CN103413175B - Based on the closed non-homogeneous B spline curve method for fairing of genetic algorithm - Google Patents

Abstract

The invention discloses a kind of closed non-homogeneous B spline curve method for fairing based on genetic algorithm, for solving the slow-footed technical matters of existing closed non-homogeneous B spline curve method for fairing.Technical scheme between two data points occurring reverse curvature, increases data point re-start curve interpolation, and the position of newly-increased data point adopts genetic algorithm to determine under the constraint of fairing criterion, and then the shape of adjustment curve makes its fairing.The method makes again the curve of interpolation not only strictly by preliminary offset point, and solves the reverse curvature problem that original curve occurs, than curve fairing more disclosed in background technology.There is the phenomenon of pit in the closed cross-section line simultaneously effectively solving the stitching portion of trailing edge and blade back and leaf basin, make the more fairing of blade profile line, and the method is applicable to multiple Three-dimensional CAD Software platform, thus effectively compensate for the deficiency of existing nurbs curve interpolation research, and improve fairing speed.

Description

Based on the closed non-homogeneous B spline curve method for fairing of genetic algorithm

Technical field

The present invention relates to a kind of closed non-homogeneous B spline curve method for fairing, particularly a kind of closed non-homogeneous B spline curve method for fairing based on genetic algorithm.

Background technology

Complex product, three-dimensional model as blade of aviation engine or generator blade constructs, the data point that usual utilization obtains from pneumatic (or other calculate) data, to construct blade profile, namely constructs blade profile by " cross section curve interpolation data point-curved surface crosses cross section curve ".The front/rear edge of current blade be mostly to provide the front/rear edge center of circle with radial location as known conditions, be connected by the single order geometry continuum of front/rear edge and blade back and leaf basin and create section line, thus complete surface modeling.And the development trend of section line formative method uses data point direct representation shape more and more, created the section line of a second order geometry continuum by the direct interpolation of data point.But because the Curvature varying of blade trailing edge is larger, shape is very responsive to aeroperformance, therefore very close at trailing edges place data point, then relative sparse with the data point on leaf basin at blade back, the closed cross-section line of the stitching portion of trailing edge and blade back and leaf basin can be caused thus to occur pit, thus affect blade profile.Therefore how to process realistic problem when this pit makes its fairing, existing Three-dimensional CAD Software system cannot solve problems.

Non-uniform rational B-spline is (hereinafter referred to as NURBS, Non-UniformRationalB-Spline) method representation curve and surface becomes the standard expression-form of CAD system already, it not only solves the inconsistent problem that free curve curved surface and elementary parsing curve and surface describe, and overcome Bezier, the deficiency of B-spline method, weight factor and non-uniform knot vector make it possible to more effectively control the shape of curve and surface simultaneously, and can make in a CAD system strictly with a kind of unified mathematical model definition product geometric configuration, system is simplified, be easy to data management, be convenient to engineering staff use, improve surface modeling ability simultaneously.

For the nurbs curve generated by interpolation, the place of often comparatively dredging place transition compared with Mi Chu to data point at data point occurs that curvature is reverse, causes curve to occur the phenomenon of not fairing.At present, for the situation of the not fairing of NURBS interpolation curve, mainly contain the method for fairing such as amendment bad point, adjustment weight factor and knot modification vector, but these methods all also exist deficiency.If data point is accurately, so adopt the data point that the method meeting artificial destruction of amendment bad point is originally correct; In the middle of engineer applied, the data point of nurbs curve interpolation does not often all have weight factor, and therefore, the shape being adjusted nurbs curve by the power of amendment factor can not be widely used; Prove by experiment, knot modification vector is not solve the most effective method of curve reverse curvature problem.

Document " based on the research of the curve smoothing of genetic algorithm, China Mechanical Engineering the 13rd volume, the 13rd phase, first half of the month in February, 2002 " discloses a kind of curve smoothing method based on genetic algorithm.The method, on the basis of traditional fairing, one of proposes using the variance of curvature of curve extreme value as the standard weighing curve smoothing, introduces genetic algorithm and fuzzy mathematics controlling mechanism.The method mainly studies the Smoothing Problem after grating vector, has certain limitation, and in addition when data point is more, utilize the method for curvature of curve extreme value variance, speed is slower.

Summary of the invention

In order to overcome the slow-footed deficiency of existing closed non-homogeneous B spline curve method for fairing, the invention provides a kind of closed non-homogeneous B spline curve method for fairing based on genetic algorithm.The method re-starts curve interpolation by increasing data point between two data points occurring reverse curvature, and the position of newly-increased data point adopts genetic algorithm to determine under the constraint of fairing criterion, and then the shape of adjustment curve makes its fairing.The method makes again the curve of interpolation not only strictly by preliminary offset point, and solves the reverse curvature problem that original curve occurs, than the fairing more of the curve disclosed in background technology.There is the phenomenon of pit in the closed cross-section line simultaneously effectively solving the stitching portion of trailing edge and blade back and leaf basin, make the more fairing of blade profile line, and the method is applicable to multiple Three-dimensional CAD Software platform, thus effectively compensate for the deficiency of existing nurbs curve interpolation research, and speed is fast.

The technical solution adopted for the present invention to solve the technical problems: a kind of closed non-homogeneous B spline curve method for fairing based on genetic algorithm, is characterized in comprising the following steps:

Step one, determine closed nurbs curve interpolation method, adopt three closed nurbs curves to carry out interpolation.Be provided with m+1 data point q ₀, q ₁, q ₂... q _m, and q ₀=q _m, getting data point is curvilinear inner connection segment point, i.e. q _ithere is nodal value u _i+3.This nurbs curve is by n+1 control vertex d ₀, d ₁, d ₂... .d _nwith knot vector U=[u ₀, u ₁..., u _n+4] define, field of definition is u ∈ [u ₃, u _n+1]=[0,1].Wherein n=m+2, total m+3 unknown control vertex.

The method of 1.1 employing accumulation chord lengths, calculates parameter value sequence t ₀, t ₁, t ₂... t _m, field of definition internal segment point value is u ₃=t ₀, u ₄=t ₁, u ₅=t ₂... u _m=u _m+3, the node outside field of definition is defined as u ₀=u _n-2-1, u ₁=u _n-1-1, u ₂=u _n-1, u _n+2=u ₄+ 1, u _n+3=u ₅+ 1, u _n+4=u ₆+ 1.

1.2 is anticaustic in interpolation m+1 data point q ₀, q ₁, q ₂... q _mand q ₀=q _mthree closed nurbs curve the Representation Equation be

$p\left(u\right)=\underset{j=0}{\overset{n}{\mathrm{\Σ}}}{d}_j{R}_{j,3}\left(u\right)=\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{d}_j{R}_{j,3}\left(u\right),u\∈[u_i,u_{i+1}]\⋐[u_3,u_{n+1}],$

Wherein, $R_{i,3}\left(u\right)=\frac{w_j{N}_{j,k}\left(u\right)}{\underset{j=0}{\overset{n}{\mathrm{\Σ}}}{w}_j{N}_{j,k}\left(u\right)}$ Be three rational basis functions.

By curve definitions territory interior nodal value substitutes into equation, meets interpolation condition, namely

$p\left(u_i\right)=\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{d}_j{R}_{j,3}\left(u_i\right)=q_{i-3},i=\mathrm{3,4},\·\·\·,n$

Above formula is altogether containing n-2 equation.First and last three control vertex coincidence d _n-2=d ₀, d _n-1=d ₁, d _n=d ₂, unknown control vertex number is reduced to n-2.N-2 unknown control vertex is solved from the system of linear equations chasing method be made up of n-2 equation.

1.3 are solving control vertex d _ibefore, d need be obtained _icorresponding weight factor w _i, i=0,1 ..., n.If known each data point q _iweight factor i=0,1 ..., m, then

$\left\{\begin{array}{c}\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{w}_j{R}_{j,3}\left(u_i\right)=\stackrel{\‾}{w_{i-3}},i=\mathrm{3,4},...,n\\ w_{n-2}=w_0,w_{n-1}=w_1,w_n=w_2\end{array}\right.$

The above-mentioned system of equations of simultaneous, obtains control vertex d _iweight factor w _i.

Step 2, determine a q _kwith a q _k+1, wherein at q _kand q _k+1reverse curvature not fairing is there is between two data points.

Step 3, employing genetic algorithm calculation level q _kwith a q _k+1between the position of newly-increased data point.

3.1 hypothesis are at q _kand q _k+1reverse curvature not fairing is there is, wherein q between two data points _kand q _k+1manually select. q _k(x _k, y _k) and q _k+1(x _k+1, y _k+1) between the data point that newly increases, Δ x is q _k+0.5(x _k+0.5, y _k+0.5) edge the bias in direction, Δ y is perpendicular to bias on direction.Through calculating, obtain:

$\left\{\begin{array}{c}{x}_{k+0.5}=x_k+\mathrm{\Δx}\·\cos \mathrm{\θ}+\mathrm{\Δy}\·\cos \mathrm{\η}\\ y_{k+0.5}=y_k+\mathrm{\Δx}\·\sin \mathrm{\θ}+\mathrm{\Δy}\·\sin \mathrm{\η}\end{array}\right.$

Wherein, $\mathrm{\&theta;}=\arctan \frac{y_{k+1}-y_k}{x_{k+1}-x_k},$ $\mathrm{\&eta;}=\arctan (-\frac{x_{k+1}-x_k}{y_{k+1}-y_k}),$ $0<\mathrm{\&Delta;x}<\left|\stackrel{\&RightArrow;}{q_k{q}_{k+1}}\right|.$

Calculate Δ x and Δ y, obtain newly-increased data point q _k+0.5(x _k+0.5, y _k+0.5), therefore, Δ x and Δ y is as the gene of two on genetic algorithm chromosome.

The energy definition of 3.2 curves is E=∫ k ²ds, wherein k is curvature, and s is arc length; Define the maximal value that a variable Q represents Curvature varying, the objective function of curve smoothing is min (f), and wherein f=α E+ β Q, α are the weight factors of curve strain energy changing value, and β is the weight factor of curve maximum curvature changing value, alpha+beta=1.

The objective function of curve smoothing is min (f (Δ x, Δ y)); Fitness is defined as wherein Δ x and Δ y is two genes on chromosome.

3.3 adopt coded systems to be floating-point encoding, and two gene Δ x on chromosome and Δ y to retain after radix point three respectively; The scale of population is 10, and each individuality of initial population produces at random.

3.4 genetic operators comprise selection, crossover and mutation.System of selection adopts wheel disc stake method; Cross method adopts single-point to intersect, and point of crossing produces at random; Variation method adopts Gaussian mutation method.

3.5 start genetic algorithm, calculate the position of newly-increased data point.

Step 4, by preliminary offset point and newly-increased data point, the nurbs curve that interpolation makes new advances.

If step 5 curve also exists reverse curvature, then jump to step 2, again fairing is carried out to curve; If curve has met fairing requirement, then export current interpolation curve as net result.

Weight factor α=0.7 of described curve strain energy changing value.

Weight factor β=0.3 of described curve maximum curvature changing value.

The invention has the beneficial effects as follows: because the method re-starts curve interpolation by increasing data point between two data points occurring reverse curvature, the position of newly-increased data point adopts genetic algorithm to determine under the constraint of fairing criterion, and then the shape of adjustment curve makes its fairing.The method makes again the curve of interpolation not only strictly by preliminary offset point, and solves the reverse curvature problem that original curve occurs, than the fairing more of the curve disclosed in background technology.There is the phenomenon of pit in the closed cross-section line simultaneously effectively solving the stitching portion of trailing edge and blade back and leaf basin, make the more fairing of blade profile line, and the method is applicable to multiple Three-dimensional CAD Software platform, thus effectively compensate for the deficiency of existing nurbs curve interpolation research, and improve fairing speed.

Below in conjunction with drawings and Examples, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is newly-increased data point schematic diagram.

Fig. 2 is the schematic diagram of blade Cross-sectional data point.

Fig. 3 is the partial enlarged drawing of blade cross section trailing edge partial data point.

Fig. 4 is the initial blade section line by blade Cross-sectional data point structure.

Fig. 5 is the curvature comb that reverse curvature place appears in blade section line.

Fig. 6 is the data point schematic diagram that reverse curvature place appears in blade section line, wherein at data point p ₁and p ₂between there is reverse curvature not fairing, at data point q ₁and q ₂between there is reverse curvature not fairing.

Fig. 7 is the blade section line schematic diagram after fairing.

Fig. 8 is the curvature comb after curve smoothing.

Embodiment

With reference to Fig. 1-8, for the blade section line interpolation of certain type blade, take VisualStudio2010 as developing instrument, design software NX7.5 platform utilizes NXOpenAPI develop and realize describing the present invention in detail.

Step 1: determine closed nurbs curve interpolation method, adopts three closed nurbs curves to carry out interpolation.Be provided with m+1 data point q ₀, q ₁, q ₂... q _m, and q ₀=q _m, getting data point is curvilinear inner connection segment point, i.e. q _ithere is nodal value u _i+3.This nurbs curve is by n+1 control vertex d ₀, d ₁, d ₂... .d _nwith knot vector U=[u ₀, u ₁..., u _n+4] define, field of definition is u ∈ [u ₃, u _n+1]=[0,1].Wherein n=m+2, i.e. more than data point number 2 of the number of control vertex, total m+3 unknown control vertex.

1.1 determine knot vector.Adopt the method for accumulation chord length, calculate parameter value sequence t ₀, t ₁, t ₂... t _m, field of definition internal segment point value is u ₃=t ₀, u ₄=t ₁, u ₅=t ₂... u _m=u _m+3, the node outside field of definition is defined as u ₀=u _n-2-1, u ₁=u _n-1-1, u ₂=u _n-1, u _n+2=u ₄+ 1, u _n+3=u ₅+ 1, u _n+4=u ₆+ 1.

1.2 control of reverse computing summits.For interpolation m+1 data point q ₀, q ₁, q ₂... q _mand q ₀=q _mthree closed nurbs curve the Representation Equation be

$p\left(u\right)=\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{d}_j{R}_{j,3}\left(u\right)=\underset{j=i-3}{\overset{i}{\mathrm{\&Sigma;}}}{d}_j{R}_{j,3}\left(u\right),u\&Element;[u_i,u_{i+1}]\&Subset;[u_3,u_{n+1}],$

Wherein $R_{i,3}\left(u\right)=\frac{w_j{N}_{j,k}\left(u\right)}{\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}{w}_j{N}_{j,k}\left(u\right)}$ Be three rational basis functions.

By curve definitions territory interior nodal value substitutes into equation, meets interpolation condition, namely

$p\left(u_i\right)=\underset{j=i-3}{\overset{i}{\mathrm{\&Sigma;}}}{d}_j{R}_{j,3}\left(u_i\right)=q_{i-3},i=\mathrm{3,4},\&CenterDot;\&CenterDot;\&CenterDot;,n$

Above formula is altogether containing n-2 equation.First and last three control vertex coincidence d _n-2=d ₀, d _n-1=d ₁, d _n=d ₂, unknown control vertex number is reduced to n-2.N-2 unknown control vertex is solved from the system of linear equations chasing method be made up of n-2 equation.

1.3 determine control vertex weight factor.Solving control vertex d _ibefore, d need be obtained _icorresponding weight factor w _i, i=0,1 ..., n.If known each data point q _iweight factor i=0,1 ..., m, then

$\left\{\begin{array}{c}\underset{j=i-3}{\overset{i}{\mathrm{\&Sigma;}}}{w}_j{R}_{j,3}\left(u_i\right)=\stackrel{\&OverBar;}{w_{i-3}},i=\mathrm{3,4},...,n\\ w_{n-2}=w_0,w_{n-1}=w_1,w_n=w_2\end{array}\right.$

The above-mentioned system of equations of simultaneous, obtains control vertex d _iweight factor w _i.

Step 2: determine a q voluntarily _kwith a q _k+1, wherein at q _kand q _k+1reverse curvature not fairing is there is between two data points.

Step 3: adopt genetic algorithm calculation level q _kwith a q _k+1between the position of newly-increased data point.

3.1 chromosomes determining genetic algorithm.Suppose at q _kand q _k+1reverse curvature not fairing is there is, wherein q between two data points _kand q _k+1manually select.Q _k+0.5(x _k+0.5, _yk+0.5) be q _k(x _k, y _k) and q _k+1(x _k+1, y _k+1) between the data point that newly increases, Δ x is q _k+0.5(x _k+0.5, y _k+0.5) edge the bias in direction, Δ y is perpendicular to bias on direction.Through calculating, obtain:

$\left\{\begin{array}{c}{x}_{k+0.5}=x_k+\mathrm{\&Delta;x}\&CenterDot;\cos \mathrm{\&theta;}+\mathrm{\&Delta;y}\&CenterDot;\cos \mathrm{\&eta;}\\ y_{k+0.5}=y_k+\mathrm{\&Delta;x}\&CenterDot;\sin \mathrm{\&theta;}+\mathrm{\&Delta;y}\&CenterDot;\sin \mathrm{\&eta;}\end{array}\right.$

Wherein, $\mathrm{\&theta;}=\arctan \frac{y_{k+1}-y_k}{x_{k+1}-x_k},$ $\mathrm{\&eta;}=\arctan (-\frac{x_{k+1}-x_k}{y_{k+1}-y_k}),$ $0<\mathrm{\&Delta;x}<\left|\stackrel{\&RightArrow;}{q_k{q}_{k+1}}\right|.$

Calculate Δ x and Δ y, obtain newly-increased data point q _k+0.5(x _k+0.5, y _k+0.5), therefore, Δ x and Δ y is as the gene of two on genetic algorithm chromosome.

3.2 calculate genetic algorithm fitness.Article one, the curve of fairing generally will meet following condition: curve second order geometry continuum; There is no singular point and unnecessary flex point; Curvature varying is even; Strain energy is little.Consider Curvature varying and strain energy two aspects herein, propose a kind of reasonably fairing criterion.

The energy definition of curve is E=∫ k ²ds, wherein k is curvature, and s is arc length; Define the maximal value that a variable Q represents Curvature varying, be 1000 points by curve discrete, utilize the function of analytic curve curvature just to go out E and Q.And then the objective function of trying to achieve curve smoothing is min (f), wherein f=α E+ β Q, α and β is respectively the weight factor of curve strain energy and maximum curvature changing value, and this example gets α=0.7 and β=0.3.The fitness of genetic algorithm $\mathrm{fitness}=\frac{1}{f(\mathrm{\&Delta;x},\mathrm{\&Delta;y})}.$

In genetic algorithm, evaluate individual good and bad degree with the size of ideal adaptation degree, thus determine the size of its hereditary chance.The objective function of curve smoothing is min (f (Δ x, Δ y)), and f (Δ x, Δ y) the less individuality of value is more outstanding, and therefore, fitness is defined as wherein Δ x and Δ y is two genes on chromosome.

3.3 determine coding and initial population.Employing coded system is floating-point encoding, and two gene Δ x on chromosome and Δ y to retain after radix point three respectively; The scale of population is 10, and namely population is made up of 10 individualities, and each individuality of initial population produces at random.

3.4 determine genetic operator.Genetic operator comprises selection, crossover and mutation.System of selection adopts wheel disc stake method; Cross method adopts single-point to intersect, and point of crossing produces at random; Variation method adopts Gaussian mutation method.

The fitness of genetic algorithm is utilized to evaluate population.If meet genetic algebra, then terminate program, export final curves; Otherwise chromosomal gene carries out selecting, the computing of crossover and mutation, wherein system of selection adopts wheel disc stake method; Cross method adopts single-point to intersect, and crossover probability Pc gets 0.8, and point of crossing produces at random; Variation method adopts Gaussian mutation method, and mutation probability Pm gets 0.8.

3.5 start genetic algorithm, calculate the position of newly-increased data point.

Step 4: by preliminary offset point and newly-increased data point, the nurbs curve that interpolation makes new advances.

Step 5: if curve also exists the place of reverse curvature, then jump to step 2, carries out fairing to curve again; If curve has met fairing requirement, then export current interpolation curve as net result.

Claims (3)

1., based on a closed non-homogeneous B spline curve method for fairing for genetic algorithm, it is characterized in that comprising the following steps:

Step one, determine closed nurbs curve interpolation method, adopt three closed nurbs curves to carry out interpolation; Be provided with m+1 data point q ₀, q ₁, q ₂... q _m, and q ₀=q _m, getting data point is curvilinear inner connection segment point, i.e. q _ithere is nodal value u _i+3, i=0,1 ... m; This nurbs curve is by n+1 control vertex d ₀, d ₁, d ₂... .d _nwith knot vector U=[u ₀, u ₁..., u _n+4] define, field of definition is u ∈ [u ₃, u _n+1]=[0,1]; Wherein n=m+2, total m+3 unknown control vertex;

The method of 1.1 employing accumulation chord lengths, calculates parameter value sequence t ₀, t ₁, t ₂... t _m, field of definition internal segment point value is u ₃=t ₀, u ₄=t ₁, u ₅=t ₂... u _m=t _m-3, the node outside field of definition is defined as u ₀=u _n-2-1, u ₁=u _n-1-1, u ₂=u _n-1, u _n+2=u ₄+ 1, u _n+3=u ₅+ 1, u _n+4=u ₆+ 1;

1.2 is anticaustic in interpolation m+1 data point q ₀, q ₁, q ₂... q _mand q ₀=q _mthree closed nurbs curve the Representation Equation be

$p\left(u\right)=\underset{j=0}{\overset{n}{\&Sigma;}}{d}_j{R}_{j,3}\left(u\right)=\underset{j=e-3}{\overset{e}{\&Sigma;}}{d}_j{R}_{j,3}\left(u\right),u\&Element;\&lsqb;u_e,u_{e+1}\&rsqb;\&Subset;\&lsqb;u_3,u_{n+1}\&rsqb;,e=3,4,...n$

Wherein, be three rational basis functions;

By curve definitions territory interior nodal value substitutes into equation, meets interpolation condition, namely

above formula is altogether containing n-2 equation; First and last three control vertex coincidence d _n-2=d ₀, d _n-1=d ₁, d _n=d ₂, unknown control vertex number is reduced to n-2; N-2 unknown control vertex is solved from the system of linear equations chasing method be made up of n-2 equation;

1.3 are solving control vertex d _jbefore, d need be obtained _jcorresponding weight factor w _j, j=0,1 ... n; If known each data point q _iweight factor i=0,1 ..., m, then

$\left\{\begin{array}{c}\underset{j=e-3}{\overset{e}{\&Sigma;}}{w}_j{R}_{j,3}\left(u_e\right)=\stackrel{\&OverBar;}{W_{e-3}},e=3,4,...,n\\ w_{n-2}=w_0,w_{n-1}=w_1,w_n=w_2\end{array}\right.$

The above-mentioned system of equations of simultaneous, obtains control vertex d _iweight factor w _i;

Step 2, determine a q _kwith a q _k+1, wherein at q _kand q _k+1reverse curvature not fairing is there is between two data points;

Step 3, employing genetic algorithm calculation level q _kwith a q _k+1between the position of newly-increased data point;

3.1 hypothesis are at q _kand q _k+1reverse curvature not fairing is there is, wherein q between two data points _kand q _k+1manually select; q _k+0.5(x _k+0.5, y _k+0.5) be q _k(x _k, y _k) and q _k+1(x _k+1, y _k+1) between the data point that newly increases, △ x is q _k+0.5(x _k+0.5, y _k+0.5) edge the bias in direction, △ y is perpendicular to bias on direction; Through calculating, obtain:

$\left\{\begin{array}{c}{x}_{k+0.5}=x_k+\mathrm{\&Delta;}x\&CenterDot;cos\mathrm{\&theta;}+\mathrm{\&Delta;}y\&CenterDot;cos\mathrm{\&eta;}\\ y_{k+0.5}=y_k+\mathrm{\&Delta;}x\&CenterDot;sin\mathrm{\&theta;}+\mathrm{\&Delta;}y\&CenterDot;sin\mathrm{\&eta;}\end{array}\right.$

Wherein,

Calculate △ x and △ y, obtain newly-increased data point q _k+0.5(x _k+0.5, y _k+0.5), therefore, △ x and △ y is as the gene of two on genetic algorithm chromosome;

The energy definition of 3.2 curves is E=∫ k ²ds, wherein k is curvature, and s is arc length; Define the maximal value that a variable Q represents Curvature varying, the objective function of curve smoothing is min (f), and wherein f=α E+ β Q, α are the weight factors of curve strain energy changing value, and β is the weight factor of curve maximum curvature changing value, alpha+beta=1;

The objective function of curve smoothing is min (f (△ x, △ y)); Fitness is defined as wherein △ x and △ y is two genes on chromosome;

3.3 adopt coded systems to be floating-point encoding, and two gene △ x on chromosome and △ y to retain after radix point three respectively; The scale of population is 10, and each individuality of initial population produces at random;

3.4 genetic operators comprise selection, crossover and mutation; System of selection adopts wheel disc stake method; Cross method adopts single-point to intersect, and point of crossing produces at random; Variation method adopts Gaussian mutation method;

3.5 start genetic algorithm, calculate the position of newly-increased data point;

Step 4, by preliminary offset point and newly-increased data point, the nurbs curve that interpolation makes new advances;

If step 5 curve also exists reverse curvature, then jump to step 2, again fairing is carried out to curve; If curve has met fairing requirement, then export current interpolation curve as net result.

2. the closed non-homogeneous B spline curve method for fairing based on genetic algorithm according to claim 1, is characterized in that: weight factor α=0.7 of described curve strain energy changing value.

3. the closed non-homogeneous B spline curve method for fairing based on genetic algorithm according to claim 1, is characterized in that: weight factor β=0.3 of described curve maximum curvature changing value.