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CN113887107A - Hexahedron volume calculation method and system based on digital twin body - Google Patents

Hexahedron volume calculation method and system based on digital twin body Download PDF

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CN113887107A
CN113887107A CN202111194573.9A CN202111194573A CN113887107A CN 113887107 A CN113887107 A CN 113887107A CN 202111194573 A CN202111194573 A CN 202111194573A CN 113887107 A CN113887107 A CN 113887107A
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CN113887107B (en
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郑文杰
杨祎
李�杰
辜超
林颖
白德盟
秦佳峰
刘萌
崔其会
黄锐
吕俊涛
邢海文
任敬国
李程启
王江伟
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Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
State Grid Corp of China SGCC
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Abstract

本申请实施例公开了基于数字孪生体的六面体体积计算方法及系统，所述方法包括：根据设定编号规则对目标六面体的八个顶点进行编号；确定目标六面体的八个顶点的坐标；进一步根据顶点的坐标计算目标六面体的每个面的对角线向量坐标；将对角线向量组成矩阵，计算矩阵行列式；最终将每个面的矩阵行列式的结果相加，得到目标六面体的体积。针对现有的计算六面体体积浮点数计算繁琐，消耗大量计算资源等问题，从构造四角化六面体出发，将四角化六面体的体积分解成六个子体积之和，减少了计算六面体体积的浮点数运算次数。

Figure 202111194573

The embodiment of the present application discloses a method and system for calculating the volume of a hexahedron based on a digital twin. The method includes: numbering eight vertices of a target hexahedron according to a set numbering rule; determining the coordinates of the eight vertices of the target hexahedron; The coordinates of the vertices calculate the diagonal vector coordinates of each face of the target hexahedron; the diagonal vectors are formed into a matrix, and the matrix determinant is calculated; finally, the results of the matrix determinants of each face are added to obtain the volume of the target hexahedron. Aiming at the problems that the existing calculation of hexahedral volume is cumbersome and consumes a lot of computing resources, the volume of the tetragonal hexahedron is decomposed into the sum of six sub-volumes starting from the construction of tetragonal hexahedron, which reduces the number of floating-point operations for calculating hexahedral volume. .

Figure 202111194573

Description

Hexahedron volume calculation method and system based on digital twin body
Technical Field
The embodiment of the application relates to the technical field of computers, in particular to a hexahedron volume calculation method and system based on a digital twin body.
Background
The digital twin technology is a comprehensive multi-physical field, multi-scale and probabilistic over-the-reality simulation that uses the most appropriate physical model, sensory data and historical data to mirror real-world machine equipment and reflect its real-time operating state.
In the mathematical model solution of the digital twin, a smooth finite element is often used for the solution. While the calculation of smooth finite elements requires the use of hexahedral volumes. The volume of each region must therefore be calculated in each time step, which takes up a significant portion of the calculation time of the problem, and it is therefore necessary to perform the volume calculation in as few floating point operations as possible.
The hexahedral area is specified by the positions of eight nodes logically connected as a cube. The conventional method used in the quadrangular hexahedron needs 264 steps of floating point number operation, and has the problems of complex floating point number calculation, large consumption of calculation resources and the like.
Disclosure of Invention
Therefore, the embodiment of the application provides a hexahedron volume calculation method and system based on a digital twin body, and the problem that the number of times of calculation for calculating the hexahedron volume floating point number is large is solved. The volume of the quadrangular hexahedron is decomposed into the sum of six sub-volumes, then the calculation formula is further simplified, the floating point number operation frequency of the hexahedron volume is reduced to 72 steps, the calculation steps can be greatly reduced, the calculation time is shortened, the calculation efficiency is improved, and the method can be applied to digital twin solving calculation.
In order to achieve the above object, the embodiments of the present application provide the following technical solutions:
according to a first aspect of embodiments of the present application, there is provided a digital twin-based hexahedral volume calculation method, the method including:
numbering eight vertexes of the target hexahedron according to a set numbering rule;
determining coordinates of eight vertexes of the target hexahedron;
calculating the diagonal vector coordinate of each surface of the target hexahedron according to the coordinate of the vertex;
forming diagonal vectors into a matrix, and calculating a matrix determinant;
and adding the matrix determinant results of each surface to obtain the volume of the target hexahedron.
Optionally, the diagonal vector coordinates of each face of the target hexahedron are calculated according to the coordinates of the vertex, and the diagonal vector coordinates of each face are respectively:
Figure BDA0003302522950000021
Figure BDA0003302522950000022
Figure BDA0003302522950000023
Figure BDA0003302522950000024
Figure BDA0003302522950000025
Figure BDA0003302522950000026
wherein,
Figure BDA0003302522950000027
respectively, the coordinates of the eight vertices of the target hexahedron.
Optionally, the result of the matrix determinant of each face is added to obtain the volume of the target hexahedron, according to the following formula:
VTH＝V1375+V4576+V2376+V0231+V0451+V0462
wherein, V1375、V4576、V2376、V0231、V0451、V0462Respectively, the volumes of the six faces of the target hexahedron.
Optionally, the V1375Calculated according to the following formula:
Figure BDA0003302522950000031
the V is4576Calculated according to the following formula:
Figure BDA0003302522950000032
the V is2376Calculated according to the following formula:
Figure BDA0003302522950000033
optionally, the V0231Calculated according to the following formula:
Figure BDA0003302522950000034
the V is0451Calculated according to the following formula:
Figure BDA0003302522950000035
the V is0231Calculated according to the following formula:
Figure BDA0003302522950000036
optionally, the method further comprises: will vector V1Defined as the Jacobian of the conversion of the xc point from logical space to physical space, then vector V1Expressed according to the following formula:
Figure BDA0003302522950000037
further simplifying as follows:
Figure BDA0003302522950000038
further transformation is as follows:
Figure BDA0003302522950000039
unfolding and binding V by the property of determinantTHThe formula yields:
Figure BDA0003302522950000041
optionally, the method further comprises: according to 16V after simplification1Equation and 12VTHThe formula obtains the volume formula of the target hexahedron:
Figure BDA0003302522950000042
according to a second aspect of embodiments of the present application, there is provided a digital twin-based hexahedral volume calculation system, the system including:
the numbering module is used for numbering eight vertexes of the target hexahedron according to a set numbering rule;
the coordinate module is used for determining coordinates of eight vertexes of the target hexahedron;
the diagonal coordinate module is used for calculating the diagonal vector coordinate of each surface of the target hexahedron according to the coordinate of the vertex;
the matrix determinant module is used for forming the diagonal vectors into a matrix and calculating a matrix determinant;
and the hexahedron volume module is used for adding the matrix determinant results of each surface to obtain the volume of the target hexahedron.
Optionally, the diagonal vector coordinates of each face in the diagonal coordinate module are respectively:
Figure BDA0003302522950000043
Figure BDA0003302522950000044
Figure BDA0003302522950000045
Figure BDA0003302522950000046
Figure BDA0003302522950000047
Figure BDA0003302522950000051
wherein,
Figure BDA0003302522950000052
respectively, the coordinates of the eight vertices of the target hexahedron.
Optionally, the hexahedral volume module is specifically calculated according to the following formula:
VTH＝V1375+V4576+V2376+V0231+V0451+V0462
wherein, V1375、V4576、V2376、V0231、V0451、V0462Respectively, the volumes of the six faces of the target hexahedron.
Optionally, the V1375Calculated according to the following formula:
Figure BDA0003302522950000053
the V is4576According to the following formulaAnd (3) calculating:
Figure BDA0003302522950000054
the V is2376Calculated according to the following formula:
Figure BDA0003302522950000055
optionally, the V0231Calculated according to the following formula:
Figure BDA0003302522950000056
the V is0451Calculated according to the following formula:
Figure BDA0003302522950000057
the V is0231Calculated according to the following formula:
Figure BDA0003302522950000058
optionally, the hexahedral volume module is further configured to:
will vector V1Defined as the Jacobian of the conversion of the xc point from logical space to physical space, then vector V1Expressed according to the following formula:
Figure BDA0003302522950000061
further simplifying as follows:
Figure BDA0003302522950000062
further transformation is as follows:
Figure BDA0003302522950000063
unfolding and binding V by the property of determinantTHThe formula yields:
Figure BDA0003302522950000064
optionally, the hexahedral volume module is further configured to:
according to 16V after simplification1Equation and 12VTHThe formula obtains the volume formula of the target hexahedron:
Figure BDA0003302522950000065
according to a third aspect of embodiments herein, there is provided an apparatus comprising: the device comprises a data acquisition device, a processor and a memory; the data acquisition device is used for acquiring data; the memory is to store one or more program instructions; the processor is configured to execute one or more program instructions to perform the method of any of the first aspect.
According to a fourth aspect of embodiments herein, there is provided a computer-readable storage medium having one or more program instructions embodied therein for performing the method of any of the first aspects.
In summary, the embodiment of the present application provides a hexahedron volume calculation method and system based on a digital twin body, and eight vertexes of a target hexahedron are numbered by setting a numbering rule; determining coordinates of eight vertexes of the target hexahedron; further calculating the diagonal vector coordinate of each surface of the target hexahedron according to the coordinate of the vertex; forming diagonal vectors into a matrix, and calculating a matrix determinant; and finally, adding the matrix determinant results of each surface to obtain the volume of the target hexahedron. Aiming at the problems that the existing calculation of the floating point number of the hexahedron volume is complicated, a large amount of calculation resources are consumed, and the like, starting from the construction of the four-corner hexahedron, the volume of the four-corner hexahedron is decomposed into the sum of six sub-volumes, and the number of floating point number calculation times for calculating the hexahedron volume is reduced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so that those skilled in the art can understand and read the present invention, and do not limit the conditions for implementing the present invention, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the functions and purposes of the present invention, should still fall within the scope of the present invention.
Fig. 1 is a schematic flow chart of a digital twin-based hexahedron volume calculation method according to an embodiment of the present application;
FIG. 2 is a schematic view of a hexahedron provided by an embodiment of the present application;
FIG. 3 is another schematic view of the hexahedron according to the embodiment of the present application;
FIG. 4 is a schematic view of a rectangular pyramid provided by an embodiment of the present application;
FIG. 5 is a schematic polyhedral diagram provided by an embodiment of the present application;
fig. 6 is a schematic flow chart of a specific application of the hexahedral unit volume efficient calculation method in the digital twin according to the embodiment of the present application;
FIG. 7 is a schematic diagram illustrating an example of a hexahedral volume calculation according to an embodiment of the present disclosure;
FIG. 8 is a diagram illustrating a comparison of floating-point operations required according to an embodiment of the present application;
fig. 9 is a block diagram of a digital twin-based hexahedral volume calculation system according to an embodiment of the present application.
Detailed Description
The present invention is described in terms of particular embodiments, other advantages and features of the invention will become apparent to those skilled in the art from the following disclosure, and it is to be understood that the described embodiments are merely exemplary of the invention and that it is not intended to limit the invention to the particular embodiments disclosed. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 shows a flow chart of a digital twin-based hexahedron volume calculation method provided by an embodiment of the application, and the method includes the following steps:
step 101: numbering eight vertexes of the target hexahedron according to a set numbering rule;
step 102: determining coordinates of eight vertexes of the target hexahedron;
step 103: calculating the diagonal vector coordinate of each surface of the target hexahedron according to the coordinate of the vertex;
step 104: forming diagonal vectors into a matrix, and calculating a matrix determinant;
step 105: and adding the matrix determinant results of each surface to obtain the volume of the target hexahedron.
As shown in fig. 2, the hexahedral volumetric region is specified by the positions of eight nodes. Since nodes are allowed to move independently of each other in physical simulation, four edges around one face of a logical cube are not generally coplanar, and thus a plane boundary of a hexahedral cell is constructed by dividing the hexahedral face into triangles. Each face is divided into four triangles and the hexahedron is defined by a 24-sided triangular polyhedron called a 24-sided hexahedron. As shown in fig. 3. The center of gravity divides each surface into four triangles, and such a hexahedron is called a quadrangular hexahedron (TH).
In a possible implementation manner, in step 103, the diagonal vector coordinates of each face of the target hexahedron are calculated according to the coordinates of the vertex, and the diagonal vector coordinates of each face are respectively shown in formula group (1):
Figure BDA0003302522950000081
Figure BDA0003302522950000082
Figure BDA0003302522950000083
Figure BDA0003302522950000091
Figure BDA0003302522950000092
Figure BDA0003302522950000093
wherein,
Figure BDA0003302522950000094
respectively, the coordinates of the eight vertices of the target hexahedron.
In a possible embodiment, in step 105, the result of the matrix determinant for each face is added to obtain the volume of the target hexahedron, according to the following formula (2):
VTH＝V1375+V4576+V2376+V0231+V0451+V0462formula (2)
Wherein, V1375、V4576、V2376、V0231、V0451、V0462Respectively, the volumes of the six faces of the target hexahedron.
In one possible embodiment, said V1375Calculated according to the following equation (3):
Figure BDA0003302522950000095
the V is4576Calculated according to the following equation (4):
Figure BDA0003302522950000096
the V is2376Calculated according to the following equation (5):
Figure BDA0003302522950000097
in one possible embodiment, said V0231Calculated according to the following equation (6):
Figure BDA0003302522950000098
the V is0451Calculated according to the following equation (7):
Figure BDA0003302522950000101
the V is0231Calculated according to the following equation (8):
Figure BDA0003302522950000102
in one possible embodiment, the method further comprises: will vector V1Defined as xc points from logical space to physical spaceConverted jacobian, vector V1Expressed by the following formula (9):
Figure BDA0003302522950000103
further simplified to formula (10):
Figure BDA0003302522950000104
further transformed into formula (11):
Figure BDA0003302522950000105
unfolding and binding V by the property of determinantTHThe formula yields formula (12):
Figure BDA0003302522950000106
in one possible embodiment, the method further comprises: according to 16V after simplification1Equation and 12VTHThe formula obtains the volume formula of the target hexahedron, such as formula (13):
Figure BDA0003302522950000107
the embodiment of the application aims at the problem that the number of times of calculation of the hexahedron volume floating point number is large, starting from the construction of a four-cornered hexahedron, the volume of the four-cornered hexahedron is decomposed into the sum of six sub-volumes, then the calculation formula is further simplified, and the number of times of calculation of the hexahedron volume floating point number is reduced. The number of floating point number operations of the hexahedron volume is reduced to 72 steps, and the calculation efficiency is improved. And can be applied to digital twin solving calculations.
The methods provided in the examples of the present application are further illustrated below with reference to specific illustrations:
as shown in fig. 4, the sum of the volumes of two tetrahedrons can be considered for a rectangular pyramid. The tetrahedral volume calculation formula (14) is:
Figure BDA0003302522950000111
as shown in fig. 5, the volume of a polyhedron formed by vertices 0,1,3,5,7 is:
Figure BDA0003302522950000112
for convenience will
Figure BDA0003302522950000113
It is briefly described as
Figure BDA0003302522950000114
Figure BDA0003302522950000115
Substituting formula set (1) into (16) to simplify:
Figure BDA0003302522950000116
the same can be obtained:
Figure BDA0003302522950000117
Figure BDA0003302522950000118
for a plane S including node 00231The volume can be simplified as:
Figure BDA0003302522950000119
the same principle is that:
Figure BDA0003302522950000121
Figure BDA0003302522950000122
the volume of the whole tetragonal hexahedron is as follows:
VTH＝V1375+V4576+V2376+V0231+V0451+V0462formula (23)
Will vector V1Defined as the jacobian of the transition of the xc point from logical space to physical space.
Figure BDA0003302522950000123
The simplification is as follows:
Figure BDA0003302522950000124
the transform of equation (25) is written as:
Figure BDA0003302522950000125
and (3) expanding the matrix by using the property of the determinant and comparing the matrix with the matrix to obtain:
Figure BDA0003302522950000126
substituting (25) into (27) to obtain
Figure BDA0003302522950000127
In recent years, with the dramatic increase and progress of the internet of things and sensing technology, a novel monitoring technology enters the visual field of people, namely a digital twin technology. The first formal definition of digital twins came from the research of NASA in the united states in 2010 and pointed out that this is one of the biggest challenges in the next 10-20 years, and the digital twins technology is a comprehensive multi-physics, multi-scale, probabilistic, super-reality simulation that uses the most appropriate physical models, sensory data, and historical data to mirror real-world machine devices and reflect their real-time operating states. Fig. 6 shows a specific application of the hexahedral cell volume efficient calculation method provided by the embodiment of the present application in the digital twins.
As shown in fig. 6, the smooth finite element method is involved in solving the mathematical model of the twin. In the calculation step of the smoothing finite element method, VIJ(VIJTo contain the volume of the I, J point units) involves volume calculations of hexahedrons. The need to calculate the hexahedral volume consumes computational resources. The traditional hexahedron volume calculation method needs a large number of floating point number operations.
The efficient hexahedron volume calculation method adopted by the invention can reduce the calculation times of floating point numbers and is beneficial to efficiently solving the digital twin problem.
The following is a simple hexahedral volume calculation example. As shown in FIG. 7, the coordinates of each point are
x0(0,0,0)x1(2,0,0)x2(0,2,0)x3(2,2,0)
x4(0,0,2)x5(2,0,2)x6(0,2,2)x7(2,2,2)
According to formula (29) and formula (30):
Figure BDA0003302522950000131
Figure BDA0003302522950000132
equal to the hexahedral actual volume.
The floating point number count number comparison is according to equation (31) and equation (32) as follows:
the traditional method comprises the following steps:
Figure BDA0003302522950000133
the invention comprises the following steps:
Figure BDA0003302522950000134
FIG. 8 shows a comparison of the number of floating-point operations required by the method of the present invention versus the conventional method. The floating-point number operation times required by the traditional method is 264, and the floating-point number operation times required by the method is only 72 times, which is reduced by 72.7 percent compared with the traditional method. The computing resources of the computer are greatly saved, and the efficient solving of the digital twin model is facilitated.
The embodiment of the application aims at the problem that the number of times of calculation of the hexahedron volume floating point number is large, starting from the construction of a four-cornered hexahedron, the volume of the four-cornered hexahedron is decomposed into the sum of six sub-volumes, then the calculation formula is further simplified, and the number of times of calculation of the hexahedron volume floating point number is reduced. The number of floating point number operations of the hexahedron volume is reduced to 72 steps, and the calculation efficiency is improved. Can be applied to digital twin solving calculations.
In summary, the embodiment of the present application provides a hexahedron volume calculation method based on a digital twin body, in which eight vertexes of a target hexahedron are numbered by setting a numbering rule; determining coordinates of eight vertexes of the target hexahedron; further calculating the diagonal vector coordinate of each surface of the target hexahedron according to the coordinate of the vertex; forming diagonal vectors into a matrix, and calculating a matrix determinant; and finally, adding the matrix determinant results of each surface to obtain the volume of the target hexahedron. Aiming at the problems that the existing calculation of the floating point number of the hexahedron volume is complicated, a large amount of calculation resources are consumed, and the like, starting from the construction of the four-corner hexahedron, the volume of the four-corner hexahedron is decomposed into the sum of six sub-volumes, and the number of floating point number calculation times for calculating the hexahedron volume is reduced.
Based on the same technical concept, the embodiment of the present application further provides a digital twin-based hexahedron volume calculation system, as shown in fig. 9, the system includes:
a numbering module 901, configured to number eight vertexes of the target hexahedron according to a set numbering rule;
a coordinate module 902, configured to determine coordinates of eight vertices of the target hexahedron;
a diagonal coordinate module 903, configured to calculate a diagonal vector coordinate of each face of the target hexahedron according to the coordinates of the vertex;
a matrix determinant module 904, configured to form diagonal vectors into a matrix, and calculate a matrix determinant;
and a hexahedron volume module 905, configured to add the results of the matrix determinant for each surface to obtain a volume of the target hexahedron.
In one possible embodiment, the diagonal vector coordinates of each surface in the diagonal coordinate module 903 are respectively shown in formula group (1).
In one possible embodiment, the hexahedral volume module 905 is calculated according to equation (2).
In one possible embodiment, the hexahedral volume module 905 is further configured to: will vector V1Defined as the Jacobian of the conversion of the xc point from logical space to physical space, then vector V1Expressed according to formula (9).
In one possible embodiment, the hexahedral volume module 905 is further configured to: according to 16V after simplification1Equation and 12VTHThe formula obtains the volume formula (13) of the target hexahedron.
Based on the same technical concept, an embodiment of the present application further provides an apparatus, including: the device comprises a data acquisition device, a processor and a memory; the data acquisition device is used for acquiring data; the memory is to store one or more program instructions; the processor is configured to execute one or more program instructions to perform the method.
Based on the same technical concept, the embodiment of the present application also provides a computer-readable storage medium, wherein the computer-readable storage medium contains one or more program instructions, and the one or more program instructions are used for executing the method.
In the present specification, each embodiment of the method is described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. Reference is made to the description of the method embodiments.
It is noted that while the operations of the methods of the present invention are depicted in the drawings in a particular order, this is not a requirement or suggestion that the operations must be performed in this particular order or that all of the illustrated operations must be performed to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions.
Although the present application provides method steps as in embodiments or flowcharts, additional or fewer steps may be included based on conventional or non-inventive approaches. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. When an apparatus or client product in practice executes, it may execute sequentially or in parallel (e.g., in a parallel processor or multithreaded processing environment, or even in a distributed data processing environment) according to the embodiments or methods shown in the figures. The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the presence of additional identical or equivalent elements in a process, method, article, or apparatus that comprises the recited elements is not excluded.
The units, devices, modules, etc. set forth in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. For convenience of description, the above devices are described as being divided into various modules by functions, and are described separately. Of course, in implementing the present application, the functions of each module may be implemented in one or more software and/or hardware, or a module implementing the same function may be implemented by a combination of a plurality of sub-modules or sub-units, and the like. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
Those skilled in the art will also appreciate that, in addition to implementing the controller as pure computer readable program code, the same functionality can be implemented by logically programming method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Such a controller may therefore be considered as a hardware component, and the means included therein for performing the various functions may also be considered as a structure within the hardware component. Or even means for performing the functions may be regarded as being both a software module for performing the method and a structure within a hardware component.
The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
From the above description of the embodiments, it is clear to those skilled in the art that the present application can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present application may be embodied in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, or the like, and includes several instructions for enabling a computer device (which may be a personal computer, a mobile terminal, a server, or a network device) to execute the method according to the embodiments or some parts of the embodiments of the present application.
The embodiments in the present specification are described in a progressive manner, and the same or similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. The application is operational with numerous general purpose or special purpose computing system environments or configurations. For example: personal computers, server computers, hand-held or portable devices, tablet-type devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.
The above-mentioned embodiments are further described in detail for the purpose of illustrating the invention, and it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (16)

1.基于数字孪生体的六面体体积计算方法，其特征在于，所述方法包括：1. a hexahedral volume calculation method based on a digital twin, wherein the method comprises: 根据设定编号规则对目标六面体的八个顶点进行编号；Number the eight vertices of the target hexahedron according to the set numbering rule; 确定目标六面体的八个顶点的坐标；Determine the coordinates of the eight vertices of the target hexahedron; 根据顶点的坐标计算目标六面体的每个面的对角线向量坐标；Calculate the diagonal vector coordinates of each face of the target hexahedron according to the coordinates of the vertices; 将对角线向量组成矩阵，计算矩阵行列式；Form the diagonal vector into a matrix and calculate the matrix determinant; 将每个面的矩阵行列式的结果相加，得到目标六面体的体积。Add the results of the matrix determinants for each face to get the volume of the target hexahedron. 2.如权利要求1所述的方法，其特征在于，所述根据顶点的坐标计算目标六面体的每个面的对角线向量坐标，所述每个面的对角线向量坐标分别为：2. The method according to claim 1, wherein the diagonal vector coordinates of each face of the target hexahedron are calculated according to the coordinates of the vertices, and the diagonal vector coordinates of each face are respectively:
Figure FDA0003302522940000011
Figure FDA0003302522940000011
Figure FDA0003302522940000012
Figure FDA0003302522940000012
Figure FDA0003302522940000013
Figure FDA0003302522940000013
Figure FDA0003302522940000014
Figure FDA0003302522940000014
Figure FDA0003302522940000015
Figure FDA0003302522940000015
Figure FDA0003302522940000016
Figure FDA0003302522940000016
 其中，
Figure FDA0003302522940000017
分别是目标六面体的八个顶点的坐标。in,
Figure FDA0003302522940000017
are the coordinates of the eight vertices of the target hexahedron, respectively. 3.如权利要求1所述的方法，其特征在于，所述将每个面的矩阵行列式的结果相加，得到目标六面体的体积，按照如下公式：3. The method of claim 1, wherein the result of the matrix determinant of each surface is added to obtain the volume of the target hexahedron, according to the following formula: VTH＝V1375+V4576+V2376+V0231+V0451+V0462 V TH =V 1375 +V 4576 +V 2376 +V 0231 +V 0451 +V 0462 其中，V1375、V4576、V2376、V0231、V0451、V0462分别为目标六面体的六个面的体积。Wherein, V 1375 , V 4576 , V 2376 , V 0231 , V 0451 , and V 0462 are the volumes of the six faces of the target hexahedron, respectively. 4.如权利要求3所述的方法，其特征在于，所述V1375按照如下公式计算：4. The method of claim 3, wherein the V 1375 is calculated according to the following formula:
Figure FDA0003302522940000021
Figure FDA0003302522940000021
 所述V4576按照如下公式计算：The V 4576 is calculated according to the following formula:
Figure FDA0003302522940000022
Figure FDA0003302522940000022
 所述V2376按照如下公式计算：The V 2376 is calculated according to the following formula:
Figure FDA0003302522940000023
Figure FDA0003302522940000023
 5.如权利要求3所述的方法，其特征在于，所述V0231按照如下公式计算：5. The method of claim 3, wherein the V 0231 is calculated according to the following formula:
Figure FDA0003302522940000024
Figure FDA0003302522940000024
 所述V0451按照如下公式计算：The V 0451 is calculated according to the following formula:
Figure FDA0003302522940000025
Figure FDA0003302522940000025
 所述V0231按照如下公式计算：The V 0231 is calculated according to the following formula:
Figure FDA0003302522940000026
Figure FDA0003302522940000026
 6.如权利要求1至3任一项所述的方法，其特征在于，所述方法还包括：将向量V1定义为xc点从逻辑空间到物理空间的转换的雅可比行列式，则向量V1按照如下公式表示：6. The method according to any one of claims 1 to 3, wherein the method further comprises: defining the vector V1 as the Jacobian determinant of the transformation of point xc from logical space to physical space, then the vector V1 is represented by the following formula :
Figure FDA0003302522940000027
Figure FDA0003302522940000027
 进一步化简为：Simplify further to:
Figure FDA0003302522940000028
Figure FDA0003302522940000028
 进一步变换为：It is further transformed to:
Figure FDA0003302522940000031
Figure FDA0003302522940000031
 利用行列式的性质展开并结合VTH公式得到：Using the properties of the determinant to expand and combine the V TH formula to get:
Figure FDA0003302522940000032
Figure FDA0003302522940000032
 7.如权利要求6所述的方法，其特征在于，所述方法还包括：根据化简后的16V1公式和12VTH公式得到目标六面体的体积公式：7. The method of claim 6, wherein the method further comprises: obtaining the volume formula of the target hexahedron according to the simplified 16V 1 formula and the 12V TH formula:
Figure FDA0003302522940000033
Figure FDA0003302522940000033
 8.基于数字孪生体的六面体体积计算系统，其特征在于，所述系统包括：8. A hexahedral volume calculation system based on a digital twin, wherein the system comprises: 编号模块，用于根据设定编号规则对目标六面体的八个顶点进行编号；The numbering module is used to number the eight vertices of the target hexahedron according to the set numbering rule; 坐标模块，用于确定目标六面体的八个顶点的坐标；The coordinate module is used to determine the coordinates of the eight vertices of the target hexahedron; 对角线坐标模块，用于根据顶点的坐标计算目标六面体的每个面的对角线向量坐标；The diagonal coordinate module is used to calculate the diagonal vector coordinates of each face of the target hexahedron according to the coordinates of the vertices; 矩阵行列式模块，用于将对角线向量组成矩阵，计算矩阵行列式；The matrix determinant module is used to form a matrix with diagonal vectors and calculate the matrix determinant; 六面体体积模块，用于将每个面的矩阵行列式的结果相加，得到目标六面体的体积。The hexahedral volume module is used to add the results of the matrix determinants of each face to obtain the volume of the target hexahedron. 9.如权利要求8所述的系统，其特征在于，所述对角线坐标模块中的每个面的对角线向量坐标分别为：9. The system of claim 8, wherein the diagonal vector coordinates of each face in the diagonal coordinate module are respectively:
Figure FDA0003302522940000034
Figure FDA0003302522940000034
Figure FDA0003302522940000035
Figure FDA0003302522940000035
Figure FDA0003302522940000036
Figure FDA0003302522940000036
Figure FDA0003302522940000037
Figure FDA0003302522940000037
Figure FDA0003302522940000041
Figure FDA0003302522940000041
Figure FDA0003302522940000042
Figure FDA0003302522940000042
 其中，
Figure FDA0003302522940000043
分别是目标六面体的八个顶点的坐标。in,
Figure FDA0003302522940000043
are the coordinates of the eight vertices of the target hexahedron, respectively. 10.如权利要求8所述的系统，其特征在于，所述六面体体积模块，具体按照如下公式计算：10. The system of claim 8, wherein the hexahedral volume module is specifically calculated according to the following formula: VTH＝V1375+V4576+V2376+V0231+V0451+V0462 V TH =V 1375 +V 4576 +V 2376 +V 0231 +V 0451 +V 0462 其中，V1375、V4576、V2376、V0231、V0451、V0462分别为目标六面体的六个面的体积。Wherein, V 1375 , V 4576 , V 2376 , V 0231 , V 0451 , and V 0462 are the volumes of the six faces of the target hexahedron, respectively. 11.如权利要求10所述的系统，其特征在于，所述V1375按照如下公式计算：11. The system of claim 10, wherein the V 1375 is calculated according to the following formula:
Figure FDA0003302522940000044
Figure FDA0003302522940000044
 所述V4576按照如下公式计算：The V 4576 is calculated according to the following formula:
Figure FDA0003302522940000045
Figure FDA0003302522940000045
 所述V2376按照如下公式计算：The V 2376 is calculated according to the following formula:
Figure FDA0003302522940000046
Figure FDA0003302522940000046
 12.如权利要求10所述的系统，其特征在于，所述V0231按照如下公式计算：12. The system of claim 10, wherein the V 0231 is calculated according to the following formula:
Figure FDA0003302522940000047
Figure FDA0003302522940000047
 所述V0451按照如下公式计算：The V 0451 is calculated according to the following formula:
Figure FDA0003302522940000048
Figure FDA0003302522940000048
 所述V0231按照如下公式计算：The V 0231 is calculated according to the following formula:
Figure FDA0003302522940000051
Figure FDA0003302522940000051
 13.如权利要求8至10任一项所述的系统，其特征在于，所述六面体体积模块，还用于：13. The system according to any one of claims 8 to 10, wherein the hexahedral volume module is further used for: 将向量V1定义为xc点从逻辑空间到物理空间的转换的雅可比行列式，则向量V1按照如下公式表示：Define the vector V 1 as the Jacobian determinant of the transformation of the xc point from the logical space to the physical space, then the vector V 1 is represented by the following formula:
Figure FDA0003302522940000052
Figure FDA0003302522940000052
 进一步化简为：Simplify further to:
Figure FDA0003302522940000053
Figure FDA0003302522940000053
 进一步变换为：It is further transformed to:
Figure FDA0003302522940000054
Figure FDA0003302522940000054
 利用行列式的性质展开并结合VTH公式得到：Using the properties of the determinant to expand and combine the V TH formula to get:
Figure FDA0003302522940000055
Figure FDA0003302522940000055
 14.如权利要求8所述的系统，其特征在于，所述六面体体积模块还用于：14. The system of claim 8, wherein the hexahedral volume module is further configured to: 根据化简后的16V1公式和12VTH公式得到目标六面体的体积公式：According to the simplified 16V 1 formula and 12V TH formula, the volume formula of the target hexahedron is obtained:
Figure FDA0003302522940000056
Figure FDA0003302522940000056
 15.一种设备，其特征在于，所述设备包括：数据采集装置、处理器和存储器；15. A device, characterized in that the device comprises: a data acquisition device, a processor and a memory; 所述数据采集装置用于采集数据；所述存储器用于存储一个或多个程序指令；所述处理器，用于执行一个或多个程序指令，用以执行如权利要求1-7任一项所述的方法。The data collection device is used to collect data; the memory is used to store one or more program instructions; the processor is used to execute one or more program instructions to execute any one of claims 1-7 the method described. 16.一种计算机可读存储介质，其特征在于，所述计算机存储介质中包含一个或多个程序指令，所述一个或多个程序指令用于执行如权利要求1-7任一项所述的方法。16. A computer-readable storage medium, wherein the computer storage medium contains one or more program instructions, and the one or more program instructions are used to execute any one of claims 1-7 Methods.
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