Dense monocular Simultaneous Localization and Mapping by direct surfel optimization

This work presents a novel approach for monocular dense Simultaneous Localization and Mapping. The surface to be estimated is represented as a piecewise planar surface, defined as a group of surfels each having as parameters its position and normal. These parameters are then directly estimated from the raw camera pixels measurements, by a Gauss-Newton iterative process. The representation of the surface as a group of surfels has several advantages. It allows the recovery of robust and accurate pixel depths, without the need to use a computationally demanding depth regularization schema. This has the further advantage of avoiding the use of a physically unlikely surface smoothness prior. New surfels can be correctly initialized from the information present in nearby surfels, avoiding also the need to use an expensive initialization routine commonly needed in Gauss-Newton methods. The method was written in the GLSL shading language, allowing the usage of GPU thus achieving real-time. The method was tested against several datasets, showing both its depth and normal estimation correctness, and its scene reconstruction quality. The results presented here showcase the usefulness of the more physically grounded piecewise planar scene depth prior, instead of the more commonly pixel depth independence and smoothness prior.

Weakly reducible H′-splittings of 3-manifolds

We introduce the [Formula: see text]-splittings for 3-manifolds as follows. For a compact connected surface [Formula: see text] properly embedded in a compact connected orientable 3-manifold [Formula: see text], if [Formula: see text] decomposes [Formula: see text] into two handlebodies [Formula: see text] and [Formula: see text], then [Formula: see text] is called an [Formula: see text]-splitting for [Formula: see text]. Clearly, when [Formula: see text] is closed, this is just the Heegaard splitting for [Formula: see text]; when [Formula: see text] is with boundary, the [Formula: see text]-splitting for [Formula: see text] is different from the Heegaard splitting for [Formula: see text]. In this paper, we first show that any compact connected orientable 3-manifold admits an [Formula: see text]-splitting, then generalize Casson–Gordon theorem on weakly reducible Heegaard splitting to the [Formula: see text]-splitting case in the following version: if [Formula: see text] is a weakly reducible [Formula: see text]-splitting for a compact connected orientable 3-manifold [Formula: see text], then (1) [Formula: see text] contains an incompressible closed surface of positive genus or (2) the [Formula: see text]-splitting [Formula: see text] is reducible or (3) there is an essential 2-sphere [Formula: see text] in [Formula: see text] such that [Formula: see text] is a collection of essential disks in [Formula: see text] and [Formula: see text] is an incompressible and not boundary parallel planar surface in [Formula: see text] with at least two boundary components, where [Formula: see text] or (4) [Formula: see text] is stabilized.

Ультразвуковой адаптивный томограф бетонных изделий с нестандартной конфигурацией

It is shown that should be used adaptive antenna arrays, the shape of which can take the form of a non-planar surface of the tested product, for ultrasonic tomography of concrete building structures with a non-standard surface configuration. It should also be used adaptive methods of ultrasound tomography, which allows both to determine the coordinates of defects and the velocity of ultrasound in concrete, as well as adjust the parameters of the probing signals to the characteristics of concrete products.

Biomimetic apposition compound eye fabricated using microfluidic-assisted 3D printing

After half a billion years of evolution, arthropods have developed sophisticated compound eyes with extraordinary visual capabilities that have inspired the development of artificial compound eyes. However, the limited 2D nature of most traditional fabrication techniques makes it challenging to directly replicate these natural systems. Here, we present a biomimetic apposition compound eye fabricated using a microfluidic-assisted 3D-printing technique. Each microlens is connected to the bottom planar surface of the eye via intracorporal, zero-crosstalk refractive-index-matched waveguides to mimic the rhabdoms of a natural eye. Full-colour wide-angle panoramic views and position tracking of a point source are realized by placing the fabricated eye directly on top of a commercial imaging sensor. As a biomimetic analogue to naturally occurring compound eyes, the eye’s full-colour 3D to 2D mapping capability has the potential to enable a wide variety of applications from improving endoscopic imaging to enhancing machine vision for facilitating human–robot interactions.

A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Accurate prediction of the natural frequency for the lateral oscillation of a liquid drop pinned on a vertical planar surface is important to many drop applications. The natural oscillation frequency, normalized by the capillary frequency, is mainly a function of the equilibrium contact angle and the Bond number ( $Bo$ ), when the contact lines remain pinned. Parametric numerical and experimental studies have been performed to establish a comprehensive understanding of the oscillation dynamics. An inviscid model has been developed to predict the oscillation frequency for wide ranges of $Bo$ and the contact angle. The model reveals the scaling relation between the normalized frequency and $Bo$ , which is validated by the numerical simulation results. For a given equilibrium contact angle, the lateral oscillation frequency decreases with $Bo$ , implying that resonance frequencies will be magnified if the drop oscillations occur in a reduced gravity environment.

Algorithm for the Conformal 3D Printing on Non-Planar Tessellated Surfaces: Applicability in Patterns and Lattices

In contrast to the traditional 3D printing process, where material is deposited layer-by-layer on horizontal flat surfaces, conformal 3D printing enables users to create structures on non-planar surfaces for different and innovative applications. Translating a 2D pattern to any arbitrary non-planar surface, such as a tessellated one, is challenging because the available software for printing is limited to planar slicing. The present research outlines an easy-to-use mathematical algorithm to project a printing trajectory as a sequence of points through a vector-defined direction on any triangle-tessellated non-planar surface. The algorithm processes the ordered points of the 2D version of the printing trajectory, the tessellated STL files of the target surface, and the projection direction. It then generates the new trajectory lying on the target surface with the G-code instructions for the printer. As a proof of concept, several examples are presented, including a Hilbert curve and lattices printed on curved surfaces, using a conventional fused filament fabrication machine. The algorithm’s effectiveness is further demonstrated by translating a printing trajectory to an analytical surface. The surface is tessellated and fed to the algorithm as an input to compare the results, demonstrating that the error depends on the resolution of the tessellated surface rather than on the algorithm itself.

Optimal local unitary encoding circuits for the surface code

The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006) showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size L, however the most efficient known method for encoding an unknown state, introduced by Dennis et al. (2002), has O(L2) time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly 2L time steps to encode an unknown state in a distance L planar code. We further show how an O(L) complexity local unitary encoder for the toric code can be found by enforcing locality in the O(log⁡L)-depth non-local renormalisation encoder. We relate these techniques by providing an O(L) local unitary circuit to convert between a toric code and a planar code, and also provide optimal encoders for the rectangular, rotated and 3D surface codes. Furthermore, we show how our encoding circuit for the planar code can be used to prepare fermionic states in the compact mapping, a recently introduced fermion to qubit mapping that has a stabiliser structure similar to that of the surface code and is particularly efficient for simulating the Fermi-Hubbard model.

Analysis of Spectral Transmission in Si Solar Cell With Pyramidal Texturization by Using PC3S Simulation

Management of light is a crucial task in solar cell design and structure because it increases the path length of the light inside, which in turn increases the probability of electron-hole pair generation. This study addresses the impact of a pyramidal textured structure on spectral transmission in the morphology of silicon. The morphology of silicon wafers was investigated using PC3S spectral transmission software to study the spectral transmission, reflectance, collection probability, mobility, carriers, electric field, velocity, current and surface recombination. Spectral transmission on the front surface with pyramidal texture showed a better transmission percentage than the planar surface. The texture with a depth of 20 µm and base length of 20 µm exhibited good performance in front spectral transmission, spectral reflectance, electric field, velocity, current and surface recombination from the top to the bottom of the sample. The planar surface had more reflectance and lower collection probability than the other pyramidal textured samples due to its low mobility, carriers, electric field, velocity and current but high surface recombination.