Continuous smooth lofting curved surface body modeling method and application thereof

Abstract

The invention discloses a continuous smooth lofting curved surface body modeling method, which comprises the following steps: carrying out conformal mapping on a lofting surface to obtain mapping parameter domains, distributing and arranging all the mapping parameter domains according to a lofting curved surface structure, and carrying out normalization processing according to the distribution and arrangement direction; setting interpolation points to complete local spline interpolation on the normalized mapping parameter domain by using a plurality of segmented spline curves to form a parameter curved edge polyhedral area; according to the parameter curved edge polyhedron area, performing normalization processing according to the direction of local spline interpolation to obtain a unit cube structure to which the lofting curved surface structure is correspondingly mapped; and calculating according to mapping between the unit cube structure and the lofting curved surface structure to obtain a continuous and smooth lofting curved surface body structure model. The problem that curved surfaces at interpolation endpoints are discontinuous due to the fact that a linear interpolation method is adopted for lofting of multiple plane domains can be solved.

Description

Technical Field

[0001] The present application relates to the technical field of structural optimization design, and in particular to a method for modeling a continuous smooth lofted curved surface body, a device for modeling a continuous smooth lofted curved surface body, an electronic device, and a computer-readable storage medium. Background Art

[0002] Lofting is the process of using multiple two-dimensional objects as the section surface of the structure and sweeping them along a certain direction to form a complex three-dimensional object. It is often used in the generation of complex curved surfaces such as blades, and is a common surface and curved surface generation operation in mechanical structure design. The core idea of ​​surface lofting is to interpolate each intermediate surface / curve through a set of compatible intermediate structures, and achieve a continuous and uniform transition between the two Jordan regions through interpolation methods.

[0003] However, if only lofting is performed between two plane curve domains, it is feasible to further solve the shape of the intermediate state according to the linear interpolation method. However, for multiple plane domains, if the linear interpolation method is still adopted, the surface at the interpolation endpoints will be discontinuous. However, if the traditional continuous interpolation method is used for the expansion quotient, including polynomial interpolation, spline interpolation, etc., the following situations will easily occur: (1) If the expansion quotients mapped between multiple regions are the same, in order to ensure that the interpolation function passes through the specified data points, jitter will occur; (2) The global interpolation method is prone to more exceedance points, that is, the interpolation function value in some intervals will be higher or lower than the maximum or minimum interpolation point, resulting in inaccurate shape interpolation. Summary of the invention

[0004] In order to overcome the defects of the above-mentioned prior art, an embodiment of the present invention provides a method and application for modeling a continuous smooth lofted surface body, which can solve the problem of surface discontinuity at the interpolation endpoints caused by the linear interpolation method used for lofting multiple plane domains, and the problem of inaccurate shape interpolation caused by the use of traditional continuous interpolation methods such as polynomial interpolation and spline interpolation.

[0005] On the one hand, an embodiment of the present invention proposes a method for modeling a continuous and smooth lofted surface body, comprising: obtaining a mapping parameter domain by conformal mapping of a lofted surface, arranging all the mapping parameter domains according to the lofted surface structure distribution, and normalizing them in the direction of the distribution arrangement; setting interpolation points to perform local spline interpolation of the normalized mapping parameter domain using multiple piecewise spline curves to form a parametric curved edge polyhedron region; normalizing the parametric curved edge polyhedron region in the direction of the local spline interpolation to obtain a unit cube structure mapped to the lofted surface structure; and obtaining a continuous and smooth lofted surface body construction model based on the mapping calculation between the unit cube structure and the lofted surface structure.

[0006] In one embodiment of the present invention, the interpolation points are set to normalize the mapping parameter domain using multiple piecewise spline curves to complete local spline interpolation, including: setting the interpolation points so that the tangent vector directions of the two connected piecewise spline curves at the connected endpoints are the same, so that the lofted surface structure that completes the local spline interpolation has geometrical numerical continuity at the connection points.

[0007] In one embodiment of the present invention, the local spline interpolation is completed to form a parametric curved-edge polyhedron region, including: calculating the affine stretch transformation between the mapping parameter domains according to the conformal mapping; combining the conformal mapping with the affine stretch transformation to obtain the Teichmuller space mapping between the mapping parameter domains; and obtaining the expansion and contraction quotient between the mapping parameter domains according to the local spline interpolation based on the Teichmuller space mapping.

[0008] In one embodiment of the present invention, after obtaining the expansion quotient between the mapping parameter domains according to the local spline interpolation based on the Teichmuller space mapping, it also includes: interpolating the amplitude angle of the mapping parameter domain to the parameter curved hexahedron region according to the expansion quotient to obtain the Beltrami coefficient of the mapping parameter domain; calculating each intermediate cross-sectional shape of the mapping parameter domain to the parameter curved hexahedron region according to the Beltrami coefficient; and calculating the modeling equation of the lofted surface structure according to the intermediate cross-sectional shapes.

[0009] In one embodiment of the present invention, the lofted surface includes a plurality of triangular facets in the form of triangulation, and the calculation of each intermediate cross-sectional shape of the mapping parameter domain mapped to the parameter curved hexahedron region according to the Beltrami coefficients includes: obtaining the surface shape of each triangular facet after mapping according to the Beltrami coefficients, and assembling and stitching all the mapped surface shapes to obtain the interpolation shape between the mapping parameter domains.

[0010] In one embodiment of the present invention, the method of obtaining the surface shape after each triangular facet is mapped according to the Beltrami coefficient includes: obtaining the vertex set and connection relationship of the triangular facets to determine the original triangulation mesh and the target triangulation mesh composed of the triangular facets on the two lofting surfaces; using a piecewise linear function to approximate the mapping of the original triangulation mesh to the target triangulation mesh to obtain the linear change of each triangular facet in the original triangulation mesh mapped to the target triangulation mesh; and calculating the area of ​​each triangular facet and the Beltrami coefficient according to the linear change to construct the surface shape after each triangular facet is mapped.

[0011] On the other hand, an embodiment of the present invention further proposes a continuous smooth lofted surface body modeling device, including: a conformal mapping module, used to obtain a mapping parameter domain by conformal mapping of the lofted surface, arrange all the mapping parameter domains according to the lofted surface structure distribution, and normalize them according to the direction of the distribution arrangement; a local spline interpolation module, used to set the interpolation points to complete local spline interpolation of the normalized mapping parameter domain using multiple segmented spline curves to form a parameter curved edge polyhedron area; a unit cube structure mapping module, used to normalize the parameter curved edge polyhedron area according to the direction of the local spline interpolation to obtain the unit cube structure mapped to the lofted surface structure; a lofted surface body model construction module, used to obtain a continuous and smooth lofted surface body construction model based on the mapping calculation between the unit cube structure and the lofted surface structure.

[0012] In one embodiment of the present invention, the local spline interpolation module is specifically used to: set the interpolation points so that the tangent vector directions of the two connected segmented spline curves at the connected endpoints are the same, so that the geometric values ​​of the lofted surface structure that completes the local spline interpolation are continuous at the connecting points.

[0013] On the other hand, an embodiment of the present invention further proposes an electronic device, comprising: a memory and one or more processors connected to the memory, the memory storing a computer program, and the processor being used to execute the computer program to implement the continuous smooth lofting surface body modeling method as described in any one of the above embodiments.

[0014] On the other hand, an embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to execute the continuous smooth lofting surface body modeling method as described in any one of the above embodiments.

[0015] It can be seen from the above that, compared with the prior art, the above embodiments of the present invention can have at least one or more of the following beneficial effects:

[0016] A local spline interpolation method is proposed to realize continuous and smooth modeling of lofted surface bodies. Compared with the traditional global spline interpolation method, the local interpolation has a better effect of continuous and smooth transition when multiple points are collinear; and overfitting rarely occurs in local spline interpolation. Therefore, when the local spline interpolation method is used to obtain the expansion quotient variation curve, there are fewer points that exceed the expansion quotient variation range obtained by the lofted surface, which avoids the jitter of the interpolation function passing through the specified data points and ensures the accuracy of shape interpolation; in addition, the position of each point on the curve in the local spline interpolation is only controlled by several surrounding points, so the generation and modification of the lofted surface body can be easier to control. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0018] Figure 1 A flow chart of a method for modeling a continuous smooth lofted curved surface provided by an embodiment of the present invention;

[0019] Figure 2 A schematic diagram of conformal parameterization of a lofted surface provided by an embodiment of the present invention;

[0020] Figure 3 A schematic diagram of modeling and parameterization of a lofted curved surface provided in an embodiment of the present invention;

[0021] Figure 4 A schematic diagram of connecting points of a cubic Bézier curve provided by an embodiment of the present invention;

[0022] Figure 5 A schematic diagram of the tangent vector length of a cubic Bézier curve provided in an embodiment of the present invention;

[0023] Figure 6 A comparison diagram of a local interpolation curve and a global interpolation curve provided in an embodiment of the present invention;

[0024] Figure 7 A schematic diagram for comparing the lofted surface structure modeling method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0025] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described below with reference to the accompanying drawings and in combination with the embodiments.

[0026] In order to enable ordinary technicians in the field to better understand the technical solution of the present invention, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments, and all should belong to the protection scope of the present invention.

[0027] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are applicable to distinguishing similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition. The terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or are proprietary to these processes, methods, products or devices.

[0028] It should also be noted that the division of multiple embodiments in the present invention is only for the convenience of description and should not constitute a special limitation. The features in various embodiments can be combined and referenced to each other without contradiction.

[0029] like Figure 1 As shown, the first embodiment of the present invention proposes a method for modeling a continuous and smooth lofted surface body, for example, including: step S1, obtaining a mapping parameter domain by conformal mapping of the lofted surface, arranging all the mapping parameter domains according to the lofted surface structure distribution, and normalizing them according to the direction of the distribution arrangement; step S2, setting interpolation points to complete local spline interpolation of the normalized mapping parameter domain using multiple piecewise spline curves to form a parameter curved edge polyhedron area; step S3, normalizing the parameter curved edge polyhedron area according to the direction of the local spline interpolation to obtain the unit cube structure mapped to the lofted surface structure; step S4, obtaining a continuous and smooth lofted surface body construction model according to the mapping calculation between the unit cube structure and the lofted surface structure.

[0030] Specifically, for the two lofted surfaces Jordan region S m and S n Smooth shape interpolation between m and S n Conformally mapped to R m and R n Two mapping parameter domains, and obtain the affine stretching transformation h between the mapping parameter domains [m，n] : R m →R n , two conformal mappings and a stretching affine transformation g m , g n -1 and h [m，n] The compound obtained from S m and S n Teichmüller Mapping:

[0031]

[0032] The mapping f can be calculated [m，n] After obtaining the expansion quotient K(f), we introduce the control variable t∈[0,1] into the two Jordan regional interpolation problems and select a suitable interpolation function to establish the relationship between the expansion quotient and the variable t. t (f), calculate the corresponding Beltrami coefficient and the relationship between the variable t μ t (f). Theoretically, given the Beltrami coefficient μ t (f), there must be a smooth mapping f t Correspondingly, a smooth shape interpolation is achieved between the Jordan regions of the two lofted surfaces.

[0033] Therefore, if Figure 2 As shown, for S 0 To S n The expansion quotient of each of the n+1 Jordan regions of the lofted surface to the Teichmuller space mapping of the previous region is:

[0034]

[0035] At the same time, it can be obtained that each lofting area S i For the first region S 0 The expansion quotient is:

[0036]

[0037] If only lofting is performed between two plane curve domains, according to the interpolation method given above, and the expansion quotient K is t (f) is a linear function of t, and it is feasible to further solve the shape of the intermediate state. k , k∈{0, 2, ..., n}, if the linear interpolation method is still used, the surface at the interpolation endpoint will be discontinuous. If the traditional continuous interpolation method is used for the stretch quotient, including polynomial interpolation, spline interpolation, etc., the following situations will easily occur: (1) If the stretch quotients mapped between multiple regions are the same, in order to ensure that the interpolation function passes through the specified data points, jitter will occur; (2) The global interpolation method is prone to more exceedance points, that is, the interpolation function value in some intervals will be higher or lower than the maximum or minimum interpolation point, resulting in inaccurate shape interpolation.

[0038] Therefore, in step S1 of this embodiment, combined with Figure 3As shown, the mapping parameter domain after conformal mapping is arranged according to the structure of the lofted surface. In order to facilitate parameterized calculation, the height area of ​​the mapping parameter domain distribution is normalized. Therefore, the value range of the global parameter between all mapping parameter domains is t∈[0,1], and t=0 corresponds to S 0 , t = 1 corresponds to S n .

[0039] In step S2, for example, Perform local spline interpolation for the interpolation points to obtain the curve Then the expansion quotient corresponding to each isoparametric surface is calculated as It can be concluded that:

[0040]

[0041] like Figure 4 As shown in the figure, the calculation steps of the local interpolation method are explained by taking cubic spline as an example. Local spline interpolation is a method of using multiple piecewise spline curves to complete the interpolation of data points through given data points. During the interpolation process, it is necessary to ensure that the geometric G at the points where the spline curves meet is 1 Continuity, that is, the tangent vectors of the two segmented curves have the same direction at the endpoints. If the tangent vectors are equal in magnitude and direction, the interpolation curve has a numerical G 1 Continuity.

[0042] like Figure 5 As shown, for a family of point sets in space, let:

[0043] q k =Q k -Q k-1 ,

[0044] All interpolation methods are one of the following two forms:

[0045] D k =(1-a k )d k =a k d k+1

[0046] V k =(1-a k )q k +a k q k+1

[0047] Among them, α k It can be calculated by the coordinates of three points.

[0048]

[0049] Substituting into the first form we get:

[0050]

[0051] Substituting further into the second form, a derivative T at the intermediate point is calculated through five points. k The advantage of this calculation method is that when Q k-1 , Q k , Q k+1 When they are collinear, the resulting tangent vector is collinear with the straight line connecting the three points. k-2 , Q k-1 , Q k and Q k , Q k+1 , Q k+2 When they are collinear, the denominator of the second form is zero, so we can assign a value between [0, 1] to αk. For a cubic Bézier curve, assuming P 0 and P 3 are the first and last points of this curve, T 0 and T 3 For the corresponding unit tangent vector, we can get a cubic curve C(u), u∈[0,1], such as Figure 6 As shown, it satisfies:

[0052]

[0053] At the same time, the derivative of the Bézier curve at the endpoint is:

[0054] C′(0)=n(P 1 -P 0 ), C″(0)=n(n-1)(P 2 -2P 1 +P 0 ),

[0055] C′(1)=n(P n -P n-1 ), C″(1)=n(n-1)(P n -2P n-1 +P n-2 ).

[0056] Therefore, we can get:

[0057]

[0058] Using de Casteljau's algorithm at u = 1 / 2, let have:

[0059]

[0060] Consider bisecting the parameter interval, we can get:

[0061]

[0062] Let the velocity at the midpoint be α, square both sides of the equation and reorganize it into a quadratic equation with respect to α:

[0063] (16-|T 0 +T 3 | 2 )α 2 +[12(P 3 -P 0 )·(T 3 +T 0 )]α-36|P 3 -P 0 | 2 =0

[0064] Through the above calculation method, when there is a set of data points {Q k}(k=0,1,…,n), we can calculate the value of Q for each pair of adjacent data points k Solve the above quadratic equation and record the control point of this Bezier curve as P k，0 =Q k , P k，1 , P k，2 and P k，3 =Q k+1 α and P can be calculated by solving the positive root of the equation k，1 and P k，2 , and order The n Bezier curve segments generated by this scheme are in each parameter interval The rates of the endpoints and intermediate parameter points of Q are all 1. Therefore, a line interpolated at Q k C 1 The continuous cubic B-spline curve is composed of control points {Q 0 , P 0，1 , P 0，2 , P 1，1 , P 1，2 ,…,,P n-2，2 , P n-1，1 , P n-1，2 , Q n} and node vector

[0065]

[0066] Defined by . Based on this, we can get the interpolation function:

[0067]

[0068] Among them, N i，p (u) is the B-spline basis function.

[0069] like Figure 7 As shown in the figure, compared with the traditional global spline interpolation method, the local interpolation has a better effect of continuous smooth transition when multiple points are collinear; and overfitting is less likely to occur in the local spline interpolation. Therefore, when the local spline interpolation method is used to obtain the expansion quotient variation curve, there are fewer points that exceed the expansion quotient variation range obtained by the lofted surface, which ensures the accuracy of the shape interpolation. In addition, the position of each point on the curve in the local spline interpolation is only controlled by several surrounding points, so the generation and modification of the lofted surface body can be easier to control.

[0070] Furthermore, the lofted surface includes, for example, a plurality of triangular facets in the form of triangulation. In order to obtain the specific Beltrami coefficient of each triangular facet, it is necessary to interpolate the argument of the mapping parameter domain of each lofted surface to the parameter curved edge hexahedron region, that is:

[0071]

[0072] Therefore, we have:

[0073]

[0074] In step S3, the shape interpolation method can be used to calculate the shape of each intermediate cross-sectional area of ​​the parameter domain mapped to the parameter curved hexahedron region. The parametric curved edge polyhedron region is normalized according to the direction of local spline interpolation to obtain the unit cube structure to which the lofted surface structure is mapped.

[0075] In step S4, the modeling equation of the lofted surface body can be calculated according to the intermediate cross-sectional shape, and the equation for defining the continuous swept body is:

[0076]

[0077] Where T(t) is the trace and M(t) is the matrix that records the scaling and rotation with t as the parameter. When parallelism is maintained and there is no scaling, M(t) is the unit matrix; when there is rotation and scaling, it can be decomposed into A(t)Z(t), where A(t) is the local coordinate [r(t); e 1 (t), e 2 (t), e 3 (t)] is transformed into the global coordinate system {O; X, Y, Z}, where Z(t) is a three-dimensional vector-valued function representing scaling.

[0078] Furthermore, the shape interpolation method calculates the expansion quotient and Beltrami coefficient corresponding to any intermediate variable t through the mapping relationship between the Jordan regions of the two lofted surfaces. Theoretically, given the Beltrami coefficient μ t (f), there must be a smooth mapping f t Corresponding to it. However, in the actual operation process, it is impossible to obtain the expected piecewise linear mapping by directly solving the Beltrami equation. At the same time, since in the actual calculation of piecewise mapping, the Beltrami coefficient depends on the triangle face (i.e., the connection relationship F) rather than the coordinate point, the obtained equation cannot be solved for the discrete triangulation grid whose number of points is often only half of the number of faces. Therefore, for example, the solution of the mapping is divided into two steps: first, the shape of each triangle face after mapping is calculated under the specified stretch quotient and Beltrami coefficient, and then all the triangle faces are assembled and stitched together to obtain the target interpolation result.

[0079] Furthermore, using S m = {V m , F} to represent the region S m The triangulation grid on which X m is a set of triangle vertices, and F represents the connection relationship of the triangles. f=u+iv is the original mesh S m = {V m , F} to the target grid S n = {V n , F}, where the grid S m and S n The number of vertices is the same and they have the same connectivity F. Use piecewise linear functions to approximate the mapping f. Specifically, f is in each triangle F = [v i , v j , v k ] is a linear function:

[0080] f| F (x, y) = (a F x+b F y+p F )+i(c F x+d F y+q F )

[0081] where v i , v j and v k are the vertices of triangle F in counter-clockwise order.

[0082] For each triangle, its Beltrami coefficient can be assumed to be μ t (F) = ρ t(F)+iτ t (F). If the point before mapping is v = g + ih, and the point after mapping is w = s + it, that is:

[0083]

[0084] Then for each triangle, according to the linear change, we can get:

[0085]

[0086] Among them, there are:

[0087]

[0088] Among them, A F is the area of ​​the triangle. At the same time, the Beltrami coefficient can be calculated on this triangle:

[0089]

[0090] Assume e k is the longest side of this triangle. For the corresponding local triangle, when assuming F′=[v i ′ v j ′v k ′], and v i ′=(0,0),v j '=(1,0), then we can establish the equation:

[0091]

[0092] To solve for v′ kx and v′ kx .

[0093] Furthermore, after obtaining the shape of each triangle, all triangles need to be stitched together to form a new interpolated shape. In order to ensure that the shape of the triangle does not change, for example, each triangle is rotated and scaled proportionally so that all triangles can be seamlessly stitched together to form a new triangulated mesh.

[0094] In summary, the first embodiment of the present invention realizes continuous and smooth modeling of the lofted surface body by proposing a local spline interpolation method. Compared with the traditional global spline interpolation method, the local interpolation has a better effect of continuous and smooth transition when multiple points are collinear; and overfitting is less likely to occur in the local spline interpolation. Therefore, when the local spline interpolation method is used to obtain the expansion quotient change curve, there are fewer points that exceed the expansion quotient change range obtained by the lofted surface, which avoids the jitter of the interpolation function passing through the specified data points and ensures the accuracy of the shape interpolation; in addition, the position of the point on each curve in the local spline interpolation is only controlled by several surrounding points, so that the generation and modification of the lofted surface body can be easier to control.

[0095] In addition, the second embodiment of the present invention further provides a continuous smooth lofted curved surface modeling device, including: a conformal mapping module, a local spline interpolation module, a unit cube structure mapping module and a lofted curved surface model construction module.

[0096] Among them, the conformal mapping module is used to obtain a mapping parameter domain by conformal mapping of the lofted surface, arrange all the mapping parameter domains according to the lofted surface structure distribution, and normalize them according to the direction of the distribution arrangement. The local spline interpolation module is used to set the interpolation points to complete the local spline interpolation of the normalized mapping parameter domain using multiple segmented spline curves to form a parametric curved edge polyhedron area. The unit cube structure mapping module is used to perform normalization processing according to the parametric curved edge polyhedron area in the direction of the local spline interpolation to obtain the unit cube structure mapped to the lofted surface structure. The lofted surface body model construction module is used to obtain a continuous and smooth lofted surface body construction model based on the mapping calculation between the unit cube structure and the lofted surface structure.

[0097] Furthermore, the local spline interpolation module is specifically used to: set the interpolation points so that the tangent vector directions of the two connected segmented spline curves at the connected endpoints are the same, so that the geometric values ​​of the lofted surface structure that completes the local spline interpolation are continuous at the connecting points.

[0098] The continuous smooth lofted curved surface body modeling method implemented by the continuous smooth lofted curved surface body modeling device disclosed in the second embodiment of the present invention is as described in the first embodiment above, so it will not be described in detail here. Optionally, the various modules and the above-mentioned other operations or functions in the second embodiment are respectively for implementing the method described in the first embodiment, and the beneficial effects of the continuous smooth lofted curved surface body modeling device provided by this embodiment are the same as the beneficial effects of the continuous smooth lofted curved surface body modeling method provided by the first embodiment above, and for the sake of brevity, they will not be repeated here.

[0099] The third embodiment of the present invention further proposes an electronic device, for example, comprising: at least one processing unit, and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit executes the method described in the first embodiment, and the beneficial effects of the electronic device provided by this embodiment are the same as the beneficial effects of the continuous smooth lofting surface body modeling method provided by the first embodiment.

[0100] The fourth embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps of the above method are implemented, and the beneficial effects of the computer-readable storage medium provided by this embodiment are the same as the beneficial effects of the continuous smooth lofting surface body modeling method provided by the first embodiment.

[0101] Among them, computer-readable storage media may include, but are not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives and magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0102] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0103] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0104] In the several embodiments provided in the present application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are only schematic, such as the division of the units, which is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some service interfaces, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0105] 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 distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0106] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0107] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a memory, including a number of instructions to enable a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned memory includes: U disk, read-only memory (ROM), random access memory (RAM), mobile hard disk, disk or optical disk and other media that can store program code.

[0108] A person skilled in the art may understand that all or part of the steps in the various methods of the above embodiments may be completed by entering a program to instruct the relevant hardware. The program may be stored in a computer-readable memory, and the memory may include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0109] The above is only an exemplary embodiment of the present disclosure, and the scope of the present disclosure cannot be limited thereto. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the technical field not recorded in the present disclosure. The description and examples are regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0110] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0111] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling a continuous smooth lofted surface, characterized in that: include: Obtain mapping parameter domains by conformal mapping the lofted surface, arrange all the mapping parameter domains according to the structure of the lofted surface, and perform normalization processing according to the direction of the distribution arrangement; Setting the interpolation points to normalize the mapping parameter domain using multiple piecewise spline curves to complete local spline interpolation to form a parameter curved edge polyhedron region; Normalizing the parameter curved edge polyhedron region according to the direction of the local spline interpolation to obtain a unit cube structure to which the lofted curved surface structure is mapped; A continuous and smooth lofted surface body construction model is obtained according to the mapping calculation between the unit cube structure and the lofted surface structure.

2. The continuous smooth lofting curved surface modeling method according to claim 1, characterized in that: The setting of the interpolation points to normalize the mapping parameter domain uses a plurality of piecewise spline curves to complete local spline interpolation, including: The interpolation points are set so that the tangent vector directions of the two connected segmented spline curves at the connected endpoints are the same, so that the geometric values ​​of the lofted surface structure that completes the local spline interpolation are continuous at the connected points.

3. The continuous smooth lofting curved surface modeling method according to claim 1, characterized in that: The method of completing local spline interpolation to form a parameter curved edge polyhedron region includes: Calculating an affine stretch transformation between the mapping parameter domains according to the conformal mapping; Combining the conformal mapping with the affine stretch transformation to obtain a Teichmuller space mapping between the mapping parameter domains; The expansion and contraction quotient between the mapping parameter domains is obtained according to the Teichmuller space mapping and the local spline interpolation.

4. The continuous smooth lofting curved surface modeling method according to claim 3, characterized in that: After obtaining the expansion quotient between the mapping parameter domains according to the Teichmuller space mapping and the local spline interpolation, the method further includes: Interpolating the argument of the mapping parameter domain to the parameter curved hexahedron region according to the expansion and contraction quotient to obtain the Beltrami coefficient of the mapping parameter domain; Calculate each intermediate cross-sectional shape of the mapping parameter domain to the parameter curved hexahedron region according to the Beltrami coefficient; The modeling equation of the lofted surface structure is calculated according to the intermediate cross-sectional shape.

5. The continuous smooth lofting curved surface modeling method according to claim 4, characterized in that: The lofted surface includes a plurality of triangular facets in a triangulated form, and the step of calculating each intermediate cross-sectional shape of the mapping parameter domain mapped to the parameter curved hexahedron region according to the Beltrami coefficients includes: The curved surface shape of each triangular facet after mapping is obtained according to the Beltrami coefficients, and all the mapped curved surface shapes are assembled and stitched to obtain the interpolation shape between the mapping parameter domains.

6. The continuous smooth lofting curved surface modeling method according to claim 5, characterized in that: The step of obtaining the surface shape of each triangular face after mapping according to the Beltrami coefficients includes: Acquire the vertex set and connection relationship of the triangular facets to determine the original triangulation mesh and the target triangulation mesh composed of the triangular facets on the two lofted surfaces; Using a piecewise linear function to approximate the mapping of the original triangulated mesh to the target triangulated mesh, and obtaining a linear change of each triangular patch in the original triangulated mesh mapped to the target triangulated mesh; The area of ​​each triangular facet and the Beltrami coefficient are calculated according to the linear change to construct the surface shape after each triangular facet is mapped.

7. A continuous smooth lofting curved surface modeling device, characterized in that: include: A conformal mapping module, used to obtain mapping parameter domains by conformal mapping of the lofted surface, arrange all the mapping parameter domains according to the structure of the lofted surface, and perform normalization processing according to the direction of the distribution arrangement; A local spline interpolation module, used for setting the interpolation points to perform local spline interpolation on the normalized mapping parameter domain using multiple piecewise spline curves to form a parameter curved edge polyhedron region; A unit cube structure mapping module, used to perform normalization processing according to the direction of the local spline interpolation according to the parameter curved edge polyhedron area, to obtain the unit cube structure to which the lofted surface structure is mapped; The lofted curved surface body model construction module is used to obtain a continuous and smooth lofted curved surface body construction model according to the mapping calculation between the unit cube structure and the lofted curved surface structure.

8. The continuous smooth lofting curved surface modeling device according to claim 7, characterized in that: The local spline interpolation module is specifically used for: The interpolation points are set so that the tangent vector directions of the two connected segmented spline curves at the connected endpoints are the same, so that the geometric values ​​of the lofted surface structure that completes the local spline interpolation are continuous at the connected points.

9. An electronic device, characterized in that: include: A memory and one or more processors connected to the memory, the memory storing a computer program, the processor being used to execute the computer program to implement the continuous smooth lofting surface body modeling method as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable commands, and the computer-executable commands are used to execute the continuous smooth lofting surface body modeling method as described in any one of claims 1-6.

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