Incomplete Surfaces Research Articles

Measurement method for large aperture angle incomplete spherical surface stitching based on confocal focusing

In traditional stitching measurements, the central sub-aperture is usually used as the reference and is not suitable for incomplete spherical surfaces without central sub-aperture. The measurement of each sub-aperture requires manual readjusting the position and attitude of the measured component, resulting in low measurement accuracy and low measurement efficiency. In response to this issue, this study proposed a method based on confocal focusing for large aperture angle incomplete spherical surface stitching measurement. Automatically and accurately determine the position of the common focus through confocal focusing technology, the positioning accuracy of the measured component is improved. A sub-aperture stitching model was built, coordinate mapping rotation algorithm and overlapping area error compensation algorithm were applied to the surface shape of each sub-aperture, achieving stitching measurement of large aperture angle incomplete spherical surfaces. Finally, the confocal interference stitching measurement system was built to carry out stitching experiments of sphere and large aperture angle incomplete spherical surface. The stitching experimental results indicated that the method increases the measurement accuracy of PV by 2.2 times, increases the measurement accuracy of RMS by 2.3 times, and increases the measurement efficiency by 1.6 times. Therefore, this method provides a high-precision measurement method for detecting large aperture angle spherical surface shape.

CONTROL OF HEAT AND COOLING FLOWS
 IN RAPID MACHINING OF INCOMPLETE SPHERICAL SURFACES
 OF MACHINE PARTS

Combined rapid machining of incomplete spherical surfaces of parts is considered, formulas for calculating
 the cutting temperature taking into account the angle of contact between the tool and the workpiece are derived, the
 results of experimental studies of the temperature of the part and chips depending on the processing time, as well as
 modeling of cooling air flows in the tool and the cutting zone are presented.

A 3D finite element spectral integral (FESI) method for acoustics

We present a novel hybrid method that integrates the spectral integral method (SIM) with finite element for pressure acoustics in an inhomogeneous medium surrounded by spherical or incomplete spherical surfaces. Our approach, called the finite element spectral integral (FESI) method, enables efficient calculations of the pressure field in near-field and far-field zones. It is more efficient than the conventional finite element method hybridized with the boundary element method (i.e., the FEBI method). Furthermore, we construct a symmetric coefficient matrix using the proposed symmetric coupling to speed up the FESI method. We demonstrate through several examples that our FESI method offers significantly improved efficiency and lower memory consumption compared to the FEM combined with the perfect matching layer method while achieving higher accuracy.

Object-Aware View Planning for Autonomous 3-D Model Reconstruction of Buildings Using a Mobile Robot

Active mapping ranks among the most critical applications of autonomous mobile robots. In this article, we focus on 3D model reconstruction of buildings using an outdoor ground robot equipped with a solid-state LiDAR and a gimbal. A view-planning approach is proposed to generate and evaluate view sequences with reference to the characteristics of solid-state LiDAR and the robot configuration. To reconstruct the specific buildings while ignoring unrelated objects in the environment, we introduce object awareness into the map representation, and frontier- and sampling-based strategies are combined to plan the view sequences for the effective observation of a target building. Instead of greedily maximizing information gain, frontier clusters indicating the mapped object’s incomplete surfaces are used to evaluate the sampled views, and sampling the minimum view set generates view sequences able to efficiently cover the clusters. Moreover, using object awareness to partition the area of sampled views around the building facilitates a divide-and-conquer strategy that overcomes local characteristics and guides a complete reconstruction. Simulation and real-world experiments revealed that our approach allows the thorough and efficient active reconstruction of various buildings and even outperforms state-of-the-art approaches.

Process Optimization of Non-Holonomic Surface Milling for Al-Si7Mg Component

Milling process enhancement for an aluminium alloy component with a large bore and variable wall thickness for incomplete circular surfaces, research on the optimization of milling process parameters based on machining stability and machining deformation control was carried out. Analysis of the formation mechanism of the regeneration effect caused by casting defects in cast aluminium parts, the stability lobe diagrams are plotted by the zero-order frequency domain analysis method, and the effects of radial depth of cut, cis-reverse milling and the dynamics parameters of the milling system on the boundary range of the stability lobe diagram were investigated. By orthogonal simulation analysis of milling deformation, determine the primary and secondary relationship between the influence of each process parameter on the machining deformation and the optimal combination of each process parameter in the test range. The results show that in the milling process, reducing the radial depth of cut, using a more rigid milling cutter and reverse milling can all be effective in improving the stability of the process; The significant influence of process parameters on the amount of machining distortion is: radial depth of cut > feed rate > cutter’s speed, the optimal combination of process parameters is: cutter’s speed 600 r/min, radial depth of cut 0.2 mm, feed rate 150 mm/min.The process parameters are used for machining verification, the surface roughness of the annular hole was improved from 6.3 to 3.2 before the optimization, and the coaxiality was improved from 0.12mm to 0.05mm before the optimization. The results show that Optimised milling process parameters improve part quality.

Fault surface extraction from a global perspective

Fault surface extraction plays a vital role in structural interpretation and structural modeling, which can enhance our understanding of geologic structures. Significant effort has been invested in fault surface extraction in the past few years. These contributions can be roughly divided into two types: one constructs fault sticks or fault patches and links them to form fault surfaces, and the other constructs a complete fault surface by roughly determining the location of a fault. The former is likely to extract incomplete fault surfaces in areas with low data quality or complex fault structures. The latter has problems dealing with faults in the case of complex fault structures, such as intersecting faults. To effectively address these problems, we have developed a novel fault extraction workflow from a global perspective, which can extract fault surfaces on the premise of obtaining the fault distribution of the entire data set. First, we introduce a multilayer complex network to characterize the overall distribution of faults, in which nodes represent faults, node attributes cover information, such as the location of the faults, and edge attributes give the relationship between faults. Then, for each fault represented by the node, we develop a fault surface extraction method based on computational topology, which can guarantee the completeness of the fault surfaces. We apply our method to synthetic data and field seismic data to evaluate the method quantitatively and qualitatively, respectively. The results indicate that the proposed approach extracts the fault effectively, ensures the completeness of the fault surface, and has high performance in areas with complex faults. Thus, the approach can work well in complex situations, such as intersecting faults.

A three-dimensional approach to visualize pairwise morphological variation and its application to fragmentary palaeontological specimens.

Classifying isolated vertebrate bones to a high level of taxonomic precision can be difficult. Many of Australia’s Cretaceous terrestrial vertebrate fossil-bearing deposits, for example, produce large numbers of isolated bones and very few associated or articulated skeletons. Identifying these often fragmentary remains beyond high-level taxonomic ranks, such as Ornithopoda or Theropoda, is difficult and those classified to lower taxonomic levels are often debated. The ever-increasing accessibility to 3D-based comparative techniques has allowed palaeontologists to undertake a variety of shape analyses, such as geometric morphometrics, that although powerful and often ideal, require the recognition of diagnostic landmarks and the generation of sufficiently large data sets to detect clusters and accurately describe major components of morphological variation. As a result, such approaches are often outside the scope of basic palaeontological research that aims to simply identify fragmentary specimens. Herein we present a workflow in which pairwise comparisons between fragmentary fossils and better known exemplars are digitally achieved through three-dimensional mapping of their surface profiles and the iterative closest point (ICP) algorithm. To showcase this methodology, we compared a fragmentary theropod ungual (NMV P186153) from Victoria, Australia, identified as a neovenatorid, with the manual unguals of the megaraptoran Australovenator wintonensis (AODF604). We discovered that NMV P186153 was a near identical match to AODF604 manual ungual II-3, differing only in size, which, given their 10–15Ma age difference, suggests stasis in megaraptoran ungual morphology throughout this interval. Although useful, our approach is not free of subjectivity; care must be taken to eliminate the effects of broken and incomplete surfaces and identify the human errors incurred during scaling, such as through replication. Nevertheless, this approach will help to evaluate and identify fragmentary remains, adding a quantitative perspective to an otherwise qualitative endeavour.

Experimental research on processing incomplete spherical surfaces of machine parts

Improving the durability and reliability of such components as ball joints of cars is very important. The article presents experimental studies to determine surface roughness of incomplete spherical surfaces of machine parts.

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 article, 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.

ПІДВИЩЕННЯ ДОВГОВІЧНОСТІ СФЕРИЧНИХ ШАРНІРІВ ЗМІЦНЕННЯМ КУЛЬОВИХ ПАЛЬЦІВ СТАТИКО-ІМПУЛЬСНОЮ ОБРОБКОЮ

The possibility of improving the durability of spherical sliding hinges due to the strengthening of the incomplete spherical surface of ball fingers by static-pulse processing is considered. The review of recent researches and publications was carried out and promising directions for increasing the durability of ball joints were established. The influence of the shock system parameters on the shape and amplitude of the impact pulse is analyzed. The recommended range of correlations of the geometric parameters of the elements of the shock system is established. On the basis of theoretical and experimental studies, a model of shock system with static load of the boom and tool, as well as a bipolar shock treatment scheme is proposed. The method of calculating the parameters of the shock system and the mathematical dependences have been developed. The model of the mechanical impulse generator of shock impact machine with static load of the boom and the tool according to the bipolar impact processing scheme is proposed. The method and algorithm of calculation of parameters of the generator of mechanical impulses of the device for strengthening of incomplete spherical surfaces is developed.

The restitution of the narthex of the Royal Church in Argeș

The narthex of the Royal Church in Curtea de Argeș offers us today an iconographic ensemble that is heterogeneous and confusing. The large incomplete surfaces of the mural paintings from the 14th century, the erosions and exfoliations provoked by infiltration and capillary humidity, have generated successive re-makings of the painted ensemble, starting from the middle of the 18th century and especially through the 19th century. The restoration from the beginning of the 20th century added the disastrous effect of the transformation of the inferior register of the narthex in an area designated for the replantation of the frescoes originating from the nave. One of the major consequences of this transformation is the loss of coherence of the lecture of key-images that defined the eschatological sense of the narthex iconography. To be more specific, the Final Judgement is fragmented in an arbitrary manner and is hard to read today in its original form.

3D Geological Modeling in Mineral Deposits (Copper Ore Body Cases)

Munella's deposit is one of the most important mineral deposits of Albania. It is rich in mineral resources such as copper, zinc, gold, etc. For this reason Geological 3D modeling is very important because it gives detailed information on management in the most optimal way to mine. In this article, 3D modeling of copper bodies was carried out through modeling software using the implicit method. This method uses advanced algorithms that are Polyharmonic Radial Basis Functions (RBF) generates the best surface area of the ore that can have some Z values and can perfectly customize the incomplete surfaces by utilizing 211 drilling data. The ore bodies that are created with this method are divided into blocks that represent the distribution of copper in%. The results achieved in this study provide an accurate overview of the most important sources of deposits and major concentrations of copper for the efficient management and exploitation of the mine.

Improvement of construction and technology of manufacture car suspension ball bearing

The necessity of improvement of spherical articulated joints is proved on the example of a ball bearing of a forward suspension bracket of a car. The purpose of the work is to improve the design and technology of manufacturing the ball hinge of the car suspension to improve its operational capabilities by increasing the durability of the spherical tribosystem «ball finger–liner». The ways of increasing the durability of spherical articulated joints by design and technological methods were formulated. The main factors of influence on the process of wear of spherical tribosystem «finger-liner» were considered. Taking into account the existing experience and results of the conducted studies, a self-regulated ball joint with an elastic element of the original design was developed. On the basis of the kinematic scheme of sphere manufacturing, a device for turning the incomplete spherical surface of a finger of high accuracy was developed. For hardening of partial spherical surfaces by surface plastic deformation developed by static-pulse device, which provides the layer with a heterogeneous structure, required physical and mechanical properties and geometrically determined lubricantretaining microrelief. The results of this work in future will be planned to generalize and used for the manufacture of competitive products that contains parts with incomplete spherical surfaces.

Evolution of stacking fault tetrahedral and work hardening effect in copper single crystals

Stacking fault tetrahedral (SFT), generated in machining of copper single crystal as one type of subsurface defects, has significant influence on the performance of workpiece. In this study, molecular dynamics (MD) simulation is used to investigate the evolution of stacking fault tetrahedral in nano-cutting of copper single crystal. The result shows that SFT is nucleated at the intersection of differently oriented stacking fault (SF) planes and SFT evolves from the preform only containing incomplete surfaces into a solid defect. The evolution of SFT contains several stress fluctuations until the complete formation. Nano-indentation simulation is then employed on the machined workpiece from nano-cutting, through which the interaction between SFT and later-formed dislocations in subsurface is studied. In the meanwhile, force-depth curves obtained from nano-indentation on pristine and machined workpieces are compared to analyze the mechanical properties. By simulation of nano-cutting and nano-indentation, it is verified that SFT is a reason of the work hardening effect.

Assessing Impact Direction in 3-point Bending of Human Femora: Incomplete Butterfly Fractures and Fracture Surfaces,.

Current literature associates bending failure with butterfly fracture, in which fracture initiates transversely at the tensile surface of a bent bone and branches as it propagates toward the impact surface. The orientation of the resulting wedge fragment is often considered diagnostic of impact direction. However, experimental studies indicate bending does not always produce complete butterfly fractures or produces wedge fragments variably in tension or compression, precluding their use in interpreting directionality. This study reports results of experimental 3-point bending tests on thirteen unembalmed human femora. Complete fracture patterns varied following bending failure, but incomplete fractures and fracture surface characteristics were observed in all impacted specimens. A flat, billowy fracture surface was observed in tension, while jagged, angular peaks were observed in compression. Impact direction was accurately reconstructed using incomplete tension wedge butterfly fractures and tension and compression fracture surface criteria in all thirteen specimens.

Surface Completion Using Laplacian Transform

Model acquisition process usually produce incomplete surfaces due to the technical constrains. This research presents the algorithm to perform surface completion using the available surface’s context. Previous works on surface completions do not handle surfaces with near-regular pattern or irregular patterns well. The main goal of this research is to synthesize surface for hole that will have similar surface’s context or geometric details as the hole’s surrounding. This research uses multi-resolution approach to decompose the model into low-frequency part and high-frequency part. The low-frequency part is filled smoothly. The high-frequency part are transformed it into the Laplacian coordinate and filled using example-based synthesize approach. The algorithm is tested with planar surfaces and curve surfaces with all kind of relief patterns. The results indicate that the holes can be completed with the geometric detail similar to the surrounding surface.

Precision and accuracy of acetabular size measures in fragmentary hominin pelves obtained using sphere‐fitting techniques

Hip joint diameter is highly correlated with body size in primates and so can potentially provide important information about the biology of fossil hominins. However, quantifying hip joint size has been difficult or impossible for many important but fragmentary specimens. New three-dimensional technologies can be used to digitally fit spheres to the acetabular lunate surface, potentially allowing hip joint diameter estimates for incomplete joint surfaces. Here we evaluate the reliability of sphere-fitting to incomplete lunate surfaces in silico using three-dimensional polygonal models of extant anthropoid hipbones. Measurement error in lunate sphere-fitting was assessed at the individual observer level, as well as between observers. Prediction error was also established for acetabular sphere size estimates for smaller divisions of the lunate surface. Sphere-fitting techniques were then applied to undistorted regions of lunate surface in Plio-Pleistocene hominin pelves, with a range of diameters constructed from extant error estimates. The results of this study indicate that digital sphere-fitting techniques are precise and that the lunate does not need to be completely preserved to accurately infer hip dimensions, although some aspects of joint size and morphology can influence sphere size estimates. Joint diameter is strongly predicted by spheres fit to the cranial and caudal halves of the lunate in all anthropoids. We present new hip joint size estimates for a number of fossil hominins, and outline additional applications for digital sphere-fitting as a morphometric technique.

Existence of solution of the logarithmic diffusion equation with bounded above Gauss curvature

We give a simple proof of an extension of the existence results of Ricci flow of Giesen and Topping (2010, 2011) [15,20], on incomplete surfaces with bounded above Gauss curvature without using the difficult Shi’s existence theorem of Ricci flow on complete non-compact surfaces and the pseudolocality theorem of Perelman [7] on Ricci flow. We will also give a simple proof of a special case of the existence theorem of Topping (2010) [16] without using the existence theorem of Shi (1989) [9].

Existence of Ricci Flows of Incomplete Surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.

Ricci flow of negatively curved incomplete surfaces

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.