A geometric constraint calculation technology suitable for free deformation parameterization

Abstract

The present invention discloses a geometric constraint calculation technology suitable for free deformation parameterization, including: p A method for calculating the intersection of a set direction #imgabs0# and a geometric shape surface, and a thickness constraint calculation method and system, a volume constraint calculation method and system using the intersection calculation method; wherein the intersection calculation method comprises: 1. triangulating the initial geometric shape surface to convert it into a discrete surface composed of multiple triangular planes; 2. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 3. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 4. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 5. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 6. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 7. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 8. calculating the thickness constraint of the initial geometric shape surface and the volume constraint of the initial geometric shape surface; 9. calculating the thickness constraint of the initial p The intersection point O′ along the set direction #imgabs1# with the triangular plane in the discrete surface p Coordinates in the Cartesian coordinate system #imgabs2#3, construct the FFD control volume based on B-spline for the geometric surface, and change the intersection point O′ p Embedded in the FFD control volume, calculate the intersection point O' p In the parameterized local coordinates of the FFD control body #imgabs3# this method can efficiently calculate the local coordinates of the intersection of a spatial point along a set direction with the geometric shape surface in the FFD control body, thereby realizing the calculation of geometric constraints under free deformation parameterization.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering design and optimization, and in particular relates to a geometric constraint calculation technology suitable for free deformation parameterization. Background Art

[0002] High-precision optimization technology is widely used in the fields of fluid dynamics and engineering structures. Geometric deformation is an important part of the overall or local shape surfaces of aerospace vehicles, ships, or automobiles. The free form deformation method (FFD) is mainly based on the idea of ​​deformation of elastic objects under force. The geometric shape surface to be deformed is embedded in a control body. When deformed, the shape of the control body is changed to indirectly change the geometric shape surface in the control body. Compared with the secondary development of conventional computer-aided design (CAD) software, it does not need to generate geometric shapes, does not require a strong reserve of geometric knowledge, has the advantages of simple deformation operation, continuous and smooth deformation process, and is applicable to arbitrary topological structures. In recent years, it has been widely used in the optimization design fields of aviation, aerospace, ships, and automobiles.

[0003] However, in the design optimization process of the overall or local shape surfaces of aerospace vehicles, ships, or automobiles, in order to meet the loading requirements of internal equipment, batteries, etc., certain geometric constraints, including thickness constraints and volume constraints, must be met. For the FFD parameterization method, each iteration step in the optimization process requires the three-dimensional geometric shape surface to be deformed by changing the shape of the control body, thereby changing its geometric constraints. Considering the difference between the FFD parameterization method and the CAD parameterization method, the traditional geometric constraint calculation method suitable for CAD parameterization is no longer applicable. Therefore, it is urgent to propose a geometric constraint calculation method suitable for free deformation parameterization to meet the geometric constraint requirements in the optimization design process of aviation, aerospace, ships, automobiles, etc. Summary of the invention

[0004] Purpose of the invention: The present invention provides a geometric constraint calculation technology suitable for free deformation parameterization, which can efficiently calculate the local coordinates of the intersection of a spatial point along a set direction and a geometric shape surface in the FFD control body, thereby realizing the calculation of geometric constraints under free deformation parameterization.

[0005] Technical solution: On the one hand, the present invention discloses a method of passing through a space point O p Along the set direction A method for calculating intersection points with a geometrical contour surface, wherein the geometrical contour surface is an overall contour surface or a partial contour surface of an aerospace vehicle, a ship, or an automobile; comprising the following steps:

[0006] S11, triangular meshing the initial geometric shape surface to convert it into a discrete surface composed of multiple triangular planes;

[0007] S12, calculate the space point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system

[0008] S13, constructing a B-spline-based FFD control volume for the geometric shape surface, embedding the intersection point O′p into the FFD control volume, and calculating the intersection point O′ p Parameterized local coordinates of the FFD control volume Specifically include:

[0009] S131. The FFD control volume enclosing the geometrical surface is:

[0010]

[0011] In the formula, (P i，j，k |i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD frame in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i，p (u), N j，p (v) and N k，p (w) are p-order B-spline basis functions in the parameterized space (u, v, w) in dimensions u, v, w respectively; the parameterized variables in dimensions u, v, w are all variables in the interval [0, 1];

[0012] S132, divide the FFD control volume equally along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into M u The parameterized space [0, 1] along the v direction is divided into M v The parameterized space [0, 1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are l=0,…,M u ; m = 0, ..., M v ; n = 0, ..., M w ;

[0013] Calculate each equally divided point and the intersection point O′ separatelyp Distance:

[0014]

[0015] Take the value such that d l，m，n The coordinates of the equal-division point with the smallest value in the parameterized space (u 0 , v 0 , w 0 ) as the initial value of Newton's method iteration;

[0016] S133, with (u 0 , v 0 , w 0 ) as the initial value, and use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume The specific optimization problem is as follows:

[0017]

[0018] stu,v,w∈[0,1]

[0019] Where V(u, v, w) is the Cartesian coordinate corresponding to the parameterized coordinate (u, v, w) in the FFD control volume;

[0020] The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold, t is the number of iterations, d t is O′ after the tth iteration p Distance error calculated at the optimized values ​​of the parameterized local coordinates of the FFD control volume;

[0021] The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume

[0022] Furthermore, the step S12 is specifically as follows:

[0023] Traverse the triangular plane in the discrete surface and determine the intersection of the triangular plane and the spatial point O p Along the set direction Is there an intersection:

[0024] According to the three vertices ap of the triangle plane 0 ,ap 1 ,ap 2 The coordinates of the equation are constructed:

[0025]

[0026] Where (x p ,y p , z p ) is the space point O p The coordinates of (x 0 ,y 0 , z 0 ) is ap 0 The coordinates of the The vector representation of (α 1 , β 1 , γ 1 ) is ap 1 to ap 0 The vector representation of (α 2 , β 2 , γ 2 ) is ap 2 to ap 0 The vector representation of ; s, t, r are the unknown quantities to be determined;

[0027] Solve the above equation. If there exists a solution of s≥0, t≥0 and s+t≤1, the triangle plane and the space point O p Along the set direction There is an intersection point, the intersection point O′ p Coordinates in Cartesian coordinate system for

[0028] On the other hand, the present invention provides a thickness constraint calculation method suitable for free deformation parameterization, comprising the following steps:

[0029] S21, determining the starting point and direction of the thickness constraint in the geometric shape surface;

[0030] S22, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the thickness constraint direction;

[0031] S23, take the starting point of the thickness constraint as the spatial point O p , the direction of the thickness constraint is the set direction The intersection points O of the starting point of the thickness constraint on the first curved surface and the second curved surface along the thickness constraint direction are calculated by using the above intersection calculation method. p ' 1 and O p ' 2 Parameterized local coordinates in the FFD control volume and The distance between the two intersection points is the thickness value of the thickness constraint.

[0032] Furthermore, it also includes:

[0033] S24. If the thickness value is not less than the thickness threshold of the thickness constraint, the thickness constraint is satisfied; otherwise, the thickness constraint is not satisfied.

[0034] Furthermore, the step 23 further includes:

[0035] When the control point of the FFD control body changes, according to the expression of the FFD control body and O p ' 1 , O p ' 2 Parameterized local coordinates in the FFD control volume and Recalculate O p ' 1 , O p ' 2 In Cartesian coordinates, the thickness value of the thickness constraint is updated according to the new values ​​of the two coordinates.

[0036] On the other hand, the present invention also provides a volume constraint calculation method suitable for free deformation parameterization, comprising the following steps:

[0037] S31, determining the boundary curve and direction of the volume constraint in the geometric shape surface, generating nodes on the boundary curve using an equal spacing method, and dividing the area enclosed by the boundary curve into a rectangular grid;

[0038] The Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve are calculated using the transfinite interpolation method;

[0039] S32, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the volume constraint direction;

[0040] S33, taking the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The above-mentioned intersection calculation method is used to calculate the parameterized local coordinates of the intersection of each rectangular mesh vertex on the first surface and the second surface along the volume constraint direction in the FFD control volume; the eight intersection points obtained from the four vertices of a rectangular mesh form a quadrangular prism; and the volume of the quadrangular prism is calculated;

[0041] S34. The volumes of all the quadrangular prisms are accumulated to obtain the volume value of the volume constraint.

[0042] Furthermore, the step 33 also includes:

[0043] When the control point of the FFD control body is changed, the coordinate value of each quadrangular prism vertex in the Cartesian coordinate system is recalculated according to the expression of the FFD control body and the parameterized local coordinates obtained in step S33; the volume of the quadrangular prism is updated according to the new coordinate values ​​of the quadrangular prism vertices.

[0044] The present invention also discloses a method for realizing the above-mentioned intersection calculation method. p Along the set direction An intersection calculation system intersecting with a geometrical contour surface, wherein the geometrical contour surface is an overall contour surface or a partial contour surface of an aerospace vehicle, a ship, or an automobile; comprising:

[0045] A triangular meshing module is used to perform triangular meshing on the initial geometric shape surface and convert it into a discrete surface composed of multiple triangular planes;

[0046] The intersection Cartesian coordinate calculation module is used to calculate the intersection point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system

[0047] The intersection point parameterized local coordinate calculation module is used to construct the FFD control volume based on B-spline for the geometric surface. p Embedded in the FFD control volume, calculate the intersection point O' p Parameterized local coordinates of the FFD control volume The specific calculation steps of the parameterized local coordinates are:

[0048] S131. The FFD control volume enclosing the geometrical surface is:

[0049]

[0050] In the formula, {P i，j，k |i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD frame in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i，p (u), N j，p (v) and N k，p(w) are p-order B-spline basis functions in the parameterized space (u, v, w) in dimensions u, v, w respectively; the parameterized variables in dimensions u, v, w are all variables in the interval [0, 1];

[0051] S132, divide the FFD control volume equally along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into M u The parameterized space [0, 1] along the v direction is divided into M v The parameterized space [0, 1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are 1=0,…,M u ; m = 0, ..., M v ; n = 0, ..., M w ;

[0052] Calculate each equally divided point and the intersection point O′ separately p Distance:

[0053]

[0054] Take the value such that d l，m，n The coordinates of the equal-division point with the smallest value in the parameterized space (u 0 , v 0 , w 0 ) as the initial value of Newton's method iteration;

[0055] S133, with (u 0 , v 0 , w 0 ) as the initial value, and use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume The specific optimization problem is as follows:

[0056]

[0057] stu,v,w∈[0,1]

[0058] Where V(u, v, w) is the Cartesian coordinate corresponding to the parameterized coordinate (u, v, w) in the FFD control volume;

[0059] The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold; t is the number of iterations, d t is O′ after the tth iteration p Distance error calculated at the optimized values ​​of the parameterized local coordinates of the FFD control volume;

[0060] The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume

[0061] On the other hand, the present invention also discloses a system for implementing the thickness constraint calculation method, comprising:

[0062] A thickness constraint starting point and direction determination module is used to determine the starting point and direction of the thickness constraint in the geometric shape surface;

[0063] A geometrical shape surface segmentation module is used to divide the geometrical shape surface into two parts, a first surface and a second surface, along a plane perpendicular to the thickness constraint direction;

[0064] Surface intersection calculation module, used to calculate the starting point of the thickness constraint as the space point O p , the direction of the thickness constraint is the set direction The above intersection calculation method is used to calculate the intersection point O′ of the thickness constraint starting point on the first curved surface and the second curved surface along the thickness constraint direction. p1 and O′ p2 Parameterized local coordinates in the FFD control volume and

[0065] Thickness value calculation module, used to calculate the thickness of the intersection point O' p1 and O′ p2 The parameterized local coordinates of the Cartesian coordinates are calculated according to the intersection point O′ p1 and O′ p2 The Cartesian coordinates of the thickness constraint are used to calculate the thickness value.

[0066] On the other hand, the present invention also provides a system for a volume constraint calculation method applicable to free deformation parameterization, comprising:

[0067] A volume constraint boundary curve and direction acquisition module is used to determine the boundary curve and direction of the volume constraint in the geometric shape surface;

[0068] A meshing module is used to generate nodes on the boundary curve using an equal spacing method and divide the area enclosed by the boundary curve into rectangular grids; a transfinite interpolation method is used to calculate the Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve;

[0069] A geometric shape surface segmentation module is used to divide the geometric shape surface into two parts, a first surface and a second surface, along a plane perpendicular to the volume constraint direction;

[0070] The surface intersection calculation module is used to take the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The above-mentioned intersection calculation method is used to calculate the parameterized local coordinates of the intersection of each rectangular mesh vertex on the first surface and the second surface along the volume constraint direction in the FFD control volume;

[0071] A quadrangular prism volume calculation module, used to calculate Cartesian coordinates according to parameterized local coordinates of the quadrangular prism vertices, and calculate the volume of the quadrangular prism according to the Cartesian coordinates of the quadrangular prism vertices, wherein the quadrangular prism is composed of eight intersection points of four vertices of a rectangular grid on the first curved surface and the second curved surface;

[0072] The volume value calculation module is used to accumulate the volumes of all quadrangular prisms to obtain the volume value of the volume constraint.

[0073] Beneficial effect: The space point O disclosed by the present invention p Along the set direction The intersection calculation method with the geometric shape surface, for the geometric shape of three-dimensional complex configuration, adopts a hybrid algorithm combining the Brute-Force method and the Newton method to efficiently calculate the local coordinates of the embedded position, and on this basis, according to the loading requirements of the internal equipment, realize the thickness constraint and volume constraint calculation under free deformation parameterization. This method can effectively solve the problem of geometric constraint calculation under free deformation parameterization, and provide technical support for the optimization design fields such as aviation, aerospace, shipbuilding, and automobiles. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 The space point O disclosed in the present invention p Along the set direction A flow chart of a method for calculating intersection points with a geometric contour surface;

[0075] Figure 2 A schematic diagram of the triangular discrete surface of the initial shape of the wing-body fused underwater glider;

[0076] Figure 3 is a schematic diagram of a B-spline or non-uniform rational B-spline surface patch;

[0077] Figure 4 It is a schematic diagram of a surface sheet represented in Plot3d format;

[0078] Figure 5 It is a schematic diagram of a surface body represented in STL format;

[0079] Figure 6 The space point O disclosed in the present invention p Along the set direction A schematic diagram of the composition of the intersection calculation system intersecting with the geometric shape surface;

[0080] Figure 7 Schematic diagram of thickness constraint in FFD control volume;

[0081] Figure 8 It is a flow chart of the thickness constraint calculation method applicable to free deformation parameterization disclosed in the present invention;

[0082] Fig. 9 A schematic diagram of the composition of a thickness constraint calculation system suitable for free deformation parameterization;

[0083] Fig.10 Schematic diagram of volume constraints in the FFD control volume;

[0084] Fig.11 It is a flow chart of the volume constraint calculation method applicable to free deformation parameterization disclosed in the present invention;

[0085] Fig.12 Schematic diagram of the composition of the volume constraint calculation system suitable for free deformation parameterization. DETAILED DESCRIPTION

[0086] The present invention is further explained below in conjunction with the accompanying drawings and specific implementation methods.

[0087] Embodiment 1:

[0088] The invention discloses a method for passing through a space point O p Along the set direction The method for calculating the intersection points of the geometrical contour surface is the overall contour surface or the partial contour surface of an aerospace vehicle, a ship, or an automobile. This embodiment takes the wing optimization design of a wing-body fused underwater glider as an example to illustrate the method. The process is as follows: Figure 1 As shown, the following steps are included:

[0089] S11, triangular meshing the initial geometric shape surface to convert it into a discrete surface composed of multiple triangular planes;

[0090] The initial geometric shapes described by different surface modeling methods are converted into discrete surfaces described by triangular meshes, such as Figure 2 The figure shows the triangular discrete surface of the initial shape of the wing-body fused underwater glider. The following describes in detail the specific process of constructing the initial geometric shape triangular discrete surface by different surface modeling methods.

[0091] (1) Construct triangular discrete surfaces from geometric shapes represented by B-spline or non-uniform rational B-spline methods. B-spline surfaces and non-uniform rational B-spline surfaces are mainly defined by the product of control point grids in two directions, two node vectors and univariate spline basis functions, where each control point grid is mainly composed of four vertices. Figure 3 The B-spline or non-uniform rational B-spline surface sheet is described. Each control point mesh is divided into two triangles, that is, triangular meshing is achieved.

[0092] (2) Constructed by a mesh file in Plot3d format. Plot3d format is a CFD mesh file format developed and widely used by NASA. It is often involved in the CFD programming process and can also be used to represent geometric surface shapes. Because it is a structured mesh, when it is used to represent a surface, each mesh unit is a quadrilateral composed of four vertices. Figure 4 It is a surface sheet represented in Plot3d format. Similarly, each control volume mesh is divided into two triangles, that is, triangular meshing is realized.

[0093] (3) Constructed from STL format files. STL was created by 3D Systems Software Company and is an unstructured triangular surface format that uses triangle unit normals and vertices (sorted by the right-hand rule) to describe the original geometric shape. It approximates the CAD model as a set of triangles and has been widely used in rapid prototyping, 3D printing and computer-aided manufacturing (CAM). Figure 5 It is a surface body represented in STL format. Since the STL format file itself is a triangular surface format, directly extracting the vertices of all triangles is the result of triangular meshing.

[0094] S12, calculate the space point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system The specific steps are:

[0095] Traverse the triangular plane in the discrete surface and determine the intersection of the triangular plane and the spatial point O p Along the set direction Is there an intersection:

[0096] The three vertices of a triangular plane are: h =(x h ,y h , z h ), 0≤h≤2}, then in the triangle from vertex ap 0 The two starting edges are:

[0097] Eh =ap h -ap 0 =(x h -x 0 ,y h -y 0 , z h -z 0 )=(α h , β h , γ h ), 1≤h≤2 (1)

[0098] Then each triangular discrete surface can be parameterized using two parameters (s, t), and any point on the triangular discrete surface can be described as the following expression:

[0099] P(s, t) = ap 0 +sE 1 +tE 2

[0100] =(x 0 +α 1 s+α 2 t,y 0 +β 1 s+β 2 t, z 0 +γ 1 s+γ 2 t)

[0101] =(x(s,t),y(s,t),z(s,t))

[0102] Wherein, when s≥0, t≥0, and s+t≤1, the point is inside the triangular discrete surface; otherwise, it is outside the discrete surface.

[0103] For any point O in space p (x p ,y p , z p ), given the projection direction After that, there is the following relationship expression between it and each triangular discrete surface:

[0104]

[0105] Converted into matrix form:

[0106]

[0107] Where (x p ,y p , z p ) is the space point O p The coordinates of (x 0 ,y0 , z 0 ) is ap 0 The coordinates of the The vector representation of (α 1 , β 1 , γ 1 ) is ap 1 to ap 0 The vector representation of the triangle side E 1 , (α 2 , β 2 , γ 2 ) is ap 2 to ap 0 The vector representation of the triangle side E 2 ; s, t, r are unknown quantities to be determined;

[0108] Solve the above equation. If there exists a solution of s≥0, t≥0 and s+t≤1, the triangle plane and the space point O p Along the set direction There is an intersection point. According to formula (3), we know that the intersection point O′ p Coordinates in Cartesian coordinate system for And when r≥0, if there is an intersection, it means that the intersection is located above the spatial point along the specified direction; when r≤0, if there is an intersection, it means that the intersection is located below the spatial point along the specified direction.

[0109] S13, construct the FFD control volume based on B-spline for the geometric shape surface, and make the intersection point O′ p Embedded in the FFD control volume, calculate the intersection point O' p Parameterized local coordinates of the FFD control volume Specifically include:

[0110] S131, the FFD control volume described by B-spline surrounding the geometrical shape surface is:

[0111]

[0112] In the formula, {P i，j，k |i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD frame in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i，p (u), N j，p (v) and Nk，p (w) are p-order B-spline basis functions in the parameterized space (u, v, w) in dimensions u, v, w respectively; the parameterized variables in dimensions u, v, w are all variables in the interval [0, 1];

[0113] Calculate the intersection point O′ p The parameterized local coordinates in the FFD control volume require the reverse solution of equation (4). Heuristic optimization algorithms (such as particle swarm algorithms, genetic algorithms, etc.) are a common local coordinate search algorithm, but their efficiency is low when solving, and in order to achieve a high convergence accuracy, the required amount of calculation is large; the Newton method can perform efficient local coordinate solutions, but it requires that the initial value of the iteration is very close to the true solution in order to converge. Therefore, the present invention adopts a hybrid algorithm that combines the Brute-Force method with the Newton method to achieve efficient solution of local coordinates. The specific process is as follows:

[0114] S132, divide the FFD control volume equally along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into M u The parameterized space [0, 1] along the v direction is divided into M v The parameterized space [0, 1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are l=0,…,M u ; m = 0, ..., M v ; n = 0, ..., M w ;

[0115] Calculate each equally divided point and the intersection point O′ separately p Distance:

[0116]

[0117] Take the value such that d l，m，n The coordinates of the equal-division point with the smallest value in the parameterized space (u 0 , v 0 , w 0 ) as the initial value of Newton's method iteration;

[0118] S133, with (u 0 , v 0 , w 0 ) as the initial value, and use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume This embodiment uses the distance error as the optimization target, and the specific optimization problem is as follows:

[0119]

[0120] stu,v,w∈[0,1]

[0121] Where V(u, v, w) is the Cartesian coordinate corresponding to the parameterized coordinate (u, v, w) in the FFD control volume;

[0122] The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold, t is the number of iterations, d t is O′ after the tth iteration p The distance error calculated in the optimized value of the parameterized local coordinates of the FFD control volume; in this embodiment, ε is set to 1e -12 .

[0123] The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume

[0124] According to the optimized value (u′, v′, w′), the intersection point O′ can be obtained p The position relationship with the FFD control body is analyzed as follows: When p Outside the FFD control body, the optimized value (u′, v′, w′) is the distance O′ inside the FFD control body. p The parameterized local coordinates of the nearest point; otherwise the intersection point O′ p Inside the FFD control volume, the optimal value (u′, v′, w′) is the intersection point O′ p The local coordinates in the FFD control volume. δ is the preset distance threshold. In this embodiment, the value of δ is 50e -12 .

[0125] This embodiment also provides a method for implementing the above-mentioned intersection calculation method through space point O p Along the set direction A system for calculating intersection points with a geometrical contour surface, wherein the geometrical contour surface is an overall contour surface or a partial contour surface of an aerospace vehicle, a ship, or an automobile; Figure 6 As shown, including:

[0126] A triangular meshing module 11 is used to perform triangular meshing on the initial geometric shape surface and convert it into a discrete surface composed of multiple triangular planes;

[0127] The intersection Cartesian coordinate calculation module 12 is used to calculate the intersection point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system

[0128] The intersection point parameterized local coordinate calculation module 13 is used to construct a B-spline-based FFD control volume for the geometric shape surface, and the intersection point O′ p Embedded in the FFD control volume, calculate the intersection point O' p Parameterized local coordinates of the FFD control volume The specific calculation steps of the parameterized local coordinates are:

[0129] S131. The FFD control volume enclosing the geometrical surface is:

[0130]

[0131] In the formula, {P i，j , k|i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD frame in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i，p (u), N j，p (v) and Nk, p (w) are p-order B-spline basis functions in the parameterized space (u, v, w) in dimensions u, v, w respectively; the parameterized variables in dimensions u, v, w are all variables in the interval [0, 1];

[0132] S132, the FFD control volume is equally divided along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into Mu equal parts, the parameterized space [0, 1] along the v direction is divided into Mv equal parts, and the parameterized space [0, 1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are l=0,…,M u ; m = 0, ..., M v ; n = 0, ..., M w ;

[0133] Calculate each equally divided point and the intersection point O′ separately p Distance:

[0134]

[0135] Take the value such that d l，m，n The coordinates of the equal-division point with the smallest value in the parameterized space (u 0 , v 0 , w 0 ) as the initial value of Newton's method iteration;

[0136] S133, with (u 0 , v 0 , w 0 ) as the initial value, and use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume The specific optimization problem is as follows:

[0137]

[0138] stu,v,w∈[0,1]

[0139] Where V(u, v, w) is the Cartesian coordinate corresponding to the parameterized coordinate (u, v, w) in the FFD control volume;

[0140] The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold; t is the number of iterations, d t is O′ after the tth iteration p Distance error calculated at the optimized values ​​of the parameterized local coordinates of the FFD control volume;

[0141] The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume

[0142] Embodiment 2:

[0143] This embodiment provides a thickness constraint calculation method suitable for free deformation parameterization. The thickness constraint mainly meets the position installation size requirements of equipment mechanisms, etc. Taking a wing-body fusion underwater glider as an example, Figure 7 A schematic diagram of the thickness constraint in the FFD control volume is given. In the figure, the dots are the intersections of the thickness constraint and the upper and lower surfaces, and the length of the line segment between the dots is the size of the thickness constraint. The key to calculating the thickness constraint is to accurately calculate the thickness of the FFD control volume after the deformation occurs. Figure 7 The position of the middle dot. Figure 8 As shown, the specific calculation includes the following steps:

[0144] S21, determining the starting point and direction of the thickness constraint in the geometric shape surface;

[0145] S22, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the thickness constraint direction;

[0146] In this embodiment, in order to simplify the calculation, the direction of the thickness constraint is used as the y-axis to establish a Cartesian coordinate system; this embodiment assumes that there are N t thickness constraints, and their corresponding starting point position coordinates are ((x h , 0, z h )|h=0,…,N t}.

[0147] S23, take the starting point of the thickness constraint as the spatial point O p , the direction of the thickness constraint is the set direction The intersection point calculation method in Example 1 is used to calculate the intersection point O′ of the thickness constraint starting point on the first curved surface and the second curved surface along the thickness constraint direction. p1 and O′ p2 Parameterized local coordinates in the FFD control volume and The distance calculated based on the Cartesian coordinates of the two intersection points is the thickness value of the thickness constraint.

[0148] S24. If the thickness value is not less than the thickness threshold of the thickness constraint, the thickness constraint is satisfied; otherwise, the thickness constraint is not satisfied.

[0149] When the control points of the FFD control body are changed, the geometric surface is deformed, and the Cartesian coordinates of the two intersection points need to be recalculated to update the thickness value of the thickness constraint. Since the parameterized local coordinates of the two intersection points in the FFD control body have been calculated in step S23, according to the expression of the FFD control body and O′ p1 , O′ p2 Parameterized local coordinates in the FFD control volume and You can calculate O′ p1 , O′ p2 The Cartesian coordinates used to update the thickness constraint's thickness value.

[0150] This embodiment also discloses a system for implementing the thickness constraint calculation method. Fig. 9 As shown, including:

[0151] A thickness constraint starting point and direction determination module 21 is used to determine the starting point and direction of the thickness constraint in the geometric shape surface;

[0152] A geometrical shape curved surface segmentation module 22 is used to segment the geometrical shape curved surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the thickness constraint direction;

[0153] The surface intersection calculation module 23 is used to calculate the starting point of the thickness constraint as the space point O p , the direction of the thickness constraint is the set direction The intersection points O of the starting point of the thickness constraint on the first curved surface and the second curved surface along the thickness constraint direction are calculated by using the above intersection calculation method. p ' 1 and O p ' 2 Parameterized local coordinates in the FFD control volume and

[0154] The thickness value calculation module 24 is used to calculate the thickness value according to the intersection point O p ' 1 and O p ' 2 The parameterized local coordinates of the Cartesian coordinates are calculated according to the intersection point O p ' 1 and O p ' 2 The Cartesian coordinates of the thickness constraint are used to calculate the thickness value.

[0155] The thickness constraint judgment module 25 is used to judge whether the thickness constraint is satisfied according to the thickness value and the thickness threshold: if the thickness value is not less than the thickness threshold of the thickness constraint, the thickness constraint is satisfied; otherwise, the thickness constraint is not satisfied.

[0156] Embodiment 3:

[0157] This embodiment discloses a volume constraint calculation method suitable for free deformation parameterization. The volume constraint requires that the specified space meets certain volume requirements, such as the space requirements required by the battery mechanism, etc. Taking the wing-body fusion underwater glider as an example, Fig.10 Schematic diagram of volume constraints in FFD control volume. Fig.10 The volume of the small and medium grid parts needs to meet certain requirements. The specific mathematical expression can be described as V≥V th , where V is the volume of the small mesh part, V th is the volume threshold required by the volume constraint. The key to volume constraint calculation is to accurately calculate the volume size of the small grid part after the FFD control body is deformed. Fig.11 As shown, the following steps are included:

[0158] S31, determining the boundary curve and direction of the volume constraint in the geometric shape surface, generating nodes on the boundary curve using an equal spacing method, and dividing the area enclosed by the boundary curve into a rectangular grid;

[0159] The transfinite interpolation (TFI) method is used to calculate the Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve;

[0160] S32, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the volume constraint direction;

[0161] S33, taking the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The above-mentioned intersection calculation method is used to calculate the parameterized local coordinates of the intersection of each rectangular mesh vertex on the first surface and the second surface along the volume constraint direction in the FFD control volume; the eight intersection points obtained from the four vertices of a rectangular mesh form a quadrangular prism; and the volume of the quadrangular prism is calculated;

[0162] S34. The volumes of all the quadrangular prisms are accumulated to obtain the volume value of the volume constraint.

[0163] If the volume value is not less than the volume threshold of the volume constraint, the volume constraint is satisfied; otherwise, the volume constraint is not satisfied.

[0164] When the control point of the FFD control body is changed, the coordinate value of each quadrangular prism vertex in the Cartesian coordinate system is recalculated according to the expression of the FFD control body and the parameterized local coordinates obtained in step S33; the volume of the quadrangular prism is updated according to the new coordinate values ​​of the quadrangular prism vertices.

[0165] This embodiment also provides a system for a volume constraint calculation method suitable for free deformation parameterization, such as Fig.12 As shown, including:

[0166] The volume constraint boundary curve and direction acquisition module 31 is used to determine the boundary curve and direction of the volume constraint in the geometric shape surface;

[0167] The gridding module 32 is used to generate nodes on the boundary curve by using an equal spacing method, and divide the area enclosed by the boundary curve into rectangular grids; and calculate the Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve by using a transfinite interpolation method;

[0168] A geometric shape surface segmentation module 33 is used to divide the geometric shape surface into two parts, a first surface and a second surface, along a plane perpendicular to the volume constraint direction;

[0169] The surface intersection calculation module 34 is used to take the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The above-mentioned intersection calculation method is used to calculate the parameterized local coordinates of the intersection of each rectangular mesh vertex on the first surface and the second surface along the volume constraint direction in the FFD control volume;

[0170] A quadrangular prism volume calculation module 35, used to calculate Cartesian coordinates according to parameterized local coordinates of the quadrangular prism vertices, and calculate the volume of the quadrangular prism according to the Cartesian coordinates of the quadrangular prism vertices, wherein the quadrangular prism is composed of eight intersection points of four vertices of a rectangular grid on the first curved surface and the second curved surface;

[0171] The volume value calculation module 36 is used to accumulate the volumes of all the quadrangular prisms to obtain the volume value of the volume constraint.

[0172] The volume constraint judgment module 37 is used to judge whether the volume constraint is satisfied according to the volume value and the volume threshold: if the volume value is not less than the volume threshold of the volume constraint, the volume constraint is satisfied; otherwise, the volume constraint is not satisfied.

Claims

1. A method of passing through a space point O p Along the set direction A method for calculating intersection points with a geometrical contour surface, wherein the geometrical contour surface is an overall contour surface or a partial contour surface of an aerospace vehicle, a ship, or an automobile; characterized in that: The following steps are involved: S11, triangular meshing the initial geometric shape surface to convert it into a discrete surface composed of multiple triangular planes; S12, calculate the space point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system S13, construct the FFD control volume based on B-spline for the geometric shape surface, and make the intersection point O′ p Embedded in the FFD control volume, calculate the intersection point O' p Parameterized local coordinates of the FFD control volume Specifically include: S131. The FFD control volume enclosing the geometrical surface is: In the formula, {P i,j,k |i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD control volume in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i,p (u), N j,p (v) and N k,p (w) are p-order B-spline basis functions in the parameterized space (u,v,w) in dimensions u,v,w respectively; the parameterized variables in dimensions u,v,w are all variables in the interval [0,1]; S132, divide the FFD control volume equally along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into M u The parameterized space [0,1] along the v direction is divided into M v The parameterized space [0,1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are l=0,…,M u ; m=0,…,M v ; n=0,…,M w ; Calculate each equally divided point and the intersection point O′ separately p Distance: Take the value such that d l,m,n The coordinates of the equal-division point with the smallest value in the parameterized space (u0, v0, w0) are used as the initial values ​​of the Newton method iteration; S133, using (u0, v0, w0) as the initial value, use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume The specific optimization problem is as follows: stu,v,w∈[0,1] Where V(u,v,w) is the Cartesian coordinate corresponding to the parameterized coordinate (u,v,w) in the FFD control volume; The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold, t is the number of iterations, d t is O′ after the tth iteration p Distance error calculated at the optimized values ​​of the parameterized local coordinates of the FFD control volume; The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume 2. The intersection calculation method according to claim 1, characterized in that: The step S12 is specifically as follows: Traverse the triangular plane in the discrete surface and determine the intersection of the triangular plane and the spatial point O p Along the set direction Is there an intersection: Construct the equation based on the coordinates of the three vertices ap0, ap1, and ap2 of the triangle plane: Where (x p ,y p ,z p ) is the space point O p The coordinates of ap0 are (x0, y0, z0), (a, b, c) are the set directions. The vector representation of ap1 to ap0; (α1, β1, γ1) is the vector representation of ap1 to ap0, (α2, β2, γ2) is the vector representation of ap2 to ap0; s, t, r are the unknown quantities to be determined; Solve the above equation. If there exists a solution of s≥0, t≥0 and s+t≤1, the triangle plane and the space point O p Along the set direction There is an intersection point, the intersection point O′ p Coordinates in Cartesian coordinate system for 3. A thickness constraint calculation method suitable for free deformation parameterization, characterized in that: The following steps are involved: S21, determining the starting point and direction of the thickness constraint in the geometric shape surface; S22, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the thickness constraint direction; S23, take the starting point of the thickness constraint as the spatial point O p , the direction of the thickness constraint is the set direction The method according to any one of claims 1 to 2 is used to respectively calculate the intersection point O′ of the starting point of the thickness constraint along the thickness constraint direction at the first curved surface and the second curved surface. p1 and O′ p2 Parameterized local coordinates in the FFD control volume and The distance between the two intersection points is the thickness value of the thickness constraint.

4. The thickness constraint calculation method suitable for free deformation parameterization according to claim 3 is characterized in that: Also includes: S24. If the thickness value is not less than the thickness threshold of the thickness constraint, the thickness constraint is satisfied; Otherwise, the thickness constraint is not satisfied.

5. The thickness constraint calculation method suitable for free deformation parameterization according to claim 3 is characterized in that: The step 23 further comprises: When the control point of the FFD control body changes, according to the expression of the FFD control body and O′ p1 , O′ p2 Parameterized local coordinates in the FFD control volume and Recalculate O′ p1 , O′ p2 In Cartesian coordinates, the thickness value of the thickness constraint is updated according to the new values ​​of the two coordinates.

6. A volume constraint calculation method suitable for free deformation parameterization, characterized in that: The following steps are involved: S31, determining the boundary curve and direction of the volume constraint in the geometric shape surface, generating nodes on the boundary curve using an equal spacing method, and dividing the area enclosed by the boundary curve into a rectangular grid; The Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve are calculated using the transfinite interpolation method; S32, dividing the geometric shape surface into two parts, a first curved surface and a second curved surface, along a plane perpendicular to the volume constraint direction; S33, taking the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The method according to any one of claims 1 to 2 is used to calculate the parameterized local coordinates of the intersection of each rectangular mesh vertex on the first surface and the second surface in the FFD control volume along the volume constraint direction; the eight intersection points obtained from the four vertices of a rectangular mesh form a quadrangular prism; and the volume of the quadrangular prism is calculated; S34. The volumes of all the quadrangular prisms are accumulated to obtain the volume value of the volume constraint.

7. The volume constraint calculation method suitable for free deformation parameterization according to claim 6, characterized in that: The step 33 further comprises: When the control point of the FFD control body is changed, the coordinate value of each quadrangular prism vertex in the Cartesian coordinate system is recalculated according to the expression of the FFD control body and the parameterized local coordinates obtained in step S33; the volume of the quadrangular prism is updated according to the new coordinate values ​​of the quadrangular prism vertices.

8. A method of passing through a space point O p Along the set direction An intersection calculation system for intersecting with a geometrical contour surface, wherein the geometrical contour surface is an overall contour surface or a partial contour surface of an aerospace vehicle, a ship, or an automobile; characterized in that: include: A triangular meshing module is used to perform triangular meshing on the initial geometric shape surface and convert it into a discrete surface composed of multiple triangular planes; The intersection Cartesian coordinate calculation module is used to calculate the intersection point O p Along the set direction The intersection point O′ with the triangular plane in the discrete surface p Coordinates in Cartesian coordinate system The intersection point parameterized local coordinate calculation module is used to construct the FFD control volume based on B-spline for the geometric surface. p Embedded in the FFD control volume, calculate the intersection point O' p Parameterized local coordinates of the FFD control volume The specific calculation steps of the parameterized local coordinates are: S131. The FFD control volume enclosing the geometrical surface is: In the formula, {P i,j,k |i=0,…,N u -1; j = 0, ..., N v -1; k = 0, ..., N w -1} is the coordinate of the control point of the FFD control volume in the Cartesian coordinate system; N u 、N v 、N w are the number of control points in the x, y, and z directions in the Cartesian coordinate system; N i,p (u), N j,p (v) and N k,p (w) are p-order B-spline basis functions in the parameterized space (u,v,w) in dimensions u,v,w respectively; the parameterized variables in dimensions u,v,w are all variables in the interval [0,1]; S132, divide the FFD control volume equally along each dimension in the parameterized space (u, v, w): the parameterized space [0, 1] along the u direction is divided into M u The parameterized space [0,1] along the v direction is divided into M v The parameterized space [0,1] along the w direction is divided into M w The coordinates of each equally divided point in the parameterized space in the Cartesian coordinate system are l=0,…,M u ; m=0,…,M v ; n=0,…,M w ; Calculate each equally divided point and the intersection point O′ separately p Distance: Take the value such that d l,m,n The coordinates of the equal-division point with the smallest value in the parameterized space (u0, v0, w0) are used as the initial values ​​of the Newton method iteration; S133, using (u0, v0, w0) as the initial value, use Newton's method to iteratively solve the intersection point O' p Parameterized local coordinates of the FFD control volume The specific optimization problem is as follows: stu,v,w∈[0,1] Where V(u,v,w) is the Cartesian coordinate corresponding to the parameterized coordinate (u,v,w) in the FFD control volume; The iterative convergence condition is: |d t -d t-1 |≤ε, ε is the preset iterative error threshold; t is the number of iterations, d t is O′ after the tth iteration p Distance error calculated at the optimized values ​​of the parameterized local coordinates of the FFD control volume; The optimized value of the parameterized local coordinates (u′, v′, w′) obtained after iteration is the intersection point O′ p Parameterized local coordinates of the FFD control volume 9. A thickness constraint calculation system suitable for free deformation parameterization, characterized in that: include: A thickness constraint starting point and direction determination module is used to determine the starting point and direction of the thickness constraint in the geometric shape surface; A geometrical shape surface segmentation module is used to divide the geometrical shape surface into two parts, a first surface and a second surface, along a plane perpendicular to the thickness constraint direction; Surface intersection calculation module, used to calculate the starting point of the thickness constraint as the space point O p , the direction of the thickness constraint is the set direction The method according to any one of claims 1 to 2 is used to respectively calculate the intersection point O′ of the starting point of the thickness constraint along the thickness constraint direction at the first curved surface and the second curved surface. p1 and O′ p2 Parameterized local coordinates in the FFD control volume and Thickness value calculation module, used to calculate the thickness of the intersection point O' p1 and O′ p2 The parameterized local coordinates of the Cartesian coordinates are calculated according to the intersection point O′ p1 and O′ p2 The Cartesian coordinates of the thickness constraint are used to calculate the thickness value.

10. A volume constraint calculation system suitable for free deformation parameterization, characterized in that: include: A volume constraint boundary curve and direction acquisition module is used to determine the boundary curve and direction of the volume constraint in the geometric shape surface; A meshing module is used to generate nodes on the boundary curve using an equal spacing method and divide the area enclosed by the boundary curve into rectangular grids; a transfinite interpolation method is used to calculate the Cartesian coordinates of each rectangular grid vertex in the inner area of ​​the boundary curve; A geometric shape surface segmentation module is used to divide the geometric shape surface into two parts, a first surface and a second surface, along a plane perpendicular to the volume constraint direction; The surface intersection calculation module is used to take the vertex of each rectangular grid in the inner area of ​​the boundary curve as the spatial point O p , the direction of the volume constraint is the set direction The method according to any one of claims 1 to 2 is used to calculate the parameterized local coordinates of each rectangular mesh vertex at the intersection of the first surface and the second surface in the FFD control volume along the volume constraint direction; A quadrangular prism volume calculation module, used to calculate Cartesian coordinates according to parameterized local coordinates of the quadrangular prism vertices, and calculate the volume of the quadrangular prism according to the Cartesian coordinates of the quadrangular prism vertices, wherein the quadrangular prism is composed of eight intersection points of four vertices of a rectangular grid on the first curved surface and the second curved surface; The volume value calculation module is used to accumulate the volumes of all quadrangular prisms to obtain the volume value of the volume constraint.

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