Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
1999-07-13
2001-03-27
McElheny, Jr., Donald E. (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C703S002000, C702S016000
Reexamination Certificate
active
06208939
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a topography information data processing method for processing ground surface data which represents bumps and hollows on the ground surface and discrete geographic data that includes height information which indicates bumps and hollows on the ground and the like.
2. Description of Related Art
In recent years, as the computer becomes more sophisticated, the topography of the land and ocean floor is actively being transformed into database as exemplified by the concept of GIS (geographic information system). To obtain such database, the topography is expressed based on 3-dimensional geographic information data such as longitude, latitude, and height.
Geographic information data is obtained using sensor devices such as a satellite and an ultrasonic distance measuring equipment. These sensor devices measure the height or depth of each of observation points located on the ground in the form of grid points. Polygonal data and mesh data are acquired based on the 3-diemnsional geographic data obtained by measurement, that is, discrete geographic data. A surface which contains bumps and hollows on the ground is represented in a 3-dimensional space by carrying out rendering based on the polygonal data.
The amount of discrete geographic data obtained by the sensor devices is enormous. If the discrete geographic data is transformed into polygonal data, the amount of data increases even more. Therefore, it is difficult just to store the obtained enormous discrete geographic data and polygonal data. Currently, most of the discrete geographic data obtained by the satellites are discarded without being stored effectively.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a topography information data processing method and apparatus capable of utilizing currently available geographic information data to provide novel topography information data representation.
This data processing method acquires ground surface data which represents bumps and hollows on the ground, generates manifold data which represents the shape of a manifold that encloses the bumps and hollows on the ground based on the ground surface data, and acquires topological geometric data applying the Morse theory to the manifold data.
According to one aspect of this method, novel shape representation is provided by using topological geometric data generated based on the Morse theory known in differential geometry and differential topology. The data amount of such topological geometric data is generally smaller than the data amount of polygonal data.
A manifold may be defined to be a surface in the 3-dimensional Euclidean space. A point on a smooth manifold may be called a critical point if the plane tangent to the manifold at the point is, for example, substantially parallel to a horizontal plane. The index of a critical point of a smooth manifold is defined to be 0 if the surface forms a pit or a bowl-shaped surface in the neighborhood of the critical point. The index of a critical point a smooth manifold is defined to be 1 if the surface forms a saddle in the neighborhood of the critical point. The index of a critical point a smooth manifold is defined to be 2 if the surface forms a peak or a cap-shaped surface in the neighborhood of the critical point.
According to the Morse theory, critical points of a smooth manifold and the indices of the critical points can be determined by prescribing an appropriate Morse function. Using these information, a space having the same homotopy type as the manifold can be reproduced. Here, two geometric objects in the 3-dimensional Euclidean space are said to be of the same homotopy type if the two geometric objects can be continuously deformed onto each other. For example, a sphere is of the same homotopy type as a tetrahedron but not of the same homotopy type as a torus.
In order to describe the shape of the manifold, it suffices to add geometric information to the space. Such geometric information can be specified by a structure graph for representing the structure of the manifold, for example, a Reeb graph known in differential topology and differential geometry. A Reeb graph of a manifold shows a skeleton of the manifold obtained by converging each of an arbitrary number of connected components of the manifold that appear on the cross sections of the manifold to a single point. Once the Morse function is determined, the critical points and the indices of the critical points are uniquely determined. Hence, the manifold may be automatically and uniquely converted to topological geometric data.
In acquiring ground surface data, boundary lines may be drawn on the ground to partition the ground into multiple regions. A region may be then cut out along the boundary line that encloses the region. The surface of the entire Earth can be regarded as a manifold. Moreover, a manifold may be formed for any region on the Earth. By partitioning a given area on the ground region into multiple regions, the topological geometric data of the given area is distributed among the regions.
In the case a manifold is formed for each region, in generating manifold data, an arbitrary virtual surface may be attached to the uneven surface of the region enclosed by the boundary line to form a closed manifold. In other words, a closed surface that encloses the ground surface of the region represented by a single uneven surface can be formed. By forming the closed manifold, the Morse theory may be applied to the closed manifold that encloses the uneven surface of the region.
In another aspect of the present invention, discrete topography data that includes the height information on the ground may be used in place of the above-mentioned ground surface data.
The topography information data processing method of the present invention may be realized not only by hardware but also software.
According to still another aspect of the present invention, a topography information data processing apparatus is provided. This apparatus comprises a data inputting device to acquire ground surface data which represents a shape of an uneven ground surface, a preprocessor to generate manifold data which represents a shape of a manifold that encloses said uneven ground surface based on said ground surface data and a modeling unit to obtain topological geometric data from said manifold data. The data inputting device may input discrete topography data having height or depth of the uneven ground surface.
REFERENCES:
patent: 5103429 (1992-04-01), Gelchinsky
patent: 5465323 (1995-11-01), Mallet
patent: 6106561 (2000-08-01), Farmer
McElheny Jr. Donald E.
Monolith Co. Ltd.
Morrison & Foerster / LLP
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