Modeling Method for Fitting Generalized Cylinder Surfaces Based on the Derived Structure of Water-Bomb Origami

Abstract

The present invention discloses a modeling method for fitting a generalized cylindrical surface based on the derivative structure of water bomb origami. First, the user interactively inputs a contour curve and the surface width, and the target generalized cylindrical surface is formed through scanning. Secondly, the size of the mine units tiled on this surface is optimized and unified. Finally, according to different cases of the height and width of the mine units, the mine units are tiled on the target generalized cylindrical surface to form the target grid model. Different from the traditional method of using origami folding of water bombs to fit the target generalized cylindrical surface, the present invention uses unfurled origami units, which on the one hand avoids the generation of corrugated surfaces and at the same time develops a new form of discretely fitting the target generalized cylindrical surface.

Description

Technical Field

[0001] The present invention relates to the field of computer origami fitting of generalized cylindrical surfaces in computer graphics, and specifically relates to a method for modeling the fitting of generalized cylindrical surfaces based on unfolded mine-derived origami units. Background Art

[0002] Origami is an ancient oriental origami art that has been used to construct three-dimensional structures by folding two-dimensional flat materials with crease patterns embedded in the design. An origami structure that meets the requirements of deployability constraints can be manufactured on a plane without cutting, which is attractive for the manufacturing industry. Such a structure can even be flat-folded, which is meaningful for efficient storage and transportation. Benefiting from scale-independent features, a preliminary prototype of origami may be applicable to applications ranging from the nanoscale, meter scale to the macroscale.

[0003] Constructing a given cylindrical surface through origami is a simple case of the inverse origami design problem because its Gaussian curvature is zero. Such cylindrical origami structures have also received extensive attention from researchers and engineers and have potential application prospects, such as biomedical foldable scaffolds, tunable mechanical memory structures, and space deployable arms. The origami structures obtained from most design methods are in a partially folded state when unfolded. Even if a finer approximation corresponding to the target surface can be generated by increasing the number of units used to synthesize the crease pattern, such an origami approximation shows a corrugated surface. In the appearance design of some specific engineering scenarios, a non-corrugated or smooth surface plays a crucial role. For example, in the case of an aircraft wing, a smooth surface allows wind and rain to easily pass through the object surface. Summary of the Invention

[0004] In the present invention, a new method for fitting a generalized cylindrical surface is proposed. The cylindrical surface is composed of unfoldable rectangular blocks, in which a crease pattern inspired by water bomb tessellation is embedded. The rectangular block is a basic unit and is unified by optimizing the width w and height h. The generated crease pattern with such unified rectangular blocks is unfoldable and can be manufactured on a flat sheet of material without additional cutting. To approximate the cylindrical target surface from the 2D crease pattern, the collinear creases between adjacent rows fold simultaneously and appropriately like a hinge, while the internal creases in each row remain unfolded. This approximation can be interpreted as a discrete version of the generalized cylindrical target surface and can still be compactly stored by folding all the embedded creases. In addition to the blocks with w = h, the present invention also studies how the other two relationships between w and h, namely w < h and w > h, affect the foldability of the unfolded structure, and introduces mine-derived units to fit the target generalized cylindrical surface and achieve control over the shape after complete folding.

[0005] To achieve the above object, the technical solutions provided by the present invention are as follows:

[0006] A modeling method for fitting a generalized cylindrical surface based on an unfolded mine-derived origami unit, comprising the following steps:

[0007] S1: Introduce the relevant concepts of using an unfolded mine unit origami to fit the target surface and construct a mesh model;

[0008] S2: The user interactively inputs configuration information to control the generation of the target surface;

[0009] S3: Optimize and unify the size of the mine units;

[0010] S4: Tile the mine units to fit the target surface and construct the target mesh model.

[0011] Further, the specific content of step S1 is as follows:

[0012] S11. Composition of the target mesh unit. The target mesh model is composed of N r ×N c mine units, that is, N r rows and N c columns. Among them, the width w of the square mine unit is equal to the height h. First, set the mine unit tiled in the odd rows as module B O , and the six creases inside the unit intersect at an internal vertex, and its crease pattern is as shown in (a) in Figure 1 . Secondly, set the mine unit module tiled in the even rows as B E , and on the basis of module B O , swap the left and right sides of the mine unit, and the crease pattern is as shown in (b) in Figure 1 . The origami units are staggered in each row, as shown in (c) in Figure 1 .

[0013] Further, the specific content of step S2 includes the following:

[0014] S21. Generate a contour curve. The user specifies curve control points, and a NURBS curve (Non-uniform rational basis spline) is generated from these control points, which is the 2D contour curve Γ of the cylindrical surface (Note: The coordinate system is a space rectangular coordinate system, composed of the x, y, and z axes respectively. At this time, the contour curve is located in the x-z plane);

[0015] S22. Generate the target surface. Given the contour curve Γ, the user inputs the surface width W, and the curve is scanned along the y-axis for a distance W, then the surface formed by its scanning path is the target surface Φ T , which is the finally fitted cylindrical surface;

[0016] Furthermore, step S3 specifically includes the following content:

[0017] S31. Sampling of the contour curve. For the contour curve Γ, take N r +1 sampling points on it, and set the vertices as s i (i = 1, …, N r +1), then the contour curve is divided into N r segments, and set the length of each segment as h j (j = 1,..., N r ), at this time h j may be different, which will cause production difficulties. To reduce production difficulties, iterative optimization is introduced at this time to reduce the height error, and the length residual r j is defined as:

[0018]

[0019] where is the average height.

[0020] An optimization objective function is established from this error value:

[0021]

[0022] Through this iterative optimization process, the height error of the mine unit can be reduced, and the production difficulty can be lowered;

[0023] Furthermore, step S4 specifically includes the following content:

[0024] During the fitting process, it is impossible to satisfy that the width of the target surface exactly meets: W = N c w every time, so the size of the mine unit needs to be adjusted flexibly. First, set the width of the mine unit as w = W / N r , at this time, there are three possible proportional relationships between w and h, and these three proportional relationships cause different folding problems. The construction research of the model is carried out for these three situations respectively:

[0025] S41. When w = h, a Square(E)-type mine origami structure is formed:

[0026] At this time, for each unfolded mine unit, the shape is a square, and the styles of the mine units in the odd rows and even rows are shown in Figure 2 (a) in Figure 2 and

[0027] (b) in

[0028] For the flat folding state of the entire origami structure, seeFigure 2 (c) in it. Place this origami structure in the x-z plane, where G r represents a direction vector parallel to the x-axis and pointing in the positive x-axis direction. When increasing the number of columns of mine units, mine modules will be added in the G r direction, and this origami structure will not self-intersect. Its border area is:

[0029]

[0030] S42. When w < h, a Tall (T)-type mine origami structure is formed:

[0031] At this time, the target grid structure constructed by the mine unit structure is shown in Figure 3 (c). When the origami model is fully folded, its final state will self-intersect (see Figure 3 (d)), so it does not meet the valid configuration and the crease pattern needs to be adjusted.

[0032] First, adjust the mine unit B O modules in the odd rows. Split the vertex C4 (see Figure 3 (a)) along the middle line into two vertices, and at this time the inner side length of this origami unit satisfies (see Figure 3 (e)):

[0033]

[0034] Similarly, adjust the mine unit B E modules in the even rows. Split the vertex D4 (see Figure 3 (b)) into vertices Split the vertex D5 into vertices and at this time the inner side length of this origami unit satisfies (see Figure 3 (f)):

[0035]

[0036] At this time, use the adjusted derivative structure of the mine unit to construct the target grid structure (see Figure 3 (g)). Its final flat fold is a regular shape and will not self-intersect (see Figure 3 (h)). At this time, place it in the x-z plane, where G r is parallel to the x-axis, representing the direction of increasing area when increasing the number of columns of mine units. Its border area is:

[0037]

[0038] S43. When w > h, a Short(S)-type origami structure is formed:

[0039] The target grid structure constructed from the S-type mine origami is shown in Figure 4 (c) of. According to the folding characteristics of the origami model, when the grid model is flat-folded (see Figure 4 (d) of), in the B O module, vertices C2 and C6 will intersect (where C2 and C6 are shown in Figure 4 (a) of), in the B E module, the point pairs D1, D6 and D3, D8 will intersect (where D1, D6 and D3, D8 are shown in Figure 4 (b) of). At this time, the mine unit needs to be adjusted:

[0040] First, for odd rows, that is, the B O module, the rectangular blocks F1C1C5F3 and C3F2F4C7 are respectively added to both sides of the mine unit, and their size is w1×h, where (see Figure 4 (e) of):

[0041]

[0042] Second, for even rows, that is, the B E module, the size of the rectangle D1D3D8D6 is changed from w×h to 2w2×h, where and rectangular blocks G1D1D4G3, G3D4D6G5, D3G2G4D5 and D5G4G6D8 with a width of w1 and a height of are respectively added to its left and right sides (see Figure 4 (f) of);

[0043] Use the derived structure of the adjusted mine unit to construct the target grid structure (see Figure 4 (g) of). Although it cannot meet the complete flat folding, the approximate structure of this origami can be completely folded and can avoid self-intersection (see Figure 4 (h) of);

[0044] When this origami structure is flat-folded, the boundary volume of this origami structure is:

[0045] V S = N c (w - h)A S

[0046] where A S is the mapping area of this origami structure to the x-z plane in the completely folded state:

[0047]

[0048] Substituting the area gives the volume as:

[0049]

[0050] S44. From the Short - type origami structure, it is found that in the fully - folded state, its contact with the lower surface consists only of points and edges with zero area (see (h) in Figure 4 ). Such sharp end - faces formed may cause damage to the lower contact surface. To solve this problem, the crease pattern is modified based on the Short - type:

[0051] Introduce a variable:

[0052] w′2 = λw2, where λ ∈ (0, 1) is a scaling factor.

[0053]

[0054] The squares C1C3C7C5 of type Short (see (a) in Figure 1 ) and D1D3D8D6 (see (b) in Figure 1 ) are converted into the "Tall" - type cases determined by the scaling parameter λ, and then the vertices are divided by referring to the "Tall" type to modify the creases in the rectangles C1C3C7C5 and D1D3D8D6.

[0055] For the odd - row unit module B O , referring to the "Tall" type (see (e) in Figure 3 ), the style is as shown in (a) in Figure 5 .

[0056] For the even - row unit module B E , since the vertices D4 and D5 are respectively split into two vertices, two additional rectangles and (see (b) in Figure 5 ) are added.

[0057] Introduce a parameter d ∈ (0, w′1), move the left side of the middle part to the left and symmetrically mirror - move the right side of the middle part to the right. Thus, the odd - row and even - row mine units are respectively divided as shown in (c) and (d) of Figure 5 . Then the width of the mine unit is divided into five parts: w″1, w′2, 2d, w′2, and w″1, where w″1 is:

[0058] w″1 = w′1 - d

[0059] At this time, this mode is called ShortII (SII), and the target grid structure constructed by it is shown in Figure 5(e). When the structure is in the fully folded state, the origami tessellation belonging to the adhesive surface, i.e., the fully folded structure, exists between two parallel planes contacted by the origami approximate surface (see Figure 5 (f)), where G c and G r respectively represent the longitudinal and transverse growth directions of the mine origami unit (where G r is parallel to the x-axis and G c is parallel to the y-axis). At this time, for this type of fully folded structure, its volume is:

[0060]

[0061] The beneficial effects of the present invention are as follows:

[0062] The present invention mainly uses the unfolded mine origami derivative structure to fit the target surface with the characteristics of a generalized cylinder. A mine is a type of origami pattern, and there are six adjacent vertices inside its pattern unit, forming six edges, among which the distribution is four valley folds and two mountain folds. The origami pattern used in the present invention is based on the mine derivative structure, which is a derivative origami structure invented considering the construction of a non-rippled surface. The unit module for constructing the generalized cylindrical surface is built using rectangular blocks, and the mine units are embedded in the rectangular blocks, and the flat folding constraint is satisfied to discretely construct the target grid model. Four different types of origami structures are constructed according to the different ratios of the height to the width of the mine derivative origami unit. The present invention has developed a new form capable of constructing a smooth surface, which can play a crucial role in specific application scenarios. For example, when using this origami model to construct the surface of an aircraft wing, the smooth surface can greatly reduce air resistance. Description of the Drawings

[0063] Figure 1 show the different styles of the mine unit and the distribution of the crease patterns;

[0064] Figure 2 The target surface Φ T and the Square type grid model;

[0065] Figure 3 The Tall type derivative structure grid model;

[0066] Figure 4 The Short type derivative structure grid model;

[0067] Figure 5 The ShortII type derivative structure grid model.

[0068] Figure 6 The flow schematic diagram of the implementation of the present invention. Detailed Implementation Manner

[0069] The present invention will be described in detail below in conjunction with the embodiments shown in the accompanying drawings. However, these embodiments do not limit the present invention, and any structural, methodical, or functional transformations made by those of ordinary skill in the art based on these embodiments are included within the scope of protection of the present invention.

[0070] As Figure 6 shown, the present invention is a modeling method for fitting a generalized cylindrical surface based on an unfolded mine-derived origami unit, including the following steps:

[0071] S1: Introduce the relevant concepts of using an unfolded mine unit origami to fit the target surface and construct a mesh model;

[0072] S2: The user interactively inputs configuration information to control the generation of the target surface;

[0073] S3: Optimize and unify the size of the mine units;

[0074] S4: Tile the mine units to fit the target surface and construct the target mesh model.

[0075] As a preferred embodiment of the present invention, the specific content of step S1 of the present invention includes:

[0076] S11. Composition of the target mesh unit. The target mesh model is composed of N r ×N c mine units, that is, N r rows and N c columns. Among them, the width w of the square mine unit is equal to the height h. First, set the mine units tiled in the odd rows as module B O , and the six creases inside the unit intersect at an internal vertex, and its crease pattern is as shown in Figure 1 (a). Secondly, set the mine unit module tiled in the even rows as B E , which, on the basis of module B O , exchanges the left and right sides of the mine unit, and the crease pattern is as shown in Figure 1 (b). The origami units are staggered in each row, as shown in Figure 1 (c).

[0077] As a preferred embodiment of the present invention, the above step S2 specifically includes the following content:

[0078] S21. Generate a contour curve. The user specifies curve control points, and a NURBS curve (Non-uniform rational basis spline) is generated from these control points, which is the 2D contour curve Γ of the cylindrical surface (Note: The coordinate system is a spatial rectangular coordinate system, composed of the x, y, and z axes respectively. At this time, this contour curve is located in the x-z plane);

[0079] S22. Generate the target surface. Given the contour curve Γ and the surface width W input by the user, scan the curve along the y-axis by a distance W, and the surface formed by the scanning path is the target surface Φ T , which is the finally fitted cylindrical surface;

[0080] As a preferred embodiment of the present invention, the specific content of step S3 of the present invention includes:

[0081] S31. Sampling of the contour curve. For the contour curve Γ, take N r +1 sampling points on it, and set the vertices as s i (i = 1,..., N r +1), then the contour curve is divided into N r segments, and set the length of each segment as h j (j = 1,... N r ), at this time h j may be different, which will cause production difficulties. To reduce production difficulties, iterative optimization is introduced at this time to reduce the height error, and the length residual r j is defined as:

[0082]

[0083] where is the average height.

[0084] An optimization objective function is established from this error value:

[0085]

[0086] Through this iterative optimization process, the height error of the mine unit can be reduced and the production difficulty can be lowered;

[0087] As a preferred embodiment of the present invention, step S4 specifically includes the following content:

[0088] During the fitting process, it is impossible to ensure that the width of the target surface exactly satisfies: W = N c w every time, so it is necessary to flexibly adjust the size of the mine unit. First, set the width of the mine unit as w = W / N r , at this time, there are three possible proportional relationships between w and h, and these three proportional relationships cause different folding problems. The construction research of the model is carried out for these three situations respectively:

[0089] S41. When w = h, a Square(E)-type mine origami structure is formed:

[0090] At this time, for each unfolded mine unit, its shape is a square, and the styles of the mine units in odd rows and even rows are shown respectively inFigure 2 in (a) and Figure 2 in (b).

[0091] For a single mine unit in the flat-folded state, its border area is:

[0092] For the entire origami structure in the flat-folded state, see Figure 2 in (c). Place this origami structure in the x-z plane, where G r represents a direction vector parallel to the x-axis and pointing in the positive x-axis direction. When increasing the number of columns of mine units, mine modules will be added in the G r direction, and this origami structure will not self-intersect. Its border area is:

[0093]

[0094] S42. When w < h, a Tall (T)-type mine origami structure is formed:

[0095] At this time, the target grid structure constructed by the mine unit structure can be seen in Figure 3 in (c). When the origami model is fully folded, its final state will self-intersect (see Figure 3 in (d)), then it does not meet the valid configuration and the crease pattern needs to be adjusted.

[0096] First, adjust the mine unit B O modules in the odd rows. Split the vertex C4 (see Figure 3 in (a)) along the middle line into two vertices, and at this time the inner side length of this origami unit satisfies (see Figure 3 in (e)), where C2 and C6 are Figure 3 the vertices in (e):

[0097]

[0098] Similarly, adjust the mine unit B E modules in the even rows. Split the vertex D4 (see Figure 3 in (b)) into vertices [[ID=5!]]Split the vertex D5 into vertices and at this time the inner side length of this origami unit satisfies (see Figure 3 in (f)):

[0099]

[0100] D1, D3, D8 are Figure 3 the vertices in (f);

[0101] At this time, the target grid structure is constructed using the adjusted mine unit derivative structure (see Figure 3 in (g)), which finally flattens and folds into a regular shape without self-intersection (see Figure 3 in (h)). At this time, it is placed in the x-z plane, where G r is parallel to the x-axis, representing the direction of increasing area by increasing the number of mine unit columns, and its border area is:

[0102]

[0103] S43. When w > h, a Short (S) type origami structure is formed:

[0104] The target grid structure is constructed from the S-type mine origami, see Figure 5 in (c). According to the folding characteristics of the origami model, when the grid model is flattened and folded (see Figure 4 in (d)), in the B O module, vertices C2 and C6 will intersect (where C2, C6 are seen in Figure 4 in (a)), and in the B E module, the point pairs D1, D6 and D3, D8 will intersect (where D1, D6 and D3, D8 are seen in Figure 4 in (b)). At this time, the mine unit needs to be adjusted:

[0105] First, for odd rows, that is, the B O module, rectangular blocks F1C1C5F3 and C3F2F4C7 are added to both sides of the mine unit respectively, with a size of w1×h, where (see Figure 4 in (e)), and w1 is the width value:

[0106]

[0107] Secondly, for even rows, that is, the B E module, the size of the rectangle D1D3D8D6 is changed from w×h to 2w2×h, where the length value and rectangular blocks G1D1D4G3, G3D4D6G5, D3G2G4D5 and D5G4G6D8 with a width of w1 and a height of are added to its left and right sides respectively (see Figure 4 in (f));

[0108] The target grid structure is constructed using the adjusted mine unit derivative structure (see Figure 4 in (g)). Although it cannot meet the requirement of complete flat folding, the approximate structure of this origami can be completely folded and can avoid self-intersection (see Figure 4 in (h));

[0109] When the origami structure is flat-folded, the boundary volume of the origami structure is:

[0110] V S = N c (w - h)A S

[0111] where A S is the mapped area of the origami structure onto the x-z plane in the fully folded state:

[0112]

[0113] Substituting the area, the volume is:

[0114]

[0115] S44. For the above-mentioned Short-type origami structure, it is found that in the fully folded state, its contact with the lower surface is only composed of points and edges with zero area (see (h) in Figure 4 ), and the sharp end faces formed in this way may cause damage to the lower contact surface. To solve this problem, the present invention modifies the crease pattern on the basis of the Short type:

[0116] Introduce a variable:

[0117] w′2 = λw2, where λ ∈ (0, 1) is a scaling factor.

[0118]

[0119] The squares C1C3C7C5 (see (a) in Figure 1 ) and D1D3D8D6 (see (b) in Figure 1 ) of type Short are converted into the "Tall" type case determined by the scaling parameter λ, and then the vertices are divided by referring to the type "Tall" to modify the creases in the rectangles C1C3C7C5 and D1D3D8D6.

[0120] For the odd-row unit module B O , referring to the type "Tall" (see (e) in Figure 3 ), the style is as shown in (a) in Figure 5 .

[0121] For the even-row unit module B E , since the vertices D4 and D5 are respectively split into two vertices, two additional rectangles and (see (b) in Figure 5 ) are added.

[0122] Introduce a parameter \(d\in(0, w_1')\), move the left side of the middle part to the left, and symmetrically mirror and move the right side of the middle part to the right. Thus, the mine units in odd rows and even rows are respectively divided into Figure 5 In (c) and (d) of

[0123] \(w_1'' = w_1' - d\)

[0124] At this time, this pattern is called ShortII (SII), and the target grid structure constructed by it can be seen in Figure 5 In (e) of Figure 5 When this structure is in the fully folded state, then this structure belongs to the origami tessellation of the adhesive surface, that is, the fully folded structure exists between two parallel planes contacted by the origami approximate surface (see c In (f) of r where \(G\) r and \(G\) c respectively represent the longitudinal and transverse growth directions of the mine origami unit (where \(G\)

[0125]

[0126] The series of detailed descriptions listed above are only specific descriptions of the feasible implementation manners of the present invention, and they are not intended to limit the protection scope of the present invention. Any equivalent manners or changes that do not depart from the technology created by the present invention should be included within the protection scope of the present invention.

Claims

1. A modeling method for fitting a generalized cylindrical surface based on the derivative structure of water bomb origami, characterized in that, It includes the following steps: S1: Introduce the use of unfolded mine units to fold and fit the target surface to construct a preliminary target mesh model; The specific method for constructing the preliminary target mesh model in S1: S11. The target grid model consists of N r × N c mine units, that is, N r rows and N c columns. The width w of the square mine unit is equal to the height h. First, set the mine units tiled in odd rows as module B O . The six creases inside the unit intersect at an internal vertex. Second, set the mine unit module tiled in even rows as B E . On the basis of module B O , swap the left and right sides of the mine unit, and the folding units are staggered in each row; S2: The user interactively inputs configuration information to control the generation of the target surface; S3: Optimize and unify the size of the mine units; S4: Tile the mine units to fit the target surface and construct the target mesh model; The specific method of S4 is as follows: Set the width of the mine unit as w = W / N r , and model construction is carried out respectively for three proportional relationships between w and h. When w = h, a Square(E)-type mine origami structure is formed; when w < h, a Tall(T)-type mine origami structure is formed; when w > h, a Short(S)-type origami structure is formed; When w = h, the method for constructing the Square(E) type mine origami structure is as follows: At this time, for each unfolded mine unit, its shape is a square; For a single mine unit in the flat-folded state, its frame area is as follows: For the entire origami structure in the flat-folded state, place the origami structure in the x-z plane, where G r is parallel to the x-axis. When the number of columns of the mine units is increased, mine modules will be added in the G r direction, and the origami structure will not self-intersect. Its border area is: When w < h, the method for constructing the Tall(T) type mine origami structure is as follows: At this time, when the origami model is fully folded, its final state will self-intersect, which does not conform to the effective configuration, and the crease pattern needs to be adjusted: First, for the mine units B in odd rows O the module is adjusted, and the vertex C4 is split along the center line into two vertices. At this time, the inner side length within the origami unit satisfies: Similarly, for the mine units B in the even rows E the module is adjusted to split vertex D4 into vertex split vertex D5 into vertex and at this time, the inner side length of the origami unit satisfies: Construct a target grid structure using the adjusted derived structure of the mine unit, which flattens and folds into a regular shape without self-intersection, and place it on the x-z plane at this time, where G r is parallel to the x-axis, representing the direction of increasing the area by increasing the number of mine unit columns, and its border area is: When w > h, the method for constructing the Short(S) type origami structure is as follows: According to the folding characteristics of the origami model, when the grid model is flat-folded, in the B O module, vertices C2 and C6 will intersect. In the B E module, point pairs D1, D6 and D3, D8 will intersect. At this time, adjust the mine unit: First, for the odd rows, namely B O module, add rectangular blocks F1C1C5F3 and C3F2F4C7 on both sides of the mine unit respectively, with a size of w1×h, where: Secondly, for the even rows, i.e., B E module, change the size of the rectangle D1D3D8D6 from w×h to 2w2×h, where and add rectangular blocks G1D1D4G3, G3D4D6G5, D3G2G4D5, and D5G4G6D8 with widths of w1 and heights of on its left and right sides respectively. When this origami structure is flat-folded, the boundary volume of this origami structure is: V S = N c (w - h)A S Where A S is the projected area of the origami structure onto the x-z plane in the fully folded state: Substitute the area to get the volume as:

2. The modeling method for fitting a generalized cylindrical surface based on the water bullet origami-derived structure according to claim 1, wherein, The specific method of S2: S21. Generate a contour curve: The user specifies curve control points, and a NURBS curve (Non-uniform rational basis spline) is generated from these control points, which is the 2D contour curve Γ of the cylindrical surface; S22. Generate the target surface: According to the contour curve Γ, with the surface width W input by the user, scan the curve along the y-axis by a distance W, and the surface formed by its scanning path is the target surface Φ T , which is the finally fitted cylindrical surface.

3. The modeling method for fitting a generalized cylindrical surface based on the derivative structure of water bullet origami according to claim 1, characterized in that The specific method of S3: S31. Sampling of contour curves: For the contour curve Γ, take N r + 1 sampling points on it, and set the vertices as s i , i = 1, …, N r + 1. Then the contour curve is divided into N r segments, and set the length of each segment as h j , j = 1, …, N r .

4. The modeling method for fitting a generalized cylindrical surface based on the water bullet origami derivative structure according to claim 3, wherein S3 further includes: When the length h j is different, iterative optimization is introduced, and the length residual r j is defined as: Among them is the average height; From the length residual r j An optimization objective function is established: Through this iterative optimization process, reduce the height error of the mine units and lower the manufacturing difficulty.

5. The modeling method for fitting a generalized cylindrical surface based on the water bullet origami-derived structure according to claim 1, characterized in that, It also includes: Modify the crease pattern based on the Short type: Introduce variables: w′2 = λw2, where λ ∈ (0, 1) is a scaling factor; The squares C1C3C7C5 and D1D3D8D6 of type Short are converted into the "Tall" type situation determined by the scaling parameter λ, and then the vertices are divided by referring to the "Tall" type to modify the creases in the rectangles C1C3C7C5 and D1D3D8D6; For the even-row unit module B E , since vertices D4 and D5 are each split into two vertices, two additional rectangles are attached and Introduce a parameter d ∈ (0, w′1), move the left side of the middle part to the left, and symmetrically mirror and move the right side of the middle part to the right. The mine units in the odd rows and even rows are respectively divided, and the width of the mine units is divided into 5 parts: w″1, w′2, 2d, w′2, and w″1, where w″1 is: w″1 = w′1 - d The pattern at this time is defined as ShortII (SII). The structure corresponding to this ShortII (SII) belongs to the foldable surface of origami tessellation, that is, the fully folded structure exists between two parallel planes in contact with the origami approximate surface, where G c and G r respectively represent the longitudinal and transverse growth directions of the mine origami unit. Among them, G r is parallel to the x-axis, and G c is parallel to the y-axis. At this time, for the fully folded structure of this ShortII (SII) type, its volume is:

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