Concave-convex polygon zooming-in and zooming-out method and related equipment

Abstract

The invention discloses a method for magnifying and reducing a concave-convex polygon and related equipment, and the method comprises the steps: firstly arranging the vertexes of the concave-convex polygon according to a sequence, and then achieving the precise magnification and reduction of the geometric shape of the polygon through giving the magnification or reduction requirements and distance parameters of the polygon. The method comprises the following steps: firstly, calculating an angular bisector of a vertex of a polygon, then calculating a new vertex coordinate (the expanded vertex is selected on the angular bisector outside the polygon, and the shrunk vertex is selected on the angular bisector inside the polygon) according to an expanded or shrunk distance, and finally outputting the expanded or shrunk polygon. According to the method, the polygon is enlarged or shrunk by calculating the vertex coordinates of the new polygon, and the problem that a traditional polygon enlarging or shrinking method is not suitable for concave polygons is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of computer graphics and geometric transformation, and specifically relates to a method for enlarging and reducing concave-convex polygons and related equipment. Background Art

[0002] The application of polygon enlargement and reduction techniques is crucial in the field of technology, especially in computer graphics, geographic information systems (GIS), engineering drawing, image processing and 3D printing. The core requirement of these technologies is to achieve accurate scaling of polygons while maintaining their original shapes, attributes and features. Traditional polygon enlargement and reduction methods, such as polygon offset algorithms, stepwise simplification of polygon curves and polygon shrinking / expansion algorithms (Polygon Offset), although they have certain effects in specific applications, often have difficulty in balancing the accuracy and efficiency of transformation when dealing with complex or irregular polygons.

[0003] In computer-aided design (CAD) and geographic information systems (GIS), polygon offset algorithms enlarge or reduce polygons by creating parallel offsets on the edges of polygons. They are widely used in terrain data processing to simulate the effects of water flow or erosion on terrain boundaries. The method of progressive simplification of polygon curves simplifies complex polygonal shapes by reducing the number of vertices of the polygon while trying to maintain its appearance characteristics. This simplification technique can reduce the amount of data and improve the efficiency of image processing in the field of image processing, especially in large-scale image analysis and pattern recognition. The polygon shrink / expand algorithm achieves enlargement or reduction by uniformly increasing or decreasing the distance on one or both sides of the polygon. It is often used in graphics editing software to create shadow effects or simulate the expansion and contraction of objects.

[0004] The proportional scaling method based on the center of gravity of polygons calculates the geometric center of the polygon, i.e., the center of gravity, and then uses the center of gravity as the reference point to scale up or down proportionally. This method allows polygons to be scaled uniformly while maintaining the shape and proportion of the polygons, and is suitable for various application scenarios that require precise control of the size and shape of polygons. For example, in architectural design, this method can be used to adjust the spatial layout to adapt to different planning requirements; in image processing, it can be used to adjust the size of objects in the image for effective feature matching and object recognition.

[0005] However, existing technologies often have difficulty balancing the accuracy and efficiency of transformations when dealing with these challenges, especially when faced with large-scale data sets or real-time processing requirements. In addition, existing methods also have limitations in maintaining polygon shape features and attributes, which is particularly prominent in applications that require precise control of polygon geometry. For example, in high-precision engineering drawings, even small scaling errors can lead to inaccurate structural dimensions, affecting the quality and performance of the final product. In GIS, the scaling of terrain data needs to take into account the continuity and consistency of the terrain to ensure the accuracy and reliability of map data.

[0006] Therefore, although the existing polygon enlargement and reduction technologies have met the needs of different fields to a certain extent, they still need to be improved in terms of accuracy, efficiency and shape preservation. Especially when dealing with complex or irregular polygons, how to achieve fast, accurate and shape-preserving enlargement and reduction is still a hot issue in this field. Summary of the invention

[0007] The invention provides a method for enlarging and reducing a concave-convex polygon and related equipment, which solves the problems of poor accuracy and low efficiency of the existing polygon enlarging and reducing technologies.

[0008] To achieve the above object, the present invention provides the following technical solutions: A method for enlarging and reducing a concave-convex polygon, comprising: Arrange the vertices of the concave and convex polygons in order; Draw the angle bisector of each vertex of the concave-convex polygon, calculate the unit vector and angle of the angle bisector of each vertex of the concave-convex polygon, and determine the concave-convexity of the vertex angle of the concave-convex polygon; According to the need of expansion or reduction, based on the angle bisector unit vector and the included angle of each vertex, the distance between the edge of the new concave-convex polygon and the corresponding edge of the original concave-convex polygon, the position of the new vertex of the enlarged or reduced concave-convex polygon is calculated; Based on the concavity and convexity of the vertex angles of the concave-convex polygon, new vertices are calculated and judged, and the new vertices are connected to obtain an enlarged or reduced concave-convex polygon.

[0009] Preferably, when the concave-convex polygon is expanded, the vertex array that can be covered by the expanded polygon is calculated and output.

[0010] Preferably, the calculation and judgment of the new vertex is specifically as follows: If shrinking, the maximum distance of polygon shrinkage is considered in the calculation process , to ensure that after shrinking, the edges of the new polygon will not have any intersection points other than vertices, The calculation method is as follows:

[0011] Among them, LL represents the distance from vertex to vertex, the distance from vertex to edge, or the distance from edge to edge; If the enlargement is for a concave polygon, if the edges of the new polygon after the enlargement have intersection points other than vertices, then the intersection points are the vertices of the new polygon, and the vertices replace the vertices in the new polygon; if the edges of the new concave and convex polygon after the enlargement have only intersection points of vertices, then the intersection points after the enlargement are the vertices of the new concave and convex polygon; If enlarged, for a convex polygon, the enlarged intersection points are the vertices of the new polygon.

[0012] Preferably, the concave-convexity of the vertex angle of the concave-convex polygon is determined as follows: Calculate the vector product of the unit vector of each edge of the polygon and the two adjacent edges of each vertex. If the number of positive vector products is greater than the number of negative vector products, the vertex angle corresponding to the positive vector product is a convex angle, and the vertex angle corresponding to the negative vector product is a concave angle; if the number of negative vector products is greater than the number of positive vector products, the vertex angle corresponding to the positive vector product is a concave angle, and the vertex angle corresponding to the negative vector product is a convex angle.

[0013] Preferably, the method for calculating the angle bisector unit vector and the angle of each vertex of the concave-convex polygon is specifically as follows:

[0014]

[0015]

[0016] in, and are the unit vectors of the two adjacent edges of the vertex, is the unit vector of the angle bisector and points to and The side with the smaller angle, is the measure of the angle subtended by the vertex.

[0017] Preferably, the direction of calculating the vertex coordinates of the enlarged or reduced concave-convex polygon is: For the enlarged case, the convex corners are along The concave angle is calculated along the direction of Calculate the direction of For the reduced case, the convex corners are along The concave angle is calculated along the direction of Calculate the direction of .

[0018] Preferably, the vertices of the concave-convex polygon are arranged in a clockwise or counterclockwise order.

[0019] A system for enlarging and reducing concave-convex polygons, comprising: Arrangement module: used to arrange the vertices of concave and convex polygons in order; Calculation and judgment module: used to make the angle bisector of each vertex of the concave-convex polygon, calculate the unit vector and angle of the angle bisector of each vertex of the concave-convex polygon, and judge the concave-convexity of the vertex angle of the concave-convex polygon; Vertex acquisition module: used to calculate the position of the new vertex of the enlarged or reduced concave convex polygon based on the unit vector and angle of the angle bisector of each vertex, the distance between the new concave convex polygon edge and the corresponding edge of the original concave convex polygon according to the needs of enlargement or reduction; Connection module: Based on the concavity of the vertices of the concave-convex polygon, the new vertices are calculated and judged, and the new vertices are connected to obtain an enlarged or reduced concave-convex polygon.

[0020] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of a method for enlarging and reducing a concave-convex polygon are implemented.

[0021] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for enlarging and reducing a concave-convex polygon.

[0022] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for enlarging and reducing a concave-convex polygon, firstly arranging the vertices of the concave-convex polygon in order, and then realizing accurate enlarging and reducing the polygonal geometric shape by giving the requirements and distance parameters for enlarging or reducing the polygon. The method first calculates the angle bisector of the polygon vertex, and then calculates the new vertex coordinates according to the enlargement or reduction distance (the enlarged vertex is selected on the angle bisector outside the polygon, and the reduced vertex is selected on the angle bisector inside the polygon), and finally outputs the enlarged or reduced polygon. This method realizes the enlargement or reduction of the polygon by calculating the new polygon vertex coordinates, and solves the problem that the traditional polygon enlargement or reduction method is not applicable to concave polygons. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart of a method for enlarging and reducing a concave-convex polygon according to the present invention; Figure 2 The figure of the initial polygon in the embodiment; Figure 3 In the embodiment, the polygon expansion distance does not exceed Graphics; Figure 4In the embodiment, the polygon is enlarged by a distance exceeding Graphics; Figure 5 The figures in the embodiments are within the allowable reduction range; Figure 6 This is a system block diagram of the present invention for enlarging and reducing concave-convex polygons. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0025] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0027] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0028] like Figure 1 As shown, the present invention provides a method for enlarging and reducing a concave-convex polygon, comprising: S101 arranges the vertices of the concave and convex polygons in order; S102: making the angle bisector of each vertex of the concave-convex polygon, calculating the unit vector and the angle of the angle bisector of each vertex of the concave-convex polygon, and determining the concave-convexity of the vertex angle of the concave-convex polygon; S103, according to the need of enlargement or reduction, based on the angle bisector unit vector and the included angle of each vertex, and the distance between the edge of the new concave-convex polygon and the corresponding edge of the original concave-convex polygon, calculate the position of the new vertex of the enlarged or reduced concave-convex polygon; S104 calculates and determines new vertices based on the concavity and convexity of the vertex angles of the concave-convex polygon, connects the new vertices, and obtains an enlarged or reduced concave-convex polygon.

[0029] The vertex coordinates of the input polygon include the following characteristics: The vertex coordinate array is a two-dimensional array, where each row represents the x and y coordinates of a vertex. Vertex coordinates are arranged in clockwise or counterclockwise order.

[0030] Select the direction to expand or reduce: If it is reduced, the maximum value of the polygon reduction distance d is considered in the calculation process , ensuring that after shrinking, the edges of the new polygon will not have any intersection points other than vertices. The calculation method is as follows:

[0031] Among them, LL represents the distance from vertex to vertex, the distance from vertex to edge (except when the vertex and edge are adjacent), and the distance from edge to edge (except when the edges are adjacent).

[0032] If the edge of the new polygon is enlarged, for a concave polygon, if there are intersection points other than vertices on the edges of the new polygon after the enlargement, then the intersection points are the vertices of the new polygon, and the vertices replace the vertices in the new polygon; if the edge of the new polygon is enlarged, the only intersection points are the vertices of the new polygon, and the intersection points after the enlargement are the vertices of the new polygon; If enlarged, for a convex polygon, the enlarged intersection points are the vertices of the new polygon.

[0033] The specific method for determining the convexity of the polygon's corners is as follows: By calculating the vector product of the unit vector of each edge of the polygon and the two adjacent edges of each vertex, the vector products of the adjacent edge vectors of each vertex are positive or negative. If the number of positive vector products is greater than the number of negative vector products, the vertex angle corresponding to the positive vector product is a convex angle, and the vertex angle corresponding to the negative vector product is a concave angle; if the number of negative vector products is greater than the number of positive vector products, the vertex angle corresponding to the positive vector product is a concave angle, and the vertex angle corresponding to the negative vector product is a convex angle.

[0034] The distance to expand or shrink is as follows: Set a parameter d that represents the distance between the enlarged or reduced polygon and the original polygon. If d is less than zero, the enlargement operation is converted to a reduction operation, and vice versa. Calculate the angle bisector unit vector and angle of each vertex of the polygon as follows:

[0035]

[0036]

[0037] in, and are the unit vectors of the two adjacent edges of the vertex, is the unit vector of the angle bisector and points to and The side with the smaller angle, is the measure of the angle subtended by the vertex.

[0038] The specific method for calculating the vertex coordinates after expansion or reduction is as follows: For the enlarged case, the convex corners are along The concave angle is calculated along the direction of calculate.

[0039] For the reduced case, the convex corners are along The concave angle is calculated along the direction of calculate.

[0040] Example 1 An embodiment of the present invention provides a method for enlarging and reducing a concave-convex polygon based on an angle bisector method, the method comprising the following steps: Arrange the vertices of the polygon in clockwise or counterclockwise order; Draw the angle bisector of each vertex of the polygon, which exists both inside and outside the polygon; Determine the convexity of the corners of a polygon: Calculate the angle bisector unit vector and angle of each vertex of the polygon; According to the need for expansion or reduction and the distance between the edge of the new polygon and the corresponding edge of the original polygon, the position of the new vertex corresponding to the expanded or reduced polygon is calculated; Connect the new vertices to get the enlarged or reduced concave and convex polygons If enlarged, calculate and output the vertex array that the enlarged polygon can cover.

[0041] Example 2 The scheme in Example 1 is further introduced below in combination with specific calculation formulas and examples, as described below for details: If it is enlarged, for a concave polygon, the edges of the new polygon after enlargement will not have any intersection points other than vertices, such as Figure 3 As shown; The method for determining the concavity and convexity of the corner of a polygon described in Example 1 is as follows: By calculating the vector product of the unit vector of each edge of the polygon and the two adjacent edges of each vertex, the vector products of the adjacent edge vectors of each vertex are either positive or negative. If the number of positive vector products is greater than the number of negative vector products, the vertex angle corresponding to the positive vector product is a convex angle, and the vertex angle corresponding to the negative vector product is a concave angle. Conversely, if the number of positive vector products is less than the number of negative vector products, the vertex angle corresponding to the positive vector product is a concave angle, and the vertex angle corresponding to the negative vector product is a convex angle.

[0042] Furthermore, the calculation of the angle bisector unit vector and the angle of each vertex of the polygon is specifically as follows:

[0043]

[0044]

[0045] in: and are the unit vectors of the two adjacent edges of the vertex, is the unit vector of the angle bisector and points to and The side with the smaller angle, is the measure of the angle subtended by the vertex.

[0046] Furthermore, the expanded vertex coordinates are calculated as follows: For the enlarged case, the convex corners are along The concave angle is calculated along the direction of calculate.

[0047] Example 3 If it is enlarged, for a concave polygon, the edges of the new polygon will have intersection points other than vertices after the expansion. At this time, the intersection points are the vertices of the new polygon, which replace the vertices in the new polygon, such as Figure 4 As shown; The expanded vertex coordinates are calculated as follows: The convex corner along The concave angle is calculated along the direction of calculate.

[0048] Example 4 If the polygon is reduced, the maximum value of the polygon reduction distance d is considered in the calculation process , to ensure that after shrinking, the edges of the new polygon will not have any intersection points other than vertices, such as Figure 5 As shown; The calculation method is:

[0049] Among them: LL represents the distance from vertex to vertex, the distance from vertex to edge (except when vertices and edges are adjacent), and the distance from edge to edge (except when adjacent edges); Furthermore, the reduced vertex coordinates are calculated as follows: When shrinking, the convex corners are along The concave angle is calculated along the direction of calculate.

[0050] like Figure 6 As shown, the present invention also provides a system for magnifying and reducing concave-convex polygons, comprising: Arrangement module: used to arrange the vertices of concave and convex polygons in order; Calculation and judgment module: used to make the angle bisector of each vertex of the concave-convex polygon, calculate the unit vector and angle of the angle bisector of each vertex of the concave-convex polygon, and judge the concave-convexity of the vertex angle of the concave-convex polygon; Vertex acquisition module: used to calculate the position of the new vertex of the enlarged or reduced concave convex polygon based on the unit vector and angle of the angle bisector of each vertex, the distance between the new concave convex polygon edge and the corresponding edge of the original concave convex polygon according to the needs of enlargement or reduction; Connection module: Based on the concavity of the vertices of the concave-convex polygon, new vertices are calculated and judged, and the new vertices are connected to obtain an enlarged or reduced concave-convex polygon.

[0051] A terminal device is provided in one embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of the modules / units in the above-mentioned device embodiments are implemented.

[0052] The computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to accomplish the present invention.

[0053] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0054] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0055] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0056] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by the processor, the steps of the above-mentioned various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0057] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive. Under the guidance of the specification, a person skilled in the art can also make many forms without departing from the scope of protection of the claims of the present invention, all of which belong to the scope of protection of the present invention.

Claims

1. A method for enlarging and reducing a concave-convex polygon, characterized in that: include: Arrange the vertices of the concave and convex polygons in order; Draw the angle bisector of each vertex of the concave-convex polygon, calculate the unit vector and angle of the angle bisector of each vertex of the concave-convex polygon, and determine the concave-convexity of the vertex angle of the concave-convex polygon; According to the need of expansion or reduction, based on the angle bisector unit vector and the included angle of each vertex, the distance between the edge of the new concave-convex polygon and the corresponding edge of the original concave-convex polygon, the position of the new vertex of the enlarged or reduced concave-convex polygon is calculated; Based on the concavity and convexity of the vertex angles of the concave-convex polygon, new vertices are calculated and judged, and the new vertices are connected to obtain an enlarged or reduced concave-convex polygon.

2. A method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: When the concave-convex polygon is expanded, the vertex array that can be covered by the expanded polygon is calculated and output.

3. The method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: The calculation and judgment of the new vertex are as follows: If shrinking, the maximum distance of polygon shrinkage is considered in the calculation process , to ensure that after shrinking, the edges of the new polygon will not have any intersection points other than vertices, The calculation method is as follows: Among them, LL represents the distance from vertex to vertex, the distance from vertex to edge, or the distance from edge to edge; If the enlargement is for a concave polygon, if the edges of the new polygon after the enlargement have intersection points other than vertices, then the intersection points are the vertices of the new polygon, and the vertices replace the vertices in the new polygon; if the edges of the new concave and convex polygon after the enlargement have only intersection points of vertices, then the intersection points after the enlargement are the vertices of the new concave and convex polygon; If enlarged, for a convex polygon, the enlarged intersection points are the vertices of the new polygon.

4. The method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: The specific method for judging the concave-convexity of the vertex angle of a concave-convex polygon is: Calculate the vector product of the unit vector of each edge of the polygon and the two adjacent edges of each vertex. If the number of positive vector products is greater than the number of negative vector products, the vertex angle corresponding to the positive vector product is a convex angle, and the vertex angle corresponding to the negative vector product is a concave angle; if the number of negative vector products is greater than the number of positive vector products, the vertex angle corresponding to the positive vector product is a concave angle, and the vertex angle corresponding to the negative vector product is a convex angle.

5. The method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: The method for calculating the angle bisector unit vector and angle of each vertex of a concave or convex polygon is as follows: in, and are the unit vectors of the two adjacent edges of the vertex, is the unit vector of the angle bisector and points to and The side with the smaller angle, is the measure of the angle subtended by the vertex.

6. The method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: The vertex coordinates of the enlarged or reduced concave and convex polygon are calculated in the following direction: For the enlarged case, the convex corners are along The concave angle is calculated along the direction of Calculate the direction of For the reduced case, the convex corners are along The concave angle is calculated along the direction of Calculate the direction of .

7. The method for enlarging and reducing a concave-convex polygon according to claim 1, characterized in that: The vertices of the concave and convex polygons are arranged in clockwise or counterclockwise order.

8. A system for enlarging and reducing concave and convex polygons, characterized in that: include: Arrangement module: used to arrange the vertices of concave and convex polygons in order; Calculation and judgment module: used to make the angle bisector of each vertex of the concave-convex polygon, calculate the unit vector and angle of the angle bisector of each vertex of the concave-convex polygon, and judge the concave-convexity of the vertex angle of the concave-convex polygon; Vertex acquisition module: used to calculate the position of the new vertex of the enlarged or reduced concave convex polygon based on the unit vector and angle of the angle bisector of each vertex, the distance between the new concave convex polygon edge and the corresponding edge of the original concave convex polygon according to the needs of enlargement or reduction; Connection module: Based on the concavity of the vertices of the concave-convex polygon, the new vertices are calculated and judged, and the new vertices are connected to obtain an enlarged or reduced concave-convex polygon.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for enlarging and reducing a concave-convex polygon as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for enlarging and reducing a concave-convex polygon as claimed in any one of claims 1 to 7 are implemented.

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