A local structure of null hypersurfaces of $\mathbb{R}_{1}^{n+1}$

In the present paper, we characterize constant mean curvature and scalar curvature null hypersurfaces of $\mathbb{R}_{1}^{n+1}$. Locally, such hypersurfaces are a product of a null curve and generalized cylinders.

Extraction of Rotational Surfaces and Generalized Cylinders from Point-Clouds Using Section Curves

In industrial facilities, there are various types of equipment composed of surfaces that have a high degree of freedom. Rotational surfaces and generalized cylinders are often used for equipment handling liquids and gases. In this paper, we propose methods for reconstructing rotational surfaces and generalized cylinders from noisy and incomplete point-clouds captured by a terrestrial laser scanner. In our method, we convert point-clouds into wireframe models and calculate the intersection points with section planes. Then, we extract ellipses from the intersection points on each section plane and reconstruct the rotational surfaces and generalized cylinders using the extracted ellipses. We also propose a method for subdividing a rotational surface into primitive surfaces. We evaluated our method using actual point-clouds of engineering facilities and confirmed that our method could successfully reconstruct rotational surfaces and generalized cylinders.

Extraction of Surfaces Using Section Curves for Engineering Plants

For simulating renovation of industrial facilities, 3D models are very useful. However, it is time-consuming to create 3D models. The terrestrial laser scanner is effective for easily capturing 3D data of large-scale facilities. So far, many researchers have proposed methods for reconstructing pipe structures in industrial plants using point-clouds. In those methods, planes and cylinders are extracted from point-clouds, but they are not enough for creating various types of equipment. Especially, in manufacturing plants for liquids and gases, rotating surfaces and generalized cylinders are typically used as well as planes and cylinders. In this paper, this paper proposes methods for extracting rotating surfaces and generalized cylinders from noisy and incomplete point-clouds. Since the section shapes of rotating surfaces and generalized cylinders are approximately ellipses, this method detects elliptic section shapes from point-clouds. Then rotating surfaces and generalized cylinders are reconstructed by extracting the center curves and section circles. Then the authors combine this method with general-purpose voxel-based shape reconstruction methods. Since this method is robust to missing points caused by occlusion, the quality of shape reconstruction can be improved even if points are partly missing due to occlusion.