CN104331933B - A kind of fabrication orientation self adaptation fast selecting method - Google Patents
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Abstract
The invention discloses threedimensional model triangle gridding is obtained obtaining Area-weighted normal vector after triangle surface by a kind of fabrication orientation self adaptation fast selecting method；Then principal component analysiss are carried out to area weighting factor method vector, and construction covariance matrix simultaneously carries out singular value decomposition, draws three characteristic vectors as candidate's fabrication orientation；Thereafter, model is layered under candidate's fabrication orientation, and after calculating layering, builds the cumulative volume error of model and archetype, the candidate's fabrication orientation corresponding to minimal overall product error is layered optimization direction.The present invention obtains three perpendicular candidate's fabrication orientations by extracting characteristic vector, and layered optimization direction is selected based on minimum volume error, need not be using the sampling of all for model surface normal vectors or space normal vector as candidate's fabrication orientation, algorithm complex is reduced while improving model accuracy, the time for obtaining layered optimization direction can be substantially reduced, it is adaptable to the complicated model of geometric properties or topological structure.
Description
Technical field
The present invention relates to a kind of data processing method, and in particular to the fabrication orientation choosing method in a kind of rapid shaping.
Background technology
3D printing is one kind of rapid shaping technique (Rapid prototyping), earliest by masschusetts, U.S.A Polytechnics
(MIT) propose, using the thought of Layered manufacturing (increasing manufacture).Rapid shaping is reverse-engineering, computer-aided design and system
Make, material removes molding, material increases molding, the general designation of the technology such as Layered manufacturing, present 3D printing has been rapid shaping technique
General designation.Layered manufacturing refer to along fabrication orientation by discrete for threedimensional model be one group of X-Y scheme, i.e., one group thin layer is (also referred to as
Section is layered), successively process, be layering to form threedimensional model entity.The technology has that equipment is simple, material cheap,
The advantages of low cost, small volume, the course of work are pollution-free, shaping speed is fast.
The data form of threedimensional model is various, such as CAD model, cloud data model, STL models etc., it is impossible to directly as
The input data of 3D printing, it is necessary to which the discernible data mode of 3D printing is converted into by delamination software.STL models are for quick
The file format of forming technique service, was proposed in 1987 first by 3D System companies of the U.S., is known as by industrial quarters
It is the reference format of data exchange between CAD system and rapid prototyping system, is therefore also adopted by 3D printing technique.STL moulds
By some by constituting the triangle surface that threedimensional model triangle gridding is obtained, each triangle surface includes three to type
Normal vector outside summit and a direction model, these triangle surfaces are disorderly arranged.Delaminating process is first to try to achieve and layering
The intersecting triangle surface of plane, then by end to end for the intersection section for the obtaining X-Y scheme for constituting current layer, that is, cut into slices, it is layered
As a result model construction precision and model construction time are directly affected.With the popularization of 3D printing technique, it is adaptable to complex model
Hierarchical algorithm is increasingly becoming study hotspot, and emphasis is the selection of lift height and fabrication orientation.
Model construction precision refers to the degree of closeness between the model entity of molding and theoretical model, typically uses model surface
Alias representing, more substantially, model error is less for the less alias of lift height.The model construction time is mainly
Refer to the time required for one complete model of structure, in general, layering number fewer structure time is shorter.The structure essence of model
Degree and structure time are affected by lift height and fabrication orientation simultaneously.
Generally consider impact of the two kinds of error to model construction precision.One kind is turned in CAD model to STL models
In change, turn to what discrete trigonometric shape dough sheet caused by smooth surface triangle, can pass through to control the minimizing of chordal errors.Another
Planting is caused by the alias that model surface is produced in delaminating process, in general in deep camber and the triangle for inclining
More obvious alias can be produced on surface, produced bigger between the model entity surface and theoretical model surface that cause structure
Error.Understand that the alias in print procedure can not be eliminated according to the principle of Layered manufacturing, but can be by adjusting
Lift height and fabrication orientation reduce.Lift height is less, alias more not substantially, the model entity surface of structure with theoretical
The surface of model closer to, then the structure precision of model is higher.On the other hand, identical model layers thickness is less, produces
Layering number more, then the model construction time is longer, so improve to build precision and reduce the structure time be simultaneously
One difficult point.
Existing hierarchical algorithm is broadly divided into Direct Slicing Algorithm and adaptive layered algorithm.Direct Slicing Algorithm is from original
CAD model generates each layer of profile information, it is to avoid the error that model trigonometric ratio is caused.Rajagopalan in Susila B,
et al.Interfacing geometric model data with rapid prototyping systems.Journal
of Intel ligent Manufacturing 1999；10：Propose in 323-9 a kind of using model whole geometry information pair
The algorithm of NURBS model direct layerings；Chakraborry is in Chakraborty D, Choudhury AR.A semi-
analytic approach for direct slicing of free form surfaces for layered
manufacturing.Rapid Prototyping Journal 2007；13：256-64 proposes a kind of based on curved surface-plane
The Direct Slicing Algorithm of friendship is sought, the algorithm generates a kind of hierarchical file.Adaptive layered algorithm is special according to the geometry of model local
Levy or desired model accuracy is layered, error effects is reduced by reducing lift height, reduce layering number and improve mould
Type builds efficiency.Dolenc and Makela is in Dolenc, A.and Makela, I. (1994), " Slicing procedures
For layered manufacturing techniques ", Computer-Aided Design, Vol.26, pp.119-26
Propose a kind of cusp height being widely used to represent error size that alias is caused, cusp height are by three
The normal vector direction of angular dough sheet is determined with the angle of fabrication orientation and lift height.According to given cusp height and three
The normal vector of angular dough sheet adjusts lift height with the angle of fabrication orientation, so as to improve model construction precision.Sabourin
A kind of algorithm of unified lift height is proposed with Cusp height as the standard of model construction error, the algorithm is first by mould
Type is divided into thicker thin layer, then carries out partial analysis to each thin layer, finally obtains an optimum lift height.Unified point
Layer thickness algorithms is finally only layered to model using a lift height, that is, the thickness of each thin layer is identical.This
Although algorithm is simple, the local geometric features of model are different in general, so such algorithm is not particularly suited for geometry spy
Levy the model of complexity.Yan adjusts lift height by adaptive cusp height and obtains higher model construction precision.?
There is extensive work model construction precision to be improved by adjusting lift height, but each layer building thickness of 3D printing equipment has
Certain threshold value, is limited by hardware condition more than lift height.
Fabrication orientation was all had a major impact to model construction precision and structure time, as shown in Fig. 2 giving different layerings
Direction drag produces different alias.In Fig. 2 (a), fabrication orientation is, composition plane AEFD, plane DFC, plane
The normal vector of the triangle surface of AEB respectively with fabrication orientationVertically, the normal vector of the triangle surface of composition plane FEBC
Respectively with fabrication orientationParallel, alias will not be produced as seen from the figure on these triangle surfaces.But composition plane
The normal vector of the triangle surface of ABCD was both neither perpendicular to nor parallel to fabrication orientation, produced sawtooth as seen from the figure on this plane
Shape step, i.e. alias.In Fig. 2 (b), fabrication orientation is, as seen from the figure same only in normal vector with fabrication orientation neither
Alias is produced in vertical and parallel plane ABCD.In Fig. 2 (c), fabrication orientation is, all trianglees of composition model
The normal vector of dough sheet is all vertical with fabrication orientation or parallel, does not produce rank effect as seen from the figure on model all surface.With
When as seen from the figure, the size of alias directly affects model accuracy, produces the alias on the model surface of alias
Less, the surface is closer to theoretical model, otherwise alias is bigger, and on model surface, error is bigger, with theoretical model more not
It coincide.In Fig. 2 (a) and Fig. 2 (b), lift height is less, and the error that alias is caused is less, but can cause excessive
Layering number so that the time-write interval excessively increases, simultaneously because mechanical reason, lift height can only value within the specific limits.
And in Fig. 2 (c), lift height can get the lift height value of maximum, layering number is reduced, while improve model accuracy
The time for printing manufacture can also be reduced.It can be seen that, fabrication orientation affects the selection of lift height simultaneously, if certain triangle surface
Parallel with fabrication orientation or vertical, then the lift height of the triangle surface can obtain maximum without in the triangle
Alias is produced on shape dough sheet.Therefore choose a good fabrication orientation before model layers to the structure precision of model and
Build time effects very big.Can be drawn to draw a conclusion with the relation of fabrication orientation by the normal vector of above triangle surface：If
The final fabrication orientation that chooses so that the projection maximum (method of triangle surface of certain triangle surface on the fabrication orientation
Vector is vertical with fabrication orientation) or minimum (normal vector of triangle surface is parallel with fabrication orientation), then the gore
The error that piece is produced on this fabrication orientation is minimum.
Existing fabrication orientation Algorithms of Selecting is mainly from raising model accuracy, minimizing structure time, minimizing supporting construction, saving
One object function of single or multiple constructions is chosen in the targets such as material, with adopting for the normal vector of model surface or space normal vector
Sample therefrom chooses the minimum candidate direction of target function value as layered optimization direction as candidate direction.Cheng W, Fuh
JYH, Nee AYC, Wong YS, Loh HT, Miyazawa T (1995) Multi-objective optimization of
part building orientation in stereolithography.RPJ 1：12-23 proposes one kind can be direct
The multi-objective Algorithm of CAD model is applied to, target includes improving model accuracy and reduces structure time etc..Model accuracy is used as master
Target, builds the time for time target, according to the target function value that the two parameters calculate each candidate direction, chooses target letter
The maximum direction of numerical value is used as candidate direction.But the algorithm needs first to find a candidate direction collection according to model geometric information
(such as using the sampling of normal vector or space vector etc. of model all surface), then therefrom chooses optimum according to object function
Fabrication orientation.Masood SH, Rattanawong W, Iovenitti P (2000) Part build orientations
based on volumetric error in fused deposition modeling.Int J Adv Manuf
Technol 19：According to the feature of FDM technology in 162-168, propose the volumetric errors that cause using Layered manufacturing to choose most
Excellent fabrication orientation.Model is rotated to an angle, and calculates the volumetric errors for carrying out that generation is layered under the direction, then most optimal sorting
Layer direction is to produce the minimum angle direction of volumetric errors.But the algorithm can only choose a side in the fixed anglec of rotation
To, and between different model layered optimization directions, do not have internal relation.Hossein Ahari, Assembly
Automation(2013)Optimization of slicing direction in laminated tooling for
A kind of fabrication orientation Algorithms of Selecting for being applied to CAD model is proposed in voulume deviation reduction, is not passed through
Other desired values such as volumetric errors or backing material are calculated, but the normal vector according to triangle surface is flat with fabrication orientation
Row or vertical relation, are added to the triangle surface set of the candidate direction.Calculate each candidate direction corresponding three
The gross area of angular dough sheet, chooses the maximum candidate direction of the gross area as fabrication orientation.The algorithm is by all of method in model
Vector is not suitable for the complicated model of geometric properties, but the algorithm can be obtained for naive model as candidate direction set
The minimum layered optimization direction of volumetric errors must be produced.Although algorithm above chooses fabrication orientation using different targets：
Model accuracy, time, supporting construction, material cost etc. is built, but they are all based on traveling through the thought that enumerates.
The basic thought of traversal enumeration is as candidate side using the normal vector of all triangle surfaces of composition model
It is linear relationship to, the candidate direction number that such method is chosen and the triangle surface number for constituting model, the geometry of model
Feature is more complicated, and triangle surface number is more, then the number of candidate direction is more, obtains the time in layered optimization direction
Also more long, that is, candidate direction complexity is 0 (n), wherein n represents the triangle number for constituting model.With 3D printing
Popularization, needs the model for printing to be not limited to the simple threedimensional model made by CAD, but more smart in real world
Thin complex model, such as person model, art work model etc., such model geometric feature are complicated, represent the triangle of model
Dough sheet enormous amount, traditional batch direction choosing method cannot meet the requirement of real-time of fabrication orientation selection.Therefore such as
It is the key factor for affecting fabrication orientation to choose that what reduces the number of candidate direction.
Content of the invention
For the deficiencies in the prior art, the present invention is intended to provide a kind of model suitable for complex geometry feature point
Layer direction fast selecting method, is weighted to its corresponding normal vector with the triangle surface area for representing threedimensional model, and
Principal component analysiss are carried out to area weighting factor method vector extracts characteristic vector acquisition layered optimization direction.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of fabrication orientation self adaptation fast selecting method, comprises the steps：
Step 1, by threedimensional model triangle gridding, obtains some triangle surfaces, and each triangle surface includes three
Normal vector outside individual summit and a direction model；
Step 2, calculates the corresponding Area-weighted normal vector of each triangle surface
Wherein,Represent the Area-weighted normal vector of m-th triangle surface, AmFace for m-th triangle surface
Product,Original unit's normal vector for m-th triangle surface；
Step 3, the new sample space that all of Area-weighted normal vector is constituted are designated asn
Number for total sample number, i.e. triangle surface；Principal component analysiss are carried out to area weighting factor method vector, and construction covariance matrix is simultaneously
Singular value decomposition is carried out, draws three characteristic vectors most comprising new samples spatial information as candidate direction；
Step 4, is layered to threedimensional model under candidate's fabrication orientation respectively；
Step 5, the model that calculating is built under three candidate's fabrication orientations is under alias and archetype between
Cumulative volume error；
Step 6, according to three cumulative volume errors that step 5 is calculated, the candidate layering side wherein corresponding to minima
To as layered optimization direction.
It should be noted that step 3 includes：
3.1) the average normal vector of n Area-weighted normal vector is calculated
3.2) each Area-weighted normal vector and the difference of average normal vector is calculated, difference value vector is obtained
3.3) covariance matrix C=(c are constructedij)3×3：
C=D*DT；
Wherein
3.4) singular value decomposition is carried out to covariance matrix C, obtains three eigenvalue γk(k=1,2,3) with each feature
It is worth corresponding characteristic vectorThe characteristic vector is candidate's fabrication orientation.
It should be noted that cumulative volume difference calculation process runs described in step 5 is as follows：
5.1) calculate in candidate's fabrication orientationUnder, the corresponding volumetric errors of each triangle surface：
Wherein, cmCorresponding alias slant height (cusp height) for m-th triangle surface, have
T is lift height, θmForWithAngle；
5.2) volumetric errors to constituting all triangle surfaces of model add up the totality drawn under corresponding candidate direction
Product error：
Explanation is needed further exist for, the lift height t is unified lift height, as fixed value.
The beneficial effects of the present invention is：The present invention obtains three perpendicular candidate's layerings by extracting characteristic vector
Direction, and layered optimization direction is selected based on minimum volume error, need not be by all for model surface normal vectors or space normal vector
Sampling as candidate's fabrication orientation, reduce algorithm complex while improving model accuracy, acquisition can be substantially reduced most
The time of excellent fabrication orientation, it is adaptable to the complicated model of geometric properties or topological structure.
Description of the drawings
Fig. 1 is the implementation process diagram of the present invention；
Fig. 2 is impact schematic diagram of the fabrication orientation to alias；
Structural representations of the Fig. 3 for model M；
Fig. 4 is the alias schematic diagram produced by model M layering in Fig. 3；
Fig. 5 is the cocked hat schematic diagram that alias is produced in Fig. 4；
Fig. 6 is perspective view of the normal vector of the triangle surface Area-weighted of model M in Fig. 3 on fabrication orientation；
Fig. 7 is the experiment schematic diagram to the Buddha models that triangle surface number is 10000；
Fig. 8 is the experiment schematic diagram to the Bunny models that triangle surface number is 69630；
Fig. 9 is the experiment schematic diagram to the Bunny models that triangle surface number is 5110；
Figure 10 is the experiment schematic diagram to the Bottle models that triangle surface number is 1240.
Specific embodiment
Below with reference to accompanying drawing, the invention will be further described, it should be noted that the present embodiment is with this technology side
Premised on case, detailed implementation steps and specific operation process is given, but protection scope of the present invention is not limited to this enforcement
Example.
As shown in figure 1, a kind of fabrication orientation self adaptation fast selecting method comprises the steps：
Step 1, by threedimensional model triangle gridding, obtains some triangle surfaces, and each triangle surface includes three
Individual summit and a normal vector pointed to outside threedimensional model；
Step 2, calculates the corresponding Area-weighted normal vector of each triangle surface
Wherein,Represent the Area-weighted normal vector of m-th triangle surface, AmFace for m-th triangle surface
Product,Original unit's normal vector for m-th triangle surface；The Area-weighted normal vector
Can regard that a point in three dimensions, its element value represent the coordinate figure in three dimensions as.
Step 3, the new sample space that all of Area-weighted normal vector is constituted are designated asn
Number of the total sample number for triangle being represented, principal component analysiss being carried out to area weighting factor method vector, construction covariance matrix is gone forward side by side
Row singular value decomposition, draws three characteristic vectors most comprising new samples spatial information as candidate direction.
These are not random distribution in three dimensions, but with certain distribution characteristics, they can be with table
It is shown as the linear combination of some characteristic vectors (or projecting direction).The main thought of principal component analysiss is exactly in whole three dimensions
The best base vector that describe these distribution characteristicss is inside found.These characteristic vectors constitute a new feature space, each
Individual sample is all the linear combination of characteristic vector.The selection of characteristic vector is to carry out spy by the covariance matrix to original sample
Value indicative is decomposed, and eigenvalue is bigger to represent that corresponding information of the characteristic vector comprising original sample of this feature value is more, is more suitable as
For base vector.
Principal component analysiss (PCA, principle component analysis) are a kind of classical multi-variate statistical analyses
Method, its target are to recalculate one group of more meaningful base to represent original hash, and original complex data is dropped
Dimension, contacting between Xin Ji and original sample is the size of variance.The advantage of PCA is to obtain each dimension by analytical data itself
The internal relation of data, each main constituent normal orthogonal for obtaining, redundancy are few, more representative.Principal component analysiss are basic
Principle is：(1) one group of given variable X1、X2、X3…Xn, one group of incoherent variable Y is obtained by linear transformation1、Y2、
Y3…Yk(2) population variance (X of variable, in this conversion, is kept1、X2、X3…XnVariance sum and Y1、Y2、Y3…YkSide
Difference sum is identical) constant, while so that Y1There is maximum variance, referred to as first principal component, Y2There is worst big variance, referred to as the
Two main constituents, the like, original n variable, it is possible to be converted to k new variables, reach the dimensionality reduction mesh to original variable
Mark.Main constituent carries out singular value decomposition by the covariance matrix to original variable and obtains, and covariance matrix carries out singular value point
After solution, to a characteristic vector, the characteristic vector of eigenvalue of maximum is the maximum first principal component of variance to each eigenvalue, it
The low-frequency information of original sample can be most represented, otherwise the characteristic vector of minimal eigenvalue represents the high-frequency information of original variable.
Above-mentioned principle is based on, step 3 specifically includes following steps：
3.1) the average normal vector of n Area-weighted normal vector is calculated
3.2) each Area-weighted normal vector and the difference of average normal vector is calculated, difference value vector is obtained
3.3) covariance matrix C=(c are constructedij)3×3：
C=D*DT；
Wherein
3.4) Eigenvalues Decomposition is carried out to covariance matrix C, obtains all eigenvalues and its corresponding characteristic vector.Due to
Covariance matrix C is real symmetric matrix, carries out singular value decomposition used here as jacobi SVD methods to covariance matrix C, obtains
To three eigenvalue γk(k=1,2,3) with the corresponding characteristic vector of each eigenvalueThe characteristic vector
As candidate direction.
Step 4, respectively in candidate's fabrication orientationUnder threedimensional model is layered, lift height for unification
Lift height；
Step 5, cumulative volume error of the model built after calculating layering under the influence of alias and archetype between；
Here, by taking model M as an example, model volumetric errors are illustrated.As shown in figure 3, wherein Fig. 3 (a) is model M
Model entity schematic diagram, Fig. 3 (b) for model M three dimensional structure diagram, direction shown in arrow be fabrication orientation, in model M
Surface F2, F3, F4 and fabrication orientation level, F5 be vertical with fabrication orientation, and F1 and fabrication orientation have certain angle.
Model M is layered using unified lift height.As shown in figure 4, after layering is completed, can produce on the F1 of surface
A series of sawtooth of stairsteppings of life, this phenomenon are referred to as alias.Lift height is less, and alias substantially, is not made
Into error less, model surface is closer to archetype.But the restriction due to hardware, lift height can only obtain limited threshold
Value.Surface F2 as shown in Figure 4, F3, F4, F5 are identical with the archetype before layering, do not produce alias, so not depositing
In volumetric errors.Lower surface analysis fabrication orientation, the impact of the normal vector and area of triangle surface to model surface precision.
As shown in Fig. 5 (a), surface F3 and F5 do not produce alias, and surface F1 generates alias；NoteFor dividing
Layer direction,For the normal vector of surface F1, thenWithAngle theta can be expressed as：
Therefore, ladder slant height (cusp height) c can be expressed as：
Wherein t is lift height, it is clear that lift height is affected with the angle theta of fabrication orientation by c and normal vector.But a mould
Type is made up of a lot of triangle surfaces, and on different triangle surfaces, normal vector direction is different, then their corresponding c are different,
The error of model is also relevant with s as shown in Figure 5 simultaneously, so c can not represent model global error.
In Fig. 5 (b), the cocked hat area AE of alias generation is：
The length that s is corresponding triangle surface in one layer of section, the area of this cocked hat obvious are less, ladder
Effect more not substantially, builds the surface of model closer to theoretical model.Equally, the error in the alias of model different piece
The area of triangle is simultaneously differed, by above formula can perception model error also with represent model triangle surface relevant, therefore miss
The area AE of difference triangle shape can not represent model global error.
For making up the defect of both the above error metrics method, volumetric errors consider fabrication orientation, gore simultaneously
The impact of the normal vector of piece, the area of triangle surface to error.The volumetric errors VE1 produced on the F1 of surface in Fig. 5 can be with table
It is shown as：
Areas of the wherein A1 for surface F1, c is the cusp height in the surface step effect.
So model cumulative volume error is：
Described above is based on, cumulative volume difference calculation process runs described in step 5 is as follows：
5.1) calculated in candidate direction respectivelyUnder, the corresponding volumetric errors of each triangle surface：
Wherein, cmCorresponding alias slant height (cusp height) for m-th triangle surface, have
T is lift height, θmForWithAngle；
5.2) volumetric errors to constituting all triangle surfaces of model are added up and are drawn under corresponding candidate fabrication orientation
Cumulative volume error：
When adopting unified lift height to be layered, t is for definite value, then error volume VE is depended on?
It is exactly projection of the normal vector of each triangle surface on fabrication orientationIt is multiplied by its area Am, it can be understood as will
Its normal vector is carried out after product weightings using corresponding areaProjection on fabrication orientationAs shown in Fig. 6 (a),Respectively surface F1, F2, F3, F4, F5
Normal vector, from Fig. 6 (b), the normal vector of Area-weightedProjection on fabrication orientation is less, the triangle
The error volume produced on dough sheet is less.If the fabrication orientation that tries to achieve causes the Area-weighted normal vector of all triangle surfacesOn fabrication orientationProjection and minimum, then the directionAs layered optimization direction.By principal component analysiss
Principle understands to obtain three comprising new samples space by carrying out the normal vector sample by Area-weighted principal component analysiss
The most characteristic vector of information, this feature vector are maximum with new samples space variance, that is, can most represent new samples space point
Cloth rule, therefore can be from these three characteristic vectors with the minimum Object selection layered optimization direction of volumetric errors.
Step 6, according to the cumulative volume error under three candidate's fabrication orientations that step 5 is calculated, wherein minima institute
Corresponding candidate's fabrication orientation is layered optimization direction.
It is applied to the complicated big data model of geometric properties below by way of the experimental verification present invention, can quickly obtains generation body
The less fabrication orientation of product error.
First, arithmetic accuracy analysis
From formula (1), model volumetric errors are affected by lift height and fabrication orientation simultaneously, therefore in different layerings
Multigroup experiment has been carried out to each model under thickness.
As shown in Fig. 7,8,9,10, (a) figure is experimental model, and (b) figure is under the layered optimization direction that each algorithm is obtained
The volumetric errors of generation, wherein, Fig. 7 (a) institutes representation model is the Buddha models for having 10000 triangle surfaces；Fig. 8 (a)
Institute's representation model is the Bunny models for having 69630 triangle surfaces；Fig. 9 (a) institutes representation model is to have 5110 gores
The Bunny models of piece；Figure 10 (a) is to have 1240 triangle surface Bottle models.It follows that Fig. 7 (a), 8 (a), 9
A the complexity of (), 10 (a) institute representation model is ordered as：Fig. 8 ＞ Fig. 7 ＞ Fig. 9 ＞ Figure 10.Fig. 7 (b), 8 (b), 9 (b), 10
In (b), volumetric errors comparison diagram of the left figure for the principal component analysiss result and result of the present invention of original unit's normal vector, right figure is
Hossein arithmetic results and the volumetric errors comparison diagram of result of the present invention, as seen from the figure, fabrication orientation choosing provided by the present invention
The method of taking is obtained in that and produces the less fabrication orientation of error volume.
The candidate's fabrication orientation that is chosen using the present invention is entered by the normal vector of all triangle surfaces to constituting model
After row Area-weighted, application PCA principal component analytical methods are extracted and are obtained, and the target function type (1) of volumetric errors is to normal vector
Area-weighted is carried out there is provided theoretical foundation, layering is carried out according to candidate direction of the present invention and can be produced less volumetric errors.
From Fig. 7,8,9,10, the model to differing complexity, this paper algorithms obtain layered optimization direction will not producing ratio other
The more error volumes of two kinds of algorithms.Model geometric feature in Fig. 9 is less, and modelling vector distribution feature substantially, is calculated herein
Three main constituents that method is obtained are close to some normal vectors existing in model, therefore are more or less the same with the result of other two kinds of algorithms.
Model geometric feature rich in Fig. 7, modelling vector distribution feature be not obvious, understands the model by covariance matrix coefficient
Normal vector degree of correlation is little, the normal vector that three main constituents not obtained with the present invention in model are close to, therefore this paper algorithms are obtained
The error volume that produces of the other two kinds of algorithms of layered optimization direction ratio less.
2nd, efficiency of algorithm analysis
From analysis above, the present invention directly carries out principal component analysiss characteristic vector to the normal vector of Area-weighted and carries
Take and have to three candidate directions, candidate direction number complexity is 0 (1), then according to the target function type of error volume
(1), layered optimization direction is obtained, and time complexity is 0 (n).And Hossein algorithms are by the normal direction of all for model triangle surfaces
Used as candidate direction, candidate direction number complexity is 0 (n) to amount, and the objective function Equation (1) also according to error volume is obtained
Layered optimization direction is taken, time complexity is 0 (n2).Numbers of the wherein n for model intermediate cam shape dough sheet, therefore the time of this algorithm
In hgher efficiency.Run time contrast of the table 1 for the present invention with Hossein algorithms under different models.
Table 1
As shown in table 1, under identical model, the time that the present invention obtains layered optimization direction is less, when model complexity journey
Degree increases, and increases not substantially, and the time required to Hossein algorithms when triangle surface number increases the time required to this paper algorithms
Increase quickly.
For a person skilled in the art, can be given various corresponding according to above technical scheme and design
Change and deform, and all these changes and deformation is should be construed as being included within the protection domain of the claims in the present invention.
Claims (3)
1. a kind of fabrication orientation self adaptation fast selecting method, it is characterised in that methods described comprises the steps：
Step 1, by threedimensional model triangle gridding, obtains some triangle surfaces, and each triangle surface is pushed up comprising three
Normal vector outside point and a direction model；
Step 2, calculates the corresponding Area-weighted normal vector of each triangle surface
Wherein,Represent the Area-weighted normal vector of m-th triangle surface, AmFor the area of m-th triangle surface,Original unit's normal vector for m-th triangle surface；
Step 3, the new sample space that all of Area-weighted normal vector is constituted are designated asN is sample
The number of this sum, i.e. triangle surface；Principal component analysiss are carried out to area weighting factor method vector, and construction covariance matrix is simultaneously carried out
Singular value decomposition, draws three characteristic vectors most comprising new samples spatial information as candidate direction；
Step 4, is layered to threedimensional model under three candidate's fabrication orientations respectively；
Step 5, the model that calculating is built under three candidate's fabrication orientations is under the influence of alias and archetype between
Cumulative volume error；
The cumulative volume difference calculation process runs are as follows：
5.1) calculate in candidate's fabrication orientationUnder, the corresponding volumetric errors of each triangle surface：
Wherein, cmCorresponding alias slant height (cusp height) for m-th triangle surface, have
T is lift height, ΔmForWithAngle；
5.2) volumetric errors to constituting all triangle surfaces of model add up the totality drawn under corresponding candidate fabrication orientation
Product error：
Step 6, according to three cumulative volume errors that step 5 is calculated, the candidate's fabrication orientation wherein corresponding to minima is
For layered optimization direction.
2. a kind of fabrication orientation self adaptation fast selecting method according to claim 1, it is characterised in that step 3 includes：
3.1) the average normal vector of n Area-weighted normal vector is calculated
3.2) each Area-weighted normal vector and the difference of average normal vector is calculated, difference value vector is obtained
3.3) covariance matrix C=(c are constructedij)3×3：
C=D*DT；
Wherein
3.4) singular value decomposition is carried out to covariance matrix C, obtains three eigenvalue γk(k=1,2,3) with each eigenvalue pair
The characteristic vector that answersThe characteristic vector is candidate's fabrication orientation.
3. a kind of fabrication orientation self adaptation fast selecting method according to claim 1, it is characterised in that the layering is thick
Degree t is unified lift height, as fixed value.
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| CN113334773A (en) * | 2021-06-11 | 2021-09-03 | 电子科技大学 | 3D printing forming direction multi-target optimization method based on self-adaptive layering |
| CN113414987A (en) * | 2021-06-23 | 2021-09-21 | 哈尔滨理工大学 | 3D printing self-adaptive layering thickness method |
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