A method, program, device, and storage medium for body-fitting free deformation of ship and marine structures based on a general convex hexahedron.

Abstract

This invention belongs to the field of digital deformation technology for ship and marine engineering structures, specifically relating to a method, program, device, and storage medium for body-fitting free deformation of ship and marine structures based on a general convex hexahedron. This invention improves upon traditional free deformation methods by replacing the cuboid control frame with a general convex hexahedron control frame. It innovatively combines coplanarity / convexity checks with trilinear interpolation to achieve the construction and verification of the convex hexahedron control frame and the generation of control points. It combines intelligent optimization methods with Bernstein basis functions and proposes a two-step screening criterion to achieve efficient parametric expression and deformation of three-dimensional geometry. This invention can maintain accurate deformation of complex three-dimensional geometry even when the deformation control frame fits the bow or stern plate, areas with large curvature changes and high tilt angles, and can also reduce the space of design variables to achieve efficient numerical optimization design.

Description

Technical Field

[0001] This invention belongs to the field of geometric digital deformation technology of ships and marine engineering structures, specifically relating to a method, program, equipment and storage medium for body-fitting free deformation of ship and marine structures based on a general convex hexahedron. Background Technology

[0002] Free deformation methods, as a classic geometric parametric approach, are widely used for local geometric adjustments of complex surfaces in fields such as shipbuilding and aerospace. Traditional free deformation methods are based on cuboid control frames, achieving global or local deformation by moving control vertices. However, in practical engineering applications, especially when optimizing the geometry of ship and marine engineering structures, traditional methods have the following limitations: When using traditional free deformation methods to handle complex local shapes of the hull, such as the bow and stern plate where curvature changes significantly and tilt angles are high, the gap between the cuboid control frame parallel to the geodetic coordinate system axis and the hull surface is large. This results in low sensitivity of control point movement to hull surface deformation, poor intuitiveness, and difficulty in determining a reasonable strategy for selecting control points.

[0003] Although many scholars have improved traditional free deformation methods and applied them in various fields, there is still a lack of body-fitting free deformation methods that are applicable to complex three-dimensional hulls and other curved surfaces, and that can achieve efficient global or local deformation of hulls and other geometric features using only a few design variables and a small deformation design space. Summary of the Invention

[0004] The purpose of this invention is to provide a method, program, device, and storage medium for the free deformation of ship and marine structures based on a general convex hexahedron.

[0005] A method for free deformation of ship and marine structures based on a general convex hexahedron includes the following steps:

[0006] Obtain the original three-dimensional geometric configuration of the ship and marine structure and its mesh point set, and determine the target deformation region;

[0007] Construct a Cartesian coordinate system and a general convex hexahedron that encompasses the target deformation region; obtain the three-dimensional coordinates of each grid point and each vertex of the general convex hexahedron in the Cartesian coordinate system in the original three-dimensional geometric configuration of the ship and marine structure.

[0008] The trilinear interpolation method is used to spatially parameterize the general convex hexahedron, determine the set of control points of the general convex hexahedron, and calculate the three-dimensional coordinates of each control point in the Cartesian coordinate system.

[0009] A cuboid control frame is inscribed outside a general convex hexahedron. The cuboid control frame completely encloses the general convex hexahedron, and all faces of the cuboid control frame are parallel to the Cartesian coordinate plane. Boundary values ​​are set according to the cuboid control frame. Based on the global coordinate maximum and minimum value criterion, the set of mesh points of the original three-dimensional geometric configuration of the ship and marine structure is initially screened to select the mesh points within the cuboid control frame, thus obtaining the initial candidate set of mesh points.

[0010] The initial candidate grid point set is further filtered based on the local parameter extremum criterion to select grid points within the target deformation region, thus obtaining the moving grid point set.

[0011] The deformation of a general convex hexahedron is performed to obtain the positions of each control point of the general convex hexahedron after deformation, and the movement vector is obtained. For each grid point in the set of moving grid points, the position after deformation is calculated based on the movement vector of each control point of the general convex hexahedron. Based on the position after deformation of each grid point, the three-dimensional geometric configuration of the ship and marine structure in the target deformation area is reconstructed, so as to realize the deformation operation of the original ship and marine structure.

[0012] Furthermore, the eight vertices of the general convex hexahedron are A, B, C, D, E, F, G, and H, and the six faces of the general convex hexahedron are ABCD, EFGH, ABFE, BCGF, CDHG, and DAEH, respectively, and all six faces are planar quadrilaterals; obtain the three-dimensional coordinates of each vertex of the general convex hexahedron in the Cartesian coordinate system:

[0013] A(x1,y1,z1), B(x2,y2,z2), C(x3,y3,z3), D(x4,y4,z4)

[0014] E(x5,y5,z5), F(x6,y6,z6), G(x7,y7,z7), H(x8,y8,z8)

[0015] Furthermore, the construction of a general convex hexahedron encompassing the target deformation region is specifically as follows:

[0016] Step 1: Construct a hexahedron that encompasses the target deformation region, and obtain the three-dimensional coordinates of each vertex of the hexahedron in the Cartesian coordinate system;

[0017] Step 2: Check whether the quadrilaterals corresponding to the six faces of the hexahedron are planar quadrilaterals; if all the quadrilaterals corresponding to the six faces are planar quadrilaterals, proceed to Step 3; otherwise, return to Step 1 to reconstruct the hexahedron that includes the target deformation region.

[0018] For quadrilateral BCGF, construct vectors. Calculate the mixed product

[0019] If m = 0, then points B, C, F, and G are coplanar, meaning that quadrilateral BCGF is a planar quadrilateral.

[0020] The same applies to the other five sides;

[0021] Step 3: Check whether the six planar quadrilaterals form a convex hexahedron;

[0022] For planar quadrilateral BCGF, establish the equation of plane BCGF:

[0023] a1x + a2y + a3z + b0 = 0

[0024] Among them, a1=(y3-y2)(z7-z2)-(z3-z2)(y7-y2), a2=(z3-z2)(x7-x2)-(x3-x2) (z7-z2), a3=(x3-x2)(y7-y2)-(y3-y2)(x7-x2), b0=-(a1x2+a2y2+a3z2);

[0025] Define function S i =a1x i +a2y i +a3z i +b0, substitute vertices A, D, E, and H that are not on the plane BCGF into the function S. i That is, i = 1, 4, 5, 8; if all S i >0 or all S i If <0, then the plane BCGF verification passes;

[0026] Similarly, the other five faces of the hexahedron are verified in turn. If all six faces pass the verification, the hexahedron is determined to be a general convex hexahedron; otherwise, return to step 1 to reconstruct the hexahedron that includes the target deformation region.

[0027] Furthermore, the method of using trilinear interpolation to spatially parameterize the general convex hexahedron and determine the set of control points for the general convex hexahedron is as follows:

[0028] Divide the 12 edges of a general convex hexahedron into 3 groups: AB, DC, EF, HG are group I, AD, BC, EH, FG are group II, and AE, BF, CG, DH are group III.

[0029] Divide each side of group I into l parts in the same way, with each part corresponding to a side with a length ratio of α. i ;

[0030] Divide each side of group II into m parts in the same way, with each part corresponding to a side length ratio of β. j ;

[0031] Divide each side of group III into n parts in the same way, with each part corresponding to a side length ratio of γ. k ;

[0032] Set parameter r i ,s j ,t k ∈[0,1], i=0,1,...,l, j=0,1,...,m, k=0,1,...,n;

[0033] r0 = s0 = t0 = 0, r l =s m =t n =1

[0034]

[0035] Determine the set of control points {P} of a general convex hexahedron. ijk}, P ijk =[r i ,s j ,t k ];

[0036] Based on the three-dimensional coordinates of the eight vertices of a general convex hexahedron in the Cartesian coordinate system, determine the three-dimensional coordinates of each control point in the control point set in the Cartesian coordinate system.

[0037]

[0038] Among them, M 0,0,0 =A,M 1,0,0 =B,M 1,1,0 =C,M 0,1,0 =D,M 0,0,1 =E,M 1,0,1 =F,M 1,1,1 =G,M 0,1,1 =H.

[0039] Furthermore, the step of setting boundary values ​​based on the cuboid control box specifically involves:

[0040] x min =min(x1,x2,…,x8), x max =max(x1,x2,…,x8)

[0041] y min =min(y1,y2,…,y8), y max =max(y1,y2,…,y8)

[0042] z min =min(z1,z2,…,z8), z max =max(z1,z2,…,z8)

[0043] For any grid point P d The three-dimensional coordinates in the Cartesian coordinate system are (x d ,y d ,z d If x d ∈[x min ,x max ], y d ∈[y min ,y max ], z d ∈[z min ,z max ], then the grid point P d Add to the initial candidate grid point set Ω1.

[0044] Furthermore, the initial candidate grid point set is further filtered based on the local parameter extremum criterion, specifically as follows:

[0045] For grid point Q in the initial candidate grid point set Ω1 e Solve the minimization problem:

[0046]

[0047] in, This means selecting i elements without replacement from l distinct elements to form a group. and Similarly;

[0048] Get grid point Q e The corresponding parameters (u,v,w); if u∈[0,1],v∈[0,1],w∈[0,1], then the grid point Q is... e Add the moving grid point set Ω2.

[0049] Furthermore, a deformation is performed on the general convex hexahedron to obtain the control points P of the general convex hexahedron. ijk Position P′ after deformation ijk , obtain the movement vector For each grid point R in the moving grid point set Ω2 f Based on the movement vectors of each control point of a general convex hexahedron Calculate the position R′ after deformation f To enable deformation operations on the original ship and marine structures;

[0050]

[0051] Based on the deformed position R′ of each grid point fReconstruct the three-dimensional geometric configuration of the ship and marine structure in the target deformation region to realize the deformation operation of the original ship and marine structure.

[0052] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method for free deformation of ship and marine structures based on a general convex hexahedron.

[0053] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for body-fitting free deformation of ship and marine structures based on a general convex hexahedron.

[0054] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the above-described method for free deformation of ship and marine structures based on a general convex hexahedron.

[0055] The beneficial effects of this invention are as follows:

[0056] This invention improves upon traditional free deformation methods by replacing the cuboid control frame with a general convex hexahedral control frame. It innovatively combines coplanarity / convexity checks with trilinear interpolation to achieve the construction, verification, and control point generation of the convex hexahedral control frame. Furthermore, it combines intelligent optimization methods with Bernstein basis functions and proposes a two-step screening criterion to achieve efficient parametric representation and deformation of 3D geometry. This invention can maintain accurate deformation of complex 3D geometry even when the deformation control frame fits closely to areas with large curvature changes and high tilt angles, such as the bow or stern plate, and can also reduce the space of design variables to achieve efficient numerical optimization design. Attached Figure Description

[0057] Figure 1 This is the overall flowchart of the present invention.

[0058] Figure 2 This is a schematic diagram illustrating the overall implementation effect of the present invention.

[0059] Figure 3 This is a schematic diagram of vertex coordinates in an embodiment of the present invention.

[0060] Figure 4 This is a flowchart illustrating the verification process of the convex hexahedral control body in an embodiment of the present invention.

[0061] Figure 5 This is a flowchart illustrating the grid point selection and local parameterization representation in an embodiment of the present invention.

[0062] Figure 6 This is a diagram showing the initial screening and local parameter calculation results of the cuboid control box in an embodiment of the present invention.

[0063] Figure 7 This is a diagram showing the secondary screening and local parameter calculation results of the convex hexahedral control frame in an embodiment of the present invention. Detailed Implementation

[0064] The present invention will now be further described with reference to the accompanying drawings.

[0065] To reduce the waste of sample points in the numerical simulation-based optimization design of ship and marine structure mechanical properties and to achieve more precise shape control over the 3D geometric model of the hull, this invention improves upon the traditional free deformation method by replacing the cuboid control frame with a convex hexahedron control frame placed at arbitrary angles. A body-fitting free deformation method based on this general convex hexahedron is proposed. This method reduces the gap between the 3D geometric configuration and the control frame, thereby achieving more accurate and intuitive deformation of complex curved surfaces such as the hull. Simultaneously, it effectively reduces the design space, laying a solid foundation for efficient numerical optimization design of the comprehensive performance of ship hulls and other structures.

[0066] A method for free deformation of ship and marine structures based on a general convex hexahedron includes the following steps:

[0067] Step 1: Obtain the original three-dimensional geometric configuration of the ship and marine structure, including the set of grid points, and construct a Cartesian coordinate system;

[0068] Step 2: Determine the target deformation region of the original ship and marine structure's three-dimensional geometric configuration, and construct a general convex hexahedron that encompasses the target deformation region;

[0069] The three-dimensional coordinates of the eight vertices of a typical convex hexahedron in Cartesian coordinates are:

[0070] A(x1,y1,z1), B(x2,y2,z2), C(x3,y3,z3), D(x4,y4,z4)

[0071] E(x5,y5,z5), F(x6,y6,z6), G(x7,y7,z7), H(x8,y8,z8)

[0072] Among them, ABCD is the bottom surface, EFGH is the top surface, and ABFE, BCGF, CDHG, and DAEH are the four side surfaces;

[0073] The construction of the general convex hexahedron that encompasses the target deformation region is specifically as follows:

[0074] Step 2.1: Construct a hexahedron that encompasses the target deformation region, and obtain the three-dimensional coordinates of each vertex of the hexahedron in the Cartesian coordinate system;

[0075] Step 2.2: Check whether the quadrilaterals corresponding to the six faces of the hexahedron are planar quadrilaterals;

[0076] If all six faces correspond to planar quadrilaterals, proceed to step 2.3; otherwise, return to step 2.1 to reconstruct the hexahedron that encompasses the target deformation region.

[0077] For quadrilateral BCGF, construct vectors. Calculate the mixed product

[0078] If m = 0, then points B, C, F, and G are coplanar, meaning that quadrilateral BCGF is a planar quadrilateral.

[0079] The same applies to the other five sides;

[0080] Step 2.3: Check whether the six planar quadrilaterals form a convex hexahedron;

[0081] Taking quadrilateral BCGF as an example, select vertices B, C, and G, and construct the vector:

[0082]

[0083] Calculate the normal vector of surface BCGF

[0084]

[0085] Using normal vectors Equation of plane BCGF with point B(x2,y2,z2):

[0086] a1x + a2y + a3z + b0 = 0

[0087] Among them, a1=(y3-y2)(z7-z2)-(z3-z2)(y7-y2), a2=(z3-z2)(x7-x2)-(x3-x2) (z7-z2), a3=(x3-x2)(y7-y2)-(y3-y2)(x7-x2), b0=-(a1x2+a2y2+a3z2);

[0088] Define function S i =a1x i +a2y i +a3z i +b0, substitute vertices A, D, E, and H that are not on the plane BCGF into the function S. i That is, i = 1, 4, 5, 8; if all S i >0 or all S i If <0, then the plane BCGF verification passes;

[0089] Similarly, verify the other five faces of the hexahedron in turn. If all six faces pass the verification, the hexahedron is determined to be a general convex hexahedron; otherwise, return to step 2.1 to reconstruct the hexahedron that includes the target deformation region.

[0090] Step 3: Divide the 12 edges of a general convex hexahedron into 3 groups: AB, DC, EF, HG are group I, AD, BC, EH, FG are group II, and AE, BF, CG, DH are group III.

[0091] The method employs trilinear interpolation to spatially parameterize the general convex hexahedron and determine the set of control points for the general convex hexahedron, specifically as follows:

[0092] Divide the 12 edges of a general convex hexahedron into 3 groups: AB, DC, EF, HG are group I, AD, BC, EH, FG are group II, and AE, BF, CG, DH are group III.

[0093] Divide each side of group I into l parts in the same way, with each part corresponding to a side with a length ratio of α. i ;

[0094] Divide each side of group II into m parts in the same way, with each part corresponding to a side length ratio of β. j ;

[0095] Divide each side of group III into n parts in the same way, with each part corresponding to a side length ratio of γ. k ;

[0096] Set parameter r i ,s j ,t k ∈[0,1], i=0,1,...,l, j=0,1,...,m, k=0,1,...,n;

[0097] r0 = s0 = t0 = 0, r l =s m =t n =1

[0098]

[0099] Parameter r i Control the normalized positions of the edges in group I, where r0 = 0 corresponds to the starting points A, D, E, and H of each edge; r l =1 corresponds to the endpoints B, C, F, and G, and the parameter r corresponds to the distance from the starting point to the endpoint. i A linear mapping from 0 to 1: 0 = r0 < r1 < r2 ... < r l =1;

[0100] Parameter s jControl the normalized positions of the edges in group II, where s0 = 0 corresponds to the starting points A, B, E, and F of each edge. m =1 corresponds to the endpoints D, C, H, and G, and the parameter s corresponds to the distance from the starting point to the endpoint. j A linear mapping from 0 to 1: 0 = s0 < s1 < s2 ... < s m =1;

[0101] Parameter t k Control the normalized position of the edges in group III, where t0 = 0 corresponds to the starting points A, B, C, and D of each edge, and t n =1 corresponds to the endpoints E, F, G, and H, and the parameter t corresponds to the distance from the starting point to the endpoint. k A linear mapping from 0 to 1: 0 = t0 < t1 < t2 ... < t n =1;

[0102] Determine the set of control points {P} of a general convex hexahedron. ijk}, P ijk =[r i ,s j ,t k ];

[0103] Based on the three-dimensional coordinates of the eight vertices of a general convex hexahedron in the Cartesian coordinate system, determine the three-dimensional coordinates of each control point in the control point set in the Cartesian coordinate system.

[0104]

[0105] Among them, M a,b,c The coordinates of the 8 vertices, i.e., M 0,0,0 =A,M 1,0,0 =B,M 1,1,0 =C,M 0,1,0 =D,M 0,0,1 =E,M 1,0,1 =F,M 1,1,1 =G,M 0,1,1 =H;

[0106] The interpolation basis functions in the x, y, and z directions are as follows:

[0107] N a (r i )=(1-r i ) 1-a r i a

[0108] N b (s j )=(1-s j ) 1-b s j b

[0109] N c (t k )=(1-t k ) 1-c t k c

[0110] Step 4: Inscribed a cuboid control frame outside the general convex hexahedron. The cuboid control frame completely encloses the general convex hexahedron, and each face of the cuboid control frame is parallel to the Cartesian coordinate plane. Set boundary values ​​according to the cuboid control frame, and perform preliminary screening of the mesh point set of the original ship and marine structure's three-dimensional geometric configuration based on the global coordinate maximum and minimum value criterion. Select the mesh points within the cuboid control frame and construct the initial candidate mesh point set Ω1.

[0111] The step of setting boundary values ​​based on the cuboid control box specifically involves:

[0112] x min =min(x1,x2,…,x8), x max =max(x1,x2,…,x8)

[0113] y min =min(y1,y2,…,y8), y max =max(y1,y2,…,y8)

[0114] z min =min(z1,z2,…,z8), z max =max(z1,z2,…,z8)

[0115] For any grid point P d The three-dimensional coordinates in the Cartesian coordinate system are (x d ,y d ,z d If x d ∈[x min ,x max ], y d ∈[y min ,y max ], z d ∈[z min ,z max ], then the grid point P d Add to the initial candidate grid point set Ω1;

[0116] Step 5: For each grid point in the initial candidate grid point set Ω1, solve the minimization problem to obtain the parameters (u,v,w) corresponding to the grid point; if u∈[0,1],v∈[0,1],w∈[0,1], then add the grid point to the moving grid point set Ω2.

[0117] Minimize the problem:

[0118]

[0119] Where u,v,w∈[0,1] are Bernstein parameters, representing the positions of grid points in the parameter space; B i,l (u),B j,m (v),B k,n (w) are Bernstein basis functions. This means selecting i elements without replacement from l distinct elements to form a group. and Similarly;

[0120] Step 6: Perform deformation on the general convex hexahedron to obtain the control points P of the general convex hexahedron. ijk Position P′ after deformation ijk , obtain the movement vector For each grid point R in the moving grid point set Ω2 f Based on the movement vectors of each control point of a general convex hexahedron Calculate the position R′ after deformation f ;

[0121]

[0122] Based on the positions of each grid point after deformation, the three-dimensional geometric configuration of the ship and marine structure in the target deformation area is reconstructed, realizing the deformation operation of the original ship and marine structure.

[0123] Example 1:

[0124] In a specific embodiment of the present invention, step S1: Select DTMB-5415 hull form as the reference hull form (where the main dimensional parameters are: length between perpendiculars is 1m, beam is 0.134m, draft is 0.043m, and depth is 0.135m), with the bow as the area to be deformed. The eight selected vertices are shown in the attached figure. Figure 3 .

[0125] In step S2, a Cartesian coordinate system is established, and the eight vertices are input in sequence, with coordinates (in meters) as follows:

[0126] A(0.3,-0.03,-0.065), B(0.498,-0.03,-0.065), C(0.498,0.03,-0.065)

[0127] D(0.3,0.03,-0.065), E(0.3,-0.0649,0.055), F(0.548,-0.0649,0.055)

[0128] G(0.548,0.0649,0.055),H(0.3,0.0649,0.055)

[0129] Determine if these eight vertices can form a general convex hexahedron: Perform a coplanarity check on the six quadrilaterals ABFE, BCGF, CDHG, DAEH, ABCD, and EFGH. The edge vectors are:

[0130]

[0131]

[0132] Taking quadrilateral BCGF as an example, construct vectors The results of calculating the mixed product m1 are as follows:

[0133]

[0134] Therefore, points B, C, F, and G are coplanar. Similarly, calculate m sequentially. i (i=2,3,4,5,6)=0, indicating that all six quadrilaterals are planar quadrilaterals.

[0135] Secondly, verify whether ABCDEFGH forms a convex hexahedron. Taking quadrilateral BCGF as an example, select vertices B, C, and G, and calculate the vectors. and the normal vector of surface BCGF

[0136]

[0137] From the cross product of vectors, we have

[0138] Based on the normal vector The equation of the plane formed by a point B(0.498, -0.03, -0.065) on the surface BCGF is:

[0139] a1(x-0.498)+a2(y+0.03)+a3(z+0.065)=0

[0140] That is, a1x + a2y + a3z + b0 = 0. Calculations yield a1 = 0.015576, a2 = 0, a3 = -0.00649, and b0 = -0.008. Substituting vertices A, E, D, and H into the function S... i =a1x i +a2y i +a3z i +b0(i=1,4,5,8), the final calculation result S i(i = 1, 4, 5, 8) < 0, the signs are consistent, and the plane BCGF is verified. Similarly, verify the other quadrilaterals, and finally verify that ABCDEFGH constitutes a general convex hexahedron.

[0141] Based on the 12 edges of the general convex hexahedron obtained from S2, they are divided into 3 groups: AB, DC, EF, HG are group I; DA, CB, HE, GF are group II; and AE, BF, CG, DH are group III. A uniform control point cloud is established at the bow, i.e., the number of control points in the three groups is set to 5×7×5. The edges of group I are evenly divided into 4 parts, and the corresponding value interval of parameter r [0,1] is discretized as follows: Divide the second group of edges evenly into 6 parts, and the corresponding value interval of parameter s [0,1] is discretized as follows: The edges of group III are evenly divided into 4 parts, and the corresponding value interval of parameter t [0,1] is discretized as follows: The global coordinates of each control point are calculated using trilinear interpolation, yielding the following expression:

[0142]

[0143] S4, Set the boundary value x of the cuboid control box based on the vertices of the hexahedron. min =0.3,x max =0.548,y min = -0.0649, y max =0.0649, z min =-0.065,z max =0.055. Based on the global coordinate extremum criterion, the mesh points on the hull surface are initially screened, and the (u,v,w) values ​​corresponding to each coordinate point within the cuboid frame are calculated. The calculation results are attached. Figure 6 As shown.

[0144] In step S6, the coordinates and corresponding (u,v,w) values ​​of the hull surface located within the convex hexahedron are selected in one step using the local parameter extremum criterion. The results are shown in the appendix. Figure 7 As shown.

[0145] Finally, as Figure 2 As shown, deformation is performed on a general convex hexahedron to obtain the positions of each control point of the general convex hexahedron after deformation, and the movement vector is obtained. For each grid point in the set of moving grid points, the position after deformation is calculated based on the movement vector of each control point of the general convex hexahedron. Based on the position after deformation of each grid point, the three-dimensional geometric configuration of the ship and marine structure in the target deformation area is reconstructed, thus realizing the deformation operation of the original ship and marine structure.

[0146] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for free deformation of ship and marine structures based on a general convex hexahedron, characterized in that: Obtain the original three-dimensional geometric configuration of the ship and marine structure and its mesh point set, and determine the target deformation region; Construct a Cartesian coordinate system and a general convex hexahedron that encompasses the target deformation region; Obtain the three-dimensional coordinates of each grid point and each vertex of a general convex hexahedron in the Cartesian coordinate system in the original three-dimensional geometric configuration of the ship and marine structure; the six faces of the general convex hexahedron are all planar quadrilaterals. The trilinear interpolation method is used to spatially parameterize the general convex hexahedron, determine the set of control points of the general convex hexahedron, and calculate the three-dimensional coordinates of each control point in the Cartesian coordinate system. A cuboid control frame is inscribed outside a general convex hexahedron. The cuboid control frame completely encloses the general convex hexahedron, and all faces of the cuboid control frame are parallel to the Cartesian coordinate plane. Boundary values ​​are set according to the cuboid control frame. Based on the global coordinate maximum and minimum value criterion, the set of mesh points of the original three-dimensional geometric configuration of the ship and marine structure is initially screened to select the mesh points within the cuboid control frame, thus obtaining the initial candidate set of mesh points. The initial candidate grid point set is further filtered based on the local parameter extremum criterion to select grid points within the target deformation region, thus obtaining the moving grid point set. For the initial set of candidate grid points within the grid , solve the minimization problem: wherein , , ; denotes a group consisting of different elements taken without replacement from different elements, and by analogy. acquiring grid points corresponding parameters if the condition is satisfied, the grid point is added to the set of mobile grid points ; The deformation of a general convex hexahedron is performed to obtain the positions of each control point of the general convex hexahedron after deformation, and the movement vector is obtained. For each grid point in the set of moving grid points, the position after deformation is calculated based on the movement vector of each control point of the general convex hexahedron. Based on the position after deformation of each grid point, the three-dimensional geometric configuration of the ship and marine structure in the target deformation area is reconstructed, so as to realize the deformation operation of the original ship and marine structure.

2. The method for free deformation of ship and marine structures based on a general convex hexahedron according to claim 1, characterized in that: The eight vertices of the general convex hexahedron are A, B, C, D, E, F, G, and H, and the six faces are ABCD, EFGH, ABFE, BCGF, CDHG, and DAEH, respectively, and all six faces are planar quadrilaterals. The three-dimensional coordinates of each vertex of the general convex hexahedron in the Cartesian coordinate system are obtained as follows: ， ， ， ， ， ， ， 。 3. The method for free deformation of ship and marine structures based on a general convex hexahedron according to claim 2, characterized in that: The construction of the general convex hexahedron that encompasses the target deformation region is specifically as follows: Step 1: Construct a hexahedron that encompasses the target deformation region, and obtain the three-dimensional coordinates of each vertex of the hexahedron in the Cartesian coordinate system; Step 2: Check whether the quadrilaterals corresponding to the six faces of the hexahedron are planar quadrilaterals; If all six faces correspond to planar quadrilaterals, proceed to step 3; otherwise, return to step 1 to reconstruct the hexahedron that includes the target deformation region. For quadrilateral BCGF, construct vectors. Calculate the mixed product ; like If points B, C, F, and G are coplanar, then quadrilateral BCGF is a planar quadrilateral. The same applies to the other five sides; Step 3: Check whether the six planar quadrilaterals form a convex hexahedron; For planar quadrilateral BCGF, establish the equation of plane BCGF: in, , , , ; Define function Substitute the vertices A, D, E, and H that are not on the plane BCGF into the function. ,Right now If all or all If so, the plane BCGF verification passes; Similarly, verify the other five faces of the hexahedron in turn. If all six faces pass the verification, the hexahedron is determined to be a general convex hexahedron. Otherwise, return to step 1 to reconstruct the hexahedron that includes the target deformation region.

4. The method for free deformation of ship and marine structures based on a general convex hexahedron according to claim 2, characterized in that: The method employs trilinear interpolation to spatially parameterize the general convex hexahedron and determine the set of control points for the general convex hexahedron, specifically as follows: Divide the 12 edges of a general convex hexahedron into 3 groups: AB, DC, EF, HG are group I, AD, BC, EH, FG are group II, and AE, BF, CG, DH are group III. Divide each side of group I into l parts in the same way, with each part corresponding to a side with a length ratio of . ; Divide each side of group II into m parts in the same way, with each part corresponding to a side with a length ratio of . ; Divide each side of group III into n parts in the same way, with each part corresponding to a side with a length ratio of . ; Setting parameters , , , ; ， ， ， Determine the set of control points for a general convex hexahedron , ; Based on the three-dimensional coordinates of the eight vertices of a general convex hexahedron in the Cartesian coordinate system, determine the three-dimensional coordinates of each control point in the control point set in the Cartesian coordinate system. in, , , , , , , , .

5. A method for free deformation of ship and marine structures based on a general convex hexahedron according to claim 2, characterized in that: The step of setting boundary values ​​based on the cuboid control box specifically involves: ， ， ， For any grid point The three-dimensional coordinates in the Cartesian coordinate system are ,like , , Then the grid point Add to the initial candidate grid point set .

6. The method for free deformation of ship and marine structures based on a general convex hexahedron according to claim 1, characterized in that: Perform deformation on a general convex hexahedron to obtain its control points. Deformed position , obtain the movement vector For moving grid point sets Each grid point in Based on the movement vectors of each control point of a general convex hexahedron Calculate the position after deformation : To enable deformation operations on the original ship and marine structures; Based on the deformed positions of each grid point Reconstruct the three-dimensional geometric configuration of the ship and marine structure in the target deformation region to realize the deformation operation of the original ship and marine structure.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 6.

9. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 6.

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