A 3-aperture triangle equal surface partitioning method based on sphere

Abstract

The present invention proposes a 3-aperture triangle equal-surface partitioning method based on a sphere, including forming a plurality of primary spherical triangles of equal area from a Platonic solid, performing 6-aperture triangle partitioning on each primary spherical triangle to form a plurality of secondary spherical triangles of equal area, performing 3-aperture triangle partitioning on the secondary spherical triangle step by step, and obtaining an equal-area, multi-level, seamless grid system adapted to the world. The method does not consider further partitioning based on regular polygons, adopts a partitioning idea based on spherical non-equilateral triangles, and approximates the earth to a sphere based on a suitable Platonic solid, establishes a sphere partitioning grid based on a spherical triangle partitioning unit, and then provides an equal-area, multi-level, seamless grid system suitable for computer model calculations on a global scale, which is convenient for establishing a unified global big data grid system.

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 method based on a sphere. Background Art

[0002] The spherical geographic gridding began with the Dymaxon world map designed by Fuller RB 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 division methods are basically based on the further division of the above polyhedrons, and they also use 3, 4, 9 and other division apertures (division aperture: the number of K+1 level division facets contained in a K-level division facet). However, they all consider further division based on regular polygons, and cannot form a multi-level division effect of equal area.

[0004] Currently, geographic data gridding is mainly aimed at method design and system application for visualization and regional calculations, but there is no relatively complete research on globally unified, multi-level, unambiguous, equal-area grids suitable for computer model calculations, especially in terms of completely equal area. There are no relevant results. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] The present invention proposes a 3-aperture triangle equal-surface partitioning method based on a sphere to solve the technical problem of how to form equal-area, multi-level and seamless sphere partitioning results.

[0007] (II) Technical solution

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

[0009] S1. Select a Platonic solid whose first-level mesh is an equilateral triangle as the basic polyhedron for meshing;

[0010] S2. Align the vertices of the selected Platonic solid polyhedron to the longitude and latitude of the sphere to form a plurality of primary spherical triangles of equal area, thereby forming a subdivided primary grid;

[0011] S3. Perform 6-aperture triangulation on each primary spherical triangle, connect the vertices and midpoints of the opposite sides of each primary spherical triangle, form multiple secondary spherical triangles of equal area, and form a divided secondary grid;

[0012] S4. Perform 3-aperture triangulation on each secondary spherical triangle to form multiple tertiary spherical triangles of equal area to form a divided tertiary grid;

[0013] S5. Perform 3-aperture triangulation on each level 3 spherical triangle to form a plurality of level 4 spherical triangles of equal area, thereby forming a divided level 4 grid.

[0014] Furthermore, the Platonic solids include the regular tetrahedron, the regular octahedron and the regular icosahedron.

[0015] Furthermore, after step S5, the four-level spherical triangles are continuously subjected to 3-aperture triangulation, and according to the grid usage requirements, the 3-aperture triangulation is continuously performed step by step to obtain an equal-area, multi-level, seamless grid system that is adapted to the whole world.

[0016] (III) Beneficial effects

[0017] The present invention proposes a 3-aperture triangle equal-surface partitioning method based on a sphere, including forming a plurality of primary spherical triangles of equal area from a Platonic solid, performing 6-aperture triangle partitioning on each primary spherical triangle to form a plurality of secondary spherical triangles of equal area, performing 3-aperture triangle partitioning on the secondary spherical triangle step by step, and obtaining an equal-area, multi-level, seamless grid system adapted to the world. The method does not consider further partitioning based on regular polygons, adopts a partitioning idea based on spherical non-equilateral triangles, and approximates the earth to a sphere based on a suitable Platonic solid, establishes a sphere partitioning grid based on a spherical triangle partitioning unit, and then provides an equal-area, multi-level, seamless grid system suitable for computer model calculations on a global scale, which is convenient for establishing a unified global big data grid system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of vertex coordinates of a regular octahedron in an embodiment of the present invention;

[0019] Figure 2 Schematic diagram of the subdivision of a spherical triangle in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] 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.

[0021] This embodiment proposes a 3-aperture triangle equal surface partitioning method based on a sphere, which specifically includes the following steps:

[0022] S1. Select a Platonic solid with a first-level mesh of regular triangles as the basic polyhedron for segmentation, that is, select a regular tetrahedron, a regular octahedron, and a regular icosahedron.

[0023] S2. Align the vertices of the selected Platonic solid polyhedron with the longitude and latitude of the sphere to form a plurality of primary spherical triangles of equal area, thereby forming a subdivided primary grid.

[0024] Among them, there are 4 first-order spherical triangles formed by the decomposition of the regular tetrahedron, 8 first-order spherical triangles formed by the decomposition of the regular octahedron, and 20 first-order spherical triangles formed by the decomposition of the regular icosahedron.

[0025] In this embodiment, a regular octahedron is used as an example for explanation. The longitude and latitude corresponding to the primary spherical triangle are as follows: Figure 1 As shown, eight first-order spherical triangles AH are formed (the vertex values ​​represent the longitude and latitude of the point respectively). The eight first-order spherical triangles are all of equal area and shape.

[0026] S3. Perform 6-aperture triangulation on each primary spherical triangle, connect the vertices and midpoints of the opposite sides of each primary spherical triangle respectively, form six secondary spherical triangles of equal area, and form a divided secondary grid.

[0027] like Figure 2 As shown in the figure, taking a primary spherical triangle as an example, the principle of 6-aperture triangulation is described. The primary spherical triangle ABC is equally divided into 6 secondary spherical triangles (ADG, ADE, BDG, BDF, CDE, CDF). Among them, points E, F, and G are the midpoints of the three sides of the spherical triangle ABC, respectively. The radius of the earth can be set to 6371.004 kilometers. Using the great circle algorithm, the coordinates of the center point D are calculated to be (45,35.264389682755). The spherical area of ​​the six secondary spherical triangles is 10626356.5082 square kilometers, forming a subdivided secondary grid.

[0028] S4. Perform 3-aperture triangulation on each secondary spherical triangle to form eighteen tertiary spherical triangles of equal area, thereby forming a divided tertiary grid.

[0029] In this embodiment, the above-mentioned 6 secondary spherical triangles (ADG, ADE, BDG, BDF, CDE, CDF) are further divided into 3-aperture triangulations to form 18 tertiary spherical triangles of equal area, forming a divided tertiary grid.

[0030] The spherical area of ​​each third-level spherical triangle is 3542118.8361 square kilometers. The coordinate points of the subdivision are calculated:

[0031] H(45,62.30671070011)、I(90,60.643405080365)、

[0032] J(90,26.50391945324), K(67.5,19.14412403714),

[0033] L(60.643405080365,0)、M(29.356594919635,0)、

[0034] N(22.5,19.14412403714), O(0,26.50391945324),

[0035] P(0,60.643405080365).

[0036] S5. Perform 3-aperture partitioning on each level 3 spherical triangle to form fifty-four level 4 spherical triangles of equal area, thereby forming a partitioned level 4 grid.

[0037] The spherical area of ​​each fourth-order spherical triangle is 1180706.2787 square kilometers. Taking triangles OBN and BMN as an example, the coordinates of the subdivision points are calculated as:

[0038] Q(13.22319977494,12.884455911948), R(0,14.702124214945), S(14.702124214945,0).

[0039] The ultimate result is an equal-area, multi-level, seamless grid system that can adapt to the entire world.

[0040] 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 and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for isosurface partitioning of three-aperture triangles based on the earth's spherical surface, characterized in that: The dissection method comprises the following steps: S1. Selecting a Platonic solid whose primary mesh is a regular triangle as a basic polyhedron for segmentation; the Platonic solid includes a regular tetrahedron, a regular octahedron and a regular icosahedron; S2. Align the vertices of the selected Platonic solid polyhedron to the longitude and latitude of the sphere to form a plurality of primary spherical triangles of equal area, thereby forming a subdivided primary grid; S3. Perform 6-aperture triangulation on each primary spherical triangle, connect the vertices and midpoints of the opposite sides of each primary spherical triangle, form multiple secondary spherical triangles of equal area, and form a divided secondary grid; S4. Perform 3-aperture triangulation on each secondary spherical triangle to form multiple tertiary spherical triangles of equal area to form a divided tertiary grid; S5. Perform 3-aperture triangulation on each level 3 spherical triangle to form multiple level 4 spherical triangles of equal area, thus forming a divided level 4 grid; continue to perform 3-aperture triangulation on the level 4 spherical triangle, and continue to perform 3-aperture triangulation step by step according to the grid usage requirements, so as to obtain an equal-area, multi-level, seamless grid system that can adapt to the whole world.

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