A 3-aperture triangle equal-surface mesh coding method based on sphere

Abstract

The present invention proposes a 3-aperture triangle equal-surface mesh coding method based on a sphere, comprising selecting a basic polyhedron type A0 of a Platonic solid used for meshing, forming a plurality of primary spherical triangles of equal area from the selected basic polyhedron, and obtaining a primary mesh number A1; dividing each primary spherical triangle into two left and right secondary spherical triangles of equal area, and obtaining a secondary mesh number A2; dividing each secondary spherical triangle into three third-level spherical triangles of equal area, and obtaining a third-level mesh number A3, and repeating for multiple times until the spherical triangle is divided into a required K-level mesh, and obtaining a K-th mesh number A1. K ; A0A1A2…A k The present invention can identify each segmented facet on the spherical surface, so that the segmented facet coding has spatial position correlation and global uniqueness, and the segmented facet coding can be used to represent the spatial position to some extent.

Description

Technical Field

[0001] The invention belongs to the field of geographic information and computer graphics technology, and in particular relates to a 3-aperture triangle equal-surface subdivision grid coding method based on a sphere. Background Art

[0002] The spherical geographic grid division began with the Dymaxon world map designed by Fuller R.B. in the 1940s. Its purpose was to describe the globe more accurately on a plane without obvious deformation (maintaining scale, orientation and shape), and to depict the world on the spherical surface as a plane with real scale, orientation and shape.

[0003] Technically speaking, only Platonic solids (tetrahedron, hexahedron or cube, octahedron, icosahedron, dodecahedron) can perfectly divide the earth's surface into regular, similar-shaped, equal-area spherical geographic grid units. The current subdivision methods are basically based on the further subdivision of the above polyhedrons, and they also use 3, 4, 9 and other subdivision apertures (subdivision aperture: the number of K+1 level subdivision facets contained in a K-level subdivision facet). At the same time, after the grid is established, it is necessary to establish a global spatial information identification code to achieve a unique spatial entity code on a global scale, which is conducive to information sharing between different platforms.

[0004] At present, only the 3-aperture triangle equal-surface partitioning method based on the sphere can form a globally unified, multi-level, unambiguous, equal-area partitioning grid system. However, there is no research result on the specific post-partitioning grid coding method. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] The present invention proposes a 3-aperture triangle equal-surface subdivision grid coding method based on a sphere to solve the problem of how to establish a global spatial information identification coding.

[0007] (II) Technical solution

[0008] In order to solve the above technical problems, the present invention proposes a 3-aperture triangle equiplanar mesh coding method based on a sphere, and the equiplanar mesh coding method comprises the following steps:

[0009] S1. Select the basic polyhedron type A0 of the Platonic solid used for meshing. When the basic polyhedron is a regular tetrahedron, the value of A0 is A; when the basic polyhedron is a regular octahedron, the value of A0 is B; when the basic polyhedron is a regular icosahedron, the value of A0 is C;

[0010] S2. The polyhedral vertices of the selected basic polyhedron correspond to the longitude and latitude of the sphere to form multiple first-level spherical triangles of equal area, forming a first-level mesh, and obtaining the first-level mesh number A1 in alphabetical order according to the longitude and latitude; wherein, the first-level spherical triangles formed by the regular tetrahedron are 4, and the value range of A1 is A to D; the first-level spherical triangles formed by the regular octahedron are 8, and the value range of A1 is A to H; the first-level spherical triangles formed by the regular icosahedron are 20, and the value range of A1 is A to T;

[0011] S3. Each primary spherical triangle is divided into two equal-area secondary spherical triangles on the left and right to form a secondary mesh, and a secondary mesh number A2 is obtained according to the left and right positions; wherein, for the secondary spherical triangle on the left, A2 is 1; and for the secondary spherical triangle on the right, A2 is 2;

[0012] S4. Each secondary spherical triangle is divided into three equal-area third-level spherical triangles to form a divided third-level grid, and a third-level grid number A3 is obtained; wherein, for the third-level spherical triangle containing the largest angle of the secondary spherical triangle, A3 is 1; for the third-level spherical triangle close to number 1, A3 is 2; for the remaining third-level spherical triangles, A3 is 3;

[0013] S5. According to the division and value-taking method of step S4, the third-level spherical triangle is further divided into 3 aperture triangles and the like, and the division is repeated multiple times until the spherical triangle is divided into the required K-level grids, and the fourth-level grid number A4, the fifth-level grid number A, the sixth-level grid number A6 are obtained in sequence, until the K-level grid number A K ;

[0014] S6. With A0A1A2…A k The encoding method is used to obtain all the mesh numbers of the Kth level, thereby determining the unique code of each subdivided face of the 3-aperture triangle equisurface subdivision mesh based on the sphere.

[0015] (III) Beneficial effects

[0016] The present invention proposes a 3-aperture triangle equal-surface mesh coding method based on a sphere, comprising selecting a basic polyhedron type A0 of a Platonic solid used for meshing, forming a plurality of primary spherical triangles of equal area from the selected basic polyhedron, and obtaining a primary mesh number A1; dividing each primary spherical triangle into two left and right secondary spherical triangles of equal area, and obtaining a secondary mesh number A2; dividing each secondary spherical triangle into three third-level spherical triangles of equal area, and obtaining a third-level mesh number A3, and repeating for multiple times until the spherical triangle is divided into a required K-level mesh, and obtaining a K-th mesh number A1. K ; A0A1A2…Ak The present invention can identify each segmented facet on the spherical surface, so that the segmented facet coding has spatial position correlation and global uniqueness, and the segmented facet coding can be used to represent the spatial position to some extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of vertex coordinates of a regular tetrahedron in an embodiment of the present invention;

[0018] Figure 2 Schematic diagram of vertex coordinates of a regular octahedron in an embodiment of the present invention;

[0019] Figure 3 Schematic diagram of vertex coordinates of a regular icosahedron in an embodiment of the present invention;

[0020] Figure 4 A schematic diagram of the numbering of the secondary grids divided in an embodiment of the present invention;

[0021] Figure 5 A schematic diagram of three-level grid numbering according to an embodiment of the present invention;

[0022] Figure 6 A schematic diagram of four-level grid numbering according to an embodiment of the present invention;

[0023] Figure 7 A schematic diagram of five-level grid numbering according to an embodiment of the present invention;

[0024] Figure 8 Schematic diagram of six-level grid numbering in an embodiment of the present invention. DETAILED DESCRIPTION

[0025] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the drawings and examples.

[0026] This embodiment proposes a 3-aperture triangle equal-surface mesh encoding method based on a sphere, which specifically includes the following steps:

[0027] S1. Select the basic polyhedron type A0 of the Platonic solid used for meshing. When the basic polyhedron is a regular tetrahedron, the value of A0 is A; when the basic polyhedron is a regular octahedron, the value of A0 is B; when the basic polyhedron is a regular icosahedron, the value of A0 is C;

[0028] S2. Align the polyhedron vertices of the selected basic polyhedron with the longitude and latitude of the sphere to form multiple primary spherical triangles of equal area, form a subdivided primary grid, and obtain the primary grid number A1 in alphabetical order according to the longitude and latitude.

[0029] like Figure 1As shown in the figure, the number of primary spherical triangles formed by the decomposition of the regular tetrahedron is 4, and the value range of A1 is A~D; Figure 2 As shown in the figure, the number of primary spherical triangles formed by the decomposition of the regular octahedron is 8, and the value range of A1 is A~H; Figure 3 As shown, there are 20 primary spherical triangles formed by the decomposition of the regular icosahedron, and the value range of A1 is A~T.

[0030] S3. Each primary spherical triangle is divided into two equal-area secondary spherical triangles on the left and right to form a secondary grid, and a secondary grid number A2 is obtained according to the left and right positions. Figure 4 As shown, for the secondary spherical triangle on the left, A2 takes the value of 1; for the secondary spherical triangle on the right, A2 takes the value of 2.

[0031] S4. Each secondary spherical triangle is divided into three equal-area tertiary spherical triangles to form a divided tertiary grid, and the tertiary grid number A3 is obtained. Figure 5 As shown, for the tertiary spherical triangle containing the largest angle of the secondary spherical triangle, A3 takes the value of 1; for the tertiary spherical triangle close to number 1, A3 takes the value of 2; for the remaining tertiary spherical triangles, A3 takes the value of 3.

[0032] S5. According to the division and value selection method of step S4, the third-level spherical triangle is further divided into 3 aperture triangles and repeated multiple times until the spherical triangle is divided into the required K-level grids, and the fourth-level grid number A4 is obtained in turn (based on Figure 5 The third-level spherical triangle is divided as shown in Figure 6 As shown; the fifth level grid number A5 (based on Figure 6 The fourth-level spherical triangle is divided as shown in Figure 7 As shown; the sixth level grid number A6 (based on Figure 7 The five-level spherical triangle is divided as shown in Figure 8 As shown; until the Kth level grid number A K .

[0033] S6. With A0A1A2…A k The encoding method is used to obtain all the grid numbers of the Kth level, thereby determining the unique code of each subdivided face of the 3-aperture triangle equiface subdivided grid based on the sphere. Figure 8 As shown, assuming that the selected Platonic solid is a regular octahedron and the first-level spherical triangle selects area A, the code of the circled sixth-level triangle face is BA11333.

[0034] Through the isosurface mesh coding method of the present invention, each mesh on the sphere can be marked, so that the mesh coding has a certain spatial position correlation and global uniqueness, and the mesh coding can be used to represent the spatial position to a certain extent. Figure 8 It can be seen that the combined triangles numbered 1 and 2 and the single combined triangle numbered 3 can form relatively independent hexagonal-like shapes, which can provide a new solution for the subdivision and encoding of spherical hexagonal grids.

[0035] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the technical principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A 3-aperture triangle equal-surface mesh coding method based on the earth's spherical surface, characterized in that: The isosurface mesh encoding method comprises the following steps: S1. Select the basic polyhedron type A0 of the Platonic solid used for meshing. When the basic polyhedron is a regular tetrahedron, the value of A0 is A; when the basic polyhedron is a regular octahedron, the value of A0 is B; when the basic polyhedron is a regular icosahedron, the value of A0 is C; S2. The polyhedral vertices of the selected basic polyhedron correspond to the longitude and latitude of the sphere to form multiple first-level spherical triangles of equal area, forming a first-level mesh, and obtaining the first-level mesh number A1 in alphabetical order according to the longitude and latitude; wherein, the first-level spherical triangles formed by the regular tetrahedron are 4, and the value range of A1 is A to D; the first-level spherical triangles formed by the regular octahedron are 8, and the value range of A1 is A to H; the first-level spherical triangles formed by the regular icosahedron are 20, and the value range of A1 is A to T; S3. Each primary spherical triangle is divided into two equal-area secondary spherical triangles on the left and right to form a secondary mesh, and a secondary mesh number A2 is obtained according to the left and right positions; wherein, for the secondary spherical triangle on the left, A2 is 1; and for the secondary spherical triangle on the right, A2 is 2; S4. Each secondary spherical triangle is divided into three equal-area third-level spherical triangles to form a divided third-level grid, and a third-level grid number A3 is obtained; wherein, for the third-level spherical triangle containing the largest angle of the secondary spherical triangle, A3 is 1; for the third-level spherical triangle close to number 1, A3 is 2; for the remaining third-level spherical triangles, A3 is 3; S5. According to the division and value selection method of step S4, the third-level spherical triangle is further divided into 3 aperture triangles and repeated multiple times until the spherical triangle is divided into the required K-level grid, and the fourth-level grid number A4, the fifth-level grid number A 、 The sixth level grid is numbered A6, until the Kth level grid is numbered A K ; S6. With A0A1A2…A k The encoding method is used to obtain all the mesh numbers of the Kth level, thereby determining the unique code of each subdivided face of the 3-aperture triangle equisurface subdivision mesh based on the sphere.

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