A method for two-way interpolation of trawl surface reconstruction and calculation of volume element volume of a trawl

Abstract

The present invention relates to a method for two-way interpolation of a trawl net surface reconstruction and volume element volume calculation, belonging to the engineering technology field of the main fishing gears in marine fisheries. Aiming at the problems of surface reconstruction and volume estimation after the underwater deformation of the trawl net, a series of trawl net surface construction techniques and volume estimation methods are constructed. In the present invention, we will use the three-dimensional spatial coordinates of the key nodes of the trawl net obtained from the flume experiment, and propose technical methods such as the longitudinal interpolation method of the trawl net surface combining cubic spline interpolation and three-Heimite interpolation, the polar coordinate spline interpolation method of the transverse cross-section, and taking the average of the combined results of the cross-section method interpolation and the vertical cross-section method interpolation to reconstruct the surface where the trawl net is located. Then, the finite element idea and the volume element method are used to calculate the volume of the trawl net after the surface reconstruction.

Description

Technical Field

[0001] The present invention relates to the engineering technology field of marine fishery, and in particular to a surface reconstruction by bidirectional interpolation method and a volume calculation by volume element method for a trawl net. Background Art

[0002] Trawl nets are important fishing gears widely used in marine fishery. The volume of a trawl net directly affects the volume of the filtered water body 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 of ocean fishing gears. Taking the mid-water trawl net most widely used in fishing operations as an example, in order to calculate the volume of the trawl net, the spatial coordinates of each mesh on the trawl net surface must be mastered, but in fact 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 bidirectional interpolation method, and then a method for calculating the volume of the trawl net by using the volume element 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 literatures have provided methods for calculating the volume of cages, basically using rough linear interpolation surfaces and volume element volume algorithms. Interpolation methods for three-dimensional space 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 to provide a brand-new technical method for reconstructing the trawl net surface by using the bidirectional interpolation method and estimating the trawl net volume by using the volume element 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, and propose a hybrid comprehensive method that combines multiple efficient interpolation methods, namely cubic spline interpolation, cubic Hermite interpolation, polar coordinate spline interpolation method, bidirectional interpolation of ring cross-section and longitudinal cross-section, etc., to reconstruct the surface where the trawl net is located, and then use the finite element idea and the volume element 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 bidirectional interpolation method and volume calculation by volume element 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 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.

[0009] (2) Along the X - axis direction, use a combination of cubic spline interpolation and cubic Hermite interpolation to interpolate the key coordinate points longitudinally on the trawl surface. Use cubic spline interpolation for the main part and cubic Hermite interpolation for the end part.

[0010] (3) On the ring of the cross - sectional ring where the key nodes are located, use the periodic polar - coordinate spline interpolation method to find the coordinates of the interpolation points on the ring.

[0011] (4) Ring - cross - section interpolation method: Divide the trawl surface into a finite number of irregular quadrilateral meshes and triangular meshes. Any interpolation point on the trawl surface must fall within a certain mesh. The cross - section perpendicular to the X - axis passing through this interpolation point has 4 intersections with each mesh. Combining the methods in steps (2) and (3) can obtain the coordinates of the interpolation point.

[0012] (5) Vertical - section interpolation method: Any interpolation point has intersections with the plane where the X - axis is located and all the rings where the key points are located. Passing through these intersections and the rearmost end - point of the trawl, using the method in step (2) for interpolation can obtain the coordinates of the interpolation point.

[0013] (6) Combine the two interpolation methods in steps (4) and (5). Take the average of the results of the two interpolation methods for the coordinates of the interpolation point to obtain the three - dimensional coordinates of each interpolation point on the trawl surface. The group of quadrilateral meshes formed by the connection lines between the transverse rings and the longitudinal interpolation points in the X - direction constitutes the trawl - located surface.

[0014] (7) Volume - element subdivision: Divide the line segment from the origin of the net - mouth center to the end - point of the rearmost end of the trawl into n equal parts along the X - axis direction. Then, starting from the first cross - sectional ring where the YZ plane of the net mouth is located, every two cross - sectional rings and the longitudinal connection lines in the X - direction of the corresponding coordinate points on the two rings together form a polyhedral geometry. Split the polyhedral geometry into a finite number of spatial tetrahedrons, and regard each tetrahedron as a volume element. The entire trawl is split into a set of tetrahedron volume elements with a finite number, connected in sequence and seamlessly joined.

[0015] (8) Use the coordinates of the interpolation points of the quadrilateral meshes on the ring and the corresponding equally - divided point coordinates on the X - axis in step (6) to calculate the volume of each tetrahedron volume element. Summing up the volumes of all volume elements can obtain the trawl volume.

[0016] The beneficial effects of the present invention are as follows: It not only proposes a novel trawl surface reconstruction technical method, but also provides a simple and easy-to-implement volume element method for calculating the volume of the trawl, 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. Description of the Drawings

[0017] Figure 1 Coordinates of 25 key trawl nodes (*) extracted through flume experiments; model net experiments at a water flow speed of 80 cm / s.

[0018] Figure 2 Local interpolation along the X-axis in the XY coordinate plane; (a) Cubic Hermite interpolation; (b) Cubic spline interpolation; (C) Hybrid cubic spline and cubic Hermite interpolation.

[0019] Figure 3 Interpolation of the net mouth coordinate points in the YOZ plane; (a) Linear interpolation; (b) Cubic Hermite interpolation; (C) Ordinary periodic cubic spline interpolation; (d) Periodic cubic spline interpolation based on polar coordinates.

[0020] Figure 4 Interpolation decomposition, origin O(0,0,0) and interpolation point P(x,y,z); (a) Interpolation of the annular cross-section, P(r,θ), x = |OC0|, y = rcosθ, z = rsinθ.; (b) Interpolation of the vertical cross-section.

[0021] Figure 5 Trawl interpolation surface obtained by the annular cross-section method (n = 60, m = 40).

[0022] Figure 6 Trawl interpolation surface obtained by the vertical cross-section method (n = 60, m = 40).

[0023] Figure 7 Trawl interpolation surface obtained by taking the average of the results of the annular cross-section method and the vertical cross-section method (n = 60, m = 40).

[0024] Figure 8 Finite volume element decomposition (n = 20, m = 16); (a) Each cake-shaped annular body is divided into sixteen parts; (b) Each "cake" part is decomposed into three tetrahedrons, such as 1, 2, and 3. Detailed Implementation Manner

[0025] In order to make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further described below with reference to specific drawings.

[0026] The present invention applies basic interpolation principles such as cubic spline interpolation, cubic Hermite interpolation, and periodic polar coordinate interpolation. (1) In the case of simple cubic spline interpolation method, the Range deformation phenomenon appears at the tail of the trawl. The curve of simple cubic Hermite interpolation is not smooth enough. Therefore, in order to obtain a longitudinally smooth interpolation curve and make the tail reasonably and realistically unchanged, we adopt a longitudinal interpolation method that combines cubic spline interpolation for the main body part and cubic Hermite interpolation for the tail part for the interpolation of key points on the longitudinal trawl surface in the X direction. (2) On the ring of the longitudinal cross-section perpendicular to the X axis, a periodic polar coordinate spline interpolation method with the center point of the ring as the origin is adopted to obtain the coordinates of each point on the trawl surface on the ring. (3) In order to obtain a more smooth and realistic trawl surface, the ring cross-section method interpolation and the vertical cross-section method interpolation are combined, and the average value of the two interpolation results is taken to reconstruct the trawl surface. (4) Utilizing the self-characteristics of the trawl reconstruction method, starting from the mouth of the net, a rotating polyhedron similar to a cylinder is formed between every two ring cross-sections. This ring-shaped polyhedron can be exactly decomposed into a finite number of tetrahedral volume elements. The vertex coordinates of these volume elements are the interpolation point coordinates and the equally divided point coordinates on the X axis, all of which are known. Therefore, the volume of each volume element can be calculated, and the sum of all volume elements is the volume of the trawl.

[0027] The above shows and describes the basic principles, main features, and advantages of the present invention.

[0028] (1) First, the spatial coordinates of the key nodes on the trawl surface in the water flow have been obtained. 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 most tail end of the trawl 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 trawl nodes have been obtained under the uniform flow experiment in the water tank (* marked points, Figure 1 );

[0029] (2) Along the X-axis direction, a combination of cubic spline interpolation and cubic Hermite interpolation is used to interpolate the key coordinate points longitudinally on the trawl surface. Taking the interpolation of the upper half of the coordinates on the XOY coordinate plane in this case as an example to illustrate the principle. The cubic Hermite interpolation curve is not smooth enough ( Figure 2 (a)). The cubic spline curve is smooth enough, but the Runge phenomenon appears near the end of the trawl ( Figure 2 (b)). We use cubic spline interpolation for the main body part and cubic Hermite interpolation for the end part, that is, cubic spline interpolation is used between the first four points, and cubic Hermite interpolation is used between the last four points, and a more ideal smooth curve can be obtained ( Figure 2 (c)). Cubic spline interpolation and cubic Hermite interpolation are very classic and commonly used interpolation methods, and their complex theoretical formulas are not given here.

[0030] (3) On the ring of the ring cross-section where the key nodes are located, use the periodic polar coordinate spline interpolation method to find the coordinates of the interpolation points on the ring. In this case, it is assumed that the period interval is [θ0, θ0 + 2π], where θ0 < θ1 < … < θ n-1 <θ n =θ0 + 2π. Then, in each interval [θ i , θ i+1 (i = 0, 1, …, n - 1), the following type of Hermite cubic spline function is:

[0031]

[0032] Here h i =θ i+1 -θ i , Δr i =(r i+1 -r i ) / h i , b i =dr(b i ) / dθ. b i+1 =dr(b i+1 ) / dθ is the first derivative at the interval endpoints. It is easy to know that the function r(θ) passes through the polar coordinate points (θ i , r i )(i = 0, 1, …, n). Calculate the first derivative bi of the spline at the nodes by minimizing the integral sum in formula (2), and then substitute bi into formula (1) to obtain the polar coordinate points (θ, r) for any given θ angle.

[0033]

[0034] For comparison, try four interpolation methods to interpolate the four key points on the plane where the net opening is located in the YOZ coordinate plane. The linear interpolation result has the largest error ( Figure 3 (a)), the cubic Hermite interpolation line is not smooth enough near the end point ( Figure 3 (b)); the shape of the ordinary cubic spline interpolation is pear-shaped and does not conform to the actual shape of the net opening ( Figure 3 (c)); only the result of the periodic polar coordinate spline interpolation is the best ( Figure 3 (d)).

[0035] For the ring cross-section with six key points along the x-axis direction (including the ring cross-section where the net opening is located), each ring cross-section passes through four key points. The circumferential angle [0, 2π] centered at the intersection of the ring cross-section and the x-axis is equally divided into n parts. After converting the three-dimensional coordinates of the four key points into polar coordinates (the high school mathematics formula is not given here) and substituting them into formulas (1) and (2), the polar coordinate points of the n equally divided points on the six ring cross-sections can be obtained.

[0036] (4) Ring-section method interpolation. The trawl surface is divided into 24 irregular quadrilateral meshes and 4 triangular meshes (at the tail) ( Figure 4 ). Any interpolation point P on the trawl surface must fall within one of the meshes. Assume that P(x, y, z) falls on the mesh as shown in the figure ( Figure 4 (a)). The four points that have a direct influence on P are A1, A2, B1, and B2. On the ring section passing through point P and parallel to the YOZ plane, assume that points C1 and C2 have been obtained through step (2), that is, point C1 can be obtained from A1 and B1 through cubic spline interpolation (if P is close to the tail, cubic Hermite interpolation is used), and similarly, C2 can be interpolated from A2 and B2. However, to obtain the coordinates of point P, C1 and C2 are not enough. We continue to obtain the coordinates of C3 and C4 in the same way, and then polarize the three-dimensional coordinates of C1, C2, C3, and C4 with C0 as the center, and perform periodic cubic spline interpolation according to the method in step (3) to obtain the polar coordinates P(r, θ). It can be transformed into three-dimensional coordinates P(x, y, z) through three formulas (x = |OC0|, y = rcosθ, z = rsinθ). B1 and B2 converge to point E at the end.

[0037] (5) Vertical-section interpolation method ( Figure 4 (b)). The perpendicular line PC0 of OE passes through P, and C0 is on the OE line. Assume that the angle between PC0 and the horizontal plane XOY is θ. Then, on the vertical section OPE passing through P, C1 is interpolated from A1, A2, A3, and A4 through periodic polar spline interpolation, and similarly, C2 can be obtained. Then, on the section OC1C2E, P(x, y, z) can be obtained from C1 and C2 through cubic Hermite interpolation or cubic spline interpolation. But here, the coordinate plane XOY needs to be rotated by an angle θ to the plane OC1C2E.

[0038] (6) Combine the two interpolation methods in steps (4) and (5), and take the average of the results of the two interpolation methods for the interpolation point coordinates to obtain the three-dimensional coordinates of each interpolation point on the trawl surface. In this case, on the X-axis, divide OE into n equal parts to obtain the sequence x0 < x1 < x2 … < x n . On the ring section parallel to the YOZ plane, with x i (i = 0, 1, 2, … n) as the center, the entire circumferential angle [0, 2π] is divided into n equal parts. In this way, the trawl surface is evenly divided into quadrilateral meshes, and then the interpolation methods described in steps (4) and (5) are used to interpolate each mesh intersection point respectively.

[0039] Only using (4) ring-section interpolation ( Figure 5 ), the trawl surface is acceptable, but the smoothness is slightly poor, especially the tail is overly rigid. Only using (5) vertical-section interpolation ( Figure 6), the trawl surface is also acceptable, but not very smooth. We combine two methods of ring-section interpolation and vertical-section interpolation, that is, for each interpolation point P, we use the interpolation methods in steps (4) and (5) respectively. The average value of the coordinates of point P obtained by the two methods is taken as the interpolation result of point P. Figure 7 ) This is the required optimal trawl interpolation surface.

[0040] (7) Subdivision of volume elements. In this case, with the center line OE of the trawl as the axis Figure 4 ), use planes parallel to YOZ to cut each layer of the grid from left to right. In turn, every two ring sections and the longitudinal connections in the X direction of the corresponding coordinate points on the two rings together form a polyhedral geometry, similar to a ring in the shape of a layer cake Figure 8 (a). Each grid on the trawl surface corresponds to a "cake" Figure 8 (b), which can be further split into three tetrahedrons (M - BCD, M - ABD, M - ABN). When N is the end point E of the trawl tail, points A, B, and N shrink to point E simultaneously, leaving only one tetrahedron M - CDE. The entire trawl is split into a set of tetrahedron volume elements with a finite number, connected in sequence and seamlessly joined.

[0041] (8) Using the coordinates of the interpolation points of the quadrilateral grids on the ring and the corresponding equally divided points on the X axis in step (6), according to the tetrahedron volume formula (3), calculate the volume of each tetrahedron volume element, and the sum of the volumes of all tetrahedrons gives the trawl volume.

[0042]

[0043] where abs is the absolute value, det is the determinant, and (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) represent the coordinates of the four vertices of each tetrahedron.

[0044] To obtain the trawl volume accurately enough, we divide OE into 600 equal parts, and at the same time divide the central angle 2π in the ring section into 600 equal parts, and the volume of the trawl model net is 0.147 cubic meters.

[0045] The present invention has been described exemplarily above 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 bidirectional interpolation of a trawl net, trawl net surface reconstruction, and volume element volume calculation, characterized in that The steps are as follows: (1) First, the spatial coordinates of the key nodes on the trawl surface in the water flow are obtained. A three-dimensional coordinate system is established with 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; (2) Along the X-axis direction, a combination of cubic spline interpolation and cubic Hermite interpolation is used to interpolate the longitudinal key coordinate points on the trawl surface. Cubic spline interpolation is used for the main part, and cubic Hermite interpolation is used for the end; (3) On the ring of the cross-section where the key nodes are located, the periodic polar coordinate spline interpolation method is used to find the coordinates of the interpolation points on the ring; Suppose the period interval is [θ0, θ0 + 2π], where θ0 < θ1 < … < θ n-1 <θ n = θ0 + 2π; Then, in each interval [θ i , θ i+1 (i = 0, 1, …, n - 1), a kind of Hermite cubic spline function is as shown in Equation (1): where h i = θ i+1 - θ i , Δr i = (r i+1 - r i ) / h i , b i = dr(b i ) / dθ; b i+1 = dr(b i+1 ) / dθ is the first derivative at the interval endpoints; It is easy to know that the function r(θ) passes through the polar coordinate points (θ i , r i )(i = 0, 1,..., n); The first derivative b of the spline at the node is calculated by minimizing the integral sum in Equation (2). i Then, b i is substituted into Equation (1) to obtain the polar coordinate point (θ, r) for any given angle θ. (4) Ring cross-section interpolation method: The trawl surface is divided into a finite number of irregular quadrilateral meshes and triangular meshes. Any interpolation point on the trawl surface must fall within a certain mesh. The cross-section perpendicular to the X-axis passing through this interpolation point has 4 intersections with each mesh. The coordinates of the interpolation point can be obtained by combining the methods in (2) and (3) above; (5) Vertical cross-section interpolation method: Any interpolation point has intersections with the plane where the X-axis is located and all the rings where the key points are located. The coordinates of the interpolation point can be obtained by interpolating through these intersections and the end point of the rearmost part of the trawl using the method in (2); (6) By combining the two interpolation methods in (4) and (5), the coordinates of the interpolation point are taken as the average of the results of the two interpolation methods to obtain the three-dimensional coordinates of each interpolation point on the trawl surface. The group of quadrilateral meshes formed by the connection lines between the transverse rings and the longitudinal interpolation points in the X direction constitutes the surface where the trawl is located; (7) Volume element subdivision: The line segment from the origin of the net mouth center to the end point of the rearmost end of the trawl is equally divided into n parts along the X-axis direction. Then, starting from the first cross-section where the YZ plane of the net mouth is located, every two cross-sections and the longitudinal connection lines in the X direction of the corresponding coordinate points on the two rings together form a polyhedral geometry; the polyhedral geometry is split into volume elements, split into a finite number of spatial tetrahedrons, and each tetrahedron is regarded as a volume element; the entire trawl is split into a set of tetrahedron volume elements with a finite number, connected in sequence and seamlessly joined; (8) Using the coordinates of the quadrilateral mesh interpolation points on the ring in (6) and the corresponding equally divided point coordinates on the X-axis, calculate the volume of each tetrahedron volume element, and the sum of the volumes of all volume elements can obtain the trawl volume.

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