Method, apparatus, electronic device, and storage medium for generating a free-form surface of a building

Abstract

The present application relates to a method, device, electronic device, and storage medium for generating a free-form surface of a building. The method includes: determining the central axis curve of the free-form surface of the building and fitting an initial surface on the central axis curve; sequentially generating at least one remaining surface on the central axis curve based on the initial surface; traversing the surface intersection points on the central axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve; traversing all the surface intersection points, searching for a target intersection point where there are three surfaces at the surface intersection point and the included angle of the remaining space is less than 180°, and continuing to fill the surface in the remaining space according to the target intersection point until no new surface can be generated or a free-form surface is formed. The present application realizes that the free-form surface has both beautiful shape and stable structure.

Description

Technical Field

[0001] This application relates to the technical field of computer systems, and in particular, to a method, apparatus, electronic device, and storage medium for generating a free-form surface of a building. Background Art

[0002] In modern architectural design and structural engineering, free-form surface structures are highly favored for their aesthetic value and structural performance. Lattice shell structures, continuous shell structures, and membrane structures are three commonly used structures to achieve free-form surfaces of buildings. Due to their advantages such as beautiful form, light weight, high efficiency, and structural stability, these structural forms are widely used in scenarios such as large-span buildings, exhibition centers, and stadiums.

[0003] A common method for designing these structures is to first define the overall surface form and then decompose it into local modules to meet construction requirements. Although the above structural forms have achieved remarkable achievements in constructing surfaces, they still face the problem of difficulty in balancing complex surface shapes and structural stability in practical applications. Specifically, lattice shell structures have difficulties in realizing complex shapes and controlling construction accuracy; continuous shell structures rely on smooth surfaces to transfer loads, and their dependence on formwork and support systems in construction makes their costs high and the construction process complex; membrane structures have high requirements for the accuracy of tension control and are easily restricted by materials and processes. The common difficulty of these structural forms is that the rationality and stability of the surface shape cannot be ensured in the design stage. Summary of the Invention

[0004] This application provides a method, apparatus, electronic device, and storage medium for generating a free-form surface of a building to solve the problem of difficulty in balancing free-form surface shape and structural stability.

[0005] In a first aspect, this application provides a method for generating a free-form surface of a building. The method includes: determining the central axis curve of the free-form surface of the building and fitting an initial surface on the central axis curve, where the central axis curve is used to guide the shape of the free-form surface, all surfaces on the central axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the covered central axis curve region; sequentially generating at least one remaining surface on the central axis curve based on the initial surface; traversing the surface intersection points on the central axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve; traversing all surface intersection points, finding a target intersection point where there are three surfaces at the surface intersection point and the included angle of the remaining space is less than 180°, and continuing to fill the surface in the remaining space according to the target intersection point until no new surface can be generated or until the free-form surface is formed. All generated surfaces are hyperbolic paraboloids, and adjacent surfaces conform to the coplanarity principle, where the coplanarity principle means that all straight lines intersecting at a point between adjacent surfaces are always coplanar.

[0006] Optionally, fitting the initial surface on the central axis curve includes: determining a unique hyperbolic paraboloid by four points in space, where the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space; determining the axial lengths of the two symmetry axes of the hyperbolic paraboloid and the axial angle between the two symmetry axes; and fitting an initial surface whose one symmetry axis conforms to the curve trend of a part of the central axis curve by adjusting the axial lengths and the axial angle.

[0007] Optionally, successively generating at least one remaining surface on the central axis curve based on the initial surface includes: determining a vertex of the initial surface located on the central axis curve, using the vertex as a common vertex, and generating, according to the coplanarity principle, a remaining surface adjacent to the initial surface and located on the central axis curve; if the initial surface is at the end position of the central axis curve, recursively adding surfaces according to the remaining surface until the added surfaces reach the length of the central axis curve; if the initial surface is at a non-end position of the central axis curve, recursively adding surfaces in both side directions according to the remaining surface and another vertex of the initial surface until the added surfaces reach the length of the central axis curve.

[0008] Optionally, using the vertex as a common vertex and generating, according to the coplanarity principle, a remaining surface adjacent to the initial surface and located on the central axis curve includes: determining two adjacent edges of the initial surface connected to the vertex and determining the initial adjacent edge vectors of the two adjacent edges, where the remaining surface and the initial surface share the vertex; generating the remaining adjacent edge vectors of the two edges connected to the vertex in the remaining surface according to a preset parameter and the initial adjacent edge vectors; generating the curvature parameter of the remaining surface according to the preset parameter; generating the remaining vector of the third edge in the remaining surface according to the initial adjacent edge vectors, the curvature parameter, and the initial vector of the third edge in the initial surface; and determining the position and shape of the remaining surface according to the remaining adjacent edge vectors of the two edges and the remaining vector of the third edge in the remaining surface.

[0009] Optionally, traversing the surface intersection points on the central axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve includes: traversing the surface intersection points on the central axis curve; if the curvature of the surface intersection point is not zero, determining the surface intersection point as a tetrahedral combination intersection point, and using a filling surface tool to generate a filling surface in each region formed by adjacent surfaces on the central axis curve with the tetrahedral combination intersection point as the vertex; if the curvature of the surface intersection point is zero, determining the surface intersection point as a hexahedral combination intersection point, and using a lateral surface generation tool and the filling surface tool to generate two filling surfaces in each region formed by adjacent surfaces on the central axis curve with the hexahedral combination intersection point as the vertex.

[0010] Optionally, using a filling surface tool to generate a filling surface in each region formed by adjacent surfaces on the central axis curve includes: using the filling surface tool to determine two filling regions formed between adjacent surfaces on the central axis curve; determining two associated curves of each surface in the adjacent surfaces associated with any one filling region, where the intersection point of the two associated curves is the adjacent point of the surface intersection point; determining two adjacent edge vectors of the filling surface according to the directed vectors of the four associated curves in the two adjacent surfaces; determining the position and shape of the filling surface according to the two adjacent edge vectors of the filling surface and the tetrahedral combination intersection point.

[0011] Optionally, using a lateral surface generation tool and the filling surface tool to generate two filling surfaces in each region formed by adjacent surfaces on the central axis curve includes: using the lateral surface generation tool to determine a target surface and a set surface adjacent on the central axis curve, where the target surface and the set surface intersect at the hexahedral combination intersection point; determining three edge vectors of the target surface, where two of the three edge vectors correspond to edges connected to the hexahedral combination intersection point; constructing two new edge vectors in each region formed by the target surface and the set surface according to the three edge vectors and preset parameters; generating a first filling surface in the region according to the two new edge vectors; using the filling surface tool to generate a second filling surface in the region between the set surface and the first filling surface.

[0012] Second aspect, the present application provides a device for generating a free-form surface of a building. The device includes: a fitting module, configured to determine a central axis curve of the free-form surface of the building and fit an initial surface on the central axis curve, wherein the central axis curve is used to guide the shape of the free-form surface, all surfaces on the central axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the area of the central axis curve it covers; a generating module, configured to sequentially generate at least one remaining surface on the central axis curve based on the initial surface; a traversing module, configured to traverse the surface intersection points on the central axis curve and fill at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve; a searching module, configured to traverse all surface intersection points, search for a target intersection point where there are three surfaces at the surface intersection point and the included angle of the remaining space is less than 180°, and continue to fill the surface in the remaining space according to the target intersection point until no new surface can be generated or until the free-form surface is formed. All generated surfaces are hyperbolic paraboloids, and adjacent surfaces conform to the coplanarity principle, where the coplanarity principle means that all straight lines intersecting at a point between adjacent surfaces are always coplanar.

[0013] Third aspect, the present application provides an electronic device, including: at least one communication interface; at least one bus connected to the at least one communication interface; at least one processor connected to the at least one bus; at least one memory connected to the at least one bus.

[0014] Fourth aspect, the present application further provides a computer storage medium storing computer-executable instructions for executing the method for generating a free-form surface of a building according to any one of the above in the present application.

[0015] The above technical solutions provided by the embodiments of the present application have the following advantages compared with the prior art: Based on the axial symmetry of the hyperbolic paraboloid itself and by following the coplanarity principle, the method provided by the embodiments of the present application realizes the splicing of multiple hyperbolic paraboloids together. The axes of symmetry of all hyperbolic paraboloids are located in the same plane. In this way, only axial forces are borne inside the generated surface, and no bending moment is generated, achieving extremely high force transmission efficiency, and realizing visual smooth continuity. The generated free-form surface combines beautiful shape and structural stability. Description of the Drawings

[0016] The drawings here are incorporated into the specification and form a part of this specification, showing embodiments consistent with the present invention and used together with the specification to explain the principles of the present invention.

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0018] One or more embodiments are exemplarily illustrated by the pictures in the corresponding drawings. These exemplary illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are represented as similar elements. Unless otherwise stated, the drawings in the figures do not constitute a proportional limitation.

[0019] Figure 1 It is a flowchart of a method for generating a free-form surface of a building provided by an embodiment of the present application;

[0020] Figure 2 It is a schematic diagram of a medial axis curve provided by an embodiment of the present application;

[0021] Figure 3 It is a schematic diagram of an initial surface provided by an embodiment of the present application;

[0022] Figure 4 It is a schematic diagram of generating multiple surfaces on the medial axis curve provided by an embodiment of the present application;

[0023] Figure 5 It is a schematic diagram of generating a filling surface on both sides of a central skeleton provided by an embodiment of the present application;

[0024] Figure 6 It is a schematic diagram of the process of filling a surface at the intersection point where three surfaces are connected provided by an embodiment of the present application;

[0025] Figure 7 It is a schematic diagram of the coplanarity principle provided by an embodiment of the present application;

[0026] Figure 8 It is a parameter schematic diagram of the initial surface provided by an embodiment of the present application;

[0027] Figure 9 It is a schematic diagram of no change in the bending direction of the main curve in the four-sided combination provided by an embodiment of the present application;

[0028] Figure 10 It is a schematic diagram of a change in the bending direction of the main curve in the six-sided combination provided by an embodiment of the present application;

[0029] Figure 11 It is a schematic diagram of generating a filling surface using a filling surface tool provided by an embodiment of the present application;

[0030] Figure 12Schematic diagram of generating a filling surface using a lateral surface generation tool provided by an embodiment of the present application;

[0031] Figure 13 Schematic structural diagram of a device for generating a free-form surface of a building provided by an embodiment of the present application;

[0032] Figure 14 Schematic structural diagram of an electronic device provided by an embodiment of the present application. Detailed implementation manners

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Apparently, the described embodiments are some but not all of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0034] The following disclosure provides many different embodiments or examples for implementing different structures of the present invention. To simplify the disclosure of the present invention, components and settings of specific examples are described below. Of course, they are only examples and are not intended to limit the present invention. In addition, the present invention may repeat reference numerals and / or letters in different examples. Such repetition is for the purpose of simplification and clarity and does not itself indicate the relationship between the various embodiments and / or settings discussed.

[0035] The present application provides a method for generating a free-form surface of a building, which is applied to a server and is used to ensure the graceful shape and structural stability of a complex surface, as Figure 1 shown. The method includes the following steps:

[0036] Step 101: Determine the central axis curve of the free-form surface of the building and fit an initial surface on the central axis curve. The central axis curve is used to guide the shape of the free-form surface. All the surfaces on the central axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the area of the central axis curve covered;

[0037] Step 102: Generate at least one remaining surface on the central axis curve in sequence according to the initial surface;

[0038] Step 103: Traverse the surface intersection points on the central axis curve, and fill at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve;

[0039] Step 104: Traverse all the surface intersection points, search for the target intersection points where there are three surfaces at the surface intersection points and the included angle of the remaining space is less than 180°, and continue to fill the surfaces in the remaining space according to the target intersection points until no new surface can be generated or until a free-form surface is formed. All the generated surfaces are hyperbolic paraboloids, and the adjacent surfaces conform to the coplanarity principle. The coplanarity principle means that all the straight lines where the adjacent surfaces intersect at a point are always coplanar.

[0040] The system generates a medial axis curve, which is used to determine the shape of the free-form surface of the building. The medial axis curve can be automatically generated by the system after the user inputs the requirements for the free-form surface at the terminal, or can be generated after the user adjusts any curve. Figure 2 For the schematic diagram of the medial axis curve, as Figure 2 shown, to achieve an axisymmetric structure, the medial axis curve should be constructed in a plane, and the medial axis curve is a curve with non-connected ends.

[0041] After the medial axis curve is generated, the system fits the first surface on the medial axis curve, that is, the initial surface. The initial surface can be set at any position on the medial axis curve. For example, it can be at the end point position or at the middle position. Figure 3 For the schematic diagram of the initial surface, as Figure 3 shown, the initial surface is set at one end of the medial axis curve, and the axis of symmetry of the initial surface conforms to the curve trend of the covered medial axis curve. Substantially, for any surface on the medial axis curve, its axis of symmetry conforms to the curve trend of the covered medial axis curve region.

[0042] The system starts from the initial surface and sequentially generates multiple diagonally adjacent surfaces until the accumulated length of the multiple surfaces reaches the length of the entire medial axis curve, thereby fitting the central skeleton of the medial axis curve. Figure 4 For the schematic diagram of the generation of multiple surfaces on the medial axis curve, Figure 4 If the displayed initial surface is located at the end point position of the medial axis curve, then multiple surfaces on the medial axis curve can only be recursively generated in one direction. If the initial surface is located at a non-end point position of the medial axis curve, then surfaces are recursively generated from both ends of the initial surface to both sides respectively, and in this way, the efficiency of generating surfaces is higher.

[0043] There is a surface intersection point between each adjacent surface connected in series on the medial axis curve, and there are also blank areas on both sides of the surface intersection point. Then, one or two filling surfaces can be filled in the blank area. The filling surfaces take the nearest surface intersection point as the vertex, so that surfaces can be continuously generated on both sides of the central skeleton. Figure 5 For the schematic diagram of generating filling surfaces on both sides of the central skeleton, Figure 5Among them, there are 3 surface intersection points between the 4 surfaces connected in series on the central axis curve. One filling surface is generated on each side of the first surface intersection point, two filling surfaces are generated on each side of the second surface intersection point, and one filling surface is generated on each side of the third surface intersection point. It should be noted that, in Figure 5 One of the filling surfaces generated at the second surface intersection point looks like a triangle, which is caused by the picture angle problem. In fact, all the generated surfaces are quadrilaterals.

[0044] Traverse Figure 5 the surface intersection points of the last figure in, it can be seen that the number of surfaces at different surface intersection points is different, and the number of surfaces includes one surface, two surfaces, three surfaces and four surfaces. For the intersection points involving one surface or two surfaces, if four surfaces are to be generated, at least two new surfaces need to be added, which will lead to an excessive system calculation amount. Therefore, this situation is not considered for the time being; for the intersection points of four surfaces, there is no free space to add new surfaces; for the intersection points of three surfaces, if the included angle of the remaining space is less than 180°, at this time, if one more surface is added at this intersection point, a unique tetrahedron region can be generated, and this structure is geometrically stable. Therefore, surfaces can be continuously filled at the intersection points where three surfaces are connected until no new surfaces can be generated or until a free surface is formed, completing the entire free surface construction process. Figure 6 FIG. is a schematic diagram of the process of filling a surface at the intersection point where three surfaces are connected.

[0045] Among them, the requirement of the coplanarity principle is that all the straight lines intersecting at one point between adjacent hyperbolic paraboloids are always coplanar. Figure 7 FIG. is a schematic diagram of the coplanarity principle. Any and on the plane ABCD and the plane CDFE are always coplanar with the side CD. In order to make two adjacent hyperbolic paraboloids satisfy the principle, the sides of the hyperbolic paraboloids represented as vectors should satisfy the following linear combination, where m, n, and t are scalars and m is not less than zero.

[0046] The sides of adjacent hyperbolic paraboloids should satisfy the following linear combination: ;

[0047] All the surfaces mentioned in the embodiments of the present application are quadrilateral hyperbolic paraboloids. The hyperbolic paraboloid itself has axial symmetry, and this symmetry helps to maintain the consistency and uniformity of the structure during splicing. By following the coplanarity principle, the present application realizes the splicing of multiple hyperbolic paraboloids together, and the axes of symmetry of all hyperbolic paraboloids are located in the same plane. In this way, only axial forces are borne inside the generated surface, and no bending moment is generated, achieving extremely high force transmission efficiency and strong structural stability. At the same time, visual smooth continuity is realized, and the generated free surface combines beautiful shape and structural stability.

[0048] In addition, the prior art generally adopts a design method from the whole to the part. The design method from the whole to the part usually requires repeated iterations to optimize details and structures. This process includes using professional tools for accurate force analysis. These tools require a high level of technology and a long computing time. In order to meet the surface form and mechanical requirements simultaneously, designers often need to repeatedly adjust and optimize, resulting in a complex and time-consuming design process. Under the condition of meeting the coplanarity principle, this application forms a complete free surface by accumulating hyperbolic paraboloids, which is different from the traditional method of first designing the whole and then dividing. This application does not require repeated force analysis and design adjustment, realizes the integration of design and shape generation, and improves the surface generation efficiency.

[0049] This application adopts the characteristics of the ruled surface of the hyperbolic paraboloid, which reduces the difficulty of construction; due to the stability of this structure, the hyperbolic paraboloid combined structure can be developed into a reticulated shell structure, a continuous shell and a membrane structure, and can be applied to a variety of building scenarios.

[0050] In step 101, fitting the initial surface on the central axis curve includes the following steps: determining a unique hyperbolic paraboloid from four points in space, where the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space; determining the axial lengths of the two symmetry axes of the hyperbolic paraboloid and the axial angle between the two symmetry axes; by adjusting the axial lengths and the axial angle, fitting an initial surface in which one of the symmetry axes conforms to the curve trend of part of the central axis curve.

[0051] The system arbitrarily selects four non-coplanar points in three-dimensional space. The two diagonals formed by the four points are perpendicular to each other in space. A unique hyperbolic paraboloid can be constructed through these four points, and a system of equations containing multiple unknowns can be constructed using the coordinate information of these four points. By solving this system of equations, the axial lengths x and y of the two symmetry axes of the hyperbolic paraboloid and the axial angle z between the two symmetry axes can be calculated. Figure 8 It is a schematic diagram of the parameters of the initial surface.

[0052] In order to more accurately fit the central axis curve, it is necessary to finely adjust the axial lengths and the axial angle. The fine adjustment process may require multiple iterations. Each time, the shape of the surface needs to be recalculated and its coincidence with the central axis curve needs to be evaluated. The finally generated initial surface not only conforms to the shape of the hyperbolic paraboloid, but also the change of one of its symmetry axes satisfies the curve change trend of the central axis curve. In order to improve the fitting accuracy, numerical optimization algorithms can be used to automatically adjust the axial lengths and the axial angle. These algorithms can find the optimal solution according to a predetermined objective function (such as minimizing the distance between the surface and the central axis curve).

[0053] In step 102, using a diagonal surface generation tool, at least one remaining surface on the central axis curve is generated successively based on the initial surface, including the following: determining a vertex on the central axis curve in the initial surface, using the vertex as a common vertex, and generating, according to the coplanarity principle, a remaining surface adjacent to the initial surface and located on the central axis curve; if the initial surface is at the end point position of the central axis curve, recursively add surfaces according to the remaining surface until the added surfaces reach the length of the central axis curve; if the initial surface is at a non-end point position of the central axis curve, recursively add surfaces in both lateral directions according to the remaining surface and another vertex of the initial surface until the added surfaces reach the length of the central axis curve.

[0054] Generating the surfaces on the central axis curve includes the following steps.

[0055] Step 1. Determine the vertex of the initial surface and the coplanarity principle.

[0056] Select a vertex on the central axis curve on the initial surface as the common vertex. This vertex is the key to connecting the initial surface and the subsequently generated remaining surfaces. To ensure that the newly generated remaining surface is coplanar with the existing surfaces, that is, they are in the same plane, the coplanarity principle needs to be met between adjacent surfaces. The coplanarity principle can ensure smooth transitions between surfaces and the integrity of the structure.

[0057] Step 2. Recursively generate the remaining surfaces.

[0058] Taking the selected vertex as the base point, generate a new hyperbolic paraboloid according to the coplanarity principle. This new surface will be adjacent to the initial surface and also located on the central axis curve. If the initial surface is at the end point position of the central axis curve, then new surfaces need to be recursively added according to the remaining surface until the required length is reached. If the initial surface is not at the end point position of the central axis curve, then in addition to the above vertex, another vertex of the initial surface located on the central axis curve needs to be used to recursively add new surfaces. When generating surfaces at non-end point positions, attention needs to be paid to maintaining the continuity with the front and rear surfaces to avoid uneven transitions or structural mutations.

[0059] Whether starting from the end point or the non-end point, the ultimate goal is to make the total length of the added surfaces reach or approach the designed length of the central axis curve. In actual operation, it may be necessary to fine-tune the length of each surface to ensure the accuracy and aesthetics of the overall structure.

[0060] Step 3. Optimize and verify.

[0061] Throughout the process, multiple iterations and optimizations may be required to ensure that each surface meets the design requirements and that the overall structure has good mechanical properties and stability. After generating all the surfaces, the entire model needs to be verified to ensure that it meets all the design specifications and usage requirements.

[0062] By generating the remaining surfaces with vertices as connection points and conforming to the coplanarity principle, smooth transitions between surfaces and the integrity of the structure can be ensured. When the total length of the surfaces reaches or approaches the designed length of the central axis curve, the central skeleton of the entire free-form surface is completed.

[0063] In step 2 above, the process of generating the remaining surfaces based on the initial surfaces is as follows: determine two adjacent edges in the initial surface connected by the vertex, and determine the initial adjacent edge vectors of the two adjacent edges, where the remaining surface and the initial surface share the vertex; generate the remaining adjacent edge vectors of the two edges connected by the vertex in the remaining surface according to the preset parameters and the initial adjacent edge vectors; generate the curvature parameters of the remaining surface according to the preset parameters; generate the remaining vector of the third edge in the remaining surface according to the initial adjacent edge vector, the curvature parameters, and the initial vector of the third edge in the initial surface; determine the position and shape of the remaining surface according to the remaining adjacent edge vectors of the two adjacent edges and the remaining vector of the third edge in the remaining surface.

[0064] During the process of generating the remaining surfaces, first, it is necessary to determine the initial adjacent edge vectors of two adjacent edges in the initial surface associated with the vertex. These vectors describe the direction and length of the surface edge and are the basis for constructing the new surface. Next, according to the preset parameters and these initial adjacent edge vectors, the remaining adjacent edge vectors of the two edges associated with the vertex in the remaining surface can be calculated. This step ensures the continuity and smooth transition between the old and new surfaces. Then, use the preset parameter surface to generate the curvature parameters of the remaining surface. The curvature parameters determine whether the bending direction of the main curve on the diagonal axis of the surface changes. Then, combining the initial adjacent edge vector, the curvature parameters, and the initial vector of the third edge in the initial surface, calculate the remaining vector of the third edge in the remaining surface. This step is the key to determining the complete boundary of the remaining surface and involves knowledge of spatial geometry and vector operations. Finally, according to the remaining adjacent edge vectors of the two adjacent edges and the remaining vector of the third edge of the remaining surface, the position and shape of the remaining surface can be determined.

[0065] When generating the remaining surfaces, through precise calculations and optimized designs, it can be ensured that each surface meets the design requirements and that the overall structure has good mechanical properties and stability.

[0066] Exemplarily, in combination with Figure 9 , the following is the process of generating surface CEGF from surface ABCD.

[0067] On the basis of determining the curved surface ABCD, the curved surface CEFG formed according to the following formula conforms to the coplanarity principle, that is, the sides BC, DC, CE, and CG are in the same plane (a, c > 0), and the generation process of the three sides of the curved surface CEFG is as follows.

[0068] ; where a and b, c and d, p and q are respectively three pairs of parameters controlling the form of the diagonal curved surface. The parameters a and b control the lengths of the two sides DC and CG connected to the intersection point C; c and d control the angle between the two sides DC and CG connected to the intersection point C, and the parameters p and q control the lengths of the two sides BC and DC connected to the intersection point C. The value of e can be obtained by the following formula, e = c * d - a * b.

[0069] When e is less than 0, a four-sided combination can be formed. A four-sided combination refers to a shape formed by four curved surfaces. When e is greater than 0, a six-sided combination can be formed. A six-sided combination refers to a shape formed by six curved surfaces.

[0070] As an optional implementation manner, traversing the surface intersection points on the central axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve includes: traversing the surface intersection points on the central axis curve; if the curvature of the surface intersection point is not zero, then determining the surface intersection point as a four-sided combination intersection point, and using the filling surface tool to generate a filling surface in each area formed by adjacent surfaces on the central axis curve with the four-sided combination intersection point as the vertex; if the curvature of the surface intersection point is zero, then determining the surface intersection point as a six-sided combination intersection point, and using the lateral surface generation tool and the filling surface tool to generate two filling surfaces in each area formed by adjacent surfaces on the central axis curve with the six-sided combination intersection point as the vertex.

[0071] Figure 4 The surface intersection points on the central axis curve are shown. The system calculates the curvature of each surface intersection point. If the curvature at this point is not zero, then the surface intersection point is a four-sided combination intersection point. A four-sided combination intersection point means that there are four curved surfaces surrounding this intersection point. Since there are already two curved surfaces on the central axis curve around this intersection point, then two more curved surfaces are needed. A blank area is formed on each side of the adjacent surfaces on the central axis curve. Then, a filling surface can be filled in each blank area, thus generating two more curved surfaces on the basis of the existing two curved surfaces. Among them, the filling surface is generated according to the filling surface tool.

[0072] If the curvature at the surface intersection point is zero, then the surface intersection point is a six-surface combination intersection point. A six-surface combination intersection point means that there are six surfaces surrounding this intersection point. Since there are already two surfaces on the central axis curve around this intersection point, then four surfaces are still lacking. On both sides of the adjacent surfaces on the central axis curve, a blank area is formed respectively. Then, two filling surfaces can be filled in each blank area, thus generating four more surfaces on the basis of the existing two surfaces. Among them, the two filling surfaces are generated by the lateral surface generation tool and the filling surface tool respectively.

[0073] In this application, two prototypes are derived from the surface combination: the four-surface combination and the six-surface combination. There is no point with zero curvature on the main curve in the diagonal axis direction of the four-surface combination, that is, the bending direction of the curve does not change, as Figure 9 shown. While the curvature of the main curve in the diagonal axis direction of the six-surface combination is zero at the central intersection point, that is, the bending direction of the curve changes, as Figure 10 shown. Among them, the main curve in the diagonal axis direction refers to the curve formed by the section or projection along the diagonal direction of a polyhedron in three-dimensional geometry.

[0074] Four-surface combination: For a solid composed of four faces (such as a tetrahedron), its diagonal axis is usually a straight line connecting opposite vertices. Looking up or projecting along this diagonal axis, the main curve obtained will reflect the contour or shape of this solid in this direction. If there is no point with zero curvature on this main curve, it means that in this direction, the shape of the solid is continuously and uniformly curved without sudden changes or inflection points.

[0075] Six-surface combination: For a solid composed of six faces (such as a cube), its diagonal axis can be a straight line connecting opposite corners. In the case of a hexahedron, the curvature of the main curve along the diagonal axis is zero at the central intersection point, which usually means that at this point, the bending direction of the curve changes. In other words, this may be a turning point from convex to concave or from concave to convex, indicating that the shape of the solid in this direction is not monotonic.

[0076] This application proposes two basic prototypes, the four-surface combination and the six-surface combination. There is no point with zero curvature on the diagonal axis curve of the four-surface combination, ensuring the continuous curvature of the curve; while there is a point with zero curvature on the diagonal axis curve of the six-surface combination, allowing the bending direction of the curve to change. This design provides the flexibility to generate diverse forms, enabling the overall shape of the free-form surface to be precisely controlled as needed.

[0077] The process of generating a four-sided combination is as follows: Use the filling surface tool to determine the two filling regions formed between adjacent surfaces on the central axis curve; determine the two associated curves of each surface among the adjacent surfaces associated with any one filling region. Among them, the intersection point of the two associated curves is the adjacent point of the surface intersection point; determine the two adjacent edge vectors of the filling surface according to the directed vectors of the four associated curves of the two adjacent surfaces; determine the position and shape of the filling surface according to the two adjacent edge vectors of the filling surface and the four-sided combination intersection point.

[0078] Figure 11 Figure 4 is a schematic diagram of generating a filling surface using the filling surface tool. From Figure 11 As can be seen, a filling region K1 and a filling region K2 are respectively formed on both sides of the adjacent surfaces ABCD and DEFG on the central axis curve. If a quadrilateral surface is to be filled in the lower filling region K1, then the two sides of the filling surface are known, which are DC and DG respectively, but the other two sides are unknown. If the other two sides are known, then the filling surface can be generated. Specifically, in any one filling region, the filling region is associated with the four sides of the adjacent surfaces on the central axis curve. For example, the filling region K1 is associated with the four sides of the two adjacent surfaces, which are BC, DC, DG, and FG respectively. Then, the adjacent edge vectors of the two sides CH and GH of the filling surface can be determined according to the directed vectors of the four sides. Finally, the position and shape of the filling surface CDGH can be determined according to the adjacent edge vectors , and the coordinates of point D.

[0079] According to Figure 11 in the example, the calculation formulas for the two adjacent edge vectors of the filling surface are: ;

[0080] The process of generating a six-sided combination is as follows: Use the lateral surface generation tool to determine the target surface and the set surface adjacent on the central axis curve, where the target surface and the set surface intersect at the six-sided combination intersection point; determine the three edge vectors of the target surface, among which two of the three edge vectors are corresponding to the edges connected to the six-sided combination intersection point; according to the three edge vectors and the set parameters, construct two new edge vectors in each region formed by the target surface and the set surface; generate the first filling surface in the region according to the two new edge vectors; use the filling surface tool to generate the second filling surface in the region between the set surface and the first filling surface.

[0081] Figure 12 Figure 5 is a schematic diagram of generating a filling surface using the lateral surface generation tool. From Figure 12It can be seen that there are currently two adjacent surfaces on the central axis curve, and there is a blank area on each of the left and right sides of the two adjacent surfaces. Assuming that the upper surface is the target surface A and the lower surface is the set surface B, the first filling surface C can be generated in the blank area on the right side according to the target surface A, and then the second filling surface D can be generated in the blank area formed by the first filling surface C and the set surface B. Of course, it is also possible to set the lower surface as the target surface and the upper surface as the set surface, so that the first filling surface is generated according to the lower surface, and then the second filling surface is generated in the remaining area. Specifically, which surface is selected as the target surface and which surface is selected as the set surface are automatically calculated by the system, and the selection condition is to meet the hyperbolic paraboloid and coplanarity principles.

[0082] First, select three edges of the target surface. These three edges must include two edges associated with the intersection points of the six-sided combination. The third edge can be arbitrarily selected from the remaining two edges. Figure 12 Three edges are selected and the edge vectors of these three edges are generated. 、 、 The system sets three parameters k, j, l and generates 、 、 and according to these three parameters. Then, based on and , an edge vector of the first filling surface is obtained. Based on and , another edge vector of the first filling surface is obtained. These two edge vectors can determine the position and shape of the first filling surface. The obtained first filling surface is as shown by the bold lines in Figure 12 .

[0083] and The calculation formulas are: ; There is still a blank area between the newly generated first filling surface and the set surface. The second filling surface can be directly generated in this area using the filling surface tool. The filling method is the same as the filling method in Figure 11 . Taking the intersection point of the six-sided combination as a vertex of the second filling surface, and directly using two edges of the first filling surface and the set surface as two edges of the second filling surface, and then calculating the other two edges of the second filling surface, the shape and position of the second filling surface can be determined.

[0084] This application provides a generation process for a free-form surface of a building, including the following steps.

[0085] Step S1: Determine the central axis curve of the free form surface of the building.

[0086] Step S2: Determine a unique hyperbolic paraboloid from four points in space, where the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space. Adjust the axis length and axis angle of the hyperbolic paraboloid to fit the initial surface on the central axis curve.

[0087] Step S3: Recursively generate the remaining surfaces on the central axis curve based on the initial surface.

[0088] Step S4: Traverse the surface intersection points on the central axis curve and determine whether the curvature at the intersection point is 0. If it is 0, execute Step S5; if it is not 0, execute Step S6.

[0089] Step S5: Use the filling surface tool to generate a filling surface at each blank area according to the existing two adjacent surfaces, so as to obtain a four-surface combination, and the intersection point of the four-surface combination is the four-surface combination intersection point.

[0090] Step S6: Use the lateral surface filling tool and the filling surface tool to generate two filling surfaces at each blank area according to the existing two surfaces, so as to obtain a six-surface combination and the intersection point of the six-surface combination.

[0091] Step S7: Traverse all surface intersection points. If there are 3 surfaces at this intersection point and the angle of the remaining space is less than 180°, a four-surface combination can be generated at this point. Use the filling surface tool to continue generating surfaces until no new surface can be directly generated or a free form surface is formed.

[0092] This application introduces a new type of free form surface structure, namely the Smooth-Piecewise-Parabolic Hyperboloid (SPHS). This structure is formed by the smooth combination of multiple hyperbolic paraboloid modules, which not only retains the excellent structural performance of the hyperbolic paraboloid but also achieves visual smooth continuity, while reducing the construction difficulty. This application forms a free form surface structure based on the accumulation of hyperbolic paraboloid modules. Utilizing the unique geometric and mechanical properties of hyperbolic paraboloid modules, through module accumulation, while ensuring controllable design form and structural stability, it simplifies the construction process and meets the design requirements for free form surface structures in modern architecture.

[0093] In addition, this application also proposes three tools, namely the diagonal surface generation tool, the filling surface tool, and the lateral surface generation tool. The diagonal surface generation tool generates the surface on the central axis. The filling surface tool generates a four-surface combination, and the lateral surface generation tool and the filling surface tool generate a six-surface combination. The combined use of multiple tools makes the surface design have more possibilities.

[0094] Based on the same technical concept, the present application provides a device for generating a free-form surface of a building, as Figure 13 shown. The device includes:

[0095] A fitting module 1301, configured to determine the central axis curve of the free-form surface of the building and fit an initial surface on the central axis curve, where the central axis curve is used to guide the form of the free-form surface, all the surfaces on the central axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the area of the central axis curve it covers;

[0096] A generating module 1302, configured to sequentially generate at least one remaining surface on the central axis curve based on the initial surface;

[0097] A traversing module 1303, configured to traverse the surface intersection points on the central axis curve and fill at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the central axis curve;

[0098] A searching module 1304, configured to traverse all the surface intersection points, search for target intersection points where there are three surfaces at the surface intersection points and the included angle of the remaining space is less than 180°, and continue to fill the surface in the remaining space according to the target intersection points until no new surface can be generated or until a free-form surface is formed. All the generated surfaces are hyperbolic paraboloids, and the adjacent surfaces conform to the coplanarity principle. The coplanarity principle means that all the straight lines where adjacent surfaces intersect at a point are always coplanar.

[0099] Optionally, the fitting module 1301 is configured to:

[0100] Determine a unique hyperbolic paraboloid from four points in space, where the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space;

[0101] Determine the axis lengths of the two axes of symmetry of the hyperbolic paraboloid and the axis angle between the two axes of symmetry;

[0102] By adjusting the axis lengths and the axis angle, fit an initial surface whose one axis of symmetry conforms to the curve trend of a part of the central axis curve.

[0103] Optionally, the generating module 1302 is configured to:

[0104] Determine a vertex on the central axis curve in the initial surface, use the vertex as a common vertex, and generate an adjacent remaining surface on the central axis curve that conforms to the coplanarity principle with the initial surface;

[0105] If the initial surface is located at the end point position of the central axis curve, recursively add surfaces according to the remaining surface until the added surfaces reach the length of the central axis curve;

[0106] If the initial surface is located at a non-endpoint position of the medial axis curve, then surfaces are recursively added in both lateral directions according to the remaining surface and another vertex of the initial surface until the added surfaces reach the length of the medial axis curve.

[0107] Optionally, the generation module 1302 is configured to:

[0108] Determine two adjacent edges in the initial surface connected by vertices, and determine the initial adjacent edge vectors of the two adjacent edges, where the remaining surface and the initial surface share a vertex;

[0109] Generate the remaining adjacent edge vectors of the two adjacent edges connected by vertices in the remaining surface according to the preset parameters and the initial adjacent edge vectors;

[0110] Generate the curvature parameters of the remaining surface according to the preset parameters;

[0111] Generate the remaining vector of the third edge in the remaining surface according to the initial adjacent edge vector, the curvature parameters, and the initial vector of the third edge in the initial surface;

[0112] Determine the position and shape of the remaining surface according to the remaining adjacent edge vectors of the two adjacent edges and the remaining vector of the third edge in the remaining surface.

[0113] Optionally, the traversal module 1303 is configured to:

[0114] Traverse the surface intersection points on the medial axis curve;

[0115] If the curvature of the surface intersection point is not zero, determine that the surface intersection point is a tetrahedral combination intersection point, and use the filling surface tool to generate a filling surface in each region formed by adjacent surfaces on the medial axis curve with the tetrahedral combination intersection point as the vertex;

[0116] If the curvature of the surface intersection point is zero, determine that the surface intersection point is a hexahedral combination intersection point, and use the lateral surface generation tool and the filling surface tool to generate two filling surfaces in each region formed by adjacent surfaces on the medial axis curve with the hexahedral combination intersection point as the vertex.

[0117] Optionally, the traversal module 1303 is configured to:

[0118] Use the filling surface tool to determine two filling regions formed between adjacent surfaces on the medial axis curve;

[0119] Determine two associated curves of each surface in the adjacent surfaces associated with any one of the filling regions, where the intersection point of the two associated curves is the adjacent point of the surface intersection point;

[0120] Determine the two adjacent edge vectors of the filling surface according to the directed vectors of the four associated curves in the two adjacent surfaces;

[0121] Determine the position and shape of the filling surface based on two adjacent edge vectors of the filling surface and the intersection points of the four-sided combination.

[0122] Optionally, the traversal module 1303 is used for:

[0123] Use the lateral surface generation tool to determine the target surface and the set surface adjacent to each other on the central axis curve, where the target surface and the set surface intersect at the six-sided combination intersection point;

[0124] Determine three edge vectors of the target surface, where two of the three edge vectors are connected to the edges corresponding to the six-sided combination intersection point;

[0125] According to the three edge vectors and preset parameters, construct two new edge vectors in each region formed by the target surface and the set surface;

[0126] Generate the first filling surface in the region according to the two new edge vectors;

[0127] Use the filling surface tool to generate the second filling surface in the region between the set surface and the first filling surface.

[0128] As Figure 14 shown, an embodiment of the present application provides an electronic device, including a processor 1401, a communication interface 1402, a memory 1403, and a communication bus 1404. Among them, the processor 1401, the communication interface 1402, and the memory 1403 complete mutual communication through the communication bus 1404.

[0129] The memory 1403 is used to store computer programs.

[0130] In an embodiment of the present application, when the processor 1401 executes the program stored on the memory 1403, it implements the method for generating a free-form surface of a building provided in any one of the foregoing method embodiments.

[0131] An embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the method for generating a free-form surface of a building provided in any one of the foregoing method embodiments.

[0132] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0133] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0134] It should be understood that the terms used herein are for the purpose of describing specific example embodiments only and are not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" as used herein may also include the plural forms. The terms "include", "comprise", "contain", and "have" are inclusive and thus specify the presence of the stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or their combinations. The method steps, processes, and operations described herein are not to be construed as necessarily requiring them to be performed in the particular order described or illustrated, unless the order of performance is explicitly stated. It should also be understood that additional or alternative steps may be used.

[0135] The above description is only the specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for generating a free-form surface of a building, characterized in that, The method includes: Determining the medial axis curve of the free-form surface of the building and fitting an initial surface on the medial axis curve, wherein the medial axis curve is used to guide the form of the free-form surface of the building, all the surfaces on the medial axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the area of the medial axis curve it covers; Generating at least one remaining surface on the medial axis curve in sequence according to the initial surface; Traversing the surface intersection points on the medial axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the medial axis curve; Traversing all the surface intersection points, finding target intersection points where there are three surfaces at the surface intersection points and the included angle of the remaining space is less than 180°, and continuously filling surfaces in the remaining space according to the target intersection points until no new surface can be generated or until the free-form surface of the building is formed, wherein the form of the free-form surface is the form of the building, all the generated surfaces are hyperbolic paraboloids, and adjacent surfaces conform to the coplanarity principle, and the coplanarity principle means that all the straight lines intersecting at one point between adjacent surfaces are always coplanar; Wherein, in the generated free-form surface, multiple hyperbolic paraboloids are spliced together, the axes of symmetry of all the hyperbolic paraboloids are located in the same plane, and only axial forces are borne inside the free-form surface without generating bending moments; Wherein, fitting the initial surface on the medial axis curve includes: Determining a unique hyperbolic paraboloid from four points in space, wherein the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space; Determining the axial lengths of the two axes of symmetry of the hyperbolic paraboloid and the axial angle between the two axes of symmetry; By adjusting the axial lengths and the axial angle, fitting an initial surface where one axis of symmetry conforms to the curve trend of a part of the medial axis curve.

2. The method according to claim 1, wherein Generating at least one remaining surface on the medial axis curve in sequence according to the initial surface includes: Determining a vertex on the medial axis curve in the initial surface, using the vertex as a common vertex, and generating a remaining surface adjacent to the initial surface and located on the medial axis curve according to the coplanarity principle; If the initial surface is located at the end point position of the medial axis curve, recursively adding surfaces according to the remaining surface until the added surfaces reach the length of the medial axis curve; If the initial surface is located at a non-end point position of the medial axis curve, recursively adding surfaces in both side directions according to the remaining surface and another vertex of the initial surface until the added surfaces reach the length of the medial axis curve.

3. The method according to claim 2, characterized in that Using the vertex as a common vertex and generating a remaining surface adjacent to the initial surface and located on the medial axis curve according to the coplanarity principle includes: Determining two adjacent edges in the initial surface connected by the vertex and determining the initial adjacent edge vectors of the two adjacent edges, wherein the remaining surface and the initial surface share the vertex; Generating remaining adjacent edge vectors of two adjacent edges connected by the vertex in the remaining surface according to preset parameters and the initial adjacent edge vectors; Generate the curvature parameters of the remaining surface according to the preset parameters; Generate the remaining vector of the third side in the remaining surface according to the initial adjacent edge vector, the curvature parameters, and the initial vector of the third side in the initial surface; Determine the position and shape of the remaining surface according to the remaining adjacent edge vectors of two adjacent sides and the remaining vector of the third side in the remaining surface.

4. The method according to claim 1, wherein Traverse the surface intersection points on the medial axis curve, and fill at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the medial axis curve, including: Traverse the surface intersection points on the medial axis curve; If the curvature of the surface intersection point is not zero, determine that the surface intersection point is a four-surface combination intersection point, and use the filling surface tool to generate a filling surface in each area formed by adjacent surfaces on the medial axis curve with the four-surface combination intersection point as the vertex; If the curvature of the surface intersection point is zero, determine that the surface intersection point is a six-surface combination intersection point, and use the lateral surface generation tool and the filling surface tool to generate two filling surfaces in each area formed by adjacent surfaces on the medial axis curve with the six-surface combination intersection point as the vertex.

5. The method according to claim 4, characterized in that, Using the filling surface tool to generate a filling surface in each area formed by adjacent surfaces on the medial axis curve includes: Use the filling surface tool to determine two filling areas formed between adjacent surfaces on the medial axis curve; Determine two associated curves of each surface in the adjacent surfaces associated with any one filling area, where the intersection point of the two associated curves is the adjacent point of the surface intersection point; Determine two adjacent edge vectors of the filling surface according to the directed vectors of the four associated curves in the two adjacent surfaces; Determine the position and shape of the filling surface according to the two adjacent edge vectors of the filling surface and the four-surface combination intersection point.

6. The method according to claim 4, wherein Using the lateral surface generation tool and the filling surface tool to generate two filling surfaces in each area formed by adjacent surfaces on the medial axis curve includes: Use the lateral surface generation tool to determine the target surface and the set surface adjacent on the medial axis curve, where the target surface and the set surface intersect at the six-surface combination intersection point; Determine the three edge vectors of the target surface, where two of the three edge vectors correspond to the edges connected to the six-surface combination intersection point; According to the three edge vectors and the preset parameters, construct two new edge vectors in each area formed by the target surface and the set surface; Generate the first filling surface in the area according to the two new edge vectors; Use the filling surface tool to generate a second filling surface in the area between the set surface and the first filling surface.

7. A generating device for a free-form surface of a building, characterized in that, The device includes: A fitting module for determining the medial axis curve of the free form surface of a building and fitting the initial surface on the medial axis curve, where the medial axis curve is used to guide the shape of the free form surface of the building, all the surfaces on the medial axis curve are diagonally adjacent surfaces, and the axis of symmetry of each surface conforms to the curve trend of the covered medial axis curve area; A generation module for sequentially generating at least one remaining surface on the medial axis curve according to the initial surface; A traversal module for traversing the surface intersection points on the medial axis curve and filling at least one filling surface with the surface intersection points as vertices between adjacent surfaces on the medial axis curve; A search module for traversing all surface intersection points, searching for target intersection points where there are three surfaces at the surface intersection points and the included angle of the remaining space is less than 180°, and continuously filling surfaces in the remaining space according to the target intersection points until no new surface can be generated or until the free form surface of the building is formed, wherein the form of the free form surface is the form of the building, all the generated surfaces are hyperbolic paraboloids, and adjacent surfaces conform to the coplanarity principle, and the coplanarity principle means that all the straight lines where adjacent surfaces intersect at a point are always coplanar; Wherein, in the generated free form surface, a plurality of hyperbolic paraboloids are spliced together, and the symmetry axes of all the hyperbolic paraboloids are located in the same plane, and only axial forces are borne inside the free form surface without generating bending moments; Wherein, the fitting module is used for: Determining a unique hyperbolic paraboloid from four points in space, wherein the four points are not coplanar with each other and the two diagonals formed by the four points are perpendicular to each other in space; Determining the axial lengths of the two symmetry axes of the hyperbolic paraboloid and the axial included angle between the two symmetry axes; By adjusting the axial length and the axial included angle, fitting an initial surface where one of the symmetry axes conforms to the curve trend of a part of the medial axis curve.

8. An electronic device, characterized in that, It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus; The memory is used for storing a computer program; The processor is used for implementing the method according to any one of claims 1-6 when executing the program stored on the memory.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the method according to any one of claims 1-6 is implemented.

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