A method for generating a G2 continuous round corner surface

Abstract

The application discloses a G2 continuous round corner surface generation method. The application comprises the following steps: firstly, determining a boundary curve and a reference curve and sampling to generate a section plane; then, determining G2 continuity information of a section curve according to the position relationship between the current section plane and the boundary curve; using a fifth-order B-spline curve to represent the section curve, and then using a Newton iteration method to optimize and iterate the control points of the section curve, so that the variable acceleration energy of the generated section curve is minimized, thereby obtaining the optimal section curve of the current section plane; repeating the sampling and optimization iteration process, and finally generating a round corner surface according to all the optimal section curves. The application provides round corner surface control parameters which are easy for users to understand, and improves the robustness of the round corner surface; and can be widely used in the scene with higher smoothness requirements for the transition between various surfaces in mechanical manufacturing modeling, such as automobile manufacturing.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of computer-aided design, and particularly relates to a G2 continuous fillet surface generation method. BACKGROUND

[0002] Fillet is a geometry processing technique widely used in the field of computer-aided design (CAD), computer-aided manufacturing (CAM), three-dimensional modeling and other engineering design. Fillet operation aims to eliminate sharp corners in the model, and achieve safety, aesthetics or stress concentration prevention, dynamics compliance and other requirements by adding smooth curved surface transition at the edge or vertex of the model.

[0003] Fillet operation involves multiple methods, including multiple steps of determining the fillet boundary through user input, generating the fillet surface and topological modification, etc. One of the key steps is the fillet surface generation method. The method generates a transition surface that meets certain continuity requirements at the boundary through the fillet surface boundary information calculated by the pre-step.

[0004] Geometric continuity is a concept used to represent the smoothness of two curve segments or surface segments at the connection, which does not change according to different parameterization modes compared to parametric continuity, and thus is more widely used. G0 continuity requires the end points of two curves or surfaces at the connection to be the same; G1 continuity additionally requires the tangent direction at the connection to be the same on the basis of G0 continuity; and G2 continuity requires the curvature at the connection of the curve or surface to be the same on the basis of G1 continuity.

[0005] There are many methods to realize the generation of rounded surface. Hartmann (Hartmann E. Parametric Gnblending of curves and surfaces [J]. The Visual Computer, 2001, 17: 1-13) proposed a method to generate rounded surface which can guarantee Cn continuity, but this method requires the parameterization of base surface, and the generated rounded surface has a specific parameter representation, which is not convenient to introduce into general CAD system. Bloor et al. (Bloor M, Wilson M. Generating blend surfaces using partial differential equations [J]. Computer-aided design, 1989, 21: 165-171) proposed a method to construct rounded surface based on solving partial differential equations, but the solution of partial differential equations is difficult and inefficient. Filkins (Filkins P, Tuohy S, Patrikalakis N. Computational methods for blending surface approximation [J]. Engineering with Computers, 1993, 9: 49-62) constructed rounded surface by using non-uniform rational B-spline (NURBS) to fit the G2 continuity information at the boundary of base surface. NURBS surface is widely used in modern CAD system due to its good properties, so this method can get good support. But this method has two shortcomings: first, the free parameters provided to control the shape of rounded surface are not intuitive enough, and users have difficulty understanding them; second, the control ability provided by the free parameters is limited. Parasolid (SIEMENS. Parasolid [EB / OL]. 2018. https: / / www.plm.automation.siemens.com / global / en / products / plm-components / parasolid.html) introduced additional control points to make it easier for users to control the shape of rounded surface, but this method depends on the tangent of rounded boundary, and in some cases it cannot generate a smooth enough rounded surface. SUMMARY

[0006] In view of the deficiencies of the prior art, the application provides a G2 continuous round corner surface generation method with easy-to-control shape. The application is based on the round corner surface fitting method of Filkins, uses a 5th order B-spline curve with 8 control points to represent the cross-sectional curve of the round corner surface, wherein the first three pairs of control points are determined by the G0, G1 and G2 continuity information of the boundary, and have four additional degrees of freedom, the fourth pair of control points are used to additionally control the shape of the round corner surface, the positions of the fourth pair of control points are determined according to user input parameters, and two additional degrees of freedom are provided. Then the surface shape is optimized by minimizing the variable acceleration energy (integral of the square of the third derivative modulus) of the curve, thereby fixing the six degrees of freedom, so that the user can obtain a round corner surface with good shape by controlling only one free parameter. In addition, by limiting the control point range of the B-spline curve, the application can still give a relatively reasonable round corner surface in the case of poor boundary conditions, and has strong robustness.

[0007] The technical scheme of the application is as follows:

[0008] One kind of G2 continuous round corner surface generation method

[0009] Step one: determine the boundary curve and the reference curve;

[0010] Step two: sample the boundary curve and the reference curve to generate a cross-sectional plane;

[0011] Step three: determine the G2 continuity information of the cross-sectional curve according to the positional relationship between the current cross-sectional plane and the boundary curve;

[0012] Step four: use a 5th order B-spline curve to represent the cross-sectional curve, based on the G2 continuity information of the cross-sectional curve, use Newton iteration method to optimize and iterate the control points of the B-spline curve, so that the variable acceleration energy of the generated cross-sectional curve is minimized, thereby obtaining the optimal cross-sectional curve of the current cross-sectional plane;

[0013] Step five: repeat steps two to four to sample the boundary curve and the reference curve again and obtain the optimal cross-sectional curve of the corresponding cross-sectional plane, and finally generate a round corner surface according to all the optimal cross-sectional curves.

[0014] In the step two, one point is sampled on each of the two boundary curves and the reference curve, and the three points obtained by sampling determine the cross-sectional plane.

[0015] In the step three, the positions, tangents, normals and curvatures of the three sampling points in the cross-sectional plane are calculated, and the intersection point P between the straight line extending along the tangent of the sampling point from one boundary curve and the straight line extending along the tangent of the sampling point from the other boundary curve is calculated. A The positions, tangents, normals and curvatures of the three sampling points and the intersection point P are used to determine the G2 continuity information of the cross-sectional curve. AG2 continuity information of the section curve composed of the positions of the control points.

[0016] The step four is specifically:

[0017] 4.1) Construct eight control point vectors with six free parameters to be determined using the G2 continuity information; set initial values of the six free parameters;

[0018] 4.2) Calculate the variable acceleration energy of the section curve generated according to the current free parameters;

[0019] 4.3) Calculate the partial derivative matrix of the variable acceleration energy with respect to the control point vectors, and calculate the partial derivative matrix D and the second-order partial derivative matrix G of the control point vectors with respect to the free parameter vectors;

[0020] 4.4) Calculate the Hessian matrix of the variable acceleration energy with respect to the free parameters through all the matrices calculated in 4.3), and calculate new free parameters through the Hessian matrix;

[0021] 4.5) Repeat 4.2)-4.4) according to the new free parameters until the free parameter vectors converge, and obtain optimal free parameters to generate the optimal section curve of the current section plane.

[0022] In 4.1), the formulas of the first to eighth control point positions C0-C7 are as follows:

[0023] C0=P0

[0024] C7=P1

[0025]

[0026] V0=l0T0

[0027] V1=l1T1

[0028] When the direction of P A The direction of P A The direction of P

[0029]

[0030] When the direction of P A The direction of P A The direction of P

[0031]

[0032] Where α0, α1, β0, β1, γ0, γ1 are the first to sixth free parameters, ρ represents the "height" of the rounded surface, P0 and P1 are the sampling point positions on the two boundary curves, T0 and T1 are the unit tangent vectors of the cross-sectional curves at sampling points P0 and P1, κ0 and κ1 are the curvatures of the cross-sectional curves at sampling points P0 and P1, and V0 and V1 are the vectors pointing from sampling points P0 and P1 to the intersection point P. A The vectors are: l0 and l1 are the lengths of vectors V0 and V1, respectively; N0 and N1 are the principal normal vectors of the cross-sectional curve at sampling points P0 and P1, respectively; || is the distance; and ER is the vector length adjustment ratio.

[0033] In section 4.2), the formula for calculating the variable acceleration energy of the cross-sectional curve is as follows:

[0034] f = aC T AC

[0035] C = [C0, C1, C2, C3, C4, C5, C6, C7] T a = 480

[0036]

[0037] Where f represents the variable acceleration energy of the cross-sectional curve, T represents the transpose operation, C represents the control point vector, C0, C1, C2, C3, C4, C5, C6, and C7 represent the positions of the first control point to the eighth control point, respectively, a represents the energy coefficient, and A represents the energy matrix.

[0038] In section 4.3), the formula for the partial derivative matrix of the control point vector with respect to the free parameter vector is as follows:

[0039]

[0040] Where α0, α1 are the first and second free parameters, P0 and P1 are the sampling point positions on the two boundary curves, T0 and T1 are the unit tangent vectors of the cross-sectional curves at sampling points P0 and P1, respectively, κ0 and k1 are the curvatures of the cross-sectional curves at sampling points P0 and P1, and V0 and V1 are the vectors pointing from sampling points P0 and P1 to the intersection point P. A The vectors are given, where l0 and l1 are the lengths of vectors V0 and V1, respectively, and N0 and N1 are the principal normal vectors of the cross-sectional curve at sampling points P0 and P1, respectively.

[0041] II. A computer device

[0042] The computer device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the method when executing the computer program.

[0043] Three, a computer readable storage medium

[0044] The storage medium stores a computer program, and the computer program implements the steps of the method when executed by a processor.

[0045] Four, a computer program product

[0046] The product comprises a computer program / instruction, which implements the steps of the method when executed by a processor.

[0047] The present application has the following advantages:

[0048] The present application uses a six-order non-uniform B-spline curve with four pairs of control points as the cross-sectional curve of the fillet surface, in addition to the G2 continuity information at the endpoints, new user control parameters are added to control the shape of the fillet surface, the controllability of the fillet surface is enhanced, and the robustness of the fillet surface is enhanced through the limitation of the data range. In addition, the variable acceleration energy is used to optimize the surface shape, and the calculation of the fillet surface can be completed with high efficiency. The method can be widely used in mechanical manufacturing modeling for scenes with high smoothness requirements for the transition between surfaces, such as automobile manufacturing. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a flowchart of the method of the present application;

[0050] Figure 2 is a schematic diagram of the cross-sectional curve and user input parameters;

[0051] Figure 3 is a result diagram of the G2 continuous fillet surface constructed by the present application;

[0052] Figure 4 is a robustness diagram of the fillet surface of the present application. DETAILED DESCRIPTION

[0053] The present application will be described in detail below according to the drawings and preferred embodiments, and the purposes and effects of the present application will become more apparent. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0054] Since the G2 continuous fillet surface is often used in the field of automobile manufacturing, the following example selects a local case in the automobile manufacturing process that can reflect the superiority of the present application. In addition to the example, the present application can also be applied to various occasions with high smoothness requirements for surface connection. Figure 3(a) is a local structure of an automobile shell, and a section thereof is intercepted for explaining the generation method.

[0055] As shown in Figure 1 , a G2 continuous round corner surface generation method according to an embodiment of the application comprises the following steps:

[0056] Step one: according to the automobile production or design needs, a designer determines the round corner range in the form of a radius or a distance parameter. According to the parameter, each boundary curve on the two base surfaces S0(u0, v0) and S1(u1, v1) is determined, the curve defines the position where the round corner surface connects with the base surface, and further determines the round corner range of the local automobile shell. The two boundary curves are parameterized, and coincide with the parameter lines u=0 and u=1 of the round corner surface. The reference curve is used to assist in determining the cross section position of the round corner surface, and can be the intersection line of the two base surfaces or the intersection line of the boundary curve offset along the normal direction of the base surface. The reference curve is parameterized with the two boundary curves. In this example, the offset amount d i i=0, 1 of each base surface is taken as the reference curve. i i Two offset surfaces are obtained by offsetting the base surfaces S i along the normal direction by a distance d i , and the reference curve R(t) is obtained by intersecting the two offset surfaces. The boundary curves B0(u0(t), v0(t)) and B1(u1(t), v1(t)) are obtained by projecting R(t) to S0(u0, v0) and S1(u1, v1).

[0057] Step two: the boundary curves and the reference curve are sampled to generate a cross section plane; specifically, a point is sampled on each of the two boundary curves and the reference curve, and the three sampling points are not collinear, and the cross section plane is determined by the three sampling points.

[0058] Step three: according to the position relationship between the current cross section plane and the boundary curves, the G2 continuity information of the cross section curve is determined; specifically, the position, tangent, normal, curvature of the three sampling points in the cross section plane are calculated, and the intersection point P A between the straight line extending along the tangent of the sampling point on one boundary curve and the straight line extending along the tangent of the sampling point on the other boundary curve is calculated. Figure 2 (a) is a cross section view of a local structure of an automobile shell before the round corner operation, and the two arc lines in the figure represent the original automobile shell surface, and P0 and P1 are sampling points on the boundary curve. The G2 continuity information of the cross section curve is composed of the position, tangent, normal, curvature of the three sampling points and the position of the intersection point P A .

[0059] The cross-sectional curve is a sixth-order non-uniform B-spline curve with nodal vectors {0,0,0,0,0,0,0.5,0.5,1,1,1,1,1,1} and 8 control points C. i i = 0, 1, ..., 7. The cross-sectional curve r(t) is expressed as: Among them B i,5 (t) is the B-spline basis function. The cross-sectional normal N = (P0 - P) r )×(P1-P r ); Base surface S i In P i Normal N at the location i ; Base surface S i In P i Tangential T at the point i =(-1) i N×N i ; Base surface S i In P i curvature κ at i .

[0060] Step 4: Use a fifth-order B-spline curve to represent the cross-sectional curve. Based on the G2 continuity information of the cross-sectional curve, use Newton's iteration method to optimize and iterate the control points of the B-spline curve, so as to minimize the variable acceleration energy of the generated cross-sectional curve, thereby obtaining the optimal cross-sectional curve of the current cutting plane.

[0061] Figure 2 (b) illustrates the eight control points of the B-spline curve. These eight control points completely control the shape of the current cross-sectional curve, which in turn controls the shape of the generated fillet surface. Figure 3 (b) is a partial view of the car body after the final rounded corner operation. The light-colored line segments in the figure represent the control points of each cross-sectional curve. The figure shows the effect of the control points on the smooth transition of the local part of the car body.

[0062] Figure 2 In (b), h is formed by Figure 2 The maximum height that the highest point of the transition fillet surface can reach after smoothing the partial car body determined by V0 and V1 (see step five) in (a) is determined. This maximum height limits the sharpness of the shape of the partial car body. ρ is a user-input parameter used to control the ratio of the actual height to the maximum height of the highest point of the fillet surface, thereby controlling the shape of the partial car body after filleting. Specifically, the larger ρ is, the "sharper" the transition fillet is, and vice versa.

[0063] Step four is as follows:

[0064] 4.1) Construct 8 control point vectors using G2 continuity information, each containing six undetermined free parameters. The 8 control points form four control point pairs. The formulas for the positions C0-C7 of the first to eighth control points are as follows:

[0065] C0 = P0

[0066] C7 = P1

[0067]

[0068]

[0069] V0 = l0T0

[0070] V1=l1T1

[0071] When P A -The direction of P0 is opposite to the direction of the unit tangent vector T0, or P A When the direction of P1 is opposite to the direction of the unit tangent vector T1:

[0072] l0 = 0.1|P0 - P1|

[0073] l1 = 0.1|P0 - P1|

[0074] When P A -P0 has the same direction as the unit tangent vector T0 and P A When the direction of P1 is the same as the direction of the unit tangent vector T1:

[0075]

[0076] Where α0, α1, β0, β1, γ0, γ1 are the first to sixth free parameters, and ρ is the user-input parameter, representing the "height" of the rounded surface, such as... Figure 2 As shown in (b), P0 and P1 are the sampling point positions on the two boundary curves, T0 and T1 are the unit tangent vectors of the cross-sectional curves at sampling points P0 and P1, respectively, κ0 and κ1 are the curvatures of the cross-sectional curves at sampling points P0 and P1, respectively, and V0 and V1 are the vectors pointing from sampling points P0 and P1 to the intersection point P. A The vectors are: l0 and l1 are the lengths of vectors V0 and V1, respectively; N0 and N1 are the principal normal vectors of the cross-sectional curve at sampling points P0 and P1, respectively; || is the distance; and ER is the vector length adjustment ratio.

[0077] Based on experience, the initial values ​​for the six free parameters are set using the following formula:

[0078] α i =3ρl i

[0079]

[0080] γ i = 0.3(1 - p)

[0081] 4.2) Based on the G2 continuity information of the cross-section curve, calculate the jerk energy of the cross-section curve generated by the control under the current free parameter;

[0082] Wherein, the jerk energy of the cross-section curve After unfolding and arranging, the calculation formula of the jerk energy of the cross-section curve is as follows:

[0083] f = aC T AC

[0084] C = [C0, C1, C2, C3, C4, C5, C6, C7] T , a = 480

[0085]

[0086] Wherein, f represents the jerk energy of the cross-section curve, T represents the transpose operation, C represents the control point vector, C0, C1, C2, C3, C4, C5, C6, C7 respectively represent the first control point position to the eighth control point position, a represents the energy coefficient, A represents the energy matrix. aA is the matrix of the quadratic form f(C), and the common factor a of the matrix elements is moved out of the matrix for convenient consideration.

[0087] 4.3) Calculate the partial derivative vector of the jerk energy with respect to the control point vector And the second-order partial derivative matrix And calculate the partial derivative matrix D and the second-order partial derivative matrix G of the control point vector with respect to the free parameter vector M;

[0088] In 4.3), the formula of the partial derivative matrix of the control point vector with respect to the free parameter vector is as follows:

[0089]

[0090] Wherein, a0, a1, are the first free parameter and the second free parameter.

[0091] The second-order partial derivative matrix G of the control point vector with respect to the free parameter vector M satisfies the following formula:

[0092]

[0093] Wherein, [] is a matrix, g ijk is the matrix element of the ijk, i = 0…7, j = 0…5, k = 0…5.

[0094] Matrix G is an 8*6*6 sparse three-dimensional matrix, only and The first element is not zero, and all other matrix elements are zero.

[0095] 4.4) Calculate the Hessian matrix of the variable acceleration energy with respect to the free parameters using all matrices obtained in 4.3), as shown in the following formula:

[0096] H=2a(D T AD+C T AG)

[0097] The new free parameters are then obtained by calculating the Hessian matrix.

[0098] 4.5) Based on the new free parameters, repeat steps 4.2)-4.4) until the free parameter vector converges (i.e. the difference between the free parameter vectors obtained from the two calculations is less than the preset value), thus obtaining the optimal free parameters and generating the optimal cross-sectional curve of the current cutting plane.

[0099] Step 5: Repeat steps 2-4 to resample the boundary curve and reference curve, and obtain the optimal cross-sectional curve r(t) for the corresponding cutting plane. i Finally, based on all the optimal cross-sectional curves, a rounded surface is generated, such as... Figure 3 As shown in (b). At this point, the rounded surface that meets the G2 continuity requirements in the automobile production process has been generated. In the subsequent modeling process, this rounded surface will replace the common edge of the two surfaces in the local shell of the automobile, as well as part of the surface, so that the two surfaces maintain a high degree of smoothness at the connection.

[0100] When max(|P) A -P0|,|P A When -P1|)>|P0-P1|, the present invention imposes restrictions on l0 and l1. These restrictions are intended to prevent the rounded curved surface from producing undesirable shapes that do not meet the actual design requirements of automobiles under unfavorable boundary conditions. Figure 4 (a) represents a poorly configured result where the generation of l0 and l1 is not restricted. Figure 4 (b) represents the generated result after restricting l0 and l1.

[0101] So far, the method steps of one embodiment of the present application have been given. Taking the smoothing operation of local surface connection in the automobile design process as an example, the present application uses a six-order non-uniform B-spline curve with four pairs of control points as the cross-sectional curve of the fillet surface, in addition to the G2 continuity information at the endpoints, new user control parameters are added to control the shape of the fillet surface, the controllability of the fillet surface is enhanced, and the robustness of the fillet surface is enhanced through the limitation of the data range. In addition, the use of variable acceleration energy to optimize the surface shape can complete the calculation of the fillet surface with higher efficiency.

[0102] In one aspect, the present application also provides a computer device, which comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the G2 continuous fillet surface generation method when executing the computer program.

[0103] In one aspect, the present application also provides a computer readable storage medium, which stores a computer program, and the computer program implements the steps of the G2 continuous fillet surface generation method when executed by a processor.

[0104] In one aspect, the present application also provides a computer program product, which comprises computer programs / instructions, and the computer programs / instructions implement the steps of the G2 continuous fillet surface generation method when executed by a processor.

[0105] Finally, it should be noted that the above embodiments and descriptions are only used to illustrate the technical solutions of the present application but not to limit the present application. Those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the technical solutions disclosed by the present application, and all of them should be covered in the protection scope of the claims of the present application.

Claims

1. A method of generating a G2-continuous round corner blend, comprising: The method comprises the following steps: Step 1: obtaining an automobile shell to be optimized, selecting a structure of the automobile shell, the structure being composed of two boundary surfaces and a common edge thereof, the two boundary surfaces being approximately parallel within a certain range from the edge, determining each boundary curve on the two boundary surfaces according to a preset fillet range, the boundary curve representing a position at which a fillet surface is connected to the boundary surface, and determining a reference curve, the reference curve being used to assist in determining a cross-section position of the fillet surface; Step 2: sampling the boundary curve and the reference curve to generate a cross-section plane; Step 3: determining G2 continuity information of a cross-section curve according to a positional relationship between the current cross-section plane and the boundary curve; Step 4: using a fifth-order B-spline curve to represent the cross-section curve, based on the G2 continuity information of the cross-section curve, using a Newton iteration method to iteratively optimize control points of the B-spline curve, so that a variation acceleration energy of the generated cross-section curve is minimized, thereby obtaining an optimal cross-section curve of the current cross-section plane; Step 5: repeatedly sampling the boundary curve and the reference curve and obtaining the optimal cross-section curve of the corresponding cross-section plane, and finally generating a fillet surface according to all the optimal cross-section curves, the fillet surface replacing the common edge and part of the surfaces of the two boundary surfaces of the selected structure of the automobile shell in Step 1, thereby obtaining a smoothness-optimized automobile shell structure.

2. The method of claim 1, wherein, In Step 2, one point is sampled on each of the two boundary curves and the reference curve, and a cross-section plane is determined by the three points obtained by the sampling.

3. The method of claim 1, wherein, In the third step, the position, tangent, normal, curvature of the three sample points in the section plane are calculated, and the intersection point P between the straight line extending from a sample point on one boundary curve along the tangent of the sample point and the straight line extending from a sample point on another boundary curve along the tangent of the sample point is calculated A The G2 continuity information of the section curve is composed of the position, tangent, normal, curvature of the three sample points and the position of the intersection point P A .

4. The method of claim 1, wherein, Step 4 specifically comprises: 4.1) using the G2 continuity information to construct eight control point vectors, wherein six free parameters to be determined are included; setting initial values of the six free parameters; 4.2) calculating variation acceleration energy of a cross-section curve generated according to the current free parameters; 4.3) Compute the partial derivative matrix of the variable acceleration energy with respect to the control point vector, and the partial derivative matrix of the control point vector with respect to the free parameter vector and the second order partial derivative matrix ; 4.4) calculating a Hessian matrix of the variation acceleration energy with respect to the free parameters by using all the matrices obtained in 4.3), and obtaining new free parameters by using the Hessian matrix; 4.5) repeating 4.2)-4.4) according to the new free parameters until the free parameter vector converges, thereby obtaining optimal free parameters and generating an optimal cross-section curve of the current cross-section plane.

5. The method of claim 4, wherein, In the 4.1), the first to the eighth control point positions The formula is as follows: When the direction of the unit tangent vector is opposite or the direction of the unit tangent vector is opposite When the direction of the unit tangent vector is the same as the direction of the unit tangent vector the direction of the unit tangent vector is the same as the direction of the unit tangent vector in, These are the first to sixth free parameters. To represent the "height" of a rounded surface, and These represent the sampling point locations on the two boundary curves. and The cross-sectional curves at the sampling points are respectively and sampling points The unit tangent vector at that point, and The cross-sectional curves at the sampling points are respectively and sampling points curvature at that point and From sampling points and sampling points Pointing to the intersection The vector, They are vectors sum vector Length, and The cross-sectional curves at the sampling points are respectively and sampling points The principal normal vector at that location, For distance, This is the ratio for adjusting the vector length.

6. The method of claim 4, wherein, In 4.2, the calculation formula of the variation acceleration energy of the cross-section curve is as follows: ， wherein, represents a variable acceleration energy of a cross-sectional curve, represents a transpose operation, represents a control point vector, are respectively a first control point position - an eighth control point position, represents an energy coefficient, represents an energy matrix.

7. The method for generating a G2 continuous rounded surface according to claim 4, characterized in that, In 4.3, the formula of the partial derivative matrix of the control point vector with respect to the free parameter vector is as follows: wherein are the first and second free parameters, and are the positions of the sampling points on the two boundary curves, respectively, and are the unit tangent vectors of the cross-sectional curve at the sampling points and , respectively, and are the curvatures of the cross-sectional curve at the sampling points and , respectively, and are the vectors from the sampling points and to the intersection point , respectively, are the lengths of the vectors and , respectively, and are the principal normal vectors of the cross-sectional curve at the sampling points and , respectively.

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

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the method of any one of claims 1 to 7.

10. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to implement the steps of the method of any one of claims 1 to 7.

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