JP4171884B2 - Data hierarchization and data reconstruction method / device / program / recording medium, data recording medium - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to hierarchization of unstructured numerical data by multiresolution representation.
[0002]
[Prior art]
Conventionally, a method for hierarchizing unstructured numerical data by multi-resolution representation is used to visualize large-scale or fine unstructured numerical data at high speed. Here, unstructured numerical data refers to map data, topographic data, three-dimensional object data, three-dimensional volume data, particle data, and the like. These are all composed of one or more nodes 41 and zero or more elements 42, as in the unstructured numerical data 40 of FIG. The shape of the element 42 is defined by a plurality of nodes 41. The element 42 corresponds to, for example, a polygon in 3D object data, a polyhedron in 3D volume data, and no equivalent to particle data. Further, the node 41 and the element 42 have associated attributes defined according to the use of the data. For example, a physical quantity such as a reflectance or transmittance is used as an accompanying attribute for a three-dimensional graphics application, and a physical quantity such as pressure or speed is used for a numerical simulation application. Hereinafter, unless otherwise specified, numerical data refers to unstructured numerical data. The multi-resolution representation is a data format that can easily generate numerical data having a plurality of levels of resolution.
[0003]
An example of a conventional method for hierarchizing unstructured numerical data by multi-resolution representation is described in Non-Patent Document 1, for example. This method was originally called MT (Multi-Triangulation or Multi-Tessellation), but later became a generalized definition that does not depend on the dimension of the target numerical data, and was named MC (Multi-Complex).
[0004]
This method uses a spatially local simplification operation to obtain a multi-resolution representation of unstructured numerical data. There are various methods for the simplification operation. One example is node removal as shown in FIG. According to this, the part 400 of the unstructured numerical data is simplified by removing some elements as in 401 by removing the node 410 after degenerating the node 410 to the node 411. Such a simplification operation is repeatedly applied to each part of the unstructured numerical data until the unstructured numerical data reaches a predetermined resolution. At that time, the simplification operations are performed in order from the least simplification error. Here, the simplification error is an amount representing a change in appearance due to the simplification operation. There are various definitions of the simplification error, but there is a method of defining the diameter of the minimum inclusion sphere in the range 400 affected by the simplification or the longest side of the minimum inclusion cuboid parallel to each coordinate axis as the simplification error. For each simplification operation, detail data, simplification error, and dependency with previous simplification operations are recorded. Here, as illustrated in FIG. 11, the detailed data 330 is information necessary for the refinement operation that is the reverse operation of the simplification operation, and corresponds to information lost by the simplification operation. The contents of the refined data vary depending on the method of the simplification operation. When the simplification operation is node removal, an insertion node 412 (removed node) generated by splitting the split node 413 (corresponding to the degenerate node 411) is generated. Coordinates and associated attributes), the range of elements to be deformed, the constituent node numbers of the elements to be inserted and the associated attributes can be considered as examples of detailed data. By the way, the simplification error can be regarded as the resolution secured by the refining operation from the viewpoint of the refining operation, and hereinafter, the simplification error is simply referred to as the resolution.
[0005]
By arranging a series of detailed data, resolution, and dependency information, the original unstructured numerical data can be expressed in the form of a dependency graph of the detailed operation as shown in FIG. In this graph, the node 24 represents the refinement operation, and the dependency link 25 represents the dependency relationship of the refinement operation. The original numerical data 20 is the lowest node, and the simplified numerical data 21 that is the result of a series of simplifications is the highest node. This graph has a hierarchical structure in a broad sense because there is a dependency relationship between nodes. This dependency graph data is called hierarchical data. The original numerical data 20 and the dependent link 250 connected to the original numerical data 20 are not necessary and will not be recorded in the hierarchical data. A series of processes for generating hierarchical data from original numerical data is called decomposition.
[0006]
By selecting and performing detailed operations suitable for convenience in the order based on this dependency relationship, it is possible to obtain numerical data in which only necessary portions are detailed. For example, as shown in FIG. 13, when it is desired to increase the resolution to some extent in a certain spatial range 26, the refinement operation corresponding to the node 24 surrounded by the dotted line 260 is not contradicted to the dependency link 25 for the simplified numerical data 21. You can do it in order. A dotted line 260 surrounds a node of the refinement operation whose influence range overlaps with the spatial range 26 and whose resolution is lower than the required resolution. In the case where it is desired to further increase the resolution in the spatial range 26, the refining operation corresponding to the node 24 surrounded by the dotted line 261 may be performed in the same manner. A series of processes for generating arbitrarily detailed numerical data from hierarchical data is called reconstruction. This hierarchical data is a highly versatile multi-resolution expression that can reconstruct numerical data whose resolution is arbitrarily changed locally.
[0007]
By utilizing this feature, even large-scale three-dimensional unstructured numerical data can be visualized at high speed with few data accesses without impairing the image quality. In other words, non-structural numerical data is re-created by reducing the resolution of parts that are outside the range of the visualized image or distant parts where details are not reflected in the image, and high-resolution important parts near the viewpoint that can be reflected in detail in the image. Configure and visualize this. The amount of data of the reconstructed non-structural numerical data is greatly reduced compared to the original non-structural numerical data before hierarchization, and the load of visualization processing can be greatly reduced. In addition, since most of the detailed data that is not involved in the detailed operation is not referred to during reconfiguration, data access can be greatly reduced.
[0008]
[Non-Patent Document 1]
Proceedings Canadian Conference on Computational Geometry, pages 202-210, August 1996 (Proceedings Canadian Conference on Computational Geometry, pages 202-210, August 1996)
[0009]
[Problems to be solved by the invention]
The first problem of the prior art is that random access frequently occurs for hierarchical data during reconfiguration. The reason is that the data structure of the hierarchical data that represents the complicated dependency of the refinement operation is irregular and unstructured, and the data required for reconstruction is distributed as fine fragments on the recording medium. This is because there are many cases. The advantage of stratification increases as the data becomes larger. However, a large-capacity recording medium for storing large-scale data is usually a magnetic disk or magnetic tape whose random access is orders of magnitude slower than continuous access, so reconfiguration is significantly delayed. There is a problem that it ends up. In order to solve this problem, it may be possible to record hierarchical data on a recording medium such as a semiconductor memory in which the delay due to random access is not significant compared to a magnetic disk or magnetic tape. The cost of is very expensive and not realistic. In addition, by interposing a buffer or cache using a semiconductor memory between the recording medium and the reconstruction device, random access can be reduced somewhat, but for this purpose, the data to be accessed is localized to some extent on the recording medium. If the data is sparsely distributed, the effect is diminished.
[0010]
The second problem is that the size of the hierarchical data is larger than the original numerical data. The reason is that the dependency link data which is redundant information is included in the hierarchical data. Dependent link data can be derived from other information such as refined data without recording, but because of the spatial irregularities of unstructured numeric data, it requires a lot of processing and flexible reconfiguration In order to perform this at high speed, it is essential to record dependent link data. However, the increase in the data size due to this becomes a problem that cannot be ignored as the numerical data to be hierarchized is larger.
[0011]
The third problem is that there is a waste in the process of searching for a necessary node from the dependency graph at the time of reconfiguration. This is because the node selection selection is determined with an accuracy higher than necessary. The selection is determined based on whether or not the influence range of the refinement operation overlaps a spatial region in which the resolution of the refinement operation represented by the node is lower than the required resolution. The overlap determination may be simplified with rough accuracy according to the resolution of the refinement operation, but is performed with fine accuracy uniformly regardless of the required resolution. In order to realize interactive visualization without stress, there is a demand for speeding up without wasteful processing for reconstruction.
[0012]
The fourth problem is that reconstruction based on a multi-dimensional standard that includes not only the resolution but also the accompanying attributes cannot be performed. This is because the conventional method does not consider any reconstruction based on a multi-dimensional standard. In areas where there is little spatial change of the accompanying attributes and the surface boundary is not included, even if it is determined that the detail needs to be refined based on the resolution standard, the refinement is performed except for the special case where the element boundary is visualized. There is no meaning of element subdivision, and in such a case, only the resolution standard causes a wasteful increase in the amount of detailed operation processing and the reconstructed numerical data. For this reason, it is necessary to perform reconstruction based on a multi-dimensional standard that also includes accompanying attributes.
[0013]
A first object of the present invention is to provide a method for hierarchizing unstructured numerical data by multi-resolution representation that can reduce random access to hierarchized data at the time of reconstruction.
[0014]
A second object of the present invention is to provide a method for hierarchizing unstructured numerical data by multi-resolution representation that can reduce the increase in size of the hierarchized data.
[0015]
A third object of the present invention is to provide a method for hierarchizing unstructured numerical data by multi-resolution representation that can efficiently perform a search process of nodes required for reconfiguration.
[0016]
A fourth object of the present invention is to provide a method for hierarchizing unstructured numerical data by multi-resolution representation, which can be reconstructed on a multi-dimensional basis in consideration of incidental attributes in addition to resolution.
[0017]
[Means for Solving the Problems]
In order to achieve the first object described above, the present invention, when generating hierarchical data, structured an irregular dependency graph using cells having a spatially regular hierarchical structure to generate a node, that is, a refinement operation. The node data is arranged on the recording medium in association with the spatial arrangement, and the probability that the spatially neighboring node data becomes the vicinity also on the recording medium is increased. In addition, the cell data in which the node data is stored is also arranged on the recording medium in consideration of the spatial arrangement, and the probability that the spatially neighboring cell data will be near on the recording medium is also increased. Since the refining operations involved in reconstruction are spatially localized, the data necessary for reconstruction is also localized on the recording medium, and the random access to hierarchical data is reduced. Can do. Even if the access is localized, it is often discontinuous. Therefore, if a cache or a buffer is interposed, the random access can be reduced even more effectively.
[0018]
In order to achieve the second object, when generating hierarchical data, the present invention does not generate a dependency link in the high resolution direction among the dependency links in the conventional method. Create a lower link for a few cells. Further, the data amount of the dependency link in the low resolution direction can be compressed using the regular structure of the cell. Furthermore, in the present invention, a discrete resolution level, not a continuous resolution, is used as a reconstruction criterion. However, since the resolution level of the refinement operation becomes obvious by the rule structure of the cell, it is stored in the node. There is no need to keep it. For these reasons, it is possible to achieve a reduction in the size increase of the hierarchical data.
[0019]
In order to achieve the above third object, according to the present invention, when generating hierarchical data, the spatial size of a cell is matched with the resolution level of a node to be stored, that is, a refining operation. Search by cell, not by node. As a result, an accuracy search according to the resolution level can be performed, and nodes in the vicinity of the accuracy below the resolution level allowance are collectively determined. In addition, while a node has a complex dependency graph with multiple parents, a cell has a simple tree structure with only one parent. Simple. For these reasons, the efficiency of node search processing in reconfiguration can be achieved.
[0020]
In order to achieve the fourth object, when the hierarchical data is generated, the present invention changes each incidental attribute and refines the surface boundary unevenness when the cells are refined to each level below the cell. In the reconstruction, even if it is determined from the resolution criteria that the cell needs to be refined, the surface boundary variation can be reduced by referring to this data. If the variation of the incidental attribute is within the specified tolerance, the sub-cell level refinement is omitted. In this way, it is possible to achieve reconstruction based on a multi-dimensional standard that considers incidental attributes in addition to resolution.
[0021]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described with reference to the drawings.
[0022]
Referring to FIG. 1, a system for performing decomposition is shown in the embodiment of the present invention, a numerical data storage device 16 for storing numerical data to be hierarchized, and a hierarchical structure by dividing numerical data. Is composed of a decomposition apparatus 10 for generating hierarchical data and adding hierarchical levels, and a hierarchical data storage apparatus 17 for storing hierarchical data during and after processing.
[0023]
The numerical data storage device 16 and the hierarchical data storage device 17 may be a semiconductor memory, a magnetic disk device, an optical disk device, or other data storage devices.
[0024]
The disassembling apparatus 10 includes a numerical data input unit 100, a simplified operation generation unit 101, a cell management unit 102, a node management unit 103, a detailed data generation unit 104, and a simplified operation execution unit 105. Yes.
[0025]
When the numerical data input unit 100 newly generates hierarchical data, the original numerical data 30 stored in the numerical data storage device 16 is hierarchized as simplified numerical data 31 that is a component of the hierarchical data. The data is stored in the data storage device 17.
[0026]
The simplification operation generation unit 101 refers to the simplified numerical data 31 stored in the hierarchical data storage device 17, generates all possible simplification operation candidates, and prioritizes them based on the simplification error. Ranking is performed, and information related to the highest-priority simplification operation is output to the cell management unit 102, the detailed data generation unit 104, and the simplification operation execution unit 105 as needed. The information related to the simplification operation includes information for specifying the simplification operation, simplification error, and range of influence of the simplification operation. The information for specifying the simplification operation is, for example, the removal node number and the degenerate node number when the simplification operation is node removal. The influence range of the simplification operation may not be a strict range represented by a polyhedron or a polygon. For simplification of processing, for example, a range of each coordinate component in the influence range may be substituted. Multiple types of simplification operations, such as node removal and edge contraction, may be used. However, it is limited to a single type of simplification operation, and it is more detailed with a smaller amount of information if the rules for refinement operations are unified. Describe data.
[0027]
The cell management unit 102 manages cell data 32 that is another component of the hierarchical data stored in the hierarchical data storage device 17. The cell is a data structure for storing a plurality of nodes in the dependency relation graph of the refinement operation, and the nodes having similar resolution and influence range are collected into one cell. As will be described later, the plurality of cells have a regular hierarchical structure based on the resolution, and cells in a parent-child relationship are connected by a lower layer link. The cell management unit 102 stores the node generated from the simplification error output from the simplification operation generation unit 101 and the influence range of the simplification operation, that is, the resolution and the influence range of the refinement operation. If a cell does not exist, it is newly generated, and a lower layer link connected to this cell is also generated and updated. In addition, information necessary for storing the node in the specified cell, for example, the position of the cell data on the recording medium is output to the node management unit 103. As the decomposition process proceeds, the data size of the simplified numerical data 31 is reduced by the simplification, but the data size of the cell data 32 is increased by the generation of the cell.
[0028]
The node management unit 103 manages node data included in the cell data 32 stored in the hierarchical data storage device 17. Based on the information output from the cell management unit 102, a node is generated in the cell, the detailed data output from the detailed data generation unit 104 is stored in the node, and a dependency link connected to this node is generated. Also update.
[0029]
The detailed data generation unit 104 refers to the simplified numerical data 31 stored in the hierarchical data storage device 17, and generates detailed data corresponding to the simplified operation output from the simplified operation generation unit 101. , Output to the node management unit 103.
[0030]
The simplification operation execution unit 105 executes the simplification operation output from the simplification operation generation unit 101 on the simplified numerical data 31 stored in the hierarchical data storage device 17.
[0031]
Next, the operation of this system will be described with reference to FIG.
[0032]
First, when generating hierarchical data newly, the numerical data input unit 100 uses the original numerical data 30 stored in the numerical data storage device 16 as the simplified numerical data 31 of the hierarchical data. 17 (step A00). This step is not necessary when adding hierarchies to existing hierarchical data by re-decomposition.
[0033]
Next, the simplification operation generation unit 101 generates all possible simplification operation candidates based on the simplified numerical data 31 stored in the hierarchical data storage device 17, and based on the simplification error. And prioritize them, and select the highest priority simplification operation. This process can be performed by updating only the simplified operation of the part where the simplified numerical data has been changed from the next time if the simplified operation candidates generated in the first time and their priority information are retained. It can be done at high speed. If there is no simplification operation candidate, the decomposition process is terminated (step A01).
[0034]
Prioritization may be performed by the simplification error itself, but the int (log ₂ (L / E)). The higher the resolution level, the higher the priority. Here, int is a function that rounds down the decimal point to an integer. L is a distance used as a reference for error, and normally the maximum value of the widths of the original numerical data in the direction of each coordinate axis is used. However, if there is another reference, this may be used. The higher the resolution level, the higher the resolution and the smaller the error. When using the resolution level with the simplified error discretized, the order of priority is higher than when using the simplified error, but since reconstruction is performed in units of cells divided by the resolution level, there is almost no difference in the results. Absent. In addition, since there are usually multiple simplification operations that have the same resolution level even if the simplification errors are different, the degree of freedom of the order of simplification operations increases, and the simplification operations of the same priority that do not conflict with the scope of influence. It is also possible to perform decomposition processing in parallel. By the way, even if the simplification operations are performed in the order of higher resolution levels in this way, the resolution level is not necessarily lower than that of the previous simplification operation. The level is set to the resolution level of the simplification operation this time, so that the resolution level does not increase in the process of decomposition.
[0035]
Next, the simplification operation generation unit 101 confirms whether the resolution level of the selected simplification operation is equal to or higher than a designated level given in advance. If not, the disassembly process ends (step A02). .
[0036]
Next, the cell management unit 102 determines a cell that stores a refinement operation node corresponding to the simplification operation generated by the simplification operation generation unit 101 based on the resolution level and the influence range of the simplification operation (step A03). ).
[0037]
A cell is a data structure for storing multiple nodes, but from a spatial point of view, a virtual cube that is spread in a lattice pattern in the space (in the case of a one-dimensional space, a line segment, in the case of a two-dimensional space) Is a square or a hypercube in the case of a multidimensional space. There are lattices of cells having different sizes for each resolution level, and a parent-child relationship is established between cells having different resolution levels. That is, a cell is contained in only one cell at each lower resolution level. In general, one side of a cell is set to a size that can accommodate the maximum range of influence that the simplification or refinement operation having the resolution level can have. If it is larger than this, the reconstruction accuracy becomes uselessly coarse, and if it is smaller than this, it becomes impossible to compress dependent link data described later. Hereinafter, the length of one side of the cell is defined as L × 2 from the definition of the resolution level R. ^-R Will be described.
[0038]
There are various methods for determining a cell for storing a node. For example, a cell having the same resolution level including the center of the minimum inclusion sphere of the influence range of the refinement operation or the center of gravity of the minimum inclusion rectangle parallel to each coordinate axis may be used. Store. If the center or center of gravity is on a cell boundary, it is stored in one of the cells sharing the boundary.
[0039]
Next, the cell management unit 102 refers to the cell data 32 stored in the hierarchical data storage device 17 to check whether or not the cell storing the node already exists (step A04). Is generated (step A05), and if an existing cell having a higher resolution level than that cell is included, a lower layer link to the cell is also generated (step A06).
[0040]
A lower layer link is a unidirectional link to a high resolution level cell that the cell directly contains. From the standpoint of decomposition processing, it is a unidirectional link to an existing cell corresponding to a direct child.
[0041]
When generating hierarchical data that can be reconfigured based on a multi-dimensional standard that also includes accompanying attributes, the lower layer link data and lower layer fluctuation data are generated and stored in the cell. The lower layer fluctuation data is data representing the fluctuation of each level of the surface boundary and each associated attribute when the cell itself and the child cells at the child and lower levels are refined. Since there are usually a plurality of child cells at each lower level, the sum of the fluctuations due to the refinement of those cells is taken as the fluctuation of that level. There are various aggregation methods. For example, there is a method of taking the maximum value of fluctuation.
[0042]
Regarding the cell data arrangement on the recording medium, the cell data is grouped by resolution level so that the access at the time of reconstruction is localized. Cell data of the same resolution level is represented by Hilbert curve, Z curve, etc. It is preferable that they are arranged on the recording medium in a line along a space filling curve with good storage stability.
[0043]
Next, the node management unit 103 generates a node in the cell arranged by the cell management unit 102 (step A07).
[0044]
Next, the detailed data generation unit 104 refers to the simplified numerical data 31 stored in the hierarchical data storage device 17, and generates detailed data corresponding to the simplified operation generated by the simplified operation generation unit 101. Then, the node management unit 103 stores the detailed data in the previously generated node (step A08).
[0045]
Next, the node management unit 103 finds the dependency relationship with the existing node based on the influence range of the refinement operation corresponding to the generated node, and generates and updates the related dependency link (step A09). ).
[0046]
The dependency link is a unidirectional link to the refinement operation that is a premise for performing the refinement operation. From the standpoint of decomposition processing, this is a unidirectional link from an existing node having a dependency relationship to a new node. Data can be compressed if the dependency link is expressed by the resolution level and relative positional relationship of the cell to which the dependent node belongs and the node number in the cell. In other words, cells that can contain dependent nodes are clearly limited by the structural arrangement of the cell, either the cell itself, a parent or higher level parent cell, or a directly adjacent cell at the same level. It becomes. For this reason, a cell can be designated with a small number of bits due to the relative positional relationship. Directly adjacent means sharing the boundary including the cell vertex. Therefore, in the three-dimensional case, there are 26 directly adjacent cells including front, back, left, right, up and down and diagonal, and the positional relationship can be expressed with 5 bits. If the resolution level is about several tens to several hundreds, the resolution level is sufficient. Moreover, although it is a node number in a cell, since the number of nodes contained in a cell is not so large, this can also be expressed with a small number of bits.
[0047]
Next, the simplification operation execution unit 105 executes the simplification operation generated by the simplification operation generation unit 101 on the simplified numerical data 31 stored in the hierarchical data storage device 17 (step A0A).
[0048]
The process is repeated again from step A01.
[0049]
These series of decomposition processes can be performed separately for elements that do not include an accompanying attribute, the geometric structure of the nodes, and the accompanying attributes. In this case, for convenience of processing, it is better to store the hierarchized data separately on the recording medium for the part related to the geometric structure and the part related to each accompanying attribute. The hierarchical data of the incidental attribute is composed of the node of the simplified numerical data and the incidental attribute data of the element, the portion related to the incidental attribute in the detailed data, and the lower-layer variation data of the incidental attribute, if any. The hierarchical data of the geometric structure omits any part related to the accompanying attribute, and instead, information corresponding to a link for referring to the hierarchical data of the accompanying attribute is inserted into the cell data. The procedure for performing the decomposition process independently is as follows. First, the accompanying attributes are ignored, and only the geometric structure is decomposed to generate and update hierarchical data of only the geometric structure. At the same time, the arrangement of each data element in the hierarchical data of the incidental attribute is calculated, information corresponding to the link to the hierarchical data of the incidental attribute is stored in the cell data, and the arrangement information of each data element is separately stored. Keep it. Next, the hierarchical data of each accompanying attribute is generated and updated with reference to the stored information. This makes it easy to add, delete, and thin out time steps in time-series data in which the accompanying attributes of the hierarchical data increase or decrease or only the accompanying attributes change over time.
[0050]
By the way, data compression can be performed by removing cells having a resolution level higher than necessary. However, since it is impossible to refine the removed resolution level, it is lossy compression. It is similar to lossy compression of image data by removing high frequency components. This data compression may be performed after generation of hierarchized data and addition of hierarchies, or during generation. The latter is a method in which cells to be removed are not generated from the beginning, and can be implemented by stopping cell generation until the resolution level of the simplification operation is lowered to a predetermined level after generation of hierarchical data is started.
[0051]
Referring to FIG. 3, the hierarchical data according to the present invention includes simplified numerical data 21, a cell 22, a lower layer link 23 that is a unidirectional link to a direct child cell, and a node 24 stored in the cell. And a dependency link 25 which is a unidirectional link to a dependent node. In the drawing, the original numerical data 20 indicated by a dotted line and the dependency link 250 starting from the numerical data 20 are not necessary and are not recorded in the hierarchical data. Compared with FIG. 12, the hierarchical data according to the present invention is different from the hierarchical data according to the conventional method in that cells and lower layer links are added, and the dependent links are unidirectional links.
[0052]
FIG. 4 is a diagram showing an example of the data structure of hierarchical data according to the present invention.
[0053]
The hierarchical data is composed of simplified numerical data 31 and cell data 32.
[0054]
The simplified numerical data 31 is composed of node data 310 and element data 311.
[0055]
The node data 310 includes the coordinates of each node and accompanying attributes. There may be no accompanying attributes or there may be many.
[0056]
The element data 311 includes a constituent node number and an associated attribute of each element. In the case of stratification of particle data, this data does not exist. There may be no accompanying attributes or there may be many. In some cases, the attribute is common to the accompanying attribute of the node, and in other cases, it is not.
[0057]
The cell data 32 includes lower layer link data 320, lower layer fluctuation data 321, and node data 33.
[0058]
The lower layer link data 320 is expressed by the position of the link destination cell data on the recording medium, or a number that can uniquely identify the cell.
[0059]
The lower layer variation data 321 is composed of variation data for each lower level of the surface boundary and each associated attribute. This data is not necessary if we do not consider reconstruction on a multidimensional basis.
[0060]
The node data 33 includes detailed data 330 and dependency link data 331.
[0061]
As described above, the dependence link data 331 includes the resolution level of the cell including the dependence destination node, the relative positional relationship between the cells, and the in-cell node number. When compression of dependent link data is not considered, this is not limited to this, and the position of the link destination node data on the recording medium or a number that can uniquely identify the node is represented.
[0062]
The node data 310, the element data 311, the lower layer variation data 321, and the detailed data 330 may be stored separately in different locations on the recording medium by separating the portions related to the accompanying attributes. This makes it easy to increase / decrease accompanying attributes in hierarchical data and to deal with time-series data, that is, to add, delete, and thin out time steps.
[0063]
Referring to FIG. 5, a system for performing reverse decomposition is shown in the embodiment of the present invention, and a numerical data storage device 16 for storing restored numerical data, and reverse decomposition of hierarchical data. , A reverse decomposition apparatus 11 that performs hierarchical reduction and numerical data restoration, and a hierarchical data storage apparatus 17 that stores hierarchical data during and after processing.
[0064]
Reverse decomposition is a reverse operation of decomposition, similar to the reconstruction described later, but is different from the reconstruction in that the hierarchical data is changed, and is mainly used for maintenance of hierarchical data. By the inverse decomposition, the hierarchy of the hierarchized data can be reduced, and if this is done to the end, the original numerical data can be restored.
[0065]
The numerical data storage device 16 and the hierarchical data storage device 17 may be a semiconductor memory, a magnetic disk device, an optical disk device, or other data storage devices.
[0066]
The inverse decomposition apparatus 11 includes a numerical data output unit 110, a cell management unit 112, a node management unit 113, a dependency relationship resolution unit 114, and a detailed operation execution unit 115.
[0067]
The numerical data output unit 110 stores the simplified numerical data 31 of the hierarchical data after reverse decomposition stored in the hierarchical data storage device 17 in the numerical data storage device 16. If the hierarchical data is completely inversely decomposed, the numerical data 30 becomes the restored original numerical data.
[0068]
The cell management unit 112 manages the cell data 32 of the hierarchical data stored in the hierarchical data storage device 17. The cell to be deleted is searched, and information necessary for accessing the cell, for example, the position of the cell data on the recording medium is output to the node management unit 113. In addition, deletion of a cell in which deletion of all nodes is completed, and deletion and update of lower layer links connected to the cell are also performed. As the reverse decomposition process progresses, the data size of the simplified numerical data 31 increases due to refinement, but the data size of the cell data 32 decreases due to cell deletion.
[0069]
The node management unit 113 manages node data included in the cell data 32 stored in the hierarchical data storage device 17. Based on the information output from the cell management unit 112, the node in the cell to be deleted is extracted, and the information necessary for accessing the node, such as the position of the node data on the recording medium, depends on the information. Output to the relationship resolution unit 114. In addition, the dependency link connected to the node that has been refined and can be deleted is also deleted and updated.
[0070]
The dependency relationship resolution unit 114 creates a list of nodes to be deleted based on the information output from the node management unit 113, and stores information such as detailed data of the listed nodes in an order that satisfies the dependency relationship. Output to the refinement operation execution unit 115. Further, the node information that can be deleted, for example, the position of the node data on the recording medium, is output to the node management unit 113.
[0071]
The refinement operation execution unit 115 performs the refinement operation on the simplified numerical data 31 stored in the hierarchical data storage device 17 based on the refinement data output from the dependency relationship resolution unit 114.
[0072]
Next, the operation of this system will be described with reference to FIG.
[0073]
First, the cell management unit 112 searches the hierarchical data stored in the hierarchical data storage device 17 for a cell to be deleted, that is, a cell whose resolution level is lower than a designated level given in advance (step A10). . The node management unit 113 extracts the node in the cell, and the dependency relationship resolution unit 114 registers the node in the list (step A11). The list may be a list such as a position of the node data on the recording medium, or may be replaced by placing a registered mark on the node itself without explicitly creating the list.
[0074]
Next, the dependency relationship resolution unit 114 satisfies the dependency relationship among the listed nodes but has not yet been processed, that is, the refinement operation corresponding to the node has not yet been performed, and all the dependency destinations have been processed. The node for which the detailed operation corresponding to the node has been completed is searched (step A12). The refinement operation execution unit 115 executes the refinement operation corresponding to the retrieved node on the simplified numerical data 31 stored in the hierarchical data storage device 17 (step A13). The node management unit 113 deletes and updates the dependency link connected to the searched node (step A14). In step A12, when the dependence destination node is simplified numerical data, it is considered that the corresponding refinement operation has been completed.
[0075]
Next, the cell management unit 112 searches for a cell to be deleted (step A15), deletes the cell together with the stored node, and deletes and updates the lower layer link connected to the cell (step A16). Since the cell search performed here is the same as step A10, the search result of step A10 may be held and the search may be omitted using this.
[0076]
Next, the numerical data output unit 110 stores the simplified numerical data 31 of the hierarchical data after reverse decomposition stored in the hierarchical data storage device 17 in the numerical data storage device 16 (step A17). If the hierarchized data is completely reverse-decomposed, this numerical data becomes the restored original numerical data. This step is not necessary if the purpose is only to reduce the hierarchy of the hierarchical data.
[0077]
Referring to FIG. 7, a system for performing reconfiguration in the embodiment of the present invention is shown. A hierarchized data storage device 17 for storing hierarchized data for reconfiguration, The reconstructing device 12 reconstructs numerical data and the reconstructed numerical data storage device 18 for storing the reconstructed numerical data.
[0078]
Reconstruction is the reverse operation of decomposition, similar to the reverse decomposition described above, but differs from reverse decomposition in that the layered data is not altered at all, mainly for visualization of layered data and reuse for numerical simulation. Use for.
[0079]
The hierarchical data storage device 17 and the reconstructed numerical data storage device 18 may be a semiconductor memory, a magnetic disk device, an optical disk device, or other data storage devices.
[0080]
The reconfiguration apparatus 12 includes a numerical data duplication unit 120, a cell management unit 122, a node management unit 123, a dependency relationship resolution unit 124, and a detailed operation execution unit 125.
[0081]
The numerical data duplication unit 120 stores the simplified numerical data 31 of the hierarchical data stored in the hierarchical data storage device 17 in the reconstructed numerical data storage device 18. The numerical data 34 is increased in data size by the subsequent refinement operation, and finally becomes reconstructed numerical data.
[0082]
The cell management unit 122 manages the cell data 32 of the hierarchical data stored in the hierarchical data storage device 17. A cell to be refined is searched, and information necessary for accessing the cell, for example, the position of the cell data on the recording medium, is output to the node management unit 123.
[0083]
The node management unit 123 manages node data included in the cell data 32 stored in the hierarchical data storage device 17. Based on the information output from the cell management unit 122, a node in the cell to be refined is extracted and information necessary for accessing the node, for example, the position of the node data on the recording medium, etc. Is output to the dependency relationship resolution unit 124. Also, the access request to the node is received from the dependency relationship resolution unit 124, and information necessary for accessing the requested node is returned to the dependency relationship resolution unit 124.
[0084]
The dependency relationship resolution unit 124 creates a list of nodes to be refined based on the information output from the node management unit 123, and obtains the dependency information such as the detailed data of the listed nodes. It outputs to the refinement operation execution part 125 in the order which satisfy | fills. When a node necessary for satisfying the dependency relationship is not registered in the list, an access request to the necessary node is issued to the node management unit 123, and the necessary node is added to the list based on the returned information.
[0085]
The refinement operation execution unit 125 executes the refinement operation on the reconfiguration numerical data 34 stored in the reconfiguration numerical data storage device 18 based on the detailed data output from the dependency relationship resolution unit 124.
[0086]
Next, the operation of this system will be described with reference to FIG.
[0087]
First, the numerical data duplication unit 120 stores the simplified numerical data 31 of the hierarchical data stored in the hierarchical data storage device 17 in the reconstructed numerical data storage device 18 (A20).
[0088]
Next, the cell management unit 122 searches the hierarchized data stored in the hierarchized data storage device 17 for a cell to be refined, that is, a cell whose resolution level is lower than a predetermined request level. (Step A21). The node management unit 123 extracts the node in the cell, and the dependency relationship resolution unit 124 registers the node in the list (step A22). The list may be a list such as a position of the node data on the recording medium, or may be replaced by placing a registered mark on the node itself without explicitly creating the list.
[0089]
The requirement level may vary depending on the location, for example, a high requirement level for a part to be refined and a low requirement level for other parts. In this case, the cell whose resolution level is lower than the required level, which is the search condition in step A21, means a cell whose resolution level is lower than the maximum required level in the area within the cell.
[0090]
The search for the cell to be refined is performed by a tree constructed by the cell and the lower layer link, but the search method may be any of depth-first search and width-first search. However, when cell data is grouped by resolution level on the recording medium, the breadth-first search has the highest access localization and is preferable.
[0091]
The search for nodes to be refined is performed on a cell-by-cell basis, and basically all nodes in the searched cell are registered in the list. Only when the search condition is not satisfied in this area, it is determined whether or not the resolution level is lower than the required level for each node, and only the nodes that pass the determination need be added to the list. Although the amount of processing increases, if the search condition is satisfied or not satisfied at all in the cell, the processing contents are not changed and the process is performed in units of cells, so the node is directly searched without using the cell. It is still faster than conventional methods.
[0092]
When there is lower layer fluctuation data in a cell, reconstruction can be performed based on a multi-dimensional standard that takes into account incidental attributes in addition to resolution. The lower layer variation data shows the variation of the surface boundary and each associated attribute when it is refined to the required level. Here, for the lower layer fluctuation data, the accompanying attribute number is i, the relative resolution level from the cell is j, and the fluctuation value of the surface boundary is S. _j , The change value of the incidental attribute is A _ij And In addition, the required level given prior to the reconstruction process is R, and the allowable error of the accompanying attribute is E. _i And The resolution level of the current cell is set to R ₀ And 0 ≦ ∀j <R−R ₀ And ∀i, S _j ≦ R and A _ij ≦ E _i If that is true, that is, if the variation of the surface boundary and all accompanying attributes when the current cell region is refined to the required level is within an allowable error, even if the above search conditions are satisfied, Excludes the current cell and its child cells from the search. Thereby, in the area where the spatial change of the accompanying attribute is small, the refinement is suppressed and the element becomes coarse, and in the area where the change is abrupt, the numerical data that is refined and the element becomes fine as usual can be reconstructed. In addition, reconstruction can be performed taking into account only surface boundary fluctuations.In this case, in the area away from the surface boundary or in the vicinity of the gentle uneven surface boundary, refinement is suppressed and the elements become rough, and fine unevenness In the vicinity of the surface boundary, it is possible to reconstruct numerical data that has been refined and refined as usual.
[0093]
Next, the dependency relationship resolution unit 124 confirms whether or not all the dependence destination nodes are registered in the list for each listed node (step A23). If there is an unregistered dependency destination node, the node management unit 123 is inquired and registered in the list (step A24). When the dependence destination node is simplified numerical data, it is not necessary to register it in the list.
[0094]
Next, the dependency relationship resolution unit 124, among the listed nodes, satisfies the dependency relationship but has not yet been processed, that is, the refinement operation corresponding to the node has not yet been performed, and all the dependency destinations A node for which the detailed operation corresponding to the node is completed is searched (step A25). The refinement operation execution unit 125 executes the refinement operation corresponding to the retrieved node on the reconstructed numerical data 34 stored in the hierarchical data storage device 18 (step A26). In step A25, when the dependence destination node is simplified numerical data, it is considered that the corresponding refinement operation has been completed.
[0095]
Referring to FIG. 9, in the simplified numerical data 21, when it is desired to increase the resolution level to 2 in a certain spatial range 26, in other words, the required level is 2 in the spatial range 26 and 0 in the other regions. In this case, by the above-described operation, the refinement operation corresponding to the node 24 included in the cell 22 surrounded by the dotted line 260 is performed on the simplified numerical data 21 in the order consistent with the dependency link 25, and the required level is satisfied. Numerical data can be reconstructed. Further, when it is desired to increase the resolution level to 4 in the spatial range 26, in other words, when the required level is 4 in the spatial range 26 with a required level and 0 in other regions, the cell 22 surrounded by the dotted line 261 in the same manner. The numerical data satisfying the required level can be reconstructed by performing the refining operation corresponding to the nodes 24 and 240 included in. Here, the node 240 is included in a cell at a required level or higher, and should not be involved in the reconfiguration originally, but is necessary to satisfy the dependency relationship of other nodes.
[0096]
The series of reconstruction processes can be performed separately for elements that do not include an accompanying attribute, a geometric structure of a node, and each accompanying attribute. In this way, when the accompanying attribute to be reconfigured is switched or increased / decreased, the reconfiguration of the geometric structure can be omitted, which is efficient.
[0097]
By the way, when performing reconfiguration | reconstruction continuously, it can also be performed as follows. First, the previous reconstruction numerical data and the node used for the reconstruction are recorded and compared with the node used for the current reconstruction. Next, a simplification operation corresponding to a node that exists only in the previous time is performed on the previous reconstruction numerical data, and further a refinement operation corresponding to a node that exists only in the current time is performed. For the nodes that are common to the previous time and the current time, neither simplification operation nor refinement operation is performed. Since reconstruction is performed based on the previous reconstruction numerical data, not simplified numerical data, it is referred to as differential reconstruction. As a guide, the differential reconstruction is more advantageous than the normal reconstruction if the number of nodes common to the previous time and this time is larger than the number of nodes that exist only in the previous time.
[0098]
The above disassembling / re-disassembling / reconfiguring system records a program for realizing its function on a computer-readable recording medium in addition to being realized by dedicated hardware. The program recorded on the computer may be read into a computer system and executed. The computer-readable recording medium refers to a storage device such as a semiconductor memory, a magnetic disk, an optical disk, other recording media, and a hard disk device built in a computer system.
[0099]
【The invention's effect】
As described above, the present invention has the following effects.
[0100]
First, decomposition has the following effects.
[0101]
Using a cell to structure an irregular dependency graph, correlate with the spatial arrangement of nodes, that is, refinement operations, place node data on the recording medium, and node data that is spatially nearby is also on the recording medium Increases the probability of becoming. In addition, the cell data is arranged on the recording medium in consideration of the spatial arrangement, and the probability that the spatially neighboring cell data is also on the recording medium is increased. For this reason, since the refining operation related to the reconstruction is spatially localized, the data necessary for the reconstruction is also localized on the recording medium, and random access to the hierarchical data can be reduced. . Even if the access is localized, it is often discontinuous. Therefore, if a cache or a buffer is interposed, random access can be reduced even more effectively.
[0102]
Further, among the bidirectional dependency links in the conventional method, a dependency link in the high resolution direction is not generated, but a lower layer link of the cell is generated instead. Since a cell contains one or more nodes, the number of cells is less than the number of nodes, and a node has one or more parents, but a cell always has only one parent, so the number of underlying links is Significantly less than the number of dependent links. For this reason, the data amount of the link in the high resolution direction can be reduced.
[0103]
Further, among the bidirectional dependency links in the conventional method, the dependency link in the low resolution direction is described by the relative positional relationship of the cell including the dependency destination node and the node number in the cell. The range of cells that can include dependent nodes is clearly limited by the structural arrangement of the cells, and the number of nodes held by the cell is not so large, so cells and nodes within the cell can be specified with a small number of bits it can. For this reason, the data amount of the link in the low resolution direction can also be reduced.
[0104]
Furthermore, it is not necessary to store the resolution of the refinement operation in the node. In the conventional method, it is necessary to store this information, which takes time to calculate, in a node for speeding up. It is not necessary to reconstruct based on discrete resolution levels, not resolution, and node resolution levels can be easily identified by the regular hierarchical structure of the cells containing the nodes. Because. For this reason, the data amount of the node can also be reduced.
[0105]
Further, the reverse decomposition has the following effects.
[0106]
Since reverse decomposition can be performed in the opposite way to decomposition, the original numerical data must be retained in case the hierarchical data with a reduced number of layers is required or the original numerical data is required. The data storage device can be used effectively.
[0107]
And in reconfiguration | reconstruction, it has the following effects.
[0108]
In the reconstruction, hierarchized data generated by the decomposition is used, and this hierarchized data has high proximity on the recording medium of spatially neighboring cell data and node data. For this reason, since the refining operation related to the reconstruction is spatially localized, the data necessary for the reconstruction is also localized on the recording medium, and random access to the hierarchical data can be reduced. . Even if the access is localized, it is often discontinuous. Therefore, if a cache or a buffer is interposed, random access can be reduced even more effectively.
[0109]
Furthermore, in the hierarchical data generated by the decomposition, the spatial size of the cell is not a node unit by utilizing the fact that the spatial size of the cell corresponds to the stored node, that is, the resolution level of the refinement operation. Search in cell units. As a result, a search with an accuracy corresponding to the resolution level can be performed, and nodes in the vicinity of the accuracy below the resolution level allowance are collectively determined, so that the search process in the reconstruction can be made efficient. In addition, while nodes constitute a complex dependency graph with multiple parents, cells constitute a simple tree structure with only one parent, so searching in units of cells is a simpler procedure. Therefore, the processing can be made more efficient.
[0110]
Furthermore, if the lower layer fluctuation data is held in the cell, it is possible to determine whether the refining operation by the cell and its child cells is necessary from the viewpoint of the surface boundary and each associated attribute. For this reason, it is possible to perform reconstruction based on a multi-dimensional reference that takes into account the surface boundary and accompanying attributes in addition to the resolution, and it is possible to avoid useless refinement operations and useless increases in the number of nodes and elements.
[0111]
Note that the present invention does not impair that data hierarchization does not depend on dimensions and does not depend on the simplified operation method. In addition, it is not impaired that numerical data such as a structural grid such as a BFC (boundary matching) grid, a superposed grid combining them, and a multi-block grid can be hierarchized.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of a disassembly system of the present invention.
FIG. 2 is a flowchart showing the operation of the decomposition system of the present invention.
FIG. 3 is a diagram showing a conceptual structure of hierarchical data according to the present invention.
FIG. 4 is a diagram showing an example of a data structure of hierarchical data according to the present invention.
FIG. 5 is a block diagram showing a configuration of a reverse decomposition system of the present invention.
FIG. 6 is a flowchart showing the operation of the reverse decomposition system of the present invention.
FIG. 7 is a block diagram showing a configuration of a reconstruction system of the present invention.
FIG. 8 is a flowchart showing the operation of the reconstruction system of the present invention.
FIG. 9 is a diagram for explaining reconstruction using hierarchical data according to the present invention;
FIG. 10 is a diagram illustrating an example of unstructured numerical data.
FIG. 11 is a diagram for explaining a simplification operation and a detail operation for unstructured numerical data.
FIG. 12 is a diagram illustrating a conceptual structure of hierarchical data according to a conventional method.
FIG. 13 is a diagram for explaining reconstruction using hierarchical data according to a conventional method.
[Explanation of symbols]
10 Disassembly equipment
100 Numerical data input section
101 Simplification operation generator
102 Cell management department
103 Node manager
104 Detailed data generator
105 Simplified operation execution unit
11 Reverse decomposition equipment
110 Numerical data output section
112 Cell Management Department
113 Node manager
114 Dependency Resolution Unit
115 Refinement operation execution part
12 Reconstruction device
120 Numeric data replication unit
122 Cell management unit
123 Node manager
124 Dependency Resolution Unit
125 Detailed operation execution part
16 Numerical data storage device
17 Hierarchical data storage device
18 Reconstructed numerical data storage device
20 original numerical data
21 Simplified numerical data
22 cells
23 Lower link
24 (represents a refinement operation) node
240 Nodes involved in reconfiguration only to satisfy dependencies
25 Dependent links
250 Dependent links that do not require recording
26 Reconstruction scope
260 Part involved in reconstruction at low resolution
261 Part involved in reconstruction at high resolution
30 original numerical data
31 Simplified numerical data
310 Node data
311 Element data
32 cell data (including node data)
320 Lower layer link data
321 Lower layer fluctuation data
33 node data
330 Detailed data
331 Dependent link data
34 Reconstructed numerical data
40 Unstructured numerical data
400 Simplified part of unstructured numeric data
401 Part to be refined in unstructured numeric data
41 nodes
410 Removal node
411 Degenerate nodes
412 Insertion node
413 Split node
42 elements
A00-A0A step
A10 to A17 steps
A20 to A26 steps

Claims (55)

In a method of hierarchizing the unstructured numerical data by multiresolution representation by executing a decomposition process for generating hierarchical data from the unstructured numerical data ,
A cell that is spread in a periodic lattice pattern in each discrete resolution level , with a resolution of a simplification error due to a simplification operation for obtaining the multi-resolution representation of the unstructured numerical data, and having a certain resolution level Providing a cell in a relationship that includes cells having a higher resolution level than the resolution level;
Storing, in a predetermined cell, nodes whose resolution and spatial position coincide with the resolution level and spatial position of the cell within a predetermined range, respectively;
Providing a lower layer link from the cell to a high resolution level cell encompassed by the cell and having nodes therein;
Have a said node is a node representing the refinement operation in the dependency graph representing the corresponding dependent link refinement operations dependency on the hierarchical data, wherein the.   The method of claim 1, further comprising adding a cell of a specific resolution level. The method according to claim 1, further comprising a step of inverse decomposition that refines the most simplified numerical data to a specific resolution level and erases cells of the resolution level.   The method according to any one of claims 1 to 3, further comprising the step of deleting all cells having a resolution level higher than a predetermined resolution level.   The method according to any one of claims 1 to 3, wherein cells having a resolution level higher than a predetermined resolution level are not provided. The method according to any one of claims 1 to 3, further comprising a step of inverse decomposition in which cells of all resolution levels are deleted and the hierarchized data is restored to the original data.   The method according to any one of claims 1 to 6, wherein decomposition processing of the same resolution level is performed in parallel.   The dependency link that is a dependency relationship between nodes is expressed by a resolution level of a cell to which the node belongs, a relative positional relationship of the cell, and a node number in the cell. The method according to item.   9. The method according to any one of claims 1 to 8, further comprising the step of generating variability data indicating the amount of change in associated attributes and / or surface boundaries when refined from a given cell to a higher resolution level cell. The method described.   The method according to claim 1, wherein the geometric structure and the associated attribute are decomposed independently.   11. The method according to claim 1, wherein data related to the cell including the node, the dependency link, the lower layer link, and the variation data is recorded on a recording medium collectively for each resolution level.   The method according to claim 11, wherein data related to the cells is recorded on the recording medium in an order along a space filling curve.   The method of claim 12, wherein the space filling curve is a Hilbert curve or a Z curve.   Data related to a cell including the node, the dependent link, the lower layer link, and the variation data generated by the method according to any one of claims 1 to 10 is recorded collectively for each resolution level. Data recording media.   The data recording medium according to claim 14, wherein data related to the cells are recorded in an order along a space filling curve.   The data recording medium according to claim 15, wherein the space filling curve is a Hilbert curve or a Z curve. The method according to any one of claims 1 to 10 , wherein the reconstructing method is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and is not accompanied by modification of the hierarchical data. A method of reconstructing the data decomposed in step 1 by searching a cell related to the refinement by the link, extracting a node in the cell, and refining it. 11. A reconstruction method that is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and that is not accompanied by modification of the hierarchical data, wherein the data decomposed by the method according to claim 9 or 10 The cell related to the refinement is searched by the link, and the refinement is omitted when the change amount is within a predetermined range, and the node within the cell when the change amount is outside the predetermined range To reconstruct by extracting and refining. The method according to any one of claims 1 to 10 , wherein the reconstructing method is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and is not accompanied by modification of the hierarchical data. A method for reconstructing the data decomposed by the process independently of the geometric structure and accompanying attributes.   When reconstructing the decomposed data continuously, the node used for the previous reconstruction is compared with the node used for the previous reconstruction, and the simplified operation is performed for the node used only for the previous reconstruction. The method according to any one of claims 17 to 19, wherein a refinement operation is performed for a node used only for the current reconfiguration.   The method according to any one of claims 17 to 20, wherein when there is an area that does not need to be refined in a cell, a node included in the area is searched, and the node does not perform refinement. The data according to any one of claims 14 to 16 , wherein the reconstruction method is a reverse operation of decomposition processing for generating hierarchical data from unstructured numerical data and is not accompanied by modification of the hierarchical data. A method of reconstructing decomposed data by reading a recording medium, searching for a cell related to detail by the link, extracting a node in the cell, and refining the cell. The data according to any one of claims 14 to 16 , wherein the reconstruction method is a reverse operation of decomposition processing for generating hierarchical data from unstructured numerical data and is not accompanied by modification of the hierarchical data. Read the recording medium, search for a cell related to the refinement by the link, omit the refinement if the change amount is within a predetermined range, and the cell if the change amount is outside the predetermined range A method of reconstructing decomposed data by extracting and refining the nodes within. The data according to any one of claims 14 to 16 , wherein the reconstruction method is a reverse operation of decomposition processing for generating hierarchical data from unstructured numerical data and is not accompanied by modification of the hierarchical data. A method of reconstructing the decomposed data independently of the geometric structure and accompanying attributes by reading the recording medium.   When reconstructing the decomposed data continuously, the node used for the previous reconstruction is compared with the node used for the previous reconstruction, and the simplified operation is performed for the node used only for the previous reconstruction. The method according to any one of claims 22 to 24, wherein a refinement operation is performed for a node that is used only for the current reconfiguration.   The method according to any one of claims 22 to 25, wherein when there is an area that does not need to be refined in a cell, a node included in the area is searched, and the node does not perform refinement.   The method according to any one of claims 22 to 26, wherein the data recording medium according to any one of claims 14 to 16 is read through a cache or a buffer. In the apparatus for hierarchizing the unstructured numerical data by multi-resolution representation by executing a decomposition process for generating hierarchical data from the unstructured numerical data ,
A cell that is spread in a periodic lattice pattern in each discrete resolution level , with a resolution of a simplification error due to a simplification operation for obtaining the multi-resolution representation of the unstructured numerical data, and having a certain resolution level Means for providing a cell in a relationship including a cell having a resolution level higher than the resolution level;
Means for storing, in a predetermined cell, nodes whose resolution and spatial position coincide with the resolution level and spatial position of the cell within a predetermined range, respectively;
Means for providing a lower layer link from the cell to a high resolution level cell encompassed by the cell and having nodes therein ;
It has a said node is a node representing the refinement operation in the dependency graph representing the corresponding dependent link refinement operations dependency on the hierarchical data, that the device according to claim.   30. The apparatus of claim 28, further comprising means for adding cells of a particular resolution level. 30. The apparatus according to claim 28 or 29, further comprising means for performing inverse decomposition by refining the most simplified numerical data to a specific resolution level and erasing cells of the resolution level.   The apparatus according to any one of claims 28 to 30, further comprising means for deleting all cells having a resolution level higher than a predetermined resolution level.   31. The apparatus according to any one of claims 28 to 30, wherein no cell having a resolution level higher than a predetermined resolution level is provided. The apparatus according to any one of claims 28 to 30, further comprising means for performing inverse decomposition by deleting cells of all resolution levels and restoring the hierarchized data to the original data.   34. The apparatus according to any one of claims 28 to 33, comprising means for performing decomposition processing of the same resolution level in parallel.   35. The means according to claim 28, further comprising means for expressing a dependency link that is a dependency relationship between nodes by a resolution level of a cell to which the node belongs, a relative positional relationship of the cell, and a node number in the cell. The apparatus according to any one of the above.   36. A means according to any one of claims 28 to 35, further comprising means for generating variation data indicating the amount of change in the associated attributes and / or surface boundaries when refined from a given cell to a higher resolution level cell. The device described.   37. Apparatus according to any one of claims 28 to 36, comprising means for resolving the geometric structure and associated attributes independently.   38. The apparatus according to any one of claims 28 to 37, further comprising means for recording data related to the nodes including the node, the dependent link, the lower layer link, and the variation data on a recording medium by resolution level.   39. The apparatus of claim 38, comprising means for recording data relating to the cells on the recording medium in an order along a space filling curve.   40. The apparatus of claim 39, wherein the space filling curve is a Hilbert curve or a Z curve. 38. An apparatus for performing reconfiguration that is a reverse operation of decomposition processing that generates hierarchical data from unstructured numerical data and that is not accompanied by modification of the hierarchical data, and is performed according to any one of claims 28 to 37. An apparatus for reconstructing the data decomposed by the apparatus in (1) by searching for a cell related to the refinement by the link, extracting a node in the cell, and refining it. 38. An apparatus for performing reconstruction that is a reverse operation of decomposition processing for generating hierarchized data from unstructured numerical data and that does not involve modification of the hierarchized data, wherein the apparatus is decomposed by the apparatus according to claim 36 or 37. The cell is searched for the data related to the refinement by the link, and the refinement is omitted when the change amount is within a predetermined range, and within the cell when the change amount is outside the predetermined range. A device that reconfigures by extracting and refining nodes. 38. An apparatus for performing reconfiguration that is a reverse operation of decomposition processing that generates hierarchical data from unstructured numerical data and that is not accompanied by modification of the hierarchical data, and is performed according to any one of claims 28 to 37. A device that reconstructs the data that was decomposed by the above device independently of the geometric structure and accompanying attributes.   When reconstructing the decomposed data continuously, the node used for the previous reconstruction is compared with the node used for the previous reconstruction, and the simplified operation is performed for the node used only for the previous reconstruction. 44. The apparatus according to any one of claims 41 to 43, further comprising means for performing a refinement operation on a node used only for the current reconfiguration.   45. The method according to any one of claims 41 to 44, wherein when there is an area that does not need to be refined in a cell, a node included in the area is searched, and the node does not perform refinement. apparatus. The apparatus according to any one of claims 14 to 16 , wherein the apparatus is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and performs reconstruction without modification of the hierarchical data. An apparatus for reconstructing the decomposed data by reading the data recording medium, retrieving a cell related to the refinement by the link, extracting a node in the cell, and refining it. The apparatus according to any one of claims 14 to 16 , wherein the apparatus is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and performs reconstruction without modification of the hierarchical data. When the change amount is within a predetermined range, the refinement is omitted, and when the change amount is out of the predetermined range, the cell is searched. An apparatus for reconstructing decomposed data by extracting and refining nodes in the cell. The apparatus according to any one of claims 14 to 16 , wherein the apparatus is a reverse operation of a decomposition process for generating hierarchical data from unstructured numerical data and performs reconstruction without modification of the hierarchical data. A device that reads the data recording medium of, and reconstructs the decomposed data independently of the geometric structure and associated attributes.   When reconstructing the decomposed data continuously, the node used for the previous reconstruction is compared with the node used for the previous reconstruction, and the simplified operation is performed for the node used only for the previous reconstruction. 49. The apparatus according to any one of claims 46 to 48, further comprising means for performing a refinement operation on a node used only for the current reconfiguration.   50. The method according to any one of claims 46 to 49, further comprising means for searching for a node included in the area when there is an area that does not need to be refined in the cell, and the node does not perform the refinement. Equipment.   The apparatus according to any one of claims 46 to 50, comprising means for reading the data recording medium according to any one of claims 14 to 16 through a cache or a buffer.   A data hierarchization program for causing a computer to execute the method according to any one of claims 1 to 13.   A computer-readable recording medium on which a data hierarchization program for causing a computer to execute the method according to any one of claims 1 to 13 is recorded.   A data reconstruction program for causing a computer to execute the method according to any one of claims 17 to 27.   A computer-readable recording medium having recorded thereon a data reconstruction program that causes a computer to execute the method according to any one of claims 17 to 27.

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