Creation Of Shape Research Articles

Creation of Accessories Shape of Buffalo Head with Source of Ideas for Unan-Unan Ceremony Using Waste Techniques

Creation of Accessories Shape of Buffalo Head with Source of Ideas for Unan-Unan Ceremony Using Waste Techniques

Outcome of modified fleur-de-lis latissimus dorsi myocutaneous flap for breast reconstruction

BackgroundReconstruction of breast following mastectomy is important in terms of rehabilitating patients of breast cancer. Numerous approaches have been used in the reconstruction process. A procedure that has gained interest of the patients is reconstruction of breast using the autologous form. Main objective of this study is to determine the outcomes of modified fleur-de-lis latissimus dorsi flap in patients undergoing breast reconstruction. MethodologyThis is a retrospective case series which was conducted at the Department of Plastic Surgery, SIMS/Services Hospital, Lahore, from January 2020 till December 2022. 184 patients age 25–60 years and Females with a history of mastectomy, who had to undergo creation of breast shape using a tissue flap from another part of the body at the site of breast following mastectomy were included. All patients were subjected to standard procedure of breast reconstruction with latissimus dorsi flap using modified fleur-de-lis technique and postoperatively weekly assessment in the first month and then monthly until 3 months was carried out and outcome of the study was analysed. ResultsThe mean age and VAS score of the patients was 49.7 ± 9.17 and 6 ± 2.21, respectively. 57.1 % patients have DCIS, benign in 38 % patients and other tumours were present in 4.9 % patients. Immediate versus delayed reconstruction was done in 63.6 % versus 36.4 % patients respectively. Good aesthetic outcome was achieved in 80.3 % patients ConclusionModified fleur-de-lis latissimus dorsi flap in patients undergoing breast reconstruction yielded a good aesthetic outcome in the majority of the patients.

Effect of high-speed steel screw drill geometry on cutting performance when machining austenitic stainless steel

Drilling into the solid material is one of the basic technological operations, which creates a cylindrical hole in an appropriate time with required quality. Drilling operation demands a favourable removal of chips from the cutting area because a creation of an undesirable shape of chips can impart a lower quality of the drilled hole corresponding with the generation of excess heat due to the intense contact of the chip with drill. The solution for a proper machining is a suitable modification of the drill geometry i.e., point and clearance angles as presented in current study. The tested drills are made of M35 high-speed steel characterized by a very thin core at the point of the drill. An interesting feature of the drills is the use of cutting speed higher than 30 m min−1, with the feed of 0.2 mm per revolution. The surface roughness (Ra and Rz lower than 1 µm and 6 µm respectively), cylindricity (0.045 mm), roundness (0.025 mm), perpendicularity of the hole axis (0.025 mm), diameters and position of the individual holes were achieved for a drill with point angle 138.32°and clearance angle 6.92 respectively. The increase of the drill point angle by 6° resulted in the decrease in the feed force of more than 150 N. In addition, an increase of the clearance angle by 1° resulted with a decrease in the feed force of 70 N. The results of the experiment showed that with the correct geometry of the tool the effective machining without using internal cooling can be realised.

Epicycle-model-guided arbitrary shaped customization of structured light

Structured light has been exploited as an important tool for particle manipulation along a desired complex path. However, generating the required structured light illumination for the creation of an arbitrary shape without an analytic expression as a guide is challenging, specifically for designing a structured beam by mapping the shape of an arbitrary object. To address this issue, we propose an effective scheme to customize structured light freely and precisely by modifying the epicycle model in astrophysics. Predesigned structured beams can be identified with or without explicit analytic expressions of the desired shapes. Moreover, we study the roles and relationships between the number of epicycles and the number of key points. The local stretching and transformation of a specific structured beam are also analyzed. The advantages of the proposed method are demonstrated by conducting dynamic manipulation experiments using polystyrene particles. This method is simple and intuitive and provides an effective toolkit for the design of structured light for more complex tasks, thus facilitating advanced applications in optical manipulations.

Деформации в нестационарной стадии прессования прутка из алюминиевого сплава с малым коэффициентом вытяжки

Introduction. It is noted that extrusion is the main procurement process in the aluminum alloys forming operations. At the same time, the process has such a disadvantage as the nonstationarity of the metal plastic flow. The work aim is to establish the inhomogeneity deformation level of the pressed rod front part by numerical simulation using the finite element method. The study objectives are to formulate the extrusion process boundary conditions, to obtain a solution and to evaluate the inhomogeneity degree. Research methods: the finite element method was used to evaluate the deformed state. The actions sequence included the creation of primary deformation zone shape and the tool configuration. The mutual movement of the tool and the deformable material is set using the appropriate boundary conditions. The deformable medium is a ductile material with power-law hardening, the physical and mechanical properties correspond to the aluminum alloy of the 6000 series. Results and discussion: It is revealed that the strain degree in the pressed rod front part is extremely nonuniform distributed; differences above 300% are recorded. The strain degree distribution dependences in the rod cross sections are constructed depending on the distance from the front end at different relative radial coordinates. It is revealed that the rod central layers acquire a constant level of the strain degree earlier than the peripheral layers. The stationary process is achieved with less metal motion. The work result application scope is the technological study of rational metal cutting of aluminum alloys at the extrusion final stage in order to use recyclable waste more rationally. Conclusions. In the extrusion process with a low elongation ratio, the strain degree is distributed nonuniform both along the press rod cross and along its length. The rod front part remains weakly deformed both at the periphery and in the center in the nonstationary initial extrusion stage. It often forces to send for remelting due to the insufficiently developed metal structure. At the same time, if the limits on the minimum possible degree of deformation are set, then using the results of the calculation by the finite element method, the minimum length of the metal to be removed can be set, thereby reducing the mass of waste sent for remelting.

Dzieje pewnej eksplozji, czyli krótka historia nacjonalizmu

A History of a Certain Explosion, or a Short History of NationalismThe article is a survey of some of numerous paradoxes connected with the history of the notion “nation”. In its contemporary meaning, this notion evolved, in a relatively short time, from a vague idea known to some eccentric thinkers into an indispensable component of the identity of each and every inhabitant of our continent. In a relatively short period the people inhabiting Europe were first classified according to many flexible criteria (such as residence, belonging to particular social strata, confessed religion, respected authority, language spoken, etc.), and later divided into national communities of several million members, apparently existing from time immemorial and separated by eternal barriers of contradictory national interests. Attempts to cross these barriers made by a human being – i.e. transferring from one community to another – are now treated as a rejection and betrayal of one’s own identity.The article tries to present how such a radical change could have happened, to what extent national ideology was a by-product of economic and social processes initiated in Europe as early as the Middle Ages, and to what degree this ideology was a stimulus for these processes. Last but not least, the study also considers to what extent national ideology contributed to the creation of the contemporary shape of the world, in which western civilization managed to win primacy and maintain it till the present day, and, moreover, impose its standards on other cultures – among them the dogma about a necessary division into rival nations, which is apparently an effect of human nature itself.

Experience nature as a basis for building strong composite structures

Introduction. The article is devoted an analytical overview of the methods of applying the Nature solutions for designing structures made of plastics reinforced with fibers, in particular, using rational curved fiber trajectories. The first section provides an overview of different structural models and some approaches to the micromechanics of composites.
 Materials and methods. Sections 2-7 discuss: analysis of rational elastic-strength properties of wood and composites for crack arrest by weak interface; methods for constructing curved paths of fibers of “flowing holes”; analyzes the applied and promising technologies for manufacturing attachment points, in which holes are formed using curvilinear fiber paths; “nature-inspired” principles of optimal design of pipe composite structures similar in structure to ladder of bamboo stalk; examples of the effective use of fibrous composites in elastic elements such as leaf springs; developing additive technologies for 3D printing of fiber composite parts with fiber laying along calculated trajectories.
 Results. Each section of the article presents conclusions related to the peculiarities of composites structures calculation and design: calculations show that in order to increase the crack resistance of fibrous composites, it is necessary to significantly increase the shear characteristics of the binder and strive for rational properties created by Nature in wood; as a result of the calculation, it turns out that the maximum stress per fiber at the optimal reinforcement structure becomes about 3–4 times less than with a uniform rectilinear laying; rational reinforcement leads to a significant reduction in local stresses per fiber, elimination of splits and damages of fibers and an increase in the carrying capacity of the assembly; it has been shown that the bamboo rings are arranged to prevent the barrel from splitting from bending compressive stresses and tangential stresses when the barrel is twisted by wind load; analyzed the relationship of equal-strength profiling with Leonardo’s rule for tree crown branching. The works on creation of bio-similar shape and structure of curvilinear reinforcement of specimens for correct determination of unidirectional composites strength at tension along fibres were discussed; analyzed the role of composite technologies in modern mechanical engineering, in particular, in the creation of composite structures in open space.
 Conclusions. The article is devoted to the analysis of the tasks of fibrous composites macromechanics, therefore, in the opinion of the authors, the three most promising and related areas in macromechanics of composites that require further research are biomechanics of strength, computer modeling of optimal structures and technological mechanics of composites.

A.R.T.E.² threads interwoven in the sea of tales

In activities developed in the projects Mar de Histórias and A.R.T.E. 2 , the perception of the line is viewed/analyzed in its poetic possibilities, as a compositional element and in different supports. The experimentation started in regular undergraduate classes, in the discipline Creation of Shape, generated proposals for practices with the Creativity Workshop on Shape, by dealing with the use of the line by different artists, throughout the history of art, applied in the Center for Mathematical and Nature Sciences (CCMN) of the Federal University of Rio de Janeiro (UFRJ).

Оценка уровня упрочнения стружки из алюминиевого сплава, предназначенной для последующей обработки давлением

Introduction. It is noted that the chip is an undesirable type of metal scrap, because it has a developed surface, which creates conditions for more intense interaction with the surrounding atmosphere. This creates conditions for oxidation and gas saturation, especially at elevated temperatures typical of remelting processes. Therefore, the process of chip utilizing is considered, bypassing the remelting stage. The aim of the work is to establish the level of work hardening of chips during the processing of aluminum alloys and to predict its effect on the subsequent processing process. Research methods: to assess the deformed state, the finite element method was applied, implemented in the RAPID-2D software package. The sequence of actions included the creation of the initial shape of the deformation region and the configuration of the tool. The mutual displacement of the tool and the deformable material is specified using the corresponding boundary conditions. The deformable medium is a viscous-plastic material with power-law hardening, the physical and mechanical properties correspond to an aluminum-magnesium alloy. Results and discussion: the solution obtained shows that the degree of shear deformation in the chips can reach a value of more than 2. In this case, a higher level of deformation is localized on the side of the convex part of the chip. The comparison of the solution with those obtained earlier by other authors is carried out and its similarity is shown. In the considered solution, the difference in the degree of work-hardening of the chips along its thickness is 36 %. A variant of the sequence of processing the workpiece first by cold deformation, and then by cutting is considered. The field of application of the results of the work is the development of methods for the processing of technogenic formations. Conclusions. During the cutting process, the plastic deformation of the chips reaches significant values. In this paper, the difference in the degree of shear deformation in the chip thickness is established, depending on the proximity of the cut layer to the surface of the cutting tool. It is proposed to take this difference into account at the subsequent stages of chip processing. The presence of the marked inhomogeneity of mechanical properties leads to consequences in the form of an inhomogeneous distribution of the temperature of the beginning of recrystallization during subsequent operations of heat treatment or hot deformation treatment. The principle of additivity of the degree of deformation obtained by the metal at the stage of plastic shaping of the workpiece and the shaping of the chip itself is introduced.

System of preliminary treatment of substrates of methantenks in the apparatus of the vortex layer with heat recovery

The studying of energy balance for the analysis of thermal processes carried out at the stage of preliminary treatment of substrates is an urgent task. The energy balance is necessary for the subsequent studying the material balance of the developed system with heat recovery and for its energy analysis. The proposed method of substrate pre-treatment in the digester apparatus of the vortex layer allows to increase the biogas yield by 7-10 percent. At the same time, a new source of low-potential energy appears in the form of a heat carrier used for cooling the vortex layer apparatus, which, with the additional use of a heat pump, will reduce energy consumption to maintain the temperature mode of the methane tank. (Research purpose) The research purpose is in creation of technological shape of the system of preliminary treatment of substrate to anaerobic digestion, developing the energy balance of the proposed scheme and determine criteria to evaluate the proposed scheme for post-processing of experimental data. (Materials and methods) Authors used information research methods, including standard analytical methods of modern system approach, processing and analysis. The article presents analytical studies based on the well-known laws of heat engineering and thermodynamics. (Results and discussion) Based on the energy balance of the proposed system, the criteria for evaluating the system of pre-treatment of the substrate for anaerobic digestion with heat recovery of the vortex layer apparatus were determined: ensuring preheating of the initial substrate to the temperature of the anaerobic fermentation process; ensuring the temperature mode of operation of the coil of the vortex layer apparatus; ensuring the energy efficiency of the proposed system. (Conclusions) It was found that the functional dependencies based on the energy balance of the proposed system allow evaluating the effectiveness of this system. It was found that further selection of technological equipment and calculation of the material balance of the proposed system is carried out based on the energy balance.

The mathematic basics of developing a 3d shoe last shape using the reverse engineering method.

A shoe making industry which can offer shoes that fit consumer needs has a decided advantage over its competitors. Next to fashion, shoe fitness and foot comfort is an important selection criterion. The shoe last is the main element that provides the of comfort shoes. Most of the scientific researches devoted to the topic of computer-aided design of lasts, are focused on finding the optimal ratio of the foot and shoe shape, on the selection of the most suitable last. However, the features of tailor made shoe production often require the creation of a new shoe last shape based on the customer's foot parameters. This paper is devoted to the development of an algorithm for the method of а new last shape designing for the tailor made shoes in a graphical 3D CAD environment and a mathematic model of its deformation in accordance with the basic parameters of the foot and the last style. The modeling of the last by reverse engineering involves scanning the original last, which is the basis for creating a new shape by performing some deformations of the original shape. Such deformations can be described mathematically as geometric transformation matrices: displacement, rotation, scale, etc. In the article for designing a new last shape, the method of calculating the parameters of deformation of the base last shape in accordance with the style and theoretical parameters of the last, obtained based on the foot sizes of the consumer, is proposed. Based on these calculations, an algorithm for the method of modeling a new shoe last using the reverse engineering method was developed and a mathematical model of the geometric deformation of its complex 3d shape, which is performed in the 3d CAD designing process, was calculated.

Spherical Mesoporous Materials from Single to Multilevel Architectures.

Mesoporous materials with various structures have attracted considerable attention due to their distinctive properties such as large pore sizes, high surface areas, tunable pore structures, and controllable framework compositions. Among them, spherical mesoporous materials (SMMs) are of great interest owing to the unique spherical shape, which show the closed packing nature and lowest surface energy. The open mesopores and short channels of SMMs not only increase the density of high accessible active sites but also facilitate the mass diffusion with short length. These characteristics are particularly useful for applications in catalysis, adsorption, energy storage and conversion, biomedicine, and so on. In addition, the creation of a spherical shape is conformable to the law of natural selection because objects in nature tend to minimize energy, while the sphere is one of the most perfect matter structures. Therefore, the design and synthesis of SMMs are very important from both fundamental and technological viewpoints. Compared to the simple single-level, SMMs with more complex multilevel structures inevitably bring unusual mechanical, electrical, and optical properties, which are highly desired for practical applications. For example, the construction of core-shell structured SMMs has inspired great attention as they can combine multiple components into one functional unit, exhibiting ameliorated or new physicochemical properties, which cannot be obtained from the isolated one. The presence of a hollow cavity in the yolk-shell structure allows sufficient exposure of the core while maintaining the protective ability of the shell, which is conducive to retaining the distance-dependent properties of the core. Multishelled hollow structures consisting of two or more mesoporous shells are expected to show superior activities in various applications compared to their bulk counterparts because more active interfaces and unique compartmentation environments can be provided. Therefore, SMMs from single to multilevel structure represent a class of advanced nanostructured materials with unique structures and fascinating properties. In this Account, we highlight the progresses on the synthesis and applications of SMMs from single to multilevel architectures. The synthetic strategies have been summarized and categorized into (i) the modified Stöber method, (ii) the hydrothermal strategy, (iii) the biphase stratification approach, (iv) the nanoemulsion assembly method, (v) the evaporation induced aggregating assembly (EIAA) method, and (vi) the confined self-assembly strategy. Special emphasis is placed on the synthetic principles and underlying mechanisms for precise control of SMMs over the particle sizes, pore sizes, pore structures and functionalities as well as different levels of architectures. Moreover, the implementation performances in catalysis, drug delivery, and energy related fields have been highlighted. Finally, the opportunities and challenges for the future development of SMMs in terms of synthesis and applications are proposed.

Development of Path Generation Method for Five-Axis 3D Printer

3D printers that use the fused deposition modeling (FDM) method are generally based on a three-linear-axis mechanism. However, because the posture of the workpiece is limited, the shape of the model that can be generated by this type of 3D printer is restricted. The 3D printer makes 3D models by stacking up materials on a plane. Because of this principle, a base to support the laminated material is necessary, and it is impossible to develop a model shape with an overhang without support parts. Although the problem is solved by making a foundation using a support material, it takes time to shape and remove the material. Therefore, this conventional method is time consuming. The purpose of this research is to laminate and make shapes that are difficult to laminate with a three-axis 3D printer without using support material. Therefore, a new five-axis 3D printer was developed with the FDM method, and its control program was designed. In addition, hardware consisting of the mechanical structure and the servo control system was developed, and the laminating path, which can exert the effect of the five-axis mechanism, was calculated. The posture of the workpiece can be controlled by mounting the B-axis, which tilts the lamination table, and the C-axis, which rotates the lamination table added on the three-axis configuration 3D printer. Furthermore, a five-axis synchronization control program was developed to control the motion of the five-axis synchronous motion. Furthermore, to correct the nozzle position due to the posture change of the workpiece, a mathematical model of shape creation theory was applied to derive the offset command value. As a result of the laminating experiments of the overhang shape model, the five-axis mechanism and laminating path were sufficiently effective, and the five-axis synchronous control of the 3D printer demonstrated the creation of the overhang shape. However, in experiments using a conventional three-axis mechanism 3D printer with the same lamination path, resins did not adhere and dripped, making shaping impossible. Because of these results, the machining time of the five-axis controlled 3D printers was shorter than that of conventional three-axis-controlled 3D printers. Here, the basic configurations and control system are reported.

An approach of modelling of irregular masses

The goal of this study is to create and evaluate a methodology for generation of realistic 3D computational models of breast tumours with irregular shapes. Methods The methodology for the creation of breast masses consists of two steps: (a) creation of the initial diffusive tumour shape, by choosing Brownian motion or nearest neighbour random walk algorithm, (b) creation of a solid tumour shape by applying a set of 3D filters, and morphological operations. The initial models were smoothed by applying a set of image processing methods. Thereafter, projection images of these 3D lesions were generated by using an in–house developed software, capable to simulate the X-ray transport through the computational phantoms. Subsequently, a technique for embedding the simulated masses in patient mammography images was developed and applied. Results Thirty irregular masses with different sizes and shapes were generated, and projection images were simulated. The realism of the projected masses on patient images was evaluated by comparison of extracted features, such as the exponential parameter of the power spectrum, fractal dimension and other statistical parameters to these extracted from patient data. The obtained results confirmed that the methodology is capable of producing realistic 3D tumour models with user defined sizes and irregular shapes. Conclusions The methodology will be used to generate unique and realistic in shape and size computational models of breast adenoma, intraductal papilloma, cysts and duct hyperplasia. These computational models are stored in an open source database to be used by all professionals working toward the creation of new technologies for breast-screening and diagnosing. Acknowledgements This research is supported by the Bulgarian National Science Fund under grant agreement DN17/2. This project also has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 692097.

Глубокая 3D-рентгенолитография на основе высококонтрастного рентгенорезиста

In the classical X-ray lithography, the X-ray beam is perpendicular to both the mask and the resist layer; the beam starts to create microstructure along its path without transverse modulation. With the advanced technique of tilting and rotating the mask/resist layer and due account of properties of X-ray resist, multiple exposure enables creation of real 3D shape with submicrometer accuracy. This paper presents a technique of creation of real 3D microstructures with application of multi-beam X-ray lithography. This technique enables creation of a large number of 3D structures.

CREATING GEOMETRIC SHAPES IN AUTODESK INVENTOR USING OF BORN (BASE ORPHAN REFERENCE NODE) TECHNIQUE

The basic concept of BORN (Base Orphan Reference Node) technique is the use of a Cartesian coordinate system as a first shape, which preceded the creation of any geometrical shape. After the establishment a Cartesian coordinate system, are obtained by three mutually normal working plane (XY, YZ and ZX), which can be used as a sketching plane, three working axes (X, Y, and Z) and a working point (the origin). Three working planes are used as a reference for dimensions and geometric constructions. Autodesk Inventor automatically adjust set of reference geometry, which consists of three working-plane, three working axes and the origin when we begin to create a new part. All of the following geometric shapes can be used by the coordinate system and / or reference geometry as sketching plane.

Synthesis, evaluation of kinetic characteristics and investigation of apoptosis of Cu2+-modified ceria nano discs

Ceria nano discs were synthesized by the stepwise thermal decomposition strategy of the oxalate precursor. A series of Ce1–xCuxO2 (x = 0, 0.02, 0.1, 0.2 and 0.3) nano sized oxide systems were prepared through thermal decomposition route. Kinetic characterization of formation of solid solution was made by isoconversional strategy under non-isothermal condition. Introduction of various reactant molar ratios of Cu2+:Ce4+ has a pivotal role in the creation of new oxygen vacancies, decomposition strategy, particle size and shape. Cu2+ doping (x = 0.02 and 0.1) damages the disc shaped morphology of ceria. Homogeneous distribution of Cu2+ on the oxalate precursor has a significant role in the catalyzing activity for the destruction of oxalate bond to oxide. 2 mol% doped Cu2+ promotes breaking of oxalate bonds in nitrogen atmosphere. In vitro cell viability assay illustrates enhanced toxicity to cancer cells with 10 mol% Cu2+ doped ceria.

Chick muscle development.

Striated muscle is the most abundant tissue in the body of vertebrates and it forms, together with the skeleton, the locomotory system required both for movement and the creation of the specific body shape of a species. Research on the embryonic development of muscles has a long tradition both in classical embryology and in molecular developmental biology. While the gene networks regulating muscle development have been discovered mostly in the mouse through genetics, our knowledge on cell lineages, muscle morphogenesis and tissue interactions regulating their formation is to a large extent based on the use of the avian model. This review highlights present knowledge of the development of skeletal muscle in vertebrate embryos. Special focus will be placed on the contributions from chicken and quail embryo model systems.

Robot-Assisted Laparoscopic Radical Cystectomy with Stentless Intracorporeal Modified Ves.Pa Neobladder: Early Experience

Abstract Introduction: Bladder cancer represents 3% of all cancers and 7% of cancer deaths in the United States.1 A majority of bladder cancer is treatable at an early stage.1 However, radical cystectomy with urinary diversion is required for muscle invasive disease.1 Traditionally, an ileal conduit is used; however, this has significant quality-of-life (QOL) changes. A neobladder can spare some of the QOL changes. All neobladders must use detubularization, double folding, creation of a spheroid shape, and efficient evacuation.2 Pure intracorporeal robot-assisted laparoscopic technique has been recently developed with a select number of high-volume centers utilizing various operative and neobladder techniques.3–5 Recently, the robotic Ves.Pa neobladder was described in a human pelvic model.6 We present our step-by-step process of the robot-modified Ves.Pa neobladder. Materials and Methods: The modified robotic Ves.Pa neobladder was completed using the da Vinci SI surgical system. Cystoprostatectomy was co...

Digitization of Structured Composite Plates with Regard to Their Numerical Simulations

A method of 3D scanning and a subsequent data reconstruction presented in this paper are focused on digitization of highly structured composite parts with regard to creation of a fully functional CAD and FEM model. The digitized parts are structured carbon composites made replication of steel templates. Production of steel templates is a technological procedure mostly based on pressing or rolling. However, the data obtained from 3D scanner are not in appropriate format, there are a cloud of points interleaved by a sufrace and it is necessary to use some aditional methods to solidify the resulting geometry. Most often with using commercial software as for example: Creo, Catia, Inventor, Rhino or Geomagic studio is the cloud of points parameterized in a continuous surface. Now, based on some next operations (intersections, blends) the desired solidified model in CAD format could be achieved. Despite the relatively rapid creation of the main shape the minor inaccuracies that occur during non-contact measurement results either in local areas or individual points with a large deflection. The aim of this thesis was to assess the appropriate method for creating geometry and compensation the inaccuracies with regards to numerical simulations, especially the meshing and convergency of a solved model. As has been quite surprisingly found, some local small step changes in the geometry could be for the calculation easier to solve than a complicated and highly approximated area. An influence to a solution does not seem important.