Subcooled liquid boiling makes it possible to remove extremely high heat flux densities (tens, and under certain conditions even hundreds of MW/m2). This method is used for cooling rocket nozzles, in metallurgy, in thermonuclear power and special installations (cooling of beam targets), pulsed magnetohydrodynamic (MHD) installations. However, the calculations of this process are based on purely empirical correlations. The lack of experimental data on the characteristics of bubbles (size evolution, life time, formation frequency) hinders the development of mathematical models and calculation methods. The paper presents a program developed in the Python 3.10 environment for automated processing of high-speed video recordings of the evolution of a single bubble during boiling of a subcooled liquid. Comparison of frame processing, carried out «manually» and with the help of the developed program, showed a fairly high agreement between the results. The developed method makes it possible to significantly reduce the time spent on processing the experimental material and to include a significantly larger array of experimental data in the analysis.
{"title":"Visualization of the Evolution of a Single Vapor Bubble During Boiling of a Subcooled Liquid: Experience in Automating the Processing of High-Speed Video Recording Results","authors":"N.V. Vasil’ev, S.N. Vavilov, Yu.A. Zeigarnik, N.A. Azarov","doi":"10.26583/sv.15.3.01","DOIUrl":"https://doi.org/10.26583/sv.15.3.01","url":null,"abstract":"Subcooled liquid boiling makes it possible to remove extremely high heat flux densities (tens, and under certain conditions even hundreds of MW/m2). This method is used for cooling rocket nozzles, in metallurgy, in thermonuclear power and special installations (cooling of beam targets), pulsed magnetohydrodynamic (MHD) installations. However, the calculations of this process are based on purely empirical correlations. The lack of experimental data on the characteristics of bubbles (size evolution, life time, formation frequency) hinders the development of mathematical models and calculation methods. The paper presents a program developed in the Python 3.10 environment for automated processing of high-speed video recordings of the evolution of a single bubble during boiling of a subcooled liquid. Comparison of frame processing, carried out «manually» and with the help of the developed program, showed a fairly high agreement between the results. The developed method makes it possible to significantly reduce the time spent on processing the experimental material and to include a significantly larger array of experimental data in the analysis.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the topic of integrating visualization tasks to be solved using the Vulkan API into virtual environment systems based on OpenGL visualization, is researched. The problem of Vulkan-OpenGL hybrid visualization and an approach to its solution, based on a modified render-to-texture technique, are described. The technology of constructing an original embeddable program shell (VK-capsule) is proposed, which allows hybrid visualization as a "black box" to be worked with, obtaining an image in the OpenGL frame buffer at the output. The paper presents the developed structure of the VK-capsule, comprising three program blocks (VK-, GL- and I-block), and describes methods and algorithms for their construction. Based on proposed technology, methods and algorithms, a VK-capsule for height field visualization task was developed, which utilizes hardware-accelerated ray tracing, Vulkan API supported by. The approbation of the developed VK-capsule was carried out, which showed that proposed solutions are effective and meet the task. The results obtained can be used in virtual environment systems, scientific visualization, video simulators, virtual laboratories, educational applications, etc.
{"title":"Hybrid Visualization with Vulkan-OpenGL: Technology and Methods of Implementation in Virtual Environment Systems","authors":"P.Yu. Timokhin, M.V. Mikhaylyuk","doi":"10.26583/sv.15.3.02","DOIUrl":"https://doi.org/10.26583/sv.15.3.02","url":null,"abstract":"In this paper, the topic of integrating visualization tasks to be solved using the Vulkan API into virtual environment systems based on OpenGL visualization, is researched. The problem of Vulkan-OpenGL hybrid visualization and an approach to its solution, based on a modified render-to-texture technique, are described. The technology of constructing an original embeddable program shell (VK-capsule) is proposed, which allows hybrid visualization as a \"black box\" to be worked with, obtaining an image in the OpenGL frame buffer at the output. The paper presents the developed structure of the VK-capsule, comprising three program blocks (VK-, GL- and I-block), and describes methods and algorithms for their construction. Based on proposed technology, methods and algorithms, a VK-capsule for height field visualization task was developed, which utilizes hardware-accelerated ray tracing, Vulkan API supported by. The approbation of the developed VK-capsule was carried out, which showed that proposed solutions are effective and meet the task. The results obtained can be used in virtual environment systems, scientific visualization, video simulators, virtual laboratories, educational applications, etc.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135298760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 2016, an article [1] was published in the Scientific Visualization No. 1 journal, which marked the beginning of a series of publications, in one way or another related to the visualization of georeferenced data. In 2023, an article [2] was published in the journal Scientific Visualization, which continued this series. This article describes step by step the process of developing and debugging a software product for visualizing geophysical data with their subsequent layout on a Yandex satellite map. The initial information for building maps was a text file containing three columns of data: two columns are geographic coordinates, the third column is a scalar parameter, such as temperature or salinity. The presented work is a direct continuation of this series. It describes the procedure for visualizing vector geophysical parameters on the Yandex satellite map, for example, such as current velocity or wind speed. The visualization procedure for vector parameters is based on a similar procedure previously developed for scalar parameters. The paper describes in detail the process of developing and debugging, modifying a software product, the ultimate goal of which is to visualize only the geophysical velocity parameter with subsequent display on the Yandex satellite map in accordance with the geographic coordinates that are set as input. The software product is a fully debugged complete module that can work both in standalone mode and in a complex aimed at superimposing the result obtained on the Yandex satellite map.
{"title":"Universal System for Visualizing Geo-Referenced Data - Speed Vector Data","authors":"N.N. Voronina, A.S. Zapevalov","doi":"10.26583/sv.15.3.03","DOIUrl":"https://doi.org/10.26583/sv.15.3.03","url":null,"abstract":"In 2016, an article [1] was published in the Scientific Visualization No. 1 journal, which marked the beginning of a series of publications, in one way or another related to the visualization of georeferenced data. In 2023, an article [2] was published in the journal Scientific Visualization, which continued this series. This article describes step by step the process of developing and debugging a software product for visualizing geophysical data with their subsequent layout on a Yandex satellite map. The initial information for building maps was a text file containing three columns of data: two columns are geographic coordinates, the third column is a scalar parameter, such as temperature or salinity. The presented work is a direct continuation of this series. It describes the procedure for visualizing vector geophysical parameters on the Yandex satellite map, for example, such as current velocity or wind speed. The visualization procedure for vector parameters is based on a similar procedure previously developed for scalar parameters. The paper describes in detail the process of developing and debugging, modifying a software product, the ultimate goal of which is to visualize only the geophysical velocity parameter with subsequent display on the Yandex satellite map in accordance with the geographic coordinates that are set as input. The software product is a fully debugged complete module that can work both in standalone mode and in a complex aimed at superimposing the result obtained on the Yandex satellite map.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Components of optoelectronic devices installed in aircrafts and space vehicles experience significant mechanical loads during their operation. Excessive and cyclic loads may lead to the defect growth or the fatigue failure. In this paper, we describe a non-destructive imaging technique for stress mapping in anisotropic crystalline materials during bench test. The technique is based on Mueller-matrix imaging and the material photoelasticity. The results of experimental studies for two observation directions coinciding with different crystallographic axes of TeO2 are presented. Main limitations and further potential development of the technique are discussed.
{"title":"Mueller-Matrix Stress Mapping in TeO2 Crystals Under Dynamic Loading","authors":"D.D. Khokhlov, A.A. Bykov, A.Yu. Marchenkov, Yu.V. Pisarevsky, Ya.A. Eliovich, V.I. Akkuratov, A.A. Khvostov","doi":"10.26583/sv.15.3.11","DOIUrl":"https://doi.org/10.26583/sv.15.3.11","url":null,"abstract":"Components of optoelectronic devices installed in aircrafts and space vehicles experience significant mechanical loads during their operation. Excessive and cyclic loads may lead to the defect growth or the fatigue failure. In this paper, we describe a non-destructive imaging technique for stress mapping in anisotropic crystalline materials during bench test. The technique is based on Mueller-matrix imaging and the material photoelasticity. The results of experimental studies for two observation directions coinciding with different crystallographic axes of TeO2 are presented. Main limitations and further potential development of the technique are discussed.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135299087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hydrodynamical structure attending a flow can be hid and hardly to reveal. One of the methods to find them is to use mode decomposition (such as Proper orthogonal decomposition, POD). The method represents the field given as a series of spatial modes multiplied by corresponding temporal coefficients. In the article the method is discussed applyingly to a complex flow with a wave attractor structure. Attractor modes present structured vortex-like figure which cannot be claimed to be aleatory. As it turns out POD modes are not just a formal decomposition but have a physical origin: they are connected with instability cascade minor frequencies, as spectral investigation shows. Another consequence of that is that one of the collateral structure maximum can be visible. This proposition is proven as the structure is found to be visible in the flow itself.
{"title":"POD-based Hydrodynamical Structures Visualization in Flows with an Internal Wave Attractor","authors":"S. Elistratov","doi":"10.26583/sv.15.2.11","DOIUrl":"https://doi.org/10.26583/sv.15.2.11","url":null,"abstract":"Hydrodynamical structure attending a flow can be hid and hardly to reveal. One of the methods to find them is to use mode decomposition (such as Proper orthogonal decomposition, POD). The method represents the field given as a series of spatial modes multiplied by corresponding temporal coefficients. In the article the method is discussed applyingly to a complex flow with a wave attractor structure. Attractor modes present structured vortex-like figure which cannot be claimed to be aleatory.\u0000 As it turns out POD modes are not just a formal decomposition but have a physical origin: they are connected with instability cascade minor frequencies, as spectral investigation shows. Another consequence of that is that one of the collateral structure maximum can be visible. This proposition is proven as the structure is found to be visible in the flow itself.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43385003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article presents the results of research on the assessment of human emotional tension by a speech signal using the developed technology of multilevel wavelet analysis. The disadvantages of polygraph systems during psychophysiological inspections of personnel are given. The data obtained by domestic and foreign experts allow us to make a confident conclusion that the characteristics of a person's oral speech correlate with changes in their condition. The characteristics of the hardware and software complex «Icar Lab» (Russia) in assessing the emotional state of the speaker, as well as the computer voice stress analyzer CVSA (USA) are considered. A new contactless technology is proposed for assessing the level of emotional tension of a person using stress biomarkers obtained on the tonal parts of speech. The WaveView-VSA program for obtaining high-precision time-frequency characteristics of a speech signal has been developed. The possibilities of the developed program for visualizing the level of emotional tension are presented. A database of audio recordings of 6th-year students who are in conditions with increased emotional stress during the exam and the defense of the graduation project has been formed and processed. The research conducted by the Scientific and Educational Medical and Technological Center of the Bauman Moscow State Technical University showed the fundamental possibility of obtaining real-time acoustocardiography data and the level of emotional tension in the examined students during express cardiodiagnostics. The developed technology provides biomarkers of stress based on a speech signal lasting several seconds.
{"title":"Visualization of a Person's Emotional Tension by a Speech Signal","authors":"Y. G. Gorshkov","doi":"10.26583/sv.15.2.09","DOIUrl":"https://doi.org/10.26583/sv.15.2.09","url":null,"abstract":"The article presents the results of research on the assessment of human emotional tension by a speech signal using the developed technology of multilevel wavelet analysis. The disadvantages of polygraph systems during psychophysiological inspections of personnel are given. The data obtained by domestic and foreign experts allow us to make a confident conclusion that the characteristics of a person's oral speech correlate with changes in their condition. The characteristics of the hardware and software complex «Icar Lab» (Russia) in assessing the emotional state of the speaker, as well as the computer voice stress analyzer CVSA (USA) are considered. A new contactless technology is proposed for assessing the level of emotional tension of a person using stress biomarkers obtained on the tonal parts of speech. The WaveView-VSA program for obtaining high-precision time-frequency characteristics of a speech signal has been developed. The possibilities of the developed program for visualizing the level of emotional tension are presented. A database of audio recordings of 6th-year students who are in conditions with increased emotional stress during the exam and the defense of the graduation project has been formed and processed. The research conducted by the Scientific and Educational Medical and Technological Center of the Bauman Moscow State Technical University showed the fundamental possibility of obtaining real-time acoustocardiography data and the level of emotional tension in the examined students during express cardiodiagnostics. The developed technology provides biomarkers of stress based on a speech signal lasting several seconds.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46259480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article discusses Takens embedding for 2D and 3D visualization of 1D time series data. The paper considers the use of topological data analysis in conjunction with Takens embedding to analyze the output information of a dynamic system - a rigid body. 3D images of curves constructed from three components of the angular velocity vector of a rigid body for various values of the main moments of inertia are constructed. Three-dimensional images of the curves constructed on the basis of the Takens embedding for the component of the angular velocity of a rigid body for various values of the principal moments of inertia are constructed. Distances between 3D images of curves are determined by constructing persistent landscape functions. Using the method of topological data analysis in conjunction with Takens embedding for image comparison allows you to classify and identify images and output information of the instrumental composition.
{"title":"Using Topological Data Analysis to Visualize Instrument Output","authors":"S. N. Chukanov, I. S. Chukanov","doi":"10.26583/sv.15.2.02","DOIUrl":"https://doi.org/10.26583/sv.15.2.02","url":null,"abstract":"The article discusses Takens embedding for 2D and 3D visualization of 1D time series data. The paper considers the use of topological data analysis in conjunction with Takens embedding to analyze the output information of a dynamic system - a rigid body. 3D images of curves constructed from three components of the angular velocity vector of a rigid body for various values of the main moments of inertia are constructed. Three-dimensional images of the curves constructed on the basis of the Takens embedding for the component of the angular velocity of a rigid body for various values of the principal moments of inertia are constructed. Distances between 3D images of curves are determined by constructing persistent landscape functions. Using the method of topological data analysis in conjunction with Takens embedding for image comparison allows you to classify and identify images and output information of the instrumental composition.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42760595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses state-of-the-art graphical text-to-image neural networks and methods for text-to-image conversion, analyzing the results achieved and samples created to date for text-to-image conversion tasks. Ways of applying neural network approaches to text-to-image transformation for environmental monitoring, infrastructure and medical data analysis tasks are proposed. In this paper the results of neural network generation and its correlation with the user input linguistic constructions of text queries are reviewed, and the typical flaws and artifacts typical of the neural network generated images are identified and classified. The rapid development of neural network technologies in this field could have a significant impact on society, the professional market and the media, which makes the task of studying neural network images and identifying them among other graphic content particularly relevant.
{"title":"Modern Neural Network Technologies Text-to-Image","authors":"N. Bondareva","doi":"10.26583/sv.15.2.06","DOIUrl":"https://doi.org/10.26583/sv.15.2.06","url":null,"abstract":"This paper discusses state-of-the-art graphical text-to-image neural networks and methods for text-to-image conversion, analyzing the results achieved and samples created to date for text-to-image conversion tasks. Ways of applying neural network approaches to text-to-image transformation for environmental monitoring, infrastructure and medical data analysis tasks are proposed. In this paper the results of neural network generation and its correlation with the user input linguistic constructions of text queries are reviewed, and the typical flaws and artifacts typical of the neural network generated images are identified and classified. The rapid development of neural network technologies in this field could have a significant impact on society, the professional market and the media, which makes the task of studying neural network images and identifying them among other graphic content particularly relevant.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43946006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The vapor explosion process is an explosive increase in the volume of vapor, accompanied by a sharp rise in pressure when a hot melt enters a cold liquid medium with a temperature above its limiting superheat temperature. This phenomenon incurs the threat of great destruction and human casualties in certain types of accidents in the nuclear, metallurgical, pulp and paper industries. Nevertheless, there are still many insufficiently studied aspects of this phenomenon, one of which is the initiation (triggering) of the process. There are a number of logically fairly consistent descriptions of the processes occurring at a given stage of a vapor explosion. However, almost all of them are based on experiments carried out with external (forced) triggering. The article describes the data obtained during spontaneous triggering, i.e. under conditions much closer to reality. In this paper, using high-speed video recording (with a frame rate of up to 180 kHz and an exposure time of up to 2 μs), the first visualization of the processes occurring during spontaneous triggering of a vapor explosion on molten NaCl salt drops in distilled water subcooled to saturation temperature is presented. It is shown that when several drops of the NaCl melt interact with water, the micro vapor explosion that occurred on one drop, with an interval of several tens of microseconds, causes explosive vaporization on neighboring drops as well. Thus, the logical descriptions of the processes received instrumental confirmation.
{"title":"Visualization of the Processes Occurring during Spontaneous Triggering of a Vapor Explosion","authors":"N. Vasil’ev, S. Vavilov, Y. Zeigarnik","doi":"10.26583/sv.15.2.04","DOIUrl":"https://doi.org/10.26583/sv.15.2.04","url":null,"abstract":"The vapor explosion process is an explosive increase in the volume of vapor, accompanied by a sharp rise in pressure when a hot melt enters a cold liquid medium with a temperature above its limiting superheat temperature. This phenomenon incurs the threat of great destruction and human casualties in certain types of accidents in the nuclear, metallurgical, pulp and paper industries. Nevertheless, there are still many insufficiently studied aspects of this phenomenon, one of which is the initiation (triggering) of the process.\u0000 There are a number of logically fairly consistent descriptions of the processes occurring at a given stage of a vapor explosion. However, almost all of them are based on experiments carried out with external (forced) triggering. The article describes the data obtained during spontaneous triggering, i.e. under conditions much closer to reality.\u0000 In this paper, using high-speed video recording (with a frame rate of up to 180 kHz and an exposure time of up to 2 μs), the first visualization of the processes occurring during spontaneous triggering of a vapor explosion on molten NaCl salt drops in distilled water subcooled to saturation temperature is presented. It is shown that when several drops of the NaCl melt interact with water, the micro vapor explosion that occurred on one drop, with an interval of several tens of microseconds, causes explosive vaporization on neighboring drops as well. Thus, the logical descriptions of the processes received instrumental confirmation.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43822101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper proposes an algorithm for calculating a composite bicubic surface with a fixed frame formed by longitudinal (along the x axis) and transverse (along the y axis) cubic splines. Frame line equations are taken as the main boundary conditions. According to the proposed algorithm, the problem is divided into two stages: first, the frame line equations are found and then the coefficients included in the equations of the bicubic portions forming the bicubic surface are calculated. This approach reduces the size of the characteristic matrix of the linear equation system by reducing the number of coefficients in the surface equation. The matrix size is reduced from 16mn to 9mn, where m and n are the number of bicubic portions along the x and y axes. Surface visualization is reduced to building a grid of longitudinal and transverse generators, the equations of which are formed from the surface equation by substituting y=const (longitudinal generators) or x=const (transverse generators). In this paper we calculate and visualize bicubic surfaces with a frame formed by a mixed set of cubic splines and straight lines. The clarity of the examples is ensured by indicating the numerical values of all calculated magnitudes with an accuracy of up to nine significant figures.
{"title":"Bicubic Surface on a Fixed Frame: Calculation and Visualization","authors":"V. Korotkiy, E. Usmanova","doi":"10.26583/sv.15.2.05","DOIUrl":"https://doi.org/10.26583/sv.15.2.05","url":null,"abstract":"The paper proposes an algorithm for calculating a composite bicubic surface with a fixed frame formed by longitudinal (along the x axis) and transverse (along the y axis) cubic splines. Frame line equations are taken as the main boundary conditions. According to the proposed algorithm, the problem is divided into two stages: first, the frame line equations are found and then the coefficients included in the equations of the bicubic portions forming the bicubic surface are calculated. This approach reduces the size of the characteristic matrix of the linear equation system by reducing the number of coefficients in the surface equation. The matrix size is reduced from 16mn to 9mn, where m and n are the number of bicubic portions along the x and y axes. Surface visualization is reduced to building a grid of longitudinal and transverse generators, the equations of which are formed from the surface equation by substituting y=const (longitudinal generators) or x=const (transverse generators).\u0000 In this paper we calculate and visualize bicubic surfaces with a frame formed by a mixed set of cubic splines and straight lines. The clarity of the examples is ensured by indicating the numerical values of all calculated magnitudes with an accuracy of up to nine significant figures.","PeriodicalId":38328,"journal":{"name":"Scientific Visualization","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41689297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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