks (5.8%)Figure 1: Base Complex (left) and our Motorcycle Complex (right) induced by the same volumetric seamless parametrization of a solid object, both providing a structured partition into cuboid blocks. The motorcycle complex often partitions the object's interior into a much smaller number of blocks, here just 5.8%, 79 instead of 1352 blocks (see the exploded views). We provide a definition of this motorcycle complex, describe algorithms for its construction, and demonstrate its use and benefits.