A method for searching a creeping wave based on a plane grid complex target model surface

Abstract

This invention discloses a method for tracking creeping waves on the surface of complex target models based on planar meshes. After preprocessing the complex model through surface-level partitioning, automatic surface type determination, and depth culling, the surface elements constituting the shadow boundary are accurately identified as the starting point of the creeping wave. Then, a series of discrete points are obtained through a recursive approach, point by point. These discrete points are linked and fitted to obtain important parameters such as the trajectory and creeping distance of the creeping wave. This invention enriches the high-frequency scattering mechanisms that planar mesh models can represent, eliminates the separation between creeping waves and other scattering mechanisms in the electromagnetic modeling of complex target mesh models, and improves the automation level of tracking. It has advantages such as high automation, high accuracy, and stability.

Description

Technical Field

[0001] This invention relates to a method for determining the shadow boundary and tracing the surface creeping wave of a complex target model based on a triangular planar mesh. This invention belongs to the field of electromagnetics, and particularly relates to the surface scattering mechanism in high-frequency methods. Background Technology

[0002] In radar target stealth research, strong scattering mechanisms, such as specular reflection, multiple interactions between planar components, and cavity scattering, have been largely suppressed. In this context, the importance of secondary scattering becomes prominent, and in some cases, it often becomes the primary scattering mechanism. With the development and widespread adoption of high-resolution radar, the detection and accurate identification of secondary scattering mechanisms are becoming increasingly urgent, escalating the contradiction and conflict between stealth and anti-stealth. Secondary scattering mechanisms include diffraction phenomena such as surface diffraction. Considering aerodynamic principles, the surface of aerial targets often has many curved structures and components, giving creeping waves a significant role in the electromagnetic characteristics of aerial targets. Furthermore, in antenna systems on complex carriers such as aircraft and ships, a large portion of the energy radiated by the antenna forms creeping waves on the carrier surface. The diffraction field generated by these creeping waves directly affects the radiation characteristics of the antenna on the carrier. Therefore, research on surface diffraction is of great value for near-field electromagnetic environment analysis, electromagnetic protection, and system-level electromagnetic integration design such as antenna layout. Besides its applications in near-field communication, electromagnetic compatibility, and electronic warfare, creeping waves are also ubiquitous. However, the practical value of creeping waves has not been fully realized in engineering. Many documents and reports, when introducing creeping waves, generally treat them only as a supplement to the main narrative, or even summarize them simply as "creeping waves decay rapidly and can be ignored." Indeed, creeping waves decay exponentially, but ignoring their existence has certain preconditions. For electrically large targets, such as individual spheres, cylinders, or large missiles with relatively simple component structures, creeping waves are generally negligible when studying the single-station scattering field of these targets. This is because when the radiation direction of the creeping wave points towards the radar receiver, its energy has already decayed to a very small amount, so the radiation field of the creeping wave is often hidden in noise and remains unknown. However, when the research scope is expanded from single-station to dual-station, and further to the multiple coupling effects of electrically large and complex targets, the influence of creeping waves is hard to ignore. This is because actual measurements in an anechoic chamber show that, in the above cases, there are some secondary scattering centers outside the scatterer, and in some cases, strong scattering centers with high brightness are formed. These scattering centers are either generated by higher-order diffraction fields or formed by the coupling of diffraction fields with other strong scattering mechanisms. This is enough to illustrate the potential value of creeping waves in various application fields.

[0003] In the past, most research on creeping waves was based on the NURBS model. This model is essentially a geometric model with a clear mathematical expression. Accurate creeping wave trajectories can be obtained relatively easily by solving the geodesic differential equation on the NURBS surface using numerical methods. Examples include Dr. Chen Xi's dissertation "Research on Electromagnetic Wave Diffraction Modeling Method for Arbitrary Smooth Convex Surfaces" from Wuhan University, Dr. Fu Song's dissertation "Research on Creeping Wave Tracking and Electromagnetic Diffraction Modeling Method for Medium-Coated Target Surfaces", and Dr. Wang Nan's dissertation "Consistent Geometric Diffraction Theory Method Based on Arbitrary Surface Modeling Technology" from Xi'an University of Electronic Science and Technology.

[0004] However, in the field of practical electromagnetic engineering, the most widely used model is the planar mesh model, which is composed of a large number of tiny polygonal elements. In this type of model, it can only be guaranteed that the endpoints of the polygons are located on the initial geometric model. The planar mesh enclosed by the endpoints may not completely fit the initial geometric model. This makes the mesh model weak in representing surface curves and difficult to solve geodesic differential equations on it, resulting in a serious disconnect between creeping waves and other scattering mechanisms. Regarding crawling wave tracing on planar mesh models, there are relevant literature and patents. For example, Ruan Yucheng's master's thesis at Southeast University, "Crawling Wave Tracing on Convex Surfaces Based on Triangular Mesh and UTD Solution Analysis of Scattering Problems," achieves crawling wave tracing on planar mesh-partitioned spheres. However, the research results are incomplete, limited to tracing on standard bodies such as spheres and cylinders, and simple, unobstructed target surfaces, without providing a complete set of electromagnetic diffraction modeling methods applicable to arbitrary mesh models. Li Yaoyao's paper, "High-Precision Adaptive Ray Tracing of Convex Surfaces Based on Normal Vector Cutting Surfaces," published in the Journal of Beijing University of Aeronautics and Astronautics, re-examines this topic. The study investigated the tracking process of creeping waves and obtained high-precision results, but lacked the ability to handle complex targets. It also did not address how to determine the starting point of creeping wave tracking—the position of the shadow boundary. The published patent "A Ray Tracking Method with Dynamic Adjustment of Cutting Surface under Triangular Mesh Surface" (Publication No.: CN106126794B) also has these problems. Similar problems also appeared in the patent "Research Method on Creeping Wave Mechanism of Electrically Large Stealth Targets" (Publication No.: CN107621633A) of Shanghai Radio Equipment Research Institute. Moreover, the patent did not demonstrate the effect of the proposed method, and its effectiveness and advantages could not be evaluated.

[0005] To date, there is no complete solution in China for tracking creeping waves on the surface of complex target models with planar meshes. Completeness here includes determining the possible locations of creeping waves, identifying the starting point, and tracking the waves. Summary of the Invention

[0006] This invention addresses the shortcomings of existing technologies by systematically providing a complete method for determining shadow boundaries and crawling wave tracing of complex target models based on planar meshes. While ensuring tracing accuracy, it overcomes the difficulties and shortcomings of previous studies and truly embodies the crawling wave scattering mechanism in complex mesh models.

[0007] The technical solution of this invention is a method for determining the shadow boundary and crawling wave tracing of complex target models based on planar meshes, comprising the following steps:

[0008] Step 1: Construct a high-precision CAD geometric model of the complex target;

[0009] Step 2: Preprocess the geometric model to obtain candidate planar elements, and then select the shadow boundary elements from them;

[0010] Step 3: Use the midpoint of the shadow boundary element as the starting point p of the crawling wave. c With the direction of the incident wave Using the initial direction as an example, a series of discrete points are obtained by recursively calculating each point. By linking the discrete points in sequence, the crawling wave trajectory can be obtained.

[0011] Step 4: Inversely synthesize the discrete point set into a curve C, calculate the length of C, and obtain the correct crawling distance;

[0012] Step 5: Stop tracking once the pre-set termination condition is met, based on actual needs.

[0013] Furthermore, the preprocessing of the geometric model in step 2 specifically includes:

[0014] (21) Decompose each component on the target geometric model constructed in step 1 into several planes or curved surfaces according to the surface properties, discretize the geometric model into a large set of triangular facets, and record the number, facet number and endpoint coordinates to obtain a mesh model with partition number.

[0015] (22) Reverse reconstruct the large number of triangular elements that make up a single surface one by one to restore the original geometric properties of each surface, and use the curvature reconstruction method to determine whether each surface-level partition is a plane or a curved surface, and record the number of the curved surface and plane partition respectively.

[0016] (23) Perform depth masking on the current planar mesh model to remove face elements in the shadow area and face elements occluded by other components.

[0017] Furthermore, the criteria for determining whether each surface-level partition is planar or curved are as follows:

[0018] (a1) If the principal radii of curvature in both directions are infinite, then the surface type is planar;

[0019] (a2) If the principal radii of curvature in both directions are finite, then the surface type is a double-curved surface;

[0020] (a3) If one principal radius of curvature is finite and the other is infinite, then the surface type is a single-curved surface.

[0021] Furthermore, the principal curvature radius is calculated as follows;

[0022] Construct a coordinate system (x1, x2, z) with the normal to any point P on the surface as the reference, where the Z-axis is the normal to point P, x1 and x2 are the tangent directions of two orthogonal curves passing through point P on the surface at that point, and the vectors are... and Let z be the principal direction of point P; assuming the surface equation of the neighborhood of point P is z = f(x1, x2), expanding this equation, we get...

[0023]

[0024] Since point P is the origin, f(P) = 0; if point P is an extreme point relative to its neighboring points, then Define the following coefficients:

[0025]

[0026] but

[0027]

[0028] Write it in matrix form

[0029]

[0030] in

[0031]

[0032] According to differential geometry theory, when the equation of the surface is expressed as At that time, the principal radius of curvature ρ at any point on the surface can be calculated using the quadratic equation of equation (6):

[0033] (Q 11 Q 12 -Q 12 2 )ρ 2 +(Q 11 +Q 22 )ρ+1=0(6)

[0034] Then the principal radius of curvature is:

[0035]

[0036] According to differential geometry theory, any point on the surface has two principal curvature directions, which correspond to two principal curvature radii, namely the two roots obtained by solving equation (6).

[0037] Furthermore, the specific process of depth culling in step (23) is as follows;

[0038] (b1) First, based on the angle between the outward normal of the target surface element and the incident wave direction, remove surfaces that cannot be seen from the rearward direction. With the outer normal of a certain surface element in the model If the dot product of the elements is greater than 0, then the element is a backward-unseeable face.

[0039] (b2) Draw the model using orthographic projection, that is, draw all the face elements on the model, start the depth test, and set the depth test type to GL_LEQUAL;

[0040] (b3) Obtain the model view matrix, projection matrix and view area matrix, and use the gluProject function to calculate the screen coordinates (x, y, z) of the center of the face element, where x and y are two-dimensional coordinates on the screen and z is the depth value; use the glReadPixels function to read the depth value of the corresponding pixel on the screen at the center of the face element. If the z value is greater than the depth value of the pixel, then the face element is a hidden face element.

[0041] After hidden surface removal, the remaining surface elements are subjected to shadow boundary determination, with the incident wave direction being... The normal vector of the surface element is Analyze each face element Whether it is less than ε, where ε is a very small negative number very close to zero, and its value is related to the quality of the model subdivision. The current face element is then a shaded boundary face element.

[0042] Furthermore, in step 3, a series of discrete points are obtained through recursion, specifically:

[0043] (c1)p c and Determine the equation of the point-directed line l, where l is related to the shaded boundary surface element T. s Find the intersection point of the lines containing the three edges, remove the point outside the face element, and then remove the points that intersect with the face element. Points in opposite directions are obtained at location T. s Point p1 on a certain edge is the first trajectory point;

[0044] (c2) Since the edge containing p1 is a common edge, the adjacent triangle is the triangular element containing the next crawling wave trajectory, denoted as T1. c Determine the equation of the line L in two-point form, with the unit direction vector as follows: Find the intersection points of L with the lines containing the three edges of T1, remove one point outside the surface element, and then remove the points that intersect with the surface element. Points in opposite directions lead to point p2 located on an edge of T1, which is the second trajectory point;

[0045] (c3) Since the edge containing p2 is a common edge, the adjacent triangle is the triangular element containing the next crawling wave trajectory, denoted as T2. p2 and p1 determine the two-point equation of the straight line L1, and the unit direction vector is... Find the intersection points of L1 with the lines containing the three edges of T2, remove the point outside the surface element, and then remove the points that intersect with the surface element. Points in opposite directions lead to point p3 located on an edge of T2, which is the third trajectory point;

[0046] (c4) Repeat (c3) to obtain a series of discrete points {p c ,p1,p2,p3,...,p n}, where p n The last discrete point before reaching the termination condition.

[0047] Furthermore, the pathfinding termination condition in step 5 is one of the following;

[0048] (d1) When the creeping wave in the current surface partition R1 propagates to the next adjacent surface partition R2, if R2 is a curved structure, the recursive tracing continues; if R2 is a plane, the tracing stops at the last discrete point of R1.

[0049] (d2) During the tracking process, the crawling distance t is calculated continuously. If t is greater than the set distance T, the tracking is stopped.

[0050] (d3) During the tracking process, the number of face elements n traversed by the crawling is recorded at all times. If n is greater than the set number N, the tracking stops.

[0051] (d4) Stop tracking when the direction of the creeping wave's radiation rays covers all the set field points.

[0052] The advantages and beneficial effects of this invention are as follows:

[0053] (1) Planar mesh model is the most widely used model format in practical electromagnetic engineering applications. This invention enriches the high-frequency scattering mechanism that the planar mesh model can embody and eliminates the separation between creeping waves and other scattering mechanisms in the electromagnetic modeling of complex target mesh models.

[0054] (2) This invention uses analytical geometry to calculate each discrete point, which is both accurate and fast in the tracking process;

[0055] (3) Before tracking, model preprocessing operations (surface-level partitioning, automatic surface type determination, and depth culling) were added, which improved the automation of tracking, accurately obtained all shadow boundary elements, and did not misjudge the position and number of shadow boundary elements.

[0056] (4) The present invention uses triangular facets as the smallest computational unit and does not rely on the macroscopic shape of the surface. Therefore, the present invention is not only applicable to creeping waves, but also applicable to the visualization study of surface wave propagation process on planar surfaces.

[0057] (5) When the mesh quality is poor, the present invention adds discrete point fitting curve operation to ensure the accuracy of the trajectory and the correct result can still be obtained. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the surface-level partitioning of a complex target model, where the model in (a) is a Tomahawk cruise missile, and the model in (b) is the SLICY calibration model commonly used in electromagnetic research.

[0059] Figure 2 This is a schematic diagram of the local coordinate system in the curvature reconstruction method.

[0060] Figure 3 These are wireframe models before and after depth scavenging. (a) is the wireframe model of the F-22 fighter jet before scavenging, and (b) is the wireframe model of the F-22 fighter jet after scavenging.

[0061] Figure 4 These are schematic diagrams of the shadow boundaries of complex targets. (a) shows the shadow boundary of the Tomahawk cruise missile surface, and (b) shows the shadow boundary of the SLICY model surface.

[0062] Figure 5 This is a schematic diagram illustrating the operation method of removing a point other than the face element.

[0063] Figure 6 This is a schematic diagram illustrating the operation of removing points that are opposite to the direction of propagation.

[0064] Figure 7 This is a schematic diagram of a straight line projected onto the surface of a triangular element.

[0065] Figure 8 This is the flowchart for step 3, which involves recursively tracing the path point by point.

[0066] Figure 9 These are the effect diagrams of tracking on the surfaces of a sphere and a cylinder. (a) shows the trajectory of a crawling wave on the surface of a sphere, with the surface elements traversed by the trajectory drawn together. (b) shows the trajectory of a crawling wave on the surface of a cylinder, with the surface elements traversed by the trajectory drawn together.

[0067] Figure 10The images show the effect of multiple creeping waves tracking on the surface of a Tomahawk cruise missile model. (a) shows θ = π / 3. Under the given attitude, the plane wave incident on the model surface excites multiple crawling wave trajectories, (b) for θ = 17π / 36. Under the given attitude, a plane wave incident on the model surface excites multiple crawling wave trajectories.

[0068] Figure 11 These are renderings of the crawling wave radiation rays on the surfaces of a sphere and a Tomahawk cruise missile model. (a) shows the crawling wave trajectory and radiation rays on the surface of the sphere, and (b) shows the crawling wave trajectory and radiation rays on the surface of the Tomahawk cruise missile.

[0069] Figure 12 This is a flowchart of the present invention. Detailed Implementation

[0070] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0071] The purpose of this invention is to accurately determine the location of the crawling wave and its starting point for any complex planar mesh model given an incident angle, and to perform line tracking point by point, thereby reflecting the strength of the surface diffraction effect of the target, and also serving as the basis for electromagnetic modeling.

[0072] like Figure 12 The flowchart shown is of the present invention, which mainly includes the following steps:

[0073] Step 1: Construct a high-precision CAD geometric model of the complex target;

[0074] Step 2: Preprocess the geometric model to obtain candidate planar elements, and select the shadow boundary elements as the starting point of the crawling wave.

[0075] In high-frequency method research, the computational domain is roughly divided into bright and shadow regions, with a boundary between them called the shadow boundary. Creeping waves, also known as surface diffraction fields, are a scattering mechanism where electromagnetic waves are excited at the shadow boundary of a curved surface and act on the shadow region (and, when the scatterer's electrical size is appropriate, may continue acting from the shadow region to the bright region). The purpose of model preprocessing is to automatically identify the curved surface structure and determine the location of the shadow boundary. Preprocessing includes the following steps:

[0076] The first step is to decompose each component of the complex target constructed in step 1 into several planes or curved surfaces based on its surface properties. Figure 1 This is a schematic diagram of the surface-level partitioning of a complex target model, with different colors representing different surface partitions.

[0077] The second step is to discretize the geometric model into a large set of triangular facets. Each facet contains information such as the number of the surface region it belongs to, the facet number, and the coordinates of its endpoints. The format of adjacent triangular facets in the mesh model file is defined as follows:

[0078] node ......

[0080] IP ix p iy p iz

[0081] i+1 p (i+1)x p (i+1)y p (i+1)z

[0082] i+2 p (i+2)x p (i+2)y p (i+2)z

[0083] i+3 p (i+3)x p (i+3)y p (i+3)z ......

[0085] triangle ......

[0087] ji i+1 i+2 m

[0088] j+1 i+1 i+2 i+3 m ......

[0090] i is the index number of the endpoint, (p ix p iy p iz Let be the coordinates of the i-th point, j be the index of the triangular element, and the last three columns be the indexes of the points that make up that element. m The index number of the surface partition to which the element belongs is the common edge, which is the line segment composed of i+1 and i+2. The index of each point is unique, and the index can be repeated when forming the element.

[0091] The third step involves reconstructing the numerous triangular facets that make up a single surface, one by one. This allows the original geometric properties of each surface to be recovered. For creeping wave tracing, it is necessary to determine whether the surface is planar or curved. The principal radius of curvature is used as an indicator to determine the surface structure type, and the criteria are as follows:

[0092] (1) If the principal radii of curvature in both directions are infinite, then the surface type is planar;

[0093] (2) If the principal radii of curvature in both directions are finite, then the surface type is a double-curved surface;

[0094] (3) If one principal radius of curvature is finite and the other is infinite, then the surface type is a single-curved surface.

[0095] Single-curved surfaces and double-curved surfaces are classified as curved surfaces.

[0096] Using the normal to any point P on the surface as a reference, we can construct Figure 2 The coordinate system shown is (x1, x2, z), where z The axis is the normal to point P, and x1 and x2 are the tangent directions of two orthogonal curves passing through point P on the surface at that point, respectively. (Vector) and Let z be the principal direction of point P. Assume the surface equation of the neighborhood of point P is z = f(x1, x2). Expanding this equation, we get...

[0097]

[0098] Since point P is the origin, f(P) = 0; if point P is an extreme point relative to its neighboring points, then make

[0099]

[0100] but

[0101]

[0102] Write it in matrix form

[0103]

[0104] in

[0105]

[0106] According to differential geometry theory, when the equation of the surface is expressed as At that time, the principal radius of curvature ρ at any point on the surface can be calculated using the quadratic equation of equation (6).

[0107] (Q 11 Q 12 -Q 12 2 )ρ 2 +(Q 11 +Q 22 )ρ+1=0(6)

[0108] Then the principal radius of curvature

[0109]

[0110] According to differential geometry theory, any point on the surface has two principal curvature directions, which correspond to two principal curvature radii, namely the two roots obtained by solving equation (6).

[0111] As can be seen from the above introduction, as long as the geometric information of the surface is provided, the coefficient Q 11 Q 12 Q 22 This can be obtained by fitting with the least squares method, and thus the principal radius of curvature at any point on the surface can be obtained.

[0112] The fourth step is to perform depth hidden surface removal on the planar mesh model. Figure 3 This is a schematic diagram of the F-22 wireframe model after depth culling. As can be seen, the shadowed areas and occluded component structures have been removed. The specific culling process of this invention is as follows:

[0113] (1) First, based on the angle between the outer normal of the target surface element and the direction of the incident wave, remove surfaces that cannot be seen from the rear. That is, if the direction of the incident wave... With the outer normal of a certain surface element in the model If the dot product of the elements is greater than 0, then the element is a backward-unseeable face.

[0114] (2) Draw the model using orthographic projection (corresponding to the glOrtho function in OpenGL), that is, draw all the face elements on the model, start the depth test, and set the depth test type to GL_LEQUAL.

[0115] (3) Obtain the Model / View Matrix, Projection Matrix, and ViewPort Matrix. Use the gluProject function to calculate the screen coordinates (x, y, z) of the center of the face element, where x and y are two-dimensional coordinates on the screen and z is the depth value. Use the glReadPixels function to read the depth value of the pixel corresponding to the center of the face element on the screen. If the z value is greater than the depth value of the pixel, then the face element is a hidden face element.

[0116] The fifth step is to determine the shadow boundaries of the remaining surface elements, with the incident wave direction being... The normal vector of the surface element is Analyze each face element Whether it is less than ε, where ε is a very small negative number very close to zero, and its value is related to the quality of the model subdivision. Then the current face element is a shaded boundary face element; Figure 4 It shows the shadow boundaries of complex targets.

[0117] Step 3: Use the midpoint of the shadow boundary element as the starting point p of the crawling wave.c With the direction of the incident wave Using the initial direction as an example, a series of discrete points are obtained by recursively calculating each point. By linking the discrete points in sequence, the crawling wave trajectory can be obtained.

[0118] After the model is preprocessed in step 2, the positions of each surface structure and shadow boundary are obtained. Recursive tracing is then performed on the surface structure starting from the shadow boundary. The specific steps are as follows:

[0119] The first step is to use the incident wave direction As the initial incident direction, a straight line l is drawn at the midpoint of the shadow boundary element. l intersects the three sides of the triangular element at three points {p1, p2, p3}. Each line can be represented in two-point form as follows:

[0120]

[0121] Where (x1, y1, z1) and (x2, y2, z2) represent any two of the three endpoints, so the coordinates of the intersection point are...

[0122]

[0123] The second step is to calculate the distances {d1, d2, d3} from the midpoint to {p1, p2, p3}. If d3 > d1 and d3 > d2, then p3 is determined to be outside the surface cell. Further checks are then performed on the other two points. Figure 5 As shown.

[0124] The third step is to... p c Let be the midpoint of the shaded boundary surface element. Then determine if p1 is in the direction of the creeping wave propagation, such as Figure 6 As shown, the first point on the trajectory is p1.

[0125] Fourth step, since the edge containing p1 is a common edge, the adjacent triangle is the triangular element containing the next crawling wave trajectory, denoted as T1. c The direction vector of the line formed by p1} is The unit normal vector of T1 is make but p1(x0,y0,z0) defines a plane

[0126] k x (x-x0)+k y (y-y0)+k z (z-z0)=0(10)

[0127] Meanwhile, the equation of the plane containing T1 is

[0128] n x (x-x0)+n y (y-y0)+n z (z-z0)=0(11)

[0129] The intersection of the two planes is the projection of the trajectory line onto the trajectory surface element. Combining (10), (11) and (8), we can solve for the coordinates of the intersection point.

[0130]

[0131]

[0132] Then, by performing the second and third steps of discrimination, the second point p2 on the crawling trajectory is obtained, as shown below. Figure 7 As shown.

[0133] Fifth step: Since the edge containing p2 is a common edge, the adjacent triangle is the triangular facet containing the next crawling wave trajectory, denoted as T2. The direction vector of the line formed by {p1, p2} is... The unit normal vector of T2 is make but p2(x0,y0,z0) defines a plane

[0134] k 1x (x-x0)+k 1y (y-y0)+k 1z (z-z0)=0(13)

[0135] Meanwhile, the equation of the plane containing T2 is

[0136] n 1x (x-x0)+n 1y (y-y0)+n 1z (z-z0)=0(14)

[0137] The intersection of the two planes is the projection of the trajectory line onto the trajectory surface element. Combining (13), (14) and (8), we can solve for the coordinates of the intersection point.

[0138]

[0139]

[0140] Then, perform the second and third steps to determine the third point p3 on the crawling trajectory. Repeat this process to obtain a series of subsequent trajectory points. The recursive flowchart for this step is as follows: Figure 8 As shown.

[0141] Step 4: Inversely synthesize the discrete point set into a curve C, calculate the length of C, and obtain the correct crawling distance;

[0142] This invention is based on an arbitrarily complex planar mesh model for creeping wave tracing. Although the mesh size is strictly defined in the calculation of electromagnetic fields in the high-frequency region, the mesh quality may not meet the requirements due to various reasons in actual calculations. In order to accurately obtain the creeping distance, a series of discrete points are fitted into a curve, and the length of this curve is calculated to obtain the creeping distance.

[0143] Step 5: Stop tracking once the pre-set termination condition is met, based on actual needs.

[0144] In electromagnetic calculations, different termination conditions exist for creeping waves depending on the desired goal and effect. Several termination conditions are as follows:

[0145] (1) When the creeping wave in the current surface partition R1 propagates to the next adjacent surface partition R2, if R2 is a curved structure, the recursive tracing continues; if R2 is a plane, the tracing stops at the last discrete point of R1.

[0146] (2) During the tracking process, the crawling distance t is calculated at all times. If t is greater than the set distance T, the tracking is stopped.

[0147] (3) During the tracking process, the number of face elements n traversed by the crawling is recorded at all times. If n is greater than the set number N, the tracking stops.

[0148] (4) Stop tracking when the direction of the creeping wave's radiation rays covers all the set field points.

[0149] like Figure 9 The diagram shows the verification of this invention on the surfaces of a sphere and a cylinder. A sphere with a radius of 0.5m exists in free space, and the incident direction is chosen to be θ = π / 4. Arbitrarily select a shaded boundary surface element for tracing. The number of trajectory surface elements is 186. Compare with the analytical data. The results are shown in Table 1. The algorithm results are correct.

[0150] There exists a cylinder in free space with a radius of 0.5m and a length of 2.0m. Ignoring the top and bottom faces, the incident direction is θ = π / 6. Arbitrarily select a shaded boundary surface element for tracing. The number of trajectory surface elements is 403. The tracing result is a spiral line. Compare it with the analytical data. The results are shown in Table 2. The algorithm result is correct.

[0151] Table 1. Comparison of Crawling Wave Tracking Results and Analytical Methods on a Spherical Surface (Length unit: m)

[0152]

[0153] Table 2 Comparison of Crawling Wave Tracking Results and Analytical Method on Cylindrical Surfaces (Length unit: m)

[0154]

[0155] The accuracy of the tracking algorithm proposed in this invention is demonstrated by a single crawling wave trajectory on the surface of a standard object. Therefore, tracking with multiple crawling waves is then performed on arbitrary curved surfaces. Figure 10 As shown, at θ = π / 3, And θ = 17π / 36, Crawling wave tracking is performed at the incident angle. When a crawling wave propagates on the surface of a scatterer, it radiates energy tangentially, such as... Figure 11 As shown, several crawling wave trajectories were randomly selected from the surfaces of the sphere and the cruise missile, illustrating the incident wave rays and the radiation rays of the crawling waves.

[0156] In summary, the method for determining the surface shadow boundary and crawling wave tracing of arbitrarily complex planar mesh models described in this invention has strong engineering applicability. Throughout the entire operation process, manual work is minimized, greatly demonstrating the automation of this invention, and the tracing results are accurate and stable. Furthermore, this invention can be extended to planar models and even models of arbitrary shapes for geodesic calculation, and still has potential application value in the characterization of surface waves.

[0157] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for tracking crawling waves on the surface of a complex target model based on a planar mesh, characterized in that, Includes the following steps: Step 1: Construct a high-precision CAD geometric model of the complex target; Step 2: Preprocess the geometric model to obtain candidate planar elements, and then select the shadow boundary elements from them; Step 3: Use the midpoint of the shadow boundary element as the starting point of the crawling wave. With the direction of the incident wave Using the initial direction as an example, a series of discrete points are obtained by recursively calculating each point. By linking the discrete points in sequence, the crawling wave trajectory can be obtained. In step 3, a series of discrete points are obtained through recursion, specifically: (c1) and Determine the equation of a point-direction line , Each with the shadow boundary element Find the intersection point of the lines containing the three edges, remove the point outside the face element, and then remove the points that intersect with the face element. Points in opposite directions, located at Points on a certain edge This point is the first trajectory point; (c2) Since the edge is a common edge, the adjacent triangle is the triangular element containing the next crawling wave trajectory, denoted as . , and Determine the equation of a straight line in two-point form. The unit direction vector is , respectively with Find the intersection point of the lines containing the three edges, remove the point outside the face element, and then remove the points that intersect with the face element. Points in opposite directions, located at Points on a certain edge This point is the second trajectory point; (c3) Since the edge is a common edge, the adjacent triangle is the triangular element containing the next crawling wave trajectory, denoted as . , and Determine the equation of a straight line in two-point form. The unit direction vector is , respectively with Find the intersection point of the lines containing the three edges, remove the point outside the face element, and then remove the points that intersect with the face element. Points in opposite directions, located at Points on a certain edge This point is the third trajectory point; (c4) Repeat (c3) to obtain a series of discrete points. ,in The last discrete point before reaching the termination condition; Step 4: Inversely synthesize the discrete point set into a curve. ,calculate The length is used to determine the correct crawling distance; Step 5: Stop tracking once the pre-set termination condition is met, based on actual needs.

2. The method for tracking crawling waves on the surface of a complex target model based on a planar mesh, as described in claim 1, is characterized in that: The specific preprocessing of the geometric model in step 2 is as follows: (21) Decompose each component on the target geometric model constructed in step 1 into several planes or curved surfaces according to the surface properties, discretize the geometric model into a large set of triangular facets, and record the number, facet number and endpoint coordinates to obtain a mesh model with partition number. (22) Reverse reconstruct the large number of triangular elements that make up a single surface one by one to restore the original geometric properties of each surface, and use the curvature reconstruction method to determine whether each surface-level partition is a plane or a curved surface, and record the number of the curved surface and the plane partition respectively. (23) Perform depth culling on the current planar mesh model to remove face elements in the shadow area and face elements occluded by other components.

3. The method for tracking crawling waves on the surface of a complex target model based on a planar mesh, as described in claim 1, is characterized in that: The criteria for determining whether each surface-level partition is a plane or a curved surface are as follows: (a1) If the principal radii of curvature in both directions are infinite, then the surface type is planar; (a2) If the principal radii of curvature in both directions are finite values, then the surface type is a double-curved surface; (a3) If one principal radius of curvature is finite and the other is infinite, then the surface type is a single-curved surface.

4. The method for tracking the surface of a complex target model based on a planar mesh according to claim 3, characterized in that: The principal curvature radius is calculated as follows; At any point on the surface Construct a coordinate system based on the normal. The Z-axis is... The normal of a point and They are respectively passing through curved surfaces The vectors of the tangents of two orthogonal curves at a point are: and for The main direction of the point; assuming The surface equation of the neighborhood of a point is Expanding this expression, we get (1) because The point is the origin of the coordinate system, therefore ;if If a point is an extreme point relative to its neighboring points, then... The coefficients are defined as follows: (2) but (3) Write it in matrix form (4) in (5) According to differential geometry theory, when the equation of the surface is expressed as When, the principal radius of curvature at any point on the surface The result is obtained by calculating using the quadratic equation in equation (6): (6) Then the principal radius of curvature is: (7) According to differential geometry theory, any point on the surface has two principal curvature directions, which correspond to two principal curvature radii, namely the two roots obtained by solving equation (6).

5. The method for tracking the surface of a complex target model based on a planar mesh according to claim 2, characterized in that: The specific process of depth culling in step (23) is as follows; (b1) First, based on the angle between the outward normal of the target surface element and the incident wave direction, remove the unseen surfaces in the rear direction. That is, if the incident wave direction... With the outer normal of a certain surface element in the model If the dot product of the elements is greater than 0, then the element is a backward-unseeable face. (b2) Draw the model using orthographic projection, that is, draw all the face elements on the model, start the depth test, and set the depth test type to GL_LEQUAL; (b3) Obtain the model view matrix, projection matrix and view area matrix, and use the gluProject function to calculate the screen coordinates (x, y, z) of the center of the face element, where x and y are two-dimensional coordinates on the screen and z is the depth value; The glReadPixels function reads the depth value of the pixel corresponding to the center of the face on the screen. If the z value is greater than the pixel depth value, then the face is a hidden face. After hidden surface removal, the remaining surface elements are subjected to shadow boundary determination, with the incident wave direction being... The normal vector of the surface element is Judge each face element one by one Is it less than ,in It is a very small negative number, very close to zero, and its value is related to the quality of the model subdivision. If so, the current face element is a shadow boundary face element.

6. The method for tracking crawling waves on the surface of a complex target model based on a planar mesh, as described in claim 2, is characterized in that: The pathfinding termination condition in step 5 is one of the following; (d1) In the current surface partition The creeping wave propagates to the next adjacent surface partition. At that time, if If it is a curved surface structure, then continue the recursive tracing. If it is a plane, then in The tracking stops at the last discrete point. (d2) Calculate the crawling distance at any time during the tracking process. ,like Greater than the set distance Stop tracking when the time comes; (d3) Record the number of facets traversed during the crawling process at any time. ,like Greater than the set number Stop tracking when the time comes; (d4) Stop tracking when the direction of the creeping wave's radiation rays covers all the set field points.

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