An irregular region cluster uniform distribution solving method based on force diffusion

Abstract

The present application relates to a kind of based on the even distribution solution method of irregular area cluster of force diffusion, based on force model, the number of certain equipment given constitutes cluster, deployment in irregular area on spherical surface, require deployment position as far as possible even, give the even distribution solution method.In the solution method, it is required that irregular area is single connected, when initialization, the point of given number is randomly generated in area, let point spread to even distribution by repulsion diffusion model, when point touches the boundary of area, then slide, at the corner of area, then stationary.This method can also be extended from spherical surface to three-dimensional and above space, be applied to the solution of unstructured grid division and generation, detection, exploration, limited coverage and other problems.

Description

Technical Field

[0001] This invention relates to a solution method for uniform distribution of irregular region clusters based on force diffusion, belonging to the field of intelligent technology for aerospace equipment modeling. Background Technology

[0002] Driven by the flexible and ever-changing requirements of missions and the irregular nature of environments, industries need the ability to uniformly fill a given environment with a particular piece of equipment. With the increasing application of artificial intelligence in aerospace equipment design and simulation, a method for uniformly distributing irregularly clustered areas based on force diffusion can meet the urgent need for rapidly generating uniform filling schemes. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a solution method for uniform distribution of irregular region clusters based on force diffusion. Based on the force expansion model, under the conditions of flexible and variable tasks and irregular model environments, a method for rapid generation of uniform filling schemes is established through the cluster uniform diffusion model. This solves the problems of poor flexibility, non-universal scenarios, and difficulty in adapting to different irregular regions in traditional modeling methods. It provides a more user-friendly and flexible scheme generation method for designers who are not simulation professionals and military users.

[0004] The technical solution of this invention is:

[0005] A method for uniformly distributing irregularly shaped equipment clusters based on force diffusion is proposed to ensure that a cluster of a given number of equipment units is uniformly distributed across an irregular region on a spherical surface. The method includes...

[0006] S1: Initialize cluster location in irregular regions:

[0007] Irregular areas are synchronously moved inward by a fixed distance to form sub-regions, which serve as hard boundaries to restrict certain equipment;

[0008] Determine the approximate center of the sub-region, and determine the dispersion region based on the minimum distance from the approximate center to the edge of the sub-region, so that the cluster is evenly distributed in the dispersion region to generate the initial position of the cluster.

[0009] S2: Determine if a piece of equipment is in an irregular area. If the equipment is outside the area, move the equipment back into the irregular area.

[0010] S3: The cluster diffuses through a repulsive force model. Starting from the initial position of the cluster, a certain piece of equipment is gradually moved until the force balance is reached, so as to achieve a uniform distribution of the equipment in the irregular area. When the maximum moving distance of the cluster in the current state is less than the threshold, it is considered that the force balance has been reached and the iteration stops.

[0011] The method for determining the approximate center of the sub-region is as follows: the vertices of the sub-region are extracted at uniform intervals, and the intersection of the mean vector of the vertex and the sphere is taken as the approximate center of the sub-region.

[0012] In step S1, determining the dispersion region based on the minimum distance from the approximate center to the edge of the sub-region includes: taking the minimum distance from the approximate center to the edge of the sub-region as the radius of the inscribed cone, establishing polar coordinates within the inscribed cone according to the center and radius, and generating the initial position of the cluster with uniform distribution of distance and direction.

[0013] The method for synchronously moving the irregular region inward by a fixed distance is as follows: move the vertices of the irregular region, and when moving the vertices, rotate the two sides of the vertices sequentially with the normal vector of the symmetry plane passing through the midpoint of each side as the axis to form two new great arcs, obtain two intersection points, and take the intersection point closer to the original vertex as the new vertex. The new vertex and the great arc between the new vertices form a sub-region.

[0014] After generating the initial position of the cluster, it is determined whether a certain piece of equipment is in the irregular area. The determination method includes: taking counterclockwise as positive, taking the vector of the adjacent vertex of the irregular area boundary relative to the equipment to calculate the directed angle, with the directed angle as the center of the sphere, the dihedral angle formed by the two adjacent vertices of the irregular area boundary and the equipment, and accumulating the directed angle along the boundary of the area. If it is 0 degrees, it means that it is outside the area; if it is 360 degrees, it means that it is inside the area; if it is other values, it means that the area boundary is surrounded in reverse or multiple times.

[0015] When the directional angle is 0 degrees, i.e., a certain piece of equipment is detected to be outside the irregular area, it is then moved back into the irregular area according to the method of initializing the cluster position.

[0016] In step S3, when the equipment moves to the edge of the hard boundary, or when the distance between the equipment and the hard boundary is less than a certain amount, the movement component perpendicular to the edge outward is set to zero, and it can slide on the edge; when the equipment moves to the vertex of the hard boundary, or when the distance between the equipment and the hard boundary is less than a certain amount, the movement component has a component outward along both sides of the vertex, and it can move; otherwise, it remains stationary.

[0017] In the repulsive force model, a certain piece of equipment The force equation is

[0018] , ,

[0019] , constant coefficients

[0020]

[0021]

[0022] in, For a point on the sphere Point of view tangent direction, for and spherical distance, Let the radius of the sphere be . Given the minimum distance threshold of the repulsive force model, , , , For given Upper and lower boundaries For a certain equipment The distance of the rotating spherical surface, For a certain equipment The rotating shaft Rotation matrix constructed for quaternions, For a certain equipment The position after rotation.

[0023] The irregular region is defined as a region enclosed by a closed curve formed by connecting the beginning and end of a point on the sphere as its vertices and the great circle arc of the sphere as its edges. The boundaries of this region do not intersect each other, and the region is simply connected.

[0024] The sphere can also be a three-dimensional or higher space.

[0025] In summary, this application includes at least the following beneficial technical effects:

[0026] This invention proposes a uniform distribution solution method for irregular regions based on force diffusion. Based on the force expansion model, and under the conditions of flexible and varied tasks and irregular model environments, a rapid method for generating uniform filling schemes is established through the uniform diffusion model of the cluster. This solves the problems of poor flexibility, non-universal scenarios, and difficulty in adapting to different irregular regions in traditional modeling methods. It provides a more user-friendly and flexible scheme generation method for designers who are not simulation professionals and military users. Attached Figure Description

[0027] Figure 1 This is a flowchart of a method for uniformly distributing irregular region clusters based on force diffusion, according to the present invention. Detailed Implementation

[0028] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0029] This invention provides a solution method for uniform distribution of irregular region clusters based on force diffusion. Based on the force expansion model, a method for rapidly generating uniform filling schemes is established through the cluster uniform diffusion model under the conditions of flexible and variable tasks and irregular model environments.

[0030] Given a cluster of a certain number of equipment units deployed in an irregular area, the goal is to achieve the most uniform deployment. A solution method for achieving uniform distribution is proposed. This method can also be extended from spherical surfaces to three-dimensional and higher spaces, and applied to unstructured mesh generation, detection, exploration, and finite coverage problems.

[0031] In terms of specific implementation methods, a solution method for uniformly distributed irregular region clusters based on force diffusion is divided into:

[0032] Irregular regions distributed on the surface of a sphere are considered as a perfect sphere, disregarding elevation and the flattening of the ellipsoid. An irregular region is defined by a closed curve formed by connecting the beginning and end of a given point as its vertex and the great circle arcs between those points as its edges. The boundaries of this region do not self-intersect, and the region is simply connected, meaning it has no internal voids or is not divided into multiple parts. This region is not necessarily a convex set.

[0033] Equipment is deployed as evenly as possible within an irregular area, meaning the minimum distance between them is maximized, including the distance to the boundary. Therefore, its distribution is essentially unstructured. The boundary of the irregular area acts as a barrier to cluster diffusion. The repulsive force model for cluster diffusion considers short-range forces and introduces a minimum distance threshold to prevent infinite repulsive forces from occurring when two points coincide.

[0034] Specifically, the steps of this invention are as follows:

[0035] like Figure 1 As shown, a method for uniformly distributing irregular region clusters based on force diffusion is proposed, and its basic steps are as follows:

[0036] 1. Let the longitude of the boundary vertices of a simply connected, non-self-intersecting irregular region (area) be... latitude for The unit vector is converted from coordinates to a rectangular coordinate system. , Initialize the cluster (well) location in an irregular region. , , .

[0037] II. The irregular region is synchronously moved inward by a fixed distance, the radius of a certain piece of equipment, serving as a hard boundary restricting the equipment. When moving a vertex, the two edges of the vertex are rotated sequentially around the normal vector of the symmetry plane passing through the midpoint of each edge, forming two new great circle arcs. Two intersection points are obtained, and the intersection point closer to the original vertex is taken as the new vertex. The new vertex and the edges between the new vertices form a sub-region.

[0038] Third, during initialization, vertices on the irregular sub-regions are reasonably extracted to ensure relatively uniform vertex spacing. The intersection of the mean of the vertex vectors and the point on the sphere is taken as the approximate center of the sub-region, and the minimum distance from the approximate center to the edge is taken as the radius of the base of the inscribed cone. Polar coordinates are established within this inscribed cone according to the center and radius. These polar coordinates, centered on the approximate center, generate the initial positions of the clusters with uniform distributions of distance and direction.

[0039] IV. Method for determining if a piece of equipment is within an irregular region: Using counter-clockwise as positive, calculate the directed angles (vectors) between adjacent vertices (vectors) of the irregular region boundary and the equipment. (The directed angle is a dihedral angle, formed by the center of the sphere, one vertex, and the equipment forming a first plane; the center of the sphere, another vertex, and the equipment forming a second plane; the angle between the first and second planes is a dihedral angle). Accumulate the directed angles along the region boundary. A value of 0 degrees indicates the equipment is outside the region; a value of 360 degrees indicates it is within the region; any other value indicates the region boundary is either reverse-enclosed or has multiple enclosing elements. If equipment is detected outside the region, it is moved back into the region using the initialization method.

[0040] 5. When a piece of equipment moves along the edge of a hard boundary (the distance between the equipment and the hard boundary is less than a certain amount, which is an empirical value, 1m in this embodiment), the outward movement component perpendicular to the edge is set to zero, and it can slide on the edge; when a piece of equipment moves along the vertex of a hard boundary (the spherical distance is less than a certain amount), if there is a component of movement along both sides of the vertex, it can move; otherwise, it remains stationary.

[0041] VI. Based on the force model, starting from the initial position of the cluster, a certain piece of equipment is gradually moved until a force equilibrium state is reached, achieving a uniform distribution of the equipment within the irregular area. When the maximum movement distance of the cluster in its current state is less than a threshold, it is considered that a force equilibrium state has been reached, and the iteration stops.

[0042] In the repulsion model, any piece of equipment The force equations are as follows

[0043] , ,

[0044] , constant coefficients

[0045]

[0046]

[0047] in, For a point on the sphere Point of view tangent direction, for and spherical distance, Let the radius of the sphere be . , For given Upper and lower boundaries For a certain equipment The distance of the rotating spherical surface, For a certain equipment The rotating shaft Rotation matrix constructed for quaternions, For a certain equipment The position after rotation.

[0048] Based on the idea of ​​simulated annealing algorithm, let s t =a×s t-1 , a = 0.99993. Let... This represents the minimum distance threshold for a given repulsive force model. Employing a high-power distance model allows the repulsive force to decay rapidly over long distances, achieving locality of the repulsive force and creating a pressure effect at the boundary.

[0049] According to iteration The rule of halving the step size after each step, a T =0.50, therefore

[0050] a=exp(ln0.50 / 10000)=0.999930687684

[0051] like Figure 1 As shown, a method for uniformly distributing irregular region clusters based on force diffusion is proposed. The specific algorithm is as follows:

[0052] I. Establish a three-dimensional rectangular coordinate system middle Around Axis rotation Angle obtained , The corresponding quaternion is ;exist Position before rotation Position after rotation ,have

[0053]

[0054]

[0055]

[0056] have to

[0057]

[0058] in

[0059]

[0060] Among them, coordinate system With the center of the sphere as A three-dimensional rectangular coordinate system with point as the origin; The axis is any given unit vector, which serves as the axis of rotation for other vectors to rotate around.

[0061] This method allows you to move points on the sphere as required, obtaining the result after the movement (around...). Axis rotation The position coordinates of the angle.

[0062] II. Latitude in Spherical Coordinate System ,longitude and vector diameter With the three axes of the rectangular coordinate system , and The conversion relationship is

[0063] ,

[0064] This method can realize the mutual conversion between spherical coordinates and rectangular coordinates of a point.

[0065] III. Two points on the sphere and The spherical distance is the angle between the sphere and the center of the sphere. With the radius of the sphere product ,in

[0066]

[0067] This method can calculate the spherical distance between two points on a sphere.

[0068] IV. Three points on the surface of a sphere that are not coplanar with the center of the sphere. , and The composition from the surface With to the face dihedral ,in

[0069] ,

[0070] ,

[0071] This method can calculate the dihedral angle formed by three points on a sphere.

[0072] V. From point on the sphere With the edge The included angle ,in

[0073]

[0074] ,

[0075] This method can calculate the angle between two points on a sphere to determine the angle between great circle arcs.

[0076] VI. Points on the surface of a sphere Point of view tangent ,in

[0077] ,

[0078] This method can calculate the tangent vector on a sphere that passes through one point and points to another.

[0079] 7. The order is counterclockwise, and the region is to the left of the boundary. Given three points on the sphere arranged sequentially along the boundary. , and Two edges are formed, and the boundary is shifted inward. Find the intersection of the two new edges. ,in

[0080] , (Midpoint of the edge)

[0081] , (The normal vector of the edge)

[0082] , (Hinge)

[0083] Constructing a quaternion attitude transformation matrix based on rotation axis and rotation angle and The normal vector of the rotated edge is obtained

[0084] , (The normal vector of the new edge)

[0085]

[0086] This method can calculate the new two great circle arcs and their intersection points after the two great circle arcs on the sphere have been moved by equal amounts.

[0087] 8. A certain piece of equipment Approaching three o'clock , and Form boundary segments and approach the midpoint. With edge A certain equipment movement vector Pass Furthermore, being tangent to the sphere, it eliminates the obstruction on one side, forming a new moving vector. ,in

[0088]

[0089] Similarly

[0090] Eliminating the obstructions on both sides creates a new movement vector. ,in

[0091] ,

[0092]

[0093]

[0094] Given a right-handed system, with the order counterclockwise, the region lies to the left of the boundary. If and Then the moving component remains stationary, if Then go Directional movement ,like Then go Directional movement .

[0095] This method can determine the movement strategy of a piece of equipment on a sphere as it approaches the boundary of a region.

[0096] 9. A point moves a certain step length (geocene angle) along its own direction of motion; a certain piece of equipment Along direction vector Movement step size get ,in

[0097] ,

[0098] This method can calculate the new position of a piece of equipment on a sphere after it has moved a certain distance along the sphere by a vector.

[0099] 10. Move the normal of a point along the edge to the edge; a certain piece of equipment. Approaching two points and Form a boundary and move along the normal to ,and , ,in

[0100] ,

[0101] ,

[0102] This method can calculate the new position of a piece of equipment on a sphere when it moves to the boundary.

[0103] 11. A point moves along the edge; a certain piece of equipment At two points and On the boundary, Step size along the boundary get ,in

[0104] ,

[0105] This method can calculate the new position of a piece of equipment on a sphere after it has moved a certain spherical distance on the boundary.

[0106] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0107] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for solving the uniform distribution of irregular region clusters based on force diffusion, characterized in that: To ensure that a given number of certain equipment units are evenly distributed across an irregular area on a spherical surface, the method includes the following steps: S1: Initialize cluster location in irregular regions: Irregular areas are synchronously moved inward by a fixed distance to form sub-regions, which serve as hard boundaries to restrict certain equipment; Determine the approximate center of the sub-region, and determine the dispersion region based on the minimum distance from the approximate center to the edge of the sub-region, so that the cluster is evenly distributed in the dispersion region to generate the initial position of the cluster. S2: Determine if a piece of equipment is in an irregular area. If the equipment is outside the area, move the equipment back into the irregular area. S3: The cluster spreads through a repulsive force model. Starting from the initial position of the cluster, a certain piece of equipment is gradually moved until the force balance is reached, so as to achieve a uniform distribution of the equipment in the irregular area. When the maximum movement distance of the cluster in the current state is less than the threshold, it is considered that the force balance has been reached and the iteration stops. After generating the initial position of the cluster, it is determined whether a certain piece of equipment is in an irregular area. The determination method includes: taking counterclockwise as positive, taking the vector of the adjacent vertex of the irregular area boundary relative to the certain piece of equipment to calculate the directed angle, with the directed angle as the center of the sphere, the dihedral angle formed by the two adjacent vertices of the irregular area boundary and the certain piece of equipment, and accumulating the directed angle along the boundary of the area. If it is 0 degrees, it means that it is outside the area; if it is 360 degrees, it means that it is inside the area; if it is other values, it means that the area boundary is surrounded in reverse or multiple times. In step S3, when the equipment moves to the edge of the hard boundary, or when the distance between the equipment and the hard boundary is less than a certain amount, the movement component perpendicular to the edge outward is set to zero, and it can slide on the edge; when the equipment moves to the vertex of the hard boundary, or when the distance between the equipment and the hard boundary is less than a certain amount, the movement component has a component outward along both sides of the vertex, and it can move; otherwise, it remains stationary.

2. The method for solving the uniform distribution of irregular region clusters based on force diffusion according to claim 1, characterized in that: The method for determining the approximate center of the sub-region is as follows: the vertices of the sub-region are extracted at uniform intervals, and the intersection of the mean vector of the vertex and the sphere is taken as the approximate center of the sub-region.

3. The method of claim 1, wherein the method is characterized by: In step S1, determining the dispersion region based on the minimum distance from the approximate center to the edge of the sub-region includes: taking the minimum distance from the approximate center to the edge of the sub-region as the radius of the inscribed cone, establishing polar coordinates within the inscribed cone according to the center and radius, and generating the initial position of the cluster with uniform distribution of distance and direction.

4. The method of claim 1, wherein the method is characterized by: The method for synchronously moving the irregular region inward by a fixed distance is as follows: move the vertices of the irregular region, and when moving the vertices, rotate the two sides of the vertices sequentially with the normal vector of the symmetry plane passing through the midpoint of each side as the axis to form two new great arcs, obtain two intersection points, and take the intersection point closer to the original vertex as the new vertex. The new vertex and the great arc between the new vertices form a sub-region.

5. The method of claim 1, wherein the method is characterized by: When the directional angle is 0 degrees, i.e., a certain piece of equipment is detected to be outside the irregular area, it is then moved back into the irregular area according to the method of initializing the cluster position.

6. The method of claim 1, wherein the method is characterized by: In the repulsive force model, the force equation of a certain equipment is ， ， , are constant in, For a point on the sphere Point of view tangent direction, for and spherical distance, Let be the radius of the sphere. Given the minimum distance threshold of the repulsive force model, , , , For given Upper and lower boundaries For a certain equipment The distance of the rotating spherical surface, For a certain equipment The rotating shaft Rotation matrix constructed for quaternions, For a certain equipment The position after rotation.

7. The method of claim 1, wherein the method is characterized by: The irregular region is defined as a region enclosed by a closed curve formed by connecting the beginning and end of a point on the sphere as its vertices and the great circle arc of the sphere as its edges. The boundaries of this region do not intersect each other, and the region is simply connected.

8. The method of claim 1, wherein the method is characterized by: The sphere is a three-dimensional or higher space.

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