I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special relativity holds. The method can be used to visualize gravitational time dilation, the horizon of black holes, and cosmological models. The idea underlying th...

Each bacterial species has a characteristic shape, but the benefits of specific morphologies remain largely unknown. To understand potential functions for cell shape, we focused on the curved bacterium Caulobacter crescentus. Paradoxically, C. crescentus curvature is robustly maintained in the wild but straight mutants have no known disadvantage in standard laboratory conditions. Here we demons...

The optimum surface-fitting method for binary images is extended in order to treat gray images, and a new method to extract edges in three-dimensional gray images is proposed. If voxels that have similar values to the voxel of interest (VOI) are distributed like a two-dimensional curved surface, it is thought that there would be a curved surface at the VOI. To apply the fitting method to gray i...

Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks from unstructured point cloud data. Our framework first generates a set of initial curved segments fitting highly curved regions. We then optimize these curved ...