PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces.Comment: Corrected typo

PRS-Net: planar reflective symmetry detection net for 3D models

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces

Improved bend waveguide design for terahertz transmission

Bending waveguides with 90 corners based on a two-dimensional photonic crystal with metallic cylinders arranged in a square lattice are studied for THz wave guiding. Considering single- and double-line defects, five different designs are investigated and assessed in terms of their transmission performance. A better structure is proposed by increasing the number of rods in the bending arc, thus achieving superior performance of the transmission characteristics in comparison to that of the former five designs. A comparison of the improved bend waveguide with a linear wave-guide shows a significant reduction of the bending losses. Trans-mission levels of up to 98% within a 2.5 THz bandwidth (from 1.2 to 3.7 THz) have been accomplished

Planck pre-launch status: HFI beam expectations from the optical optimisation of the focal plane

Planck is a European Space Agency (ESA) satellite, launched in May 2009, which will map the cosmic microwave background anisotropies in intensity and polarisation with unprecedented detail and sensitivity. It will also provide full-sky maps of astrophysical foregrounds. An accurate knowledge of the telescope beam patterns is an essential element for a correct analysis of the acquired astrophysical data. We present a detailed description of the optical design of the High Frequency Instrument (HFI) together with some of the optical performances measured during the calibration campaigns. We report on the evolution of the knowledge of the pre-launch HFI beam patterns when coupled to ideal telescope elements, and on their significance for the HFI data analysis procedure

Self-force with (3+1) codes: a primer for numerical relativists

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $< 1$. We also demonstrate consistency between $t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.Comment: 23 pages, 13 figure