Ray tracing method based on sphere bounding structure

Abstract

The application provides a ray tracing method based on a spherical envelope structure, and the implementation steps are as follows: constructing a spherical envelope structure, each sphere containing a plurality of surface elements; using the projection of the sphere center vector on the incident ray direction to complete sphere sorting; according to the sphere sorting order, the ray sequentially performs intersection detection with the spheres, and the surface elements in the sphere intersecting with the ray are reserved; the ray sequentially performs intersection detection with the surface elements in the intersecting sphere, obtains the intersection point, and reflects the ray, taking the reflected ray as the incident ray to continue the ray tracing until the ray does not intersect with any sphere or surface element, and the ray tracing result is obtained. The application sorts the multiple spherical envelope structures containing a plurality of triangular plane elements in the ray direction in sequence, and performs intersection detection on the incident ray and each spherical envelope structure, so that all the triangular surface elements in the sphere not intersecting with the ray are removed, more redundant line-surface intersection calculation can be saved, and the tracing efficiency is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and relates to a ray tracing method, specifically a ray tracing method based on a sphere-enclosed structure. Background Technology

[0002] When calculating the radar cross section of a target, the target's scattered field includes not only the field generated by the first scattering from the target surface, but also the field generated by multiple scatterings. The bouncing ray method (SBR) is an effective means of calculating the multiple scattering field of the target surface. It discretizes the incident wave into rays and tracks the paths of the rays reflected multiple times on the target surface. Based on the ray tracing results, the multiple scattering field of the target surface is obtained. Therefore, ray tracing is the core calculation content for obtaining the multiple scattering field of the target surface.

[0003] Ray tracing is a process of testing the line-plane intersection of a ray with triangular planar elements. After determining all the triangular planar elements that the ray intersects during its propagation, the first triangular planar element to intersect the ray is determined by the distance between the intersection point and the ray's origin. The reflected ray, with the intersection point of the ray and that triangular planar element as the starting point and the reflection direction as the direction, becomes the new incident ray, and ray tracing continues recursively until the ray no longer intersects with any triangular planar element. At this point, the ray is considered to have left the target surface, and ray tracing ends.

[0004] Existing ray tracing methods construct multiple wrapping spheres with the same number of triangular facets, and perform intersection detection on the ray with each wrapping sphere one by one. Then, they perform intersection detection on the ray with the triangular facets in the intersecting wrapping sphere one by one. This method can only exclude one triangular facet if a wrapping sphere is rejected, and there are still a lot of redundant ray-triangular facet intersection detections, which increases the workload of intersection detection and affects the further improvement of ray tracing efficiency. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a ray tracing method based on a sphere-enclosed structure, which aims to improve the efficiency of ray tracing while ensuring tracing accuracy.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Construct a sphere-enclosed structure:

[0008] The target geometric model is discretized, and the vertex information of the N triangular plane elements obtained from the discretization is used to construct a structure S = {S}, which is enclosed by M spheres with radius r. m |1≤m≤M}, where N≥1, M=I×J×K, where I, J, and K represent the number of structures enclosed by the sphere in the x, y, and z directions, respectively, and Sm This represents the structure enclosed by the m-th sphere;

[0009] (2) Sort all the structures enclosed by the spheres according to the vector projection of the sphere center:

[0010] Calculate the projection l = {l} of the center vector of the structure surrounded by each sphere onto the incident ray along the incident direction. m |1≤m≤M}, and sort the M spherical enclosing structures in ascending order of projection, to obtain the M spherical enclosing structures S'={S'} in the direction of incident ray propagation, ordered from near to far from the origin of the incident ray. m |1≤m≤M}, where S' m This represents the structure enclosed by the m-th sphere after sorting;

[0011] (3) Intersection detection of the incident rays with the structure enclosed by each sphere:

[0012] Determine the structure S' enclosed by each sorted sphere. m The closest distance h from the center of the sphere to the incident ray m Does the radius r of the structure enclosed by the sphere satisfy h? m If ≤r, then S' m Intersecting with the incident ray, a structure S”={S” is obtained, consisting of Q spheres that intersect with the incident ray. q If |1≤q≤Q}, then proceed to step (4); otherwise, the incident ray leaves the target surface and proceed to step (5).

[0013] (4) Perform intersection detection on the triangular plane elements within the structure surrounded by each sphere and the incident ray:

[0014] Determine the structure S” of each sphere that intersects with the incident ray obtained in step (3). q Does the simultaneous equation of the triangular plane element within the triangle have a solution? If so, then the incident ray and S” q The triangular plane elements intersect, and a reflected ray is obtained with the intersection of the incident ray and the triangular plane element as the starting point and the direction calculated using Fresnel's law as the reflection direction. The reflected ray is then used as the incident ray and step (2) is executed. Otherwise, the incident ray leaves the target surface and step (5) is executed.

[0015] (5) Obtain ray tracing results:

[0016] The structure S” obtained in step (3) is not related to the structure surrounding each sphere. q Intersecting incident rays and the non-S obtained in step (4) q The incident rays intersecting the triangular plane elements within the plane are used as the tracking result.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention first constructs multiple sphere-enclosed structures containing several triangular planar elements, and then sorts these structures sequentially along the ray direction. Next, it performs intersection detection on the incident ray with each sphere-enclosed structure to eliminate all triangular planar elements within spheres that do not intersect with the ray. This eliminates redundant line-plane intersection calculations and avoids the workload impact of numerous redundant ray-triangular planar element intersection detections caused by the rejection of a single enclosed sphere, which can only exclude one triangular planar element. This effectively improves tracking efficiency. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0020] Figure 2 This is a schematic diagram of the maximum and minimum vectors in this invention;

[0021] Figure 3 This is a schematic diagram of the sphere-enclosed structure in this invention;

[0022] Figure 4 This is a schematic diagram of the detection of the intersection of the ray and the sphere-enclosed structure in this invention;

[0023] Figure 5 This is a schematic diagram of the sphere-enclosed structure intersecting with the ray in this invention;

[0024] Figure 6 This is a schematic diagram of the intersection detection of rays and triangular plane elements in this invention;

[0025] Figure 7 This is a schematic diagram of the ray tracing visualization process in this invention;

[0026] Figure 8 This is a comparison chart of simulation results of the ray tracing accuracy of the present invention and existing technologies. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] Reference Figure 1 The present invention includes the following steps:

[0029] Step 1) Construct the sphere-enclosed structure:

[0030] The target geometric model is discretized, and the vertex information of the N triangular plane elements obtained from the discretization is used to construct a structure S = {S}, which is enclosed by M spheres with radius r. m |1≤m≤M}, where N≥1, M=I×J×K, where I, J, and K represent the number of structures enclosed by the sphere in the x, y, and z directions, respectively, and Sm This represents the structure enclosed by the m-th sphere. In this embodiment, a dihedral with dimensions of 1m×3m×3m is used as the target model, which is discretized to 1200 triangular plane elements, and 9 sphere-enclosed structures are constructed.

[0031] According to such Figure 2 The vector V, composed of the maximum coordinates of the vertices in the x, y, and z directions of the N triangular plane elements shown, is... max (x max ,y max ,z max The vector V consisting of the minimum coordinate value and the minimum coordinate value min (x min ,y min ,z min ), and V max (x max ,y max ,z max V min (x min ,y min ,z min As the maximum and minimum vectors, these two vectors are not necessarily on the triangular plane elements; they can form a coordinate axis bounding box AABB that includes all triangular plane elements, corresponding to... Figure 2 A bounding box structure with a dashed center line.

[0032] Then, the radius r of the sphere-enclosed structure is calculated, and the S of each sphere-enclosed structure is calculated using r. m The center vector C of the sphere m :

[0033]

[0034] T max =Max(T) x ,T y ,T z )

[0035]

[0036]

[0037] 1≤i≤I, 1≤j≤J, 1≤k≤K

[0038]

[0039] Among them, T max T represents the maximum dimension of the target geometric model in the x, y, and z directions. x T y and T zThese represent the dimensions of the target geometric model in the x, y, and z directions, respectively. Max(·) represents the maximum value operation. i, j, and k represent the indices of the sphere-enclosed structure in the x, y, and z axes, respectively. ceil(·) represents the round-up operation.

[0040] Through S m The radius r and the center vector C of the sphere m The sphere enclosing structure S can be m The structure is characterized in such a way that the M spheres that are constructed do not contain any triangular planar elements.

[0041] The sphere divides the triangular plane elements associated with the sphere into the interior of the sphere. Using the vector positions of the center points and three vertices of N triangular plane elements, the N triangular plane elements are divided into their corresponding spherical enclosing structures. If any point of a triangular plane element's center point or any of its three vertices lies within the spherical enclosing structure S... m Internally, the triangular planar element is divided into the spherical enclosing structure S. m In the middle, traversing N triangular plane elements, we obtain as follows: Figure 3 The structure S = {S} is surrounded by M spheres. m |1≤m≤M}. If a single triangular planar element is associated with multiple spheres, meaning its center point and three vertices are located in different spheres, then that triangular planar element is simultaneously assigned to multiple spheres. Thus, the constructed structure enclosed by M spheres contains a number of triangular planar elements, the exact number is uncertain, and each sphere may contain at least no triangular planar elements and at most all N triangular planar elements.

[0042] Step 2) Sort all the structures enclosed by the spheres according to the vector projection of the sphere's center:

[0043] Calculate the projection l = {l} of the center vector of the structure surrounded by each sphere onto the incident ray along the incident direction. m |1≤m≤M}, and sort the M spherical enclosing structures in ascending order of projection, to obtain the M spherical enclosing structures S'={S'} in the direction of incident ray propagation, ordered from near to far from the origin of the incident ray. m |1≤m≤M}, where S' m Let m represent the structure enclosed by the m-th sphere after sorting. The projection of the center vector of each enclosed structure onto the incident ray direction is given by... Calculate, where, The unit vector representing the direction of the incident ray.

[0044] Step 3) Perform intersection detection on the incident rays and the structure enclosed by each sphere:

[0045] Determine the structure S' enclosed by each sorted sphere. mThe closest distance h from the center of the sphere to the incident ray m Does the radius r of the structure enclosed by the sphere satisfy h? m If ≤r, then S' m Intersecting with the incident ray, a structure S”={S” is obtained, consisting of Q spheres that intersect with the incident ray. q If |1≤q≤Q}, then proceed to step 4); otherwise, the incident ray leaves the target surface, ray tracing ends, ray tracing is stopped, and step 5 is executed.

[0046] Each sphere surrounds the structure S' m The closest distance h between the center of the sphere and the incident ray m The positional relationship between them is as follows Figure 4 As shown. The positional relationship between the incident ray and the structure surrounded by the three spheres is as follows. Figure 5 As shown;

[0047] Sphere-enclosed structure S' m The closest distance h from the center of the sphere to the incident ray m The calculation formula is:

[0048]

[0049] Where P represents the position vector of the starting point of the incident ray, and |·| represents the modulus operation.

[0050] Step 4) Perform intersection detection on the incident ray and the triangular plane elements within the structure surrounded by each sphere:

[0051] like Figure 6 As shown, the intersection of the incident ray and the triangular plane element is detected. By determining the intersection, the structure S” is enclosed by each sphere that intersects with the incident ray. q Does the simultaneous equations of the triangular plane elements within the triangle have a solution, i.e., do the ray parametric equations... Combining this with the triangular plane parametric equation T(u,v)=(1-uv)V0+uV1+vV2, we obtain the simultaneous equations. Where V0, V1, and V2 represent the three vertex vectors of the triangular plane element, and t represents the distance the ray travels. Determine if the equation has a solution; if so, then the incident ray and S” q The triangular plane elements intersect, and the reflected ray is obtained with the intersection of the incident ray and the triangular plane element as the starting point and the direction calculated using Fresnel's law as the reflection direction. The reflected ray is then used as the incident ray and step 2) is executed, that is, ray reflection. The reflected ray is used as the new incident ray to continue ray tracing, forming a recursion. Otherwise, the incident ray leaves the target surface, the ray tracing ends, the ray tracing stops, and step 5) is executed.

[0052] like Figure 7As shown in (a), the incident ray intersects the three spheres and also intersects the triangular facet within the third sphere. The ray is reflected, generating a reflected ray as shown in (a). Figure 7 As shown in (b), the reflected ray is used as the new incident ray to continue ray tracing. The incident ray intersects with the five spheres and with the triangular facet within the fourth sphere. The ray is reflected, generating a reflected ray as shown in (b). Figure 7 As shown in (c), the reflected ray is used as the new incident ray to continue ray tracing. The incident ray intersects the three spheres, but does not intersect the triangular facets inside the three spheres, indicating that the ray leaves the target surface at this time, the ray tracing ends, and the ray tracing stops.

[0053] Step 5) Obtain the ray tracing results:

[0054] The structure S” obtained in step 3) is not related to the structure enclosed by each sphere. q Intersecting incident rays and the non-S obtained in step 4) q The incident ray that intersects the triangular plane elements within the target is used as the tracking result. This ray tracking result can be used in the SBR algorithm for subsequent far-field integration calculations to obtain the target's RCS.

[0055] The technical effects of the present invention will be illustrated below through simulation experiments.

[0056] 1. Simulation conditions and content:

[0057] The method of this invention performs accelerated ray tracing on the surface of a target model. The RCS simulation data obtained from the ray tracing results is then used to verify the effectiveness of the ray tracing results of this invention, which is more efficient than existing ray tracing methods. The experimental equipment required for this invention is a computer with a C language compilation environment. The simulation conditions for this invention are an Intel(R) Core(TM) i5 CPU with a clock speed of 3.7GHz and 8GB of memory, running on a Windows 7 system with Visual Studio 2017 installed.

[0058] The frequency of the radar incident wave is set to 10 GHz, and the calculation angle is fixed. θ changes from 0° to 90°, using HH polarization. Ray tracing of a dihedral target is performed using a ray tracing method based on a spherical enclosure structure (as described in this invention) and existing ray tracing methods. The tracing time for both methods is calculated, and the results are as follows: Figure 8 See Table 1.

[0059] Simulation 1 compares the ray tracing accuracy of the present invention with that of existing technologies. The results are as follows: Figure 8 As shown.

[0060] Simulation 2 compares the tracking accuracy of the present invention with that of the prior art, and the results are shown in Table 1.

[0061] 2. Simulation Result Analysis:

[0062] Reference Figure 8 The ray tracing method based on a sphere-enclosed structure proposed in this invention and the traditional ray tracing method yielded almost identical simulation results, demonstrating the computational correctness of the ray tracing method based on a sphere-enclosed structure proposed in this invention.

[0063] Referring to Table 1, the computation time using the method of the present invention is shorter, verifying that the ray tracing method based on a sphere-enclosed structure of the present invention improves ray tracing efficiency.

[0064] Table 1

[0065] method Average computation time per angle Existing ray tracing methods 26.36s The ray tracing method of the present invention 6.38s

Claims

1. A ray tracing method based on a sphere enclosure structure, characterized in that, The method comprises the following steps: (1) constructing a sphere enclosing structure; Discretize the target geometric model and obtain the results from the discretization. The vertex information of each triangular plane element is used to construct... A radius is spherical enclosed structure ,in , , , and These respectively represent the sphere-enclosed structure in , and Number of directions Indicates the first A spherical enclosed structure; (2) sorting all the sphere enclosing structures according to the sphere center vector projection; Calculate the projection of the center vector of each sphere enclosure on the incident direction of the incident ray , and sort the sphere enclosures in the order of the projection from small to large, obtaining sphere enclosures in the order from near to far in the propagation direction of the incident ray , wherein represents the sphere enclosure after sorting (3) performing intersection detection on an incident ray and each sphere enclosing structure; Determine the enclosing structure of each sorted sphere The closest distance from the center of the sphere to the incident ray With respect to the radius of the structure enclosed by the sphere Does it meet the requirements? If so, then Intersecting with the incident ray, we obtain the intersection with the incident ray. A spherical surrounding structure If the incident ray leaves the target surface, proceed to step (4); otherwise, proceed to step (5). (4) performing intersection detection on the incident ray and a triangular plane element in each sphere enclosing structure intersected by the incident ray; Determine the structure enclosed by each sphere that intersects with the incident ray obtained in step (3). Does the simultaneous equation of the triangular plane element within the triangle have a solution? If so, then the incident ray and... The triangular plane elements intersect, and a reflected ray is obtained with the intersection of the incident ray and the triangular plane element as the starting point and the direction calculated using Fresnel's law as the reflection direction. The reflected ray is then used as the incident ray and step (2) is executed. Otherwise, the incident ray leaves the target surface and step (5) is executed. (5) obtaining a ray tracing result; the incident rays that do not intersect with each sphere-enclosing structure the incident rays that do not intersect with the triangular plane elements inside the incident rays that do not intersect with the triangular plane elements inside 2. The method of claim 1, wherein, The constructing in step (1) A sphere with a radius of The implementation steps are as follows: (1a) according to the maximum coordinate value of the vertex in , and directions and the minimum coordinate value of the vertex in , the radius of the sphere enclosing structure is calculated , and the center vector of each sphere enclosing structure is calculated : ； ； ； ； ； wherein maximizes the size of the target geometry model in , and directions, , and denote the size of the target geometry model in , and directions, denotes a max operation, , and denote the indices of the sphere enclosing structure in , and axes, denotes a ceiling operation; (1b) By radius and the center vector of the sphere The structure surrounding the sphere Characterize and utilize The vector positions of the center point and the three vertices of the triangular plane element will be... Each triangular plane element is divided into its corresponding spherical enclosure structure. If the center point or any one of the three vertices of a triangular plane element lies within the spherical enclosure structure... Internally, the triangular planar element is divided into a sphere-enclosed structure. In the middle, traversal Given triangular plane elements, we obtain... A spherical surrounding structure .

3. The method of claim 2, wherein, Each of the spheroid-enclosing structures in step (2) encloses the projection of the spheroid center vector in the direction of the ray incidence The calculation formula is: ； wherein denotes a unit vector in the direction of the incident ray.

4. The method of claim 3, wherein, each sphere enclosing structure in step (3) the closest distance from the sphere center to the incident ray The calculation formula is: ； where P denotes the position vector of the origin of the incident ray, denotes a modulo operation.

5. The method of claim 4, wherein, The incident ray described in step (4) intersects each triangular planar element within the sphere-enclosing structure acquired in step (3) whose expression is: ； wherein, represents a ray parameter equation, represents a triangular planar element parameter equation, , and represent three vertex vectors of a triangular planar element, respectively, represents a distance of ray propagation.

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