Three-dimensional to two-dimensional coding and decoding method and drawing method for lossless dimension reduction and high-fidelity restoration

Abstract

The invention discloses a three-dimensional to two-dimensional dimension reduction coding and decoding method for lossless dimension reduction and high-fidelity restoration, which comprises the following steps of: mapping any point P in a three-dimensional space to a two-dimensional projection plane through one-time T parallel projection, and calculating to obtain coordinates of the point on the two-dimensional projection plane to finish three-dimensional to two-dimensional dimension reduction coding. Key depth information of an original three-dimensional space is implied in the two-dimensional coordinates, efficient compression and reservation of information are achieved, and lossless dimension reduction transformation from three dimensions to two dimensions can be achieved; in the decoding process, two-dimensional coordinates and projection parameters corresponding to the two-dimensional coordinates are read, an equation set with target three-dimensional point coordinates (X, Y and Z) as unknown numbers is constructed according to the mapping function relation to be solved, high-fidelity and reversible restoration from P'to P are achieved, the complex space relation can be clearly expressed in an unambiguous mode, good universality and robustness are achieved, and the method can be widely applied to the field of decoding. And compact storage, efficient transmission and accurate reconstruction of three-dimensional data are facilitated. The invention further discloses a drawing method, a computer storage medium and a drawing device.

Description

Technical Field

[0001] This invention relates to computer graphics and image processing technology, and in particular to a lossless dimensionality reduction and high-fidelity restoration method for three-dimensional to two-dimensional encoding and decoding, a drawing method, a computer storage medium, and a drawing device. Background Technology

[0002] Existing 3D to 2D dimensionality reduction coding methods mainly include: Monge descriptive geometry: As the foundation of engineering graphics, it has inherent limitations in expressing complex spatial relationships (such as a cube inscribed in a sphere). It is difficult to determine the spatial position of all points unambiguously in a single projection drawing, resulting in information loss and ambiguity.

[0003] Axonometric projection (such as isometric and oblique projection): Although widely used, this method is essentially a "lossy" projection. Its two-dimensional projection results cannot achieve a unique and accurate reconstruction of the original three-dimensional model, and it is difficult to accurately represent the spatial structure of complex inscribed / circumscribed geometries, making it impossible to draw a visual representation of an inscribed cube. The "inscribed cube" expressed by "isometric projection + oblique projection" is as follows: Figure 1 As shown, since isometric projection and oblique projection are two fundamentally different projection methods, forcibly merging them will lead to conceptual confusion and geometric distortion of several key elements such as line of sight, projection line, and projection plane.

[0004] 3D data compression and representation methods: Current mainstream technologies focus on storage efficiency and visual approximation, but fail to establish a reversible and unambiguous mapping relationship between 2D representation and 3D model in mathematics. Summary of the Invention

[0005] The technical problem to be solved by this invention is to express complex spatial relationships clearly and unambiguously, with good universality and robustness, which is conducive to compact storage, efficient transmission and accurate reconstruction of three-dimensional data.

[0006] To address the aforementioned technical problems, this invention provides a three-dimensional to two-dimensional encoding and decoding method, the encoding of which includes the following steps: S21. For any point in three-dimensional space The first set of parallel projection lines maps it onto a two-dimensional projection plane; In this system, the origin O is located at the center of the sphere, the x-axis and y-axis are located in a plane passing through the center of the sphere, and the projection plane is the normal plane passing through the center of the sphere and perpendicular to the first set of parallel projection lines. The acute angle between the direction vector of the parallel projection line and the XOY coordinate plane; The projection direction of the first set of parallel projection lines is the first-order T parallel projection direction, and the acute angle between it and the x-axis is . The angle between the x-axis and the y-axis is 90°, and the angle between the x-axis and the z-axis is... ; S22. Calculate any point Coordinates on the two-dimensional projection plane This completes the dimensionality reduction encoding from three dimensions to two dimensions; ; Its decoding includes the following steps: S31. Construct a quadratic T-parallel projection. ; when ,when , The acute angle between the direction of the second parallel projection and the XOY plane, and ; S32. Solve the system of linear equations to decode and obtain any point in three-dimensional space. ; ; .

[0007] Better .

[0008] To solve the above-mentioned technical problems, the present invention provides a drawing method based on the three-dimensional to two-dimensional encoding and decoding method, wherein the drawn shapes include spheres and regular polyhedra; The sphere is inscribed within the regular polyhedron, or all vertices of the regular polyhedron lie on the surface of the sphere; the initial side view angle of the regular polyhedron is 0°; the drawing method includes the following steps: S11. In a plane parallel to the XOY coordinate plane, the coordinates of a regular polyhedron expressed in complex form, or the point of tangency between the regular polyhedron and the sphere, are multiplied by a modulus of 1, with the complex angle being the angle of observation from the side of rotation. The complex number, while keeping the ordinate unchanged, enables the rotation operation of the vertices or tangents of a regular polyhedron in three-dimensional space; S12. The three-dimensional to two-dimensional encoding and decoding method encodes the vertices or tangent points of the regular polyhedron after rotation to obtain the viewing angle of the rotated side. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane; S13. Draw a sphere in a two-dimensional plane, and observe it from the perspective of rotating the side view. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane are connected by solid or dashed lines according to spatial relationships in the two-dimensional plane. The sphere and regular polyhedron are then drawn after rotation in the two-dimensional plane.

[0009] Preferably, the regular polyhedron is a cube; The three-dimensional coordinates of the center of the sphere are (0,0,0). The cube has an edge length of 2a, and its eight vertices have the following three-dimensional coordinates: , , , , , , , .

[0010] Preferably, the sphere is the Earth's surface, abstracted as an ideal sphere.

[0011] To solve the above-mentioned technical problems, the present invention provides a computer storage medium storing a computer program, which, when executed by a processor, implements the drawing method described above.

[0012] To solve the above-mentioned technical problems, the present invention provides a drawing device, which includes a processor and the computer storage medium; The processor, according to user settings , The graphic size control parameter a controls the execution of the computer program stored in the computer storage medium as described in claim 6, and outputs the graphic of the regular polyhedron drawn inside the sphere to the display or printer.

[0013] The 3D-to-2D dimensionality reduction encoding and decoding method of this invention maps any point P(X,Y,Z) in 3D space to a 2D projection plane through a set of parallel projection lines (first-order T-parallel projection), and calculates the coordinates P'(u1,v1) of point P on the 2D projection plane, thus completing the 3D-to-2D dimensionality reduction encoding. This 2D coordinate implicitly contains key depth information from the original 3D space, achieving efficient information compression and preservation. It enables lossless dimensionality reduction transformation from 3D to 2D and high-fidelity, reversible restoration from 2D to 3D, effectively solving the fundamental problem of irreversible loss of geometric information in traditional projection techniques. During the decoding process, the 2D coordinates P'(u1,v1) and their corresponding projection parameters (including α, etc.) are read. Based on the mapping function relationship, a 3D point coordinate (u1,v1) is constructed. X,Y,Z The system of equations with unknowns ( ) has a unique solution in all cases except for a few singularities (such as coincident projection lines), since the two-dimensional point coordinates obtained through parallel projection of T already contain the complete geometric constraints required to reconstruct the three-dimensional position. This allows for the realization of... P' arrive PThe method offers high-fidelity and reversible reconstruction. This 3D-to-2D dimensionality reduction encoding and decoding method can clearly and unambiguously express complex spatial relationships (such as a polyhedron inscribed in a sphere and a sphere inscribed in a polyhedron). It has good universality and robustness, and is conducive to the compact storage, efficient transmission and accurate reconstruction of 3D data, opening up new technical paths for basic education, scientific computing and engineering applications. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0015] Figure 1 This is a schematic diagram of an inscribed cube of a sphere expressed by existing isometric projection and oblique diopter projection. Figure 2 This is a schematic diagram of a T-parallel projection of an embodiment of the three-dimensional to two-dimensional encoding and decoding method of the present invention; Figure 3 This is a schematic diagram of two T-parallel projections onto a sphere, representing an embodiment of the three-dimensional to two-dimensional encoding and decoding method of the present invention. Figure 4 This is a schematic diagram of drawing an inscribed regular polyhedron within a sphere, according to an embodiment of the drawing method of the present invention. Figures 5a to 5f It is a drawing of a sphere-inscribed Pareto solid diagram or a sphere-circumscribed Pareto solid diagram drawn by the drawing device of the present invention; Figure 6a It is a graphic of the Earth and latitude and longitude lines drawn using the three-dimensional to two-dimensional encoding and decoding method of the present invention; Figure 6b It is a graphic representation of the minor arc path planning of a great circle between any two points on the surface of a sphere, drawn using the three-dimensional to two-dimensional encoding and decoding method of this invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The terms "first," "second," and similar words used in this application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Words such as "including" or "comprising" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," "right," "front," and "back" are used only to indicate relative positional relationships; these relative positional relationships may change accordingly when the absolute position of the described object changes.

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0019] Example 1: A lossless dimensionality reduction and high-fidelity restoration method for 3D to 2D encoding and decoding, the encoding of which includes the following steps: S21. For any point in three-dimensional space The first set of parallel projection lines maps it onto a two-dimensional projection plane; In this system, the origin O is located at the center of the sphere, the x-axis and y-axis are located in a plane passing through the center of the sphere, and the projection plane is the normal plane passing through the center of the sphere and perpendicular to the first set of parallel projection lines. The acute angle between the direction vector of the parallel projection line and the XOY coordinate plane; like Figure 2 As shown, the projection direction of the first set of parallel projection lines is the first-order T parallel projection direction, and the acute angle between it and the x-axis is . The angle between the x-axis and the y-axis is 90°, and the angle between the x-axis and the z-axis is... ; S22. Calculate any point Coordinates on the two-dimensional projection plane This completes the dimensionality reduction encoding from three dimensions to two dimensions; (Formula 1); Its decoding includes the following steps: S31. Construct a quadratic T-parallel projection. (Formula 2); when ,when , The acute angle between the direction of the second parallel projection and the XOY plane. ; S32. Solve the system of linear equations to decode and obtain any point in three-dimensional space. ; (Formula 3); .

[0020] Better .

[0021] In the projection transformation from three dimensions to two dimensions, a point Two-dimensional coordinates are obtained after encoding. It satisfies mathematical equation one, therefore it can be seen that... It includes The coupling information. However, a single projection cannot uniquely determine this. Additional constraints need to be introduced. Therefore, a quadratic T-parallel projection is constructed, using a new projection angle. To obtain new two-dimensional coordinates As can be seen from Equation 2, Also includes Information.

[0022] In Formula 3, It is known in the first dimensionality reduction, It can be calculated using preset rules; obviously, ) is a solution to this system of equations, so the solution to the system of equations in equation three exists.

[0023] The determinant of the coefficient row of this system of equations is:

[0024] because Therefore Therefore, the system of equations has a unique solution.

[0025] Further calculations:

[0026]

[0027] ;

[0028]

[0029] ; thereby, .

[0030] During the calculation, The design effectively avoids DThe singularity of =0 ensures the stability and numerical robustness of the solution. During the dynamic change of the parallel projection direction, the normal plane passing through the center of the sphere is adjusted synchronously, ensuring that the three-dimensional origin (0,0,0) always corresponds to the two-dimensional origin (0,0). Y The axis corresponds to a two-dimensional horizontal u The contour circle intercepted by the axis and normal plane has a constant size, providing a stable reference datum for compressing the three-dimensional structure into a two-dimensional plane. Other information is efficiently encoded within it, becoming an important data resource for high-fidelity reconstruction.

[0031] like Figure 3 As shown, in two parallel projections of T, the two projection planes correspond to the normal planes passing through the center of the sphere under the projection direction. The two projections have the following characteristics: ① The origins coincide; ② u Axis coincidence ( u 1= Y 0, u 2= Y 0); ③ The size of the outline circle obtained by intersecting the sphere on the projection plane remains unchanged; ④ Due to the anchoring effect of the outline circle, v The axial direction can also be considered as "overlapping".

[0032] from Figure 3 The comparison between the "3D coordinates / T-parallel projection 3D coordinates" shown indicates that in the T-parallel projection system, the line of sight and the parallel projection line are at the same height and are both parallel to the plane. XOZ The coordinate plane possesses the characteristic of an omniscient perspective. Further analysis of the correspondence between the 3D coordinates of the T-parallel projection and the 2D coordinates on the projection plane reveals a high degree of consistency in the observational experience, satisfying the need for refined visual intuition. Therefore, in lossless dimensionality reduction encoding from 3D to 2D, the core task is to perform dimensionality reduction encoding on any point in space (…). X, Y, Z Solve for its corresponding two-dimensional points (). u,v Because in the T-parallel projection, X The axial expansion coefficient of the shaft is " " Y The axis is "1". Z The axis is " Therefore, as long as the transformation relationship is satisfied: , (The negative sign "-" in the formula is due to the fact that the direction of the vertical axis of the computer screen coordinate system is opposite to the traditional convention), thus realizing that "the three-dimensional origin corresponds to the two-dimensional origin, and the three-dimensional horizontal axis..." Y The axis corresponds to the two-dimensional horizontal axis u Axis, any three-dimensional P Points are compressed into corresponding two-dimensional points. P' The goal is to achieve a "lossless" transformation from three dimensions to two dimensions (excluding points on the same projection line). This dimensionality reduction process is explicit, achieved by... , X , Z A clever combination "flattens" the information onto the normal plane of the projection lines, mapping the 3D origin to the 2D origin, and the 3D... Y Axis and Two-Dimensional u Since the axes are perfectly aligned and the projection plane is the normal plane of the projection line passing through the center of the sphere, the size of the outline circle intercepted by the sphere remains unchanged, playing a crucial anchoring role in the intuitive diagram. No positional shift or structural distortion occurs during the entire transformation process. Geometric elements on the same projection line may overlap on the projection plane, causing a temporary obscuration of depth information. This can be addressed by using variations in line thickness, density, or color intensity to visually differentiate and compensate for the loss of depth.

[0033] The 3D to 2D dimensionality reduction encoding and decoding method in Example 1, for any point in 3D space The coordinates of point P on the two-dimensional projection plane are calculated by mapping a point P onto a two-dimensional projection plane using a set of parallel projection lines (first-order T-parallel projection). This method completes dimensionality reduction encoding from 3D to 2D. The 2D coordinates implicitly contain key depth information from the original 3D space, achieving efficient information compression and preservation. It enables lossless dimensionality reduction transformation from 3D to 2D and high-fidelity, reversible restoration from 2D to 3D, effectively solving the fundamental problem of irreversible loss of geometric information in traditional projection techniques. During decoding, the 2D coordinates are read... and its corresponding projection parameters (including) (etc.), based on the mapping function relationship, construct the target three-dimensional point coordinates ( X,Y,Z The system of equations with unknowns ( ) has a unique solution in all cases except for a few singularities (such as coincident projection lines), since the two-dimensional point coordinates obtained through parallel projection of T already contain the complete geometric constraints required to reconstruct the three-dimensional position. This allows for the realization of... P' arrive P High fidelity, reversible restoration.

[0034] The 3D-to-2D dimensionality reduction encoding and decoding method in Example 1 has significant implications for reshaping spatial cognition and decision-making efficiency, and can be used to draw graphics including spheres and regular polyhedra (e.g. Figures 5a to 5f As shown), and to draw diagrams of combinations of spheres and other complex geometric shapes (such as...). Figure 6a , Figure 6b ).

[0035] This 3D-to-2D dimensionality reduction encoding and decoding method can clearly and unambiguously express complex spatial relationships (such as a polyhedron inscribed in a sphere or a sphere inscribed in a polyhedron). It possesses good universality and robustness, facilitating compact storage, efficient transmission, and accurate reconstruction of 3D data, thus opening new technological pathways for basic education, scientific computing, and engineering applications. In basic education, its adjustable parameter system can generate intuitive diagrams with a single click according to teaching needs, quickly achieving a unity of "intuitive" and "realistic" understanding, helping students build a scientific spatial cognitive system. In scientific computing, its lossless characteristics provide an efficient solution for processing complex 3D models. In engineering design, it helps improve the accuracy of 3D modeling and analysis. In virtual reality and augmented reality technologies, it can provide more realistic and intuitive visual presentation effects for virtual scene construction, providing new underlying technological support for next-generation navigation and guidance (such as real-time dynamic path planning), 3D data compression and network transmission (such as digital twins and metaverses), and computer vision (such as 3D reconstruction).

[0036] Example 2: A drawing method based on the lossless dimensionality reduction and high-fidelity restoration of the 3D to 2D encoding and decoding method in Example 1, wherein the drawn shapes include spheres and regular polyhedra; The sphere is inscribed within the regular polyhedron, or all vertices of the regular polyhedron lie on the surface of the sphere; the initial side view angle of the regular polyhedron is 0°; the drawing method includes the following steps: S11. In a plane parallel to the XOY coordinate plane, the coordinates of a regular polyhedron expressed in complex form, or the point of tangency between the regular polyhedron and the sphere, are multiplied by a modulus of 1, with the complex angle being the angle of observation from the side of rotation. The complex number, while keeping the ordinate unchanged, enables the rotation operation of the vertices or tangents of a regular polyhedron in three-dimensional space; S12. The lossless dimensionality reduction and high-fidelity restoration 3D-to-2D encoding and decoding method encodes the vertices or tangent points of the regular polyhedron after rotation to obtain the viewing angle of the rotated side. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane; S13. Draw a sphere in a two-dimensional plane, and observe it from the perspective of rotating the side view. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane are connected by solid or dashed lines according to spatial relationships in the two-dimensional plane. The sphere and regular polyhedron are then drawn after rotation in the two-dimensional plane.

[0037] The drawing method in Example 2 involves multiplying the coordinates of a point (represented as a complex number) by a modulus of 1 and a complex angle of 1 within the projection plane. By using complex numbers while keeping the ordinate unchanged, rotation of points in three-dimensional space can be achieved. Mapping the vertices of a regular polyhedron or the points of tangency between the polyhedron and a sphere to a two-dimensional projection plane, and connecting them with solid or dashed lines according to spatial relationships, allows for a unified representation of the regular polyhedron and the sphere under a unified projection system. If the regular polyhedron is viewed from the side angle... The visual representation is poor when the angle is 0°. However, by rotating the regular polyhedron, we can draw the sphere and the sphere in a two-dimensional plane after the regular polyhedron has been rotated. This will provide a more visually appealing 2D plane representation of the sphere and the regular polyhedron.

[0038] Example 3: Based on the drawing method of Example 2, the regular polyhedron is a cube; The three-dimensional coordinates of the center of the sphere are (0,0,0). The cube has an edge length of 2a, and its eight vertices have the following three-dimensional coordinates: , , , , , , , .

[0039] Assume the coordinates of the eight vertices of the cube are: , , , , , , , ; Rotation angle of complex form around the origin (center point) : ; ; / / The vertical axis remains unchanged. ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged ; ; / / The ordinate remains unchanged Mapped to two-dimensional coordinates: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; .

[0040] Preferably, the sphere is the Earth's surface, which is abstracted as an ideal sphere.

[0041] The drawing method in Example 3 involves drawing a regular polyhedron shape inside a sphere, as shown below. Figure 4As shown (α=15°, β=20°, a is the graphic size control parameter), the spatial relationship between the regular polyhedron and the sphere can be clearly expressed.

[0042] Example 4: A computer storage medium storing a computer program that, when executed by a processor, implements the drawing method of Example 2 or 3.

[0043] Preferably, a graphics device includes a processor and the computer storage medium; The processor, based on the user-defined α, β and graphic size control parameter a, controls the execution of the computer program stored in the computer storage medium, and outputs the graphic of a regular polyhedron drawn inside the sphere to a display or printer.

[0044] In lossless dimensionality reduction encoding of 3D models based on T-parallel projection, the core is to encode any point in space ( X, Y, Z Mapped to two-dimensional points ( u,v Therefore, by simply inputting the graphic size control parameter 'a', the angle α between the viewing direction and the equatorial plane of the reference sphere, and the side viewing angle 'β', the drawing device can generate a visual diagram with a single click. This drawing device only requires inputting three parameters—graphic size control parameter 'a', the angle α between the viewing direction and the equatorial plane of the reference sphere, and the side viewing angle 'β'—to generate a high-quality visual diagram with a single click.

[0045] Figure 5a Figure 5f shows a variety of typical geometric structures generated by lossless dimensionality reduction transformation, including inscribed spheres in polyhedra (e.g., inscribed spheres in cubes) and inscribed polyhedra (e.g., inscribed tetrahedrons, inscribed cubes, inscribed octahedrons, inscribed dodecahedrons, and inscribed icosahedrons), which fully demonstrates its versatility and expressive power.

[0046] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A lossless dimensionality reduction and high-fidelity restoration method for 3D to 2D encoding and decoding, characterized in that, Its encoding includes the following steps: S21. For any point in three-dimensional space The first set of parallel projection lines maps it onto a two-dimensional projection plane; In this system, the origin O is located at the center of the sphere, the x-axis and y-axis are located in a plane passing through the center of the sphere, and the projection plane is the normal plane passing through the center of the sphere and perpendicular to the first set of parallel projection lines. The acute angle between the direction vector of the parallel projection line and the XOY coordinate plane; The projection direction of the first set of parallel projection lines is the first-order T parallel projection direction, and the acute angle between it and the x-axis is . The angle between the x-axis and the y-axis is 90°, and the angle between the x-axis and the z-axis is... ; S22. Calculate any point Coordinates on the two-dimensional projection plane This completes the dimensionality reduction encoding from three dimensions to two dimensions; ； Its decoding includes the following steps: S31. Construct a quadratic T-parallel projection. ； when ,when , The acute angle between the direction of the second parallel projection and the XOY plane. ; S32. Solve the system of linear equations to decode and obtain any point in three-dimensional space. ; ； 。 2. The lossless and high-fidelity restoration method for three-dimensional to two-dimensional encoding and decoding according to claim 1, characterized in that, 。 3. A drawing method based on the lossless dimensionality reduction and high-fidelity restoration 3D-to-2D encoding and decoding method described in claim 1, characterized in that, The figures drawn include spheres and regular polyhedra; The sphere is inscribed within the regular polyhedron, or all vertices of the regular polyhedron lie on the surface of the sphere; the initial side view angle of the regular polyhedron is 0°; the drawing method includes the following steps: S11. In a plane parallel to the XOY coordinate plane, the coordinates of a regular polyhedron expressed in complex form, or the point of tangency between the regular polyhedron and the sphere, are multiplied by a modulus of 1, with the complex angle being the angle of observation from the side of rotation. The complex number, while keeping the ordinate unchanged, enables the rotation operation of the vertices or tangents of a regular polyhedron in three-dimensional space; S12. The lossless dimensionality reduction and high-fidelity restoration 3D-to-2D encoding and decoding method encodes the vertices or tangent points of the regular polyhedron after rotation to obtain the viewing angle of the rotated side. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane; S13. Draw a sphere in a two-dimensional plane, and observe it from the perspective of rotating the side view. The coordinates of the vertices or tangent points of a regular polyhedron in a two-dimensional plane are connected by solid or dashed lines according to spatial relationships in the two-dimensional plane. The sphere and regular polyhedron are then drawn after rotation in the two-dimensional plane.

4. The drawing method according to claim 3, characterized in that, The regular polyhedron is a cube; The three-dimensional coordinates of the center of the sphere are (0,0,0). The cube has an edge length of 2a, and its eight vertices have the following three-dimensional coordinates: 、 、 、 、 、 、 、 。 5. The drawing method according to claim 3 or 4, characterized in that, The sphere in question is the Earth's surface, abstracted as an ideal sphere.

6. A computer storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the drawing method described in claim 3 or 4.

7. A drawing device, characterized in that, Includes the processor and the computer storage medium; The processor, according to the user-defined settings... , The graphic size control parameter a controls the execution of the computer program stored in the computer storage medium as described in claim 6, and outputs the graphic of the regular polyhedron drawn inside the sphere to the display or printer.

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