CN103729510A - Method for computing accurate mirror symmetry of three-dimensional complex model on basis of internal implication transformation - Google Patents

Abstract

The invention discloses a method for computing accurate mirror symmetry of a three-dimensional complex model on the basis of internal implication transformation. The method includes interactively setting or computing rough symmetry planes of the model, transforming the given model according to the rough symmetry planes to enable the rough symmetry planes to coincide with a coordinate plane, and computing accurate symmetry planes according to internal implication transformation of a mirror symmetry model; transforming the model and the accurate symmetry planes to obtain accurate symmetry planes of original positions of the model. The method has the advantages that the method is based on strict internal implication transformation relations of the mirror symmetry model, the precision can be controlled, and the method is high in generalization performance and is widely applicable to the field of engineering application.

Description

Based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion

Technical field

The present invention relates to 3 d geometric modeling and calculating field, be specially a kind of based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion.

Background technology

Symmetry is the ubiquitous phenomenon of nature, no matter artificial or natural object, mostly there is symmetry in various degree in its profile, wherein with mirror image to being called master.The present invention, mainly for the artificial model with mirror symmetry of process in engineering, particularly carries out the symmetrical analysis computational problem in three-dimensional reconstruction or error analysis according to the data that gather on these mock-ups.

With natural object contrast, it is high a lot of that the symmetry precision of culture is wanted, and the accuracy requirement of this class model being carried out to symmetrical analysis calculating is generally higher.Existing symmetrical analysis computational algorithm is mainly for field application such as computer animation, computer visions, and precision generally cannot meet engineering application demand.

Along with scientific and technical development, there are symmetric complex appearance parts and in engineering, apply more and more extensively, particularly, in the manufacturing industry such as aircraft, boats and ships, automobile, bullet train, the profile of product all has mirror symmetry.This mirror symmetry has affected the presentation quality of product, and the handling of the type products such as aircraft, steamer, sport car, bullet train is also had to conclusive impact.When the profile of this series products or mock-up is carried out to three-dimensional reconstruction, guarantee that the symmetry of reconstruction model is very important; In addition, also lack effective means at present this series products profile is carried out to the analytical calculation of balanced error.Therefore, a kind of accurately mirror symmetry computing method of research and development are very important.

Summary of the invention

The object of this invention is to provide a kind of based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, for higher engineering applications of accuracy requirement such as the balanced error detections of the three-dimensional reconstruction based on mock-up or product design.

In order to achieve the above object, the technical solution adopted in the present invention is:

Based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: comprise the following steps:

(1), the rough plane of symmetry of interactive setup or calculating setting models;

(2), the rough plane of symmetry that obtains according to step (1), conversion setting models, makes the rough plane of symmetry overlap with a coordinate plane, obtains converting rear model;

(3), according to accumulateing conversion in mirror image symmetry model, the accurate plane of symmetry of model after the conversion obtaining in calculation procedure (2);

(4) model and the accurate plane of symmetry after the conversion that shift step (2) obtains, again, obtain the accurate plane of symmetry in model original position.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (1), interactive setup or the method for calculating the rough plane of symmetry are: by view rotation to approximately perpendicular to theoretical plane of symmetry position, interactive setup straight line, thereby the position of the rough plane of symmetry, the rough plane of symmetry is by a some P=(x, y, z) ^tvow V=(a, b, c) with a method ^tdefinition, wherein x, y, z is respectively three coordinate figures of P, and a, b, c are respectively three component values of vector V, a ²+ b ²+ c ²=1.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (2), conversion setting models is used homogeneous transformation matrix, and homogeneous transformation matrix is:

$\begin{array}{c}{T}_m=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ a\sin \mathrm{\α}& \cos \mathrm{\α}& c\sin \mathrm{\α}& -y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& -c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (3), establishing setting models is M setting models M and its mirror image symmetry model M about x-z coordinate plane _x-zin accumulate and be transformed to: M=R _zr _yr _xr _xr _-yr _zm _x-z+ (R _zr _yr _xr _xr _-yr _z+ I) T, wherein $R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\θ}}_x\right)& -\sin \left({\mathrm{\θ}}_x\right)\\ 0& \sin \left({\mathrm{\θ}}_x\right)& \cos \left({\mathrm{\θ}}_x\right)\end{array}\right],R_y=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_y\right)& 0& \sin \left({\mathrm{\θ}}_y\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_y\right)& 0& \cos \left({\mathrm{\θ}}_y\right)\end{array}\right],$ $R_z=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_z\right)& -\sin \left({\mathrm{\θ}}_z\right)& 0\\ \sin \left({\mathrm{\θ}}_z\right)& \cos \left({\mathrm{\θ}}_z\right)& 0\\ 0& 0& 1\end{array}\right],I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ T＝(T _x，T _y，T _z) ^T。R _x, R _y, R _zbe respectively the rotational transform matrix around x, y, z axle, θ _x, θ _y, θ _zbe respectively the anglec of rotation around x, y, z axle, T is translation transformation matrix, is unknown quantity;

Make R ^x-z=R _zr _yr _xr _xr _-yr _z, its element meets following relation:

$R_{\mathrm{1,2}}^{x-z}=-R_{\mathrm{2,1}}^{x-z},R_{\mathrm{1,3}}^{x-z}=R_{\mathrm{3,1}}^{x-z},R_{\mathrm{2,3}}^{x-z}=-R_{\mathrm{3,2}}^{x-z}.$

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: step (3) is by following process implementation:

(a), adopt model registration algorithm, obtain R ^x-Z(R ^x-z+ I) value of T;

(b), according to R in S301 ^x-zresult of calculation, obtain a Nonlinear System of Equations, adopt Solving Nonlinear Systems of Equations Algorithm for Solving, obtain sin (θ _x), cos (θ _x), sin (θ _y), cos (θ _y), sin (θ _z), cos (θ _z) value;

(c), according to the result of calculation of step (a) and step (b), obtain a system of linear equations, solve this system of linear equations and obtain T _x, T _y, T _zvalue;

(d), make y=(0,1,0) ^t, the method for the accurate plane of symmetry of model M is vowed as R _zr _yr _xy is a bit (T on it _x, T _y, T _z) ^t.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (4), after the conversion that shift step (2) obtains model and accurately the plane of symmetry use homogeneous transformation matrix, homogeneous transformation matrix is:

$\begin{array}{c}{T}_m^{-1}=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ -a\sin \mathrm{\α}& \cos \mathrm{\α}& -c\sin \mathrm{\α}& y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V,

model transferring is gone back to original position and the plane of symmetry is converted back to the plane of symmetry corresponding to model original position.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: by the setting coarse plane of symmetry, improved the reliability and stability that in step (3), model registration algorithm calculates.

Described based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: by the condition of convergence in setting model registration algorithm, can control the precision that mirror symmetry is calculated, meet the requirement of high precision engineering application.

The present invention, for applications such as the three-dimensional reconstruction based on mock-up or the balanced error detections of product design, has calculation stability, reliable, and the advantage that result precision is controlled, can meet the requirement of high precision engineering application.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the front cover for vehicle cloud data gathering for an actual measurement, adopts the accurate mirror symmetry computing method of 3 D complex model of the present invention, the mirror symmetry planes result of calculation schematic diagram obtaining.

Fig. 3 is the accurate mirror symmetry computing method that adopt the described 3 D complex model of invention, the schematic diagram of the axis of symmetry of reference axis symmetry model.

Embodiment

Based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, comprise the following steps:

(1), the rough plane of symmetry of interactive setup or calculating setting models;

(2), the rough plane of symmetry that obtains according to step (1), conversion setting models, makes the rough plane of symmetry overlap with a coordinate plane, obtains converting rear model;

(3), according to accumulateing conversion in mirror image symmetry model, the accurate plane of symmetry of model after the conversion obtaining in calculation procedure (2);

(4) model and the accurate plane of symmetry after the conversion that shift step (2) obtains, again, obtain the accurate plane of symmetry in model original position.

In step (1), interactive setup or the method for calculating the rough plane of symmetry are: by view rotation to approximately perpendicular to theoretical plane of symmetry position, interactive setup straight line, thereby the position of the rough plane of symmetry, the rough plane of symmetry is by a some P=(x, y, z) ^tvow V=(a, b, c) with a method ^tdefinition, wherein x, y, z is respectively three coordinate figures of P, and a, b, c are respectively three component values of vector V, a ²+ b ²+ c ²=1.

In step (2), conversion setting models is used homogeneous transformation matrix, and homogeneous transformation matrix is:

$\begin{array}{c}{T}_m=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ a\sin \mathrm{\α}& \cos \mathrm{\α}& c\sin \mathrm{\α}& -y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& -c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V.

In step (3), establishing setting models is M, setting models M and its mirror image symmetry model M about x-z coordinate plane _x-zin accumulate and be transformed to:

M=R _zr _yr _xr _xr _-yr _zm _x-z+ (R _zr _yr _xr _xr _-yr _z+ I) T, wherein $R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\θ}}_x\right)& -\sin \left({\mathrm{\θ}}_x\right)\\ 0& \sin \left({\mathrm{\θ}}_x\right)& \cos \left({\mathrm{\θ}}_x\right)\end{array}\right],R_y=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_y\right)& 0& \sin \left({\mathrm{\θ}}_y\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_y\right)& 0& \cos \left({\mathrm{\θ}}_y\right)\end{array}\right],$ $R_z=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_z\right)& -\sin \left({\mathrm{\θ}}_z\right)& 0\\ \sin \left({\mathrm{\θ}}_z\right)& \cos \left({\mathrm{\θ}}_z\right)& 0\\ 0& 0& 1\end{array}\right],I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ T＝(T _x，T _y，T _z) ^T。R _x, R _y, R _zbe respectively the rotational transform matrix around x, y, z axle, θ _x, θ _y, θ _zbe respectively the anglec of rotation around x, y, z axle, T is translation transformation matrix, is unknown quantity;

Make R ^x-z=R _zr _yr _xr _xr _-yr _z, its element meets following relation:

$R_{\mathrm{1,2}}^{x-z}=-R_{\mathrm{2,1}}^{x-z},R_{\mathrm{1,3}}^{x-z}=R_{\mathrm{3,1}}^{x-z},R_{\mathrm{2,3}}^{x-z}=-R_{\mathrm{3,2}}^{x-z}.$

Step (3) is pressed following process implementation:

(a), adopt model registration algorithm, obtain R ^x-z(R ^x-z+ I) value of T;

(b), according to R in S301 ^x-zresult of calculation, obtain a Nonlinear System of Equations, adopt Solving Nonlinear Systems of Equations Algorithm for Solving, obtain sin (θ _x), cos (θ _x), sin (θ _y), cos (θ _y), sin (θ _z), cos (θ _z) value;

(c), according to the result of calculation of step (a) and step (b), obtain a system of linear equations, solve this system of linear equations and obtain T _x, T _y, T _zvalue;

(d), make y=(0,1,0) ^t, the method for the accurate plane of symmetry of model M is vowed as R _zr _yr _xy is a bit (T on it _x, T _y, T _z) ^t.

In step (4), after the conversion that shift step (2) obtains, model and the accurate plane of symmetry are used homogeneous transformation matrix, and homogeneous transformation matrix is:

$\begin{array}{c}{T}_m^{-1}=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ -a\sin \mathrm{\α}& \cos \mathrm{\α}& -c\sin \mathrm{\α}& y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V, model transferring is gone back to original position and the plane of symmetry is converted back to the plane of symmetry corresponding to model original position.

By the setting coarse plane of symmetry, the reliability and stability that in step (3), model registration algorithm calculates have been improved.

By the condition of convergence in setting model registration algorithm, can control the precision that mirror symmetry is calculated, meet the requirement of high precision engineering application.

Below in conjunction with accompanying drawing 1 to 3 and embodiment, the embodiment of invention is described further.Following examples are only for the present invention is described, but are not used for limiting the scope of the invention.

The accurate mirror symmetry computing method of process flow diagram a kind of 3 D complex model as shown in Figure 1, mainly comprise step:

S1. the rough plane of symmetry of interactive setup or computation model.The method of the rough plane of symmetry of interactive setup is: by view rotation to approximately perpendicular to theoretical plane of symmetry position, interactive setup straight line, thereby the position of the rough plane of symmetry.The rough plane of symmetry is by a some P=(x, y, z) ^tvow V=(a, b, c) with a method ^tdefinition, wherein a ²+ b ²+ c ²=1.The rough plane of symmetry of model also can adopt the existing plane of symmetry computing method for other application, but from application of engineering project, the general more complicated of these algorithms, calculate time-consuming.

S2. according to the rough plane of symmetry, conversion setting models, makes the rough plane of symmetry overlap with a coordinate plane.The homogeneous transformation matrix of setting models is:

$\begin{array}{c}{T}_m=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ a\sin \mathrm{\α}& \cos \mathrm{\α}& c\sin \mathrm{\α}& -y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& -c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is three coordinate figures of P respectively, and a, b, c are respectively three component values of method arrow V.The coordinate of putting on hypothesized model is (x _i, y _i, z _i) ^t, i=O ..., n, the homogeneous coordinates after conversion are (x' _i, y' _i, z' _i, 1) ^t=T _m(x _i, y _i, z _i, 1) ^t, i=0 ..., n.The object of coordinate transform is to have good initial value when guaranteeing in S301 model registration, improves convergence.

S3. according to accumulateing conversion in mirror image symmetry model, calculate the accurate plane of symmetry.Model M by (x ' _i, y ' _i, z ' _i) ^t, i=0 ..., n definition, M and its mirror image symmetry model M about x-z coordinate plane _x-zin accumulate and be transformed to:

M＝R _zR _yR _xR _xR _-yR _zM _x-z+(R _ZR _yR _xR _xR _-yR _z+I)T

Wherein $R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\θ}}_x\right)& -\sin \left({\mathrm{\θ}}_x\right)\\ 0& \sin \left({\mathrm{\θ}}_x\right)& \cos \left({\mathrm{\θ}}_x\right)\end{array}\right],R_y=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_y\right)& 0& \sin \left({\mathrm{\θ}}_y\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_y\right)& 0& \cos \left({\mathrm{\θ}}_y\right)\end{array}\right],$ $R_z=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_z\right)& -\sin \left({\mathrm{\θ}}_z\right)& 0\\ \sin \left({\mathrm{\θ}}_z\right)& \cos \left({\mathrm{\θ}}_z\right)& 0\\ 0& 0& 1\end{array}\right],I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ T＝(T _x,T _y,T _z) ^T。R _x, R _y, R _zbe respectively the rotational transform matrix around x, y, z axle, θ _x, θ _y, θ _zbe respectively the anglec of rotation around x, y, z axle, T is translation transformation matrix, is unknown quantity.

In the present embodiment, this step mainly comprises:

S301: make R ^x-z=R _zr _yr _xr _xr _-yr _z, for M and M _x-z, adopt model registration algorithm, obtain R ^x-z(R ^x-z+ I) value of T.It is exactly ICP(Iterative Closest Points that model is registered conventional algorithm) algorithm and improvement algorithm thereof, in calculating, adopt point to plan range pattern, under this pattern, ICP convergence is better.According to concrete application needs, also can adopt other model registration or Model Matching algorithms.

S302:R ^x-zbe the matrix of a 3x3, its element meets following relation:

$R_{\mathrm{1,2}}^{x-z}=-R_{\mathrm{2,1}}^{x-z},R_{\mathrm{1,3}}^{x-z}=R_{\mathrm{3,1}}^{x-z},R_{\mathrm{2,3}}^{x-z}=-R_{\mathrm{3,2}}^{x-z},$

Therefore obtaining a variable is sin (θ _x), cos (θ _x), sin (θ _y), cos (θ _y), sin (θ _z), cos (θ _z) the Nonlinear System of Equations of 6 equations.In order to guarantee the relation between variable, need add again three equations, i.e. sin (θ _x) ²+ cos (θ _x) ²=1, sin (θ _y) ²+ cos (θ _y) ²=1, sin (θ _z) ²+ cos (θ _z) ²=1.Adopt Levenberg-Marquardt algorithm or other Solving Nonlinear Systems of Equations algorithms, obtain sin (θ _x), cos (θ _x), sin (θ _y), cos (θ _y), sin (θ _z), cos (θ _z) value;

S303: according to the result of calculation of S301 and S302, obtaining variable is T _x, T _y, T _za ternary system of homogeneous linear equations, solve this system of linear equations and obtain T _x, T _y, T _zvalue;

S304: make y=(0,1,0), the method for the accurate plane of symmetry of model M is vowed and is

(v _x, v _y, v _z)=R _zr _yr _xy is a bit (T on it _x, T _y, T _z) ^t.

S4. shift step (2) converts rear model and the accurate plane of symmetry again, obtains the accurate plane of symmetry in model original position.Model and accurately the homogeneous transformation matrix of the plane of symmetry are:

$\begin{array}{c}{T}_m^{-1}=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ -a\sin \mathrm{\α}& \cos \mathrm{\α}& -c\sin \mathrm{\α}& y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is three coordinate figures of P respectively, and a, b, c are respectively three component values of method arrow V.

model transferring is gone back to original position, $T_m^{-1}{(x_i^{\′},y_i^{\′},z_i^{\′},1)}^T={(x_i,y_i,z_i,1)}^T,i=0,...,n,$ Simultaneously the plane of symmetry is converted go back to plane of symmetry position corresponding to model original position.That is, the plane of symmetry of setting models is by 1 P=(x, y, z) ^tvow V=(a, b, c) with a method ^tdefinition, wherein ${(x,y,z,1)}^T=T_m^{-1}{(T_x,T_y,T_z,1)}^T,$ ${(a,b,c,1)}^T=T_m^{-1}{(v_x,v_y,v_z,1)}^T.$ Fig. 2 has provided one and has adopted symmetry computing method of the present invention, the mirror symmetry planes result of calculation that the front cover for vehicle cloud data that actual measurement is gathered calculates.

Above embodiment is only for illustrating the present invention; but not limitation of the present invention; the those of ordinary skill in relevant technologies field; without departing from the spirit and scope of the present invention; can also make a variety of changes and modification (for example can adopt two planes of symmetry of reference axis symmetry model of the present invention; its friendship is the axis of symmetry of model, and as shown in Figure 3), therefore all technical schemes that are equal to also belong to protection category of the present invention.

Claims (8)

1. based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: comprise the following steps:

(1), the rough plane of symmetry of interactive setup or calculating setting models;

(2), the rough plane of symmetry that obtains according to step (1), conversion setting models, makes the rough plane of symmetry overlap with a coordinate plane, obtains converting rear model;

(3), according to accumulateing conversion in mirror image symmetry model, the accurate plane of symmetry of model after the conversion obtaining in calculation procedure (2);

(4) model and the accurate plane of symmetry after the conversion that shift step (2) obtains, again, obtain the accurate plane of symmetry in model original position.

2. according to claim 1 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (1), interactive setup or the method for calculating the rough plane of symmetry are: by view rotation to approximately perpendicular to theoretical plane of symmetry position, interactive setup straight line, thereby the position of the rough plane of symmetry, the rough plane of symmetry is by a some P=(x, y, z) ^tvow V=(a, b, c) with a method ^tdefinition, wherein x, y, z is respectively three coordinate figures of P, and a, b, c are respectively three component values of vector V, a ²+ b ²+ c ²=1.

3. according to claim 1 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (2), conversion setting models is used homogeneous transformation matrix, and homogeneous transformation matrix is:

$\begin{array}{c}{T}_m=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ a\sin \mathrm{\α}& \cos \mathrm{\α}& c\sin \mathrm{\α}& -y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& -c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V.

4. according to claim 1 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (3), establishing setting models is M setting models M and its mirror image symmetry model M about x-z coordinate plane _x-zin accumulate and be transformed to: M=R _zr _yr _xr _xr _-yr _zm _x-z+ (R _zr _yr _xr _xr _-yr _z+ I) T,

Wherein $R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\θ}}_x\right)& -\sin \left({\mathrm{\θ}}_x\right)\\ 0& \sin \left({\mathrm{\θ}}_x\right)& \cos \left({\mathrm{\θ}}_x\right)\end{array}\right],R_y=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_y\right)& 0& \sin \left({\mathrm{\θ}}_y\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_y\right)& 0& \cos \left({\mathrm{\θ}}_y\right)\end{array}\right],$ $R_z=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_z\right)& -\sin \left({\mathrm{\θ}}_z\right)& 0\\ \sin \left({\mathrm{\θ}}_z\right)& \cos \left({\mathrm{\θ}}_z\right)& 0\\ 0& 0& 1\end{array}\right],I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ T＝(T _x，，R _y，T _z) ^T。R _x, R _y, R _zbe respectively the rotational transform matrix around x, y, z axle, θ _x, θ _y, θ _zbe respectively the anglec of rotation around x, y, z axle, T is translation transformation matrix, is unknown quantity;

Make R ^x-z=R _zr _yr _xr _xr _-yr _z, its element meets following relation:

$R_{\mathrm{1,2}}^{x-z}=-R_{\mathrm{2,1}}^{x-z},R_{\mathrm{1,3}}^{x-z}=R_{\mathrm{3,1}}^{x-z},R_{\mathrm{2,3}}^{x-z}=-R_{\mathrm{3,2}}^{x-z}.$

5. according to claim 1 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: step (3) is by following process implementation:

(a), adopt model registration algorithm, obtain R ^x-z(R ^x-z+ I) value of T;

(b), according to R in S301 ^x-zresult of calculation, obtain a Nonlinear System of Equations, adopt Solving Nonlinear Systems of Equations Algorithm for Solving, obtain sin (θ _x), cos (θ _x), sin (θ _y), cos (θ _y), sin (θ _z), cos (θ _z) value;

(c), according to the result of calculation of step (a) and step (b), obtain a system of linear equations, solve this system of linear equations and obtain T _x, T _y, T _zvalue;

(d), make y=(0,1,0) ^t, the method for the accurate plane of symmetry of model M is vowed as R _zr _yr _xy is a bit (T on it _x, T _y, T _z) ^t.

6. according to claim 1 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: in described step (4), after the conversion that shift step (2) obtains, model and the accurate plane of symmetry are used homogeneous transformation matrix, and homogeneous transformation matrix is:

$\begin{array}{c}{T}_m^{-1}=\\ \left[\begin{array}{cccc}{c}^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -a\cos \mathrm{\α}& -\mathrm{ac}(1-\cos \mathrm{\α})& -\mathrm{ax}\sin \mathrm{\α}\\ -a\sin \mathrm{\α}& \cos \mathrm{\α}& -c\sin \mathrm{\α}& y\cos \mathrm{\α}\\ -\mathrm{ac}(1-\cos \mathrm{\α})& c\sin \mathrm{\α}& a^2(1-\cos \mathrm{\α})+\cos \mathrm{\α}& -\mathrm{cz}\sin \mathrm{\α}\\ 0& 0& 0& 1\end{array}\right]\end{array}$ , the method that wherein α is the rough plane of symmetry is vowed the angle between V and Y-axis, and x, y, z is respectively three coordinate figures of a P, and a, b, c are respectively three component values of vector V,

model transferring is gone back to original position and the plane of symmetry is converted back to the plane of symmetry corresponding to model original position.

7. according to claim 5 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: by the setting coarse plane of symmetry, improved the reliability and stability that in step (3), model registration algorithm calculates.

8. according to claim 5 based on the interior accurate mirror symmetry computing method of 3 D complex model of accumulateing conversion, it is characterized in that: by the condition of convergence in setting model registration algorithm, can control the precision that mirror symmetry is calculated, meet the requirement of high precision engineering application.

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