A method for weight polynomial trawling surface reconstruction and central radiation volume calculation

Abstract

A method for reconstructing a weighted polynomial trawl surface and calculating the central radiation volume, which relates to the engineering technology field of the main fishing gears in marine fishery. Aiming at the problems of surface reconstruction and volume estimation after the underwater deformation of the trawl, a series of trawl surface construction techniques and volume estimation methods are constructed: In the present invention, we will use the three-dimensional space coordinates of the key nodes of the trawl obtained in the flume experiment, propose an efficient triangulation method, a new weight coefficient formula, a lateral projection method, a combination of interpolation and extrapolation, use the generalized least squares fitting of local surface patch functions and the weighted polynomial interpolation method to reconstruct the surface where the trawl is located, and then use the finite element volume element idea and the central radiation method to calculate the volume of the trawl after the surface is reconstructed.

Description

Technical Field

[0001] The present invention relates to the engineering technical field of facility ocean fishery, and particularly relates to a polynomial fitting method for surface reconstruction of a trawl net and a central radiation method for volume calculation. Background Art

[0002] Trawl nets are important fishing gears widely used in ocean fishery. The volume of a trawl net directly affects the volume of filtered water and the catch. However, the shape of a trawl net is irregular, especially the calculation of the volume of a net fishing gear after deformation underwater, which is still a world-class problem and a frontier research topic for ocean fishing gears. Taking the midwater trawl net, which is most widely used in fishing operations, as an example, in order to calculate the volume of the trawl net, it is necessary to master the spatial coordinates of each mesh on the trawl net surface. However, in reality, this is impossible underwater. Based on the key coordinate data of the trawl net experiment in a water tank, the present invention provides a technique for reconstructing the surface where the trawl net is located by using the polynomial least squares method, and then a calculation method for the volume of the trawl net by using the central radiation method.

[0003] Currently, no research on the surface reconstruction of trawl nets and the calculation of trawl net volume has been found at home and abroad. For fishing gears with regular shapes, such as cylindrical or square cages, surface reconstruction and volume calculation may be relatively easy. In recent years, a very small number of documents have provided calculation methods for the volume of cages, basically adopting rough linear interpolation surfaces and volume element volume algorithms. Interpolation methods for three-dimensional spatial data have been relatively mature, such as linear interpolation, natural boundary interpolation, polynomial interpolation, spline interpolation, etc. Summary of the Invention

[0004] The purpose of the present invention is to make up for the lack of current underwater trawl net surface reconstruction and volume calculation technologies, and provide a new technical method for reconstructing the trawl net surface by using the weighted polynomial fitting method and estimating the volume of the trawl net by using the central radiation method.

[0005] In the present invention, we will use the spatial coordinates of the key nodes of the trawl net extracted from the water tank experiment, propose an efficient triangulation method, a new weight coefficient formula, a lateral projection method, a combination of interpolation and extrapolation, use the polynomial least squares fitting of local surface patches to reconstruct the surface where the trawl net is located, and then use the finite element volume element idea and the central radiation method to calculate the volume of the trawl net after surface reconstruction.

[0006] The technical problems solved by the present invention are realized by adopting the following technical solutions:

[0007] A method for surface reconstruction of a trawl net by using the weighted polynomial method and volume calculation by using the central radiation method, comprising the following steps:

[0008] (1) First, obtain the spatial coordinates of the key nodes on the trawl surface in the water flow. Taking the center of the net mouth as the coordinate origin, the plane where the net mouth is located as the YZ plane, and the direction of the line segment from the origin to the end point of the trawl's most trailing end as the positive X-axis direction, establish a three-dimensional space coordinate system;

[0009] (2) Triangulate the adjacent key nodes on the trawl surface, and successively triangulate all the key nodes;

[0010] (3) Number each triangulated triangle and project all the triangulations onto the coordinate plane where the net mouth is located;

[0011] (4) Define the area coordinates of each triangle and any point inside the triangle;

[0012] (5) Uniformly grid the projection area of the triangulated triangle on the coordinate plane where the net mouth is located;

[0013] (6) Establish an interpolation polynomial with weight coefficients for the grid coordinate points falling within the projection of the triangle;

[0014] (7) Using the area coordinates in step (4), establish the weight function of the interpolation polynomial in step (6);

[0015] (8) Establish the general surface patch function inside each triangle;

[0016] (9) Least squares fitting. For the coordinates of each grid point in step (5), apply the coordinates of the vertices of the triangle it falls into and the coordinates of several nearest key points (the number of which can be adjusted at any time according to the fitting effect). Using (8) for least squares fitting, the X coordinate of the corresponding point on the trawl surface for the two-dimensional grid coordinate point can be obtained. Therefore, the three-dimensional coordinates of the corresponding point (or interpolation point) on the trawl surface corresponding to the grid point coordinates can be obtained. Connect the adjacent interpolation points on the trawl surface in sequence to reconstruct the trawl surface.

[0017] (10) Finite volume element subdivision method: Taking the coordinate origin at the center of the net mouth as the center, connect this center and all the interpolation points on the trawl surface. Each grid on the YZ plane corresponds to four adjacent interpolation points on the trawl surface. The coordinate origin and these four interpolation points together form a space hexahedron. Connect one pair of non-adjacent interpolation points, and the connections between the four interpolation points and the center form two space tetrahedrons; thus, all the space inside the trawl can be decomposed into a finite number of continuous and seamlessly connected tetrahedron sets.

[0018] (11) Trawl volume calculation. Calculate the volume of each tetrahedron in (10), and then sum up the volumes of all these tetrahedrons to obtain the trawl volume.

[0019] The beneficial effects of the present invention are as follows: It not only proposes a technical method for trawl surface reconstruction, but also provides a brand-new trawl volume calculation formula and method, filling the gaps in the technical methods for surface reconstruction and volume estimation of deformable and irregular underwater fishing gears at home and abroad, and providing technical support for the engineering application and development of marine fishing gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Coordinates of 25 key nodes (*) of the trawl extracted through flume experiments; model net experiments at a water flow speed of 80 cm / s.

[0021] Figure 2 The surface determined by the key points is triangulated (looking down along the X coordinate) and divided into 44 triangles.

[0022] Figure 3 Project the triangulation onto the YZ coordinate plane and sequentially number all key points and triangles.

[0023] Figure 4 For the triangle T Figure 3 in m the structure (m = 1, 2,..., 44). d i , d j and d k are the distances of PP i , PP j and PP k respectively; e i , e j and e k are the distances of P j P k , P k P i and P i P j respectively. L i , L j and L k are the areas of the triangles ΔPP m P j P k , ΔPP k P i and ΔPP i P j relative to the triangle T m ; (b) The case of the point P outside the triangle T

[0024] Figure 5 The grid of the YZ plane, n = 40 * 40, h1 = (max(Y0) - min(Y0)) / n; h2 = (max(Z0) - min(Z0)) / n; y and z are respectively Figure 3The coordinate vectors of all key points in the Y and Z directions; Y0 and Z0 are the projection coordinate vectors of 25 coordinate points of the trawl net on the YZ plane.

[0025] Figure 6 The trawl net surface reconstructed by quadratic interpolation.

[0026] Figure 7 Finite volume element subdivision (taking n = 10 mesh as an example); a) Triangulation of each rectangular grid on the YZ coordinate plane; b) Each mesh vertex on the trawl net surface is connected to the coordinate origin (0, 0, 0) to form two tetrahedrons. Specific implementation manner

[0027] In order to make the technical means, creative features, achieved purposes and effects realized by the present invention easy to understand, the present invention will be further described below with reference to specific illustrations.

[0028] The present invention borrows the polynomial interpolation principle and spatial analytic geometry method for general image pixel clarity refinement. (1) The theoretical methods based on polynomials, weight functions and least squares fitting of surface patches are usually used for interpolating pixels of two-dimensional or three-dimensional images (such as photos with poor clarity) to obtain clearer and more delicate images. However, image pixel interpolation technology belongs to the algorithm theory under the microcosm. For the application to the macroscopic trawl net surface reconstruction, the present invention proposes a series of supporting technical methods such as a brand-new weight coefficient formula, a triangulation method for key points of the trawl net surface with hierarchical co-directional spiral, a projection method for the side of the triangulated triangle to the plane where the net mouth is located, an interpolation method for obtaining a complete trawl net surface by combining internal interpolation and external interpolation, a radiation method from the net mouth center to all interpolation points on the trawl net surface, and a volume calculation formula that only needs to use the coordinates of interpolation points on the trawl net surface. (2) Spatial analytic geometry method, all formulas used in the present invention are analyzed and calculated in three-dimensional space geometry and belong to spatial analytic geometry formulas.

[0029] The above shows and describes the basic principles, main features and advantages of the present invention.

[0030] (1) First, obtain the spatial coordinates of key nodes on the trawl net surface in the water flow. Taking the center where the net mouth is located as the coordinate origin, the plane where the net mouth is located as the YZ plane, and the direction of the end point line segment from the origin to the most tail end of the trawl net as the positive direction of the X axis, a three-dimensional space coordinate system is established. In this case, the three-dimensional spatial coordinates of 25 key nodes of the trawl net have been obtained under the uniform flow experiment in the water tank (* marked points, Figure 1 )

[0031] (2) Triangulate adjacent key nodes on the trawl surface. In this case, starting from the four key nodes at the net mouth, it is hierarchically split into triangles layer by layer upwards. The layering and triangles around the trawl key points are inclined in the same direction (counterclockwise or clockwise). The purpose of this arrangement is to make the reconstructed trawl interpolation surface smoother ( Figure 2 );

[0032] (3) Number each triangulated triangle and project all triangulations onto the coordinate plane where the net mouth is located. In this case, project the triangulation onto the YZ coordinate plane of the net mouth ( Figure 3 ). For ease of subsequent calculation, number each key point (x i , y i , z i )(i = 1, 2,... 25) and P i (y i , z i )(i = 1, 2,..... 25). P i is 's projection on the YZ coordinate plane.

[0033] (4) Define the area coordinates of each triangle T m and any point P inside the triangle. Let T m (m = 1, 2,... 44) be a triangle with vertices P i , P j and P k in the triangle, and (P i , P j , P k ) follow the right-hand rule ( Figure 4 ). The distances from the midpoint P(y, z) of T m to P i , P j and P k are d i , d j and d k respectively; e i , e j and e k are the distances of the sides P j P k , P k P i and P i P j respectively, and L i , L j and L k are respectively formed by the point P and P i , P j , P kThe area of the triangle formed by the opposite sides;

[0034] The area coordinates (L i , L j , L k ) describe the coordinates of the point P(y, z) inside T m relative to the vertex positions of T m , and the calculation formula is as follows:

[0035]

[0036] where S is the area of the triangle T m , (y h , z h )(h = i, j, k) are the coordinates of the vertices P m , P i , P j and P k of T

[0037] (5) Uniformly grid the projection area of the triangulated triangle on the coordinate plane where the mesh opening is located. The projection area of the triangulated surface on the YZ plane is evenly divided into rectangular mesh cells to obtain uniform interpolation points ( Figure 5 ). In this case, this area is divided into n = 40 * 40 mesh cells in the Y direction and the Z direction respectively. The spacing in the Y direction is h1, and the spacing in the Z direction is h2. If more interpolation points are needed, n can be increased according to requirements.

[0038] (6) Establish an interpolation polynomial for the grid coordinate points falling within the triangle projection. Constructing an interpolation polynomial, spatial interpolation based on a triangle is a hybrid method that combines triangulation, least - squares approximation theory, and moving weighted approximation methods. Among them, X is regarded as a binary function of Y and Z. Therefore, the polynomial interpolation surface polynomial function x = F(y, z) at points inside the triangle T m can be written as:

[0039] F(y, z) = w i (y, z)f i (y, z) + w j (y, z)f j (y, z) + w k (y, z)f k (y, z) (2)

[0040] where w i , w j and w k are weight functions, and f i , f j and f k are the vertices of the triangle T mThe nodal functions at the three vertices. The function f h (y, z) (h = i, j, k) is defined as the surface function in the least - squares sense passing through several points closest to point P h itself. h It is also called the surface patch function. w h (y, z) (h = i, j, k) has two properties: (1) At the vertex P m of T h , there is w h (y, z) = 1 (h = i, j, k); (2) w i + w j + w k = 1. Under these two properties, then F(y h , z h ) = f h (y h , z h ) = x h (h = i, j, k), that is, the function F(y, z) passes through all the vertices of the surface patch.

[0041] (7) Using the area coordinates in step (4), establish the weight function of the interpolation polynomial in step (6). In this case, through repeated exploration and attempts, we propose the following weight function that can obtain a smooth trawl surface.

[0042]

[0043] where S is the area of triangle T m , and (L i , L j , L k ) are the area coordinates of P(y, z) within T m .

[0044] (8) Establish the general surface patch function inside each triangle. It is easy to know that f i (y, z) passes through the triangle vertices (x i , y i , z i ). The coefficients a1, a2, …, a5 can be obtained by the least - squares method, and the general form of the surface patch function is as follows

[0045] f i (y, z) = a1u 2 + a2uv + a3v 2 + a4u + a5v + x i (4)

[0046] u = y - y i , v = z - z i

[0047] (9) Perform least - squares fitting. For the two - dimensional Y and Z coordinates of each grid point in step (5), apply the vertices of the triangle in which it falls and several nearest key points (j = 1, 2,... n, n can be adjusted at any time according to the fitting effect. In this case, n is between 4 and 8) of y j and z j coordinates. Substitute them into equation (4) in step (8), and the resulting f i (y, z) function value x and the corresponding of x j The sum of the squares of the values reaches the minimum in the least - squares sense, thus obtaining the values of coefficients a1, a2,..., a5. Substitute the Y and Z coordinates of each two - dimensional grid point together with the weight function (3) into the interpolation polynomial function (2), and the X coordinate of the point on the trawl surface corresponding to each grid point can be obtained. Connect the corresponding three - dimensional coordinate points of the grid points on the trawl surface in sequence, and the reconstructed trawl surface can be obtained ( Figure 6 ).

[0048] (10) Decomposition of finite - volume elements. Taking the coordinate origin at the center of the net mouth as the center, connect this center and all interpolation points on the trawl surface. Taking Figure 7 the n = 10 * 10 mesh (rectangular grid) that falls into the net mouth as an example, decompose the finite - volume element. In actual calculation, to obtain an accurate trawl volume, n can be set as large as possible. First, we perform triangulation on the mesh that falls into the net mouth ( Figure 7 (a)), then interpolate the four vertices of each mesh on the trawl surface and connect them to the coordinate origin (0, 0, 0) through four virtual line segments. The coordinate origin and the four vertices (interpolation points) of this mesh together form a hexahedron in space. Connect one pair of non - adjacent interpolation points, and thus the connection lines between each mesh and the origin form 2 spatial tetrahedrons. In this way, all the space inside the trawl is decomposed into a finite number of continuous and seamless tetrahedron sets.

[0049] (11) Trawl volume calculation. The volume of each tetrahedron in step (10) can be calculated by formula (5), and then the sum of the volumes of all these tetrahedrons is the internal volume of the trawl surface.

[0050]

[0051] where abs is the absolute value, det is the determinant, and (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) are the three - vertex coordinates of each tetrahedron on the trawl surface.

[0052] To obtain the trawl volume accurately enough, we set n = 600 * 600 meshes in the YZ coordinate plane, and the volume of the trawl model net is 0.147 cubic meters.

[0053] The present invention has been described exemplarily in conjunction with the accompanying drawings. Obviously, the specific implementation of the present invention is not limited by the above-mentioned manner. As long as various improvements are made by adopting the method concept and technical solution of the present invention, or directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A method for weight polynomial trawl surface reconstruction and central radiation volume calculation, characterized in that It includes the following steps: (1) First, obtain the spatial coordinates of the key nodes on the trawl surface in the water flow. Taking the center of the net mouth as the coordinate origin, the plane where the net mouth is located as the YZ plane, and the direction of the end point line segment from the origin to the rearmost end of the trawl as the positive X-axis direction, establish a three-dimensional space coordinate system; (2) Triangulate the adjacent key nodes on the trawl surface, and triangulate all key nodes in turn: starting from the four key nodes of the net mouth, split them into triangles layer by layer upward in sequence. The layering and triangles around the key points of the trawl are inclined in the same counterclockwise or clockwise direction, making the reconstructed trawl interpolation surface smoother; (3) Number each triangulated triangle and project all triangulations onto the coordinate plane where the net mouth is located; (4) Define the area coordinates of each triangle and any point inside the triangle; (5) Uniformly grid the projection area of the triangulated triangles on the coordinate plane where the net mouth is located; (6) Establish an interpolation polynomial with weight coefficients for the grid coordinate points falling within the triangle projection: Construct the interpolation polynomial. Spatial interpolation based on triangles is a hybrid method that combines triangulation, least squares approximation theory, and moving weighted approximation methods; among them, X is regarded as a binary function of Y and Z; at the points within triangle T m The polynomial interpolation surface polynomial function x = F(y, z) at the points within is as shown in Equation (2): F(y,z) = w i (y,z)f i (y,z) + w j (y,z)f j (y,z) + w k (y,z)f k (y,z)(2) where w i , w j and w k are weight functions, and f i , f j and f k are nodal functions at the three vertices of triangle T m ; the function f h (y, z) (h = i, j, k) is defined as the surface function in the least squares sense through several points closest to point P h itself other than point P h ; w h (y, z) (h = i, j, k) has two properties: (1) at the vertex P m of T h , there is w h (y, z) = 1 (h = i, j, k); (2) w i + w j + w k = 1; under these two properties, F(y h , z h ) = f h (y h , z h ) = x h (h = i, j, k), and the function F(y, z) passes through all the vertices of the surface patch; (7) Using the area coordinates in step (4), establish the weight function of the interpolation polynomial in step (6). The weight function for obtaining a smooth trawl surface is as shown in Equation (3): where S is the area of triangle T m , (L i , L j , L k ) are the area coordinates of P(y, z) within T m ; (8) Establish the general surface patch function inside each triangle; (9) Least squares fitting. For the coordinates of each grid point in step (5), apply the coordinates of the vertices of the triangle it falls into and several nearest key points. The number of key points selected can be adjusted at any time according to the fitting effect; use step (8) for least squares fitting to obtain the X coordinate of the corresponding point on the trawl surface for this grid point, thereby obtaining the three-dimensional coordinates of the corresponding point or interpolation point on the trawl surface for the grid point. Connect the adjacent interpolation points on the trawl surface in sequence to reconstruct the trawl surface; (10) Finite volume element subdivision method: Taking the coordinate origin at the center of the net mouth as the center, connect this center and all interpolation points on the trawl surface. Each grid on the YZ plane corresponds to four adjacent interpolation points on the trawl surface. The coordinate origin and these four interpolation points together form a space hexahedron. Connect one pair of non-adjacent interpolation points, and the connections between these four interpolation points and the center form two space tetrahedrons; thus, all the space inside the trawl can be decomposed into a finite number of continuous and seamlessly connected tetrahedron sets; (11) Trawl volume calculation. Calculate the volume of each tetrahedron in step (10), and then sum up all the volumes of these tetrahedrons to obtain the trawl volume.

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