CN109118589A - Geometrical model full range details restorative procedure - Google Patents
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Abstract
Geometrical model full range details restorative procedure of the present invention, the restorative procedure of the original details of geometrical model is kept based on adaptive decomposition, migration reparation is carried out with the geometric detail information effectively to model surface missing, to solve the problems, such as that boundary alignment process is complicated and model is distorted.It include following steps, step (1) geometrical model full range details catabolic phase, using average curvature as the input signal of the adaptive decomposition of triangle grid model, this signal is decomposed, obtains including the full range geometric detail information for accumulateing mode function and signal margin in one group；Step (2) Patch model Optimum Matching stage；Step (1) is obtained full range geometric detail information, is migrated by similitude patch to target patch by step (3), geometry information transmitting and model full range repairing phase according to the matching result that step (2) obtains；The reconstruction that grid model is carried out for each signal obtains different geometric detail reparations as a result, to make model editable.
Description
Technical field
The present invention relates to a kind of geometrical model full range details restorative procedures of data-driven, belong to grid model data processing
With the technical field of model reparation.
Background technique
The modeling of reduction degree high for historical relic etc. substantially relies on 3-D scanning to complete, but the threedimensional model warp scanned
It often will appear damaged face, so the reparation algorithm more and more kept for model geometric details is suggested.
Main method includes voxel-based, based on textures synthesis and the method based on template library etc. at present.Mould
The problem of type reparation is an ill-posedness, because most methods can obtain relatively good reparation under particular model situation
Effect, but do not ensure that suitable for other situations.Such as some smaller cavities, it can reach and repair effect well
Fruit, but cannot repair well comprising abundant geometric detail information, the biggish hole of area.
In recent years, it was more and more emerged based on similarity measurement model restorative procedure, core concept is exactly
Define effective patch description, the benefit that the complete area most like with perforated is then found according to description
Fourth, by the patch of other regions of reconstructed model or scale model come filling-up hole.
The model restorative procedure that geometric detail based on similarity measurement is kept, mainly by replicating existing region to hole
Hole region to achieve the purpose that reparation, while also ensuring the reparation of geometric detail.But the exactly because behaviour that duplication is pasted
Make, improves computation complexity, reduce time efficiency.Because being needed when similitude region is affixed to hole target area
Carry out the boundary alignment of the two.It is difficult to define firstly, finding corresponding relationship between points needed for alignment；Secondly,
When alignment, the deformation of grid model must be carried out, it is that this is not intended to as a result, desired target is the process in reparation
In reduce repair influence of the bring to existing model area as far as possible.Therefore, how to search out a kind of reduces model degree of deformation
It alignment thereof and avoids deforming completely, becomes current technical task urgently to be solved.
In addition, the model that geometric detail is kept repair algorithm archaeology, 3D printing, manufacture in kind, mold defect detection with
The numerous areas such as rapid reparation have important role, and are also widely used, and have broad application prospects
With huge market value.However, the research of the model restorative procedure kept at present to geometric detail is also faced with lot of challenges, example
Model metamorphopsic distortion caused by the complexity and alignment procedure of as noted above hole boundary alignment process.
In view of this, special propose present patent application.
Summary of the invention
Geometrical model full range details restorative procedure of the present invention, it is above-mentioned of the existing technology its object is to solve
Problem and the restorative procedure that the original details of geometrical model is kept based on adaptive decomposition, effectively to model surface missing
Geometric detail information carries out migration reparation, to solve the problems, such as that boundary alignment process is complicated and model is distorted.
For achieving the above object, the geometrical model full range details restorative procedure includes following implementation steps:
Step (1) geometrical model full range details catabolic phase, adaptive point using average curvature as triangle grid model
The input signal of solution decomposes this signal, obtains including accumulateing mode function IMFs (Intrinsic Mode in one group
Functions, abbreviation IMFs) and signal margin (residue) full range geometric detail information；
Step (2) Patch model Optimum Matching stage is based on model damaged area contiguous structure feature, when with different time
The full range feature that anisotropy heat transfer relation weighted value in domain determines carries out Model Matching；Pass through Definition Model damaged area
Anisotropy is described son and extends to retouching for patch by vertex description by relevant demographic information description of contiguous structure feature
Son is stated, effectively lookup and the most matched similitude patch of target patch, and saves matching result；
Step (3), geometry information transmitting and model full range repairing phase, according to the matching result that step (2) obtains,
Step (1) is obtained into full range geometric detail information, is migrated by similitude patch to target patch；During migration, adjust
The weight for accumulateing mode function in different scale obtains different signals；The reconstruction of grid model is carried out for each signal respectively,
Different geometric detail reparations is obtained as a result, to make model editable.
Such as above-mentioned basic scheme, in order to solve the problems, such as that above-mentioned boundary alignment is complicated and model is distorted, the application is based on
Adaptive decomposition method proposes the model repair mode of protection geometric detail, effectively believes the geometric detail of model surface missing
Breath is repaired, and can avoid this complicated process of boundary alignment in duplication paste process.Meanwhile it is effectively real by resolving Algorithm
The migration of existing geometric detail, rather than the migration of whole patch is pasted, and the distortion level of model is reduced.
Further preferred embodiment is, in the step (1), based on set empirical mode decomposition (EEMD)
The adaptive decomposition input signal of triangle grid model is decomposed；
EEMD is the abbreviation of Ensemble Empirical Mode Decomposition, i.e. set empirical mode decomposition,
It is the noise auxiliary data analysis method proposed for the deficiency of EMD method.Its decomposition principle is when additional white noise is equal
The even different scale that when being distributed in entire time frequency space, which is just divided by filter group is at being grouped as.Work as signal
In addition the signal area of different scale will be automatically mapped to relevant to background white noise suitable when equally distributed white noise background
When scale gets on.
Based on EEMD decomposition algorithm implementation model smoothing processing, the initial repair efficiency of model can be made more preferable.
Function g:M → the R, M being defined on triangle grid model surface indicate that grid model, R indicate real number set,
Wherein, fkIt indicates k-th IMFs, k=1 ..., N, mode function sum, r is accumulate in N expressionNIndicate corresponding signal
Surplus；
Decomposable process is as follows,
Firstly, the definition of extreme point, for function g, if g (vi) meet: g (vi)≥g(vj), j ∈ N (i) or g (vi)
≤g(vj), j ∈ N (i), then vi is referred to as the maximum point or minimum point of g；
Secondly, defining according to the extreme point in upper step, extreme point is searched out, with extreme point structurally lower envelope, envelope
Solution biharmonic interpolation calculation, biharmonic interpolation are extension of the spline interpolation in three-dimension curved surface, are minimum triangles
What the energy function defined on the potential manifold surface M where grid model was realized,
∫M(ΔMφ)2dV.
Corresponding Lagrange's equation isWherein ΔMIt is the Laplace-Beltrami operator of curved surface M, tool
Body, for given interpolation point and corresponding value { (vi,g(vi)) i, ∈ C, interpolating function φ=(φ (v1),φ
(v2),...,φ(vn)) can be acquired by solving following n × n linear system:
L2φ=0, s.t., φ (vi)=g (vi),i∈C,
Wherein, C is interpolation set, and L is n × n Laplacian Matrix for triangle grid model；
Finally, the convergence of iteration screening process, in calculating after lower envelope, mould is accumulate to determine by envelope in current
State function；The convergence of screening, which is exactly whether interior the signal after determining screening is, accumulates mode function；End process is to see mark
Whether quasi- variance SD is less than given threshold value, and standard variance SD is calculated using two adjacent the selection results, standard variance SD
Formula is as follows,
Further supplement for the step (2) is that the application defines new description with refinement scheme.It should
Anisotropy based on model vertices is described son and extends to model damaged area to close on knot by description by statistical method
Relevant demographic information description of structure feature, is improved entire similitude matching result precision.Simultaneously in matching process
In, it is added to the constraint of Rigid Registration, selects registration error the smallest as best matching result in similar candidates collection.
Specifically, son is described by the relevant demographic information of Definition Model damaged area contiguous structure feature, to obtain
Similitude matching result for patch；
After giving potential manifold surface M, there are following equatioies:
Wherein, HTFor thermodynamics operator, htWhen (x, y) regards moment t as, from the heat of point x to y transmitting；
Matching process is as follows,
Firstly, carrying out feature decomposition to thermonuclear, the relevant demographic information of model damaged area contiguous structure feature is obtained
Description:
Wherein, λ itAnd ΩiRespectively one Marco Beltrami operator (Laplace-Beltramioperator of Laplce
Operator is as adjoint operator and the operator determined by exterior differentiation operator of star operator) corresponding characteristic value and and characteristic function, it is full
Sufficient equation DELTA M Ωi=λ itΩi, partial structurtes information is added in Laplacian Matrix building；
Secondly, Definition Model is damaged according to the anisotropy heat transfer relation weighted value that vertex is calculated in previous step
Contiguous structure feature relevant demographic information description in region is as follows,
Wherein, [0,1] indicates to be normalized to section [0,1], selects description of multiple time domains, i.e., each patch correspondence is more
A description；In time domain100 time points of middle sampling transmit as the anisotropic thermal of a point and close
It is weight vectors；
Finally, describing son, meter according to the relevant demographic information of defined model damaged area contiguous structure feature
The matching result between patch is calculated, using the standard of Euclidean distance, patch is calculated and describes the distance between son, for each target
Patch selects k apart from nearest, most like source patch, as candidate patches；
Define patch between matching error formula be,
Wherein, NTFor the patch number in target patch set T, D (Ti,Sj) indicate target patch TiWith source patch SjBetween lead to
Error after crossing Rigid Registration；
According to above formula, from candidate patches, the smallest patch of matching error is selected as matching result.
Further supplement for the step (3) is with refinement scheme, for the migration of implementation model surface geometry details
And full range editable, by IMFs and the signal of corresponding target patch that best patch is corresponded to different scale geological information
Surplus forms new combination.And Model Reconstruction is carried out according to this new signal, to realize the migration of geometric detail.Together
When, in migration by adjusting the weight of IMFs come the diversity boundary of implementation model.
Specifically, it is transferred to corresponding target patch by the way that mode function information will be accumulate in similitude patch, to realize
The transmitting of geometric detail；Accumulate the weight of mode function by adjusting in different levels simultaneously with implementation model full range reparation；
The set empirical mode decomposition being defined on target patch decomposes equation,
Wherein, gTIndicate the function being defined on target patch, i.e. signal；T indicates target patch；
Including following implementation steps,
Firstly, accumulateing mode function information according to obtained in the matching result of step (2) and step (1), source is mended
Accumulate mode function in fourth to migrate to target patch, obtains the new signal for being defined on model surface；
Wherein,For the new signal of formation, fk STo accumulate mode function information, ω in similar source patchkFor corresponding ruler
Spend the weight of information, rN TFor the signal margin of target patch；
Secondly, Laplacian Matrix reconfigures while previous step generates new signal, L is definedNInitially to repair
New Laplacian Matrix afterwards,For ingredient corresponding with model internal vertex in matrix,For it is corresponding with border vertices at
Point,For increase newly vertex correspondence ingredient, i.e.,The new Laplacian Matrix constructedFor original LaPlacian matrix ingredient corresponding with model internal vertex；
Finally, minimizing the side of energy using Laplce according to the signal of neotectonics and new Laplacian Matrix
Method reconstructs three-dimensional grid model, by accumulateing the weight of mode function in adjusting, obtains different repairing effects, that is, model
Edit effect.
In above-mentioned steps (1), the threshold value can be 0.1.
To sum up content, herein described geometrical model full range details restorative procedure have the advantage, that
1, present applicant proposes a kind of restorative procedures based on EEMD decomposition algorithm, on the one hand can extract full range geometry letter
Breath easily facilitates and carries out the reparation of full range geometric detail to model, on the other hand obtains geological information, also make migration of the invention
Process is not needed to carry out patch whole duplication stickup, be provided a kind of more simple and effective just for geometric detail
Method.
2, the method for comparing existing similarity measurement, the model damaged area contiguous structure feature that the application proposes are related
Demographic information describe son, the local message of model is not only reflected, while also reflecting the global information of model, for retouching
It states for patch feature, there is significant advantage.
3, the geometric detail transition process based on EEMD decomposition algorithm that the application proposes, can not only repair model
It is multiple, while model can also be edited according to user demand, to obtain diversified repair as a result, this is in game etc.
There is very big application prospect in field.
Detailed description of the invention
Fig. 1 is to the grid model full range geometric detail reparation side based on adaptive decomposition and anisotropy thermonuclear description
The process flow diagram of method；
Fig. 2 is the result that the step (1) carries out smooth treatment based on EEMD decomposition method to model；
Fig. 3 is the resulting similitude matching knot of relevant demographic information description of model damaged area contiguous structure feature
Fruit schematic diagram；
Fig. 4 is the schematic diagram of the reparation result in the simple cavity of model；
Fig. 5 is the reparation result schematic diagram of model U-shaped Void Model；
Fig. 6 is model full range edit effect schematic diagram.
Specific embodiment
The application is further described with reference to the accompanying drawings and examples.
Embodiment 1, as shown in Figure 1, giving the totality of the geometrical model full range geometric detail restorative procedure of data-driven
Process flow,
The geometrical model full range details restorative procedure, be based on EEMD decomposition algorithm carry out the reparation of full range details, and
And son is described to obtain similitude matching result according to the relevant demographic information of model damaged area contiguous structure feature, have
It is easy to operate, high-efficient, the high feature of matching precision.
Include mainly following steps:
Step (1) geometrical model full range details catabolic phase
Using average curvature as the input signal of the adaptive decomposition of triangle grid model, this signal is decomposed, is obtained
To the full range geometric detail information including accumulateing mode function and signal margin in one group；Simultaneously to only including signal margin
Signal is that new signal carries out grid reconstruction, achievees the purpose that model smoothing.
Step (2) Patch model Optimum Matching stage
Based on model damaged area contiguous structure feature, with the anisotropy heat transfer relation weight in different time time domain
The determining full range feature of value carries out Model Matching；Pass through the relevant demographic information of Definition Model damaged area contiguous structure feature
Anisotropy is described son and describes description that son extends to patch by vertex, effectively searched with target patch most by description
Matched similitude patch, and save matching result；I.e. according to description newly defined, by the smooth of initial smooth repairing
On model, the patch most like with target patch at hole is found.
Step (3), geometry information transmitting and model full range repairing phase
According to the matching result that step (2) obtains, step (1) is obtained into full range geometric detail information, by similitude patch
It migrates to target patch；During migration, the weight for accumulateing mode function in different scale is adjusted, different signals is obtained；
The reconstruction for carrying out grid model for each signal respectively obtains different geometric detail reparations as a result, to make model that can compile
Volume.
In step (1), it is necessary first to extract the full range geometric detail information of model, while also need to carry out light to model
Sliding pretreatment.Therefore, Definition Model surface of the present invention average curvature is signal, then carries out adaptive decomposition algorithm (EEMD),
The full range geometric detail information of grid model is obtained, and passes through the surface reconstruction of multi information surplus (residue), reaches mould
The smooth pretreated purpose of type.
Definition Model surface signal and to decompose Laplace operator be a Second Order Differential Operator, when expanding to three-dimensional flow pattern
When surface, referred to as Laplace-Beltrami operator can measure the deviation of lubricious thin plates curved surface, the part letter of record cast
Breath.Discrete Laplace operator is widely used for Mesh Smoothing, the geometrical models such as grid model editor and model interpolation processing behaviour
In work.The present invention further will carry out EEMD to this signal by Laplace-Beltrami operator definitions model surface signal
It decomposes.
A triangle grid model M=(V, K) is defined, wherein V indicates vertex set: { vi=(xi,yi,zi)∈R3, i=
1 ..., n }, K contains the adjacency information of grid model side and patch.By carrying out average weighted to the vertex in neighborhood, just
The discrete Laplace operator on grid model curved surface can be calculated:
Wherein, N (i) indicates vertex viA ring close on point set, Δ indicates Laplace operator, Δ viFor vertex vi's
Laplace operator.
Using cotangent weight:
ωij=cot αij+cotβij (2)
At this point, discrete Laplace vector is parallel to the normal vector on vertex,
Formula (1) will deform are as follows: Δ vi=4 | Ai|kini (3)
Wherein, αijAnd βijIndicate two angles for corresponding to side (i, j), | Ai| and kiRespectively indicate Voronoi lattice
Surface area and vertex viThe average curvature at place.
By Laplace vector Δ viWith corresponding vertex normal vector niDefinition of inner product be model surface signal:
s(vi)=(Δ vi·ni) (4)
The formula can be used as a kind of measure of average curvature, and depend on sampling density.
It can significantly find out that equation (4) have translation invariance and rotational invariance, can simultaneously serve as EEMD decomposition
The input signal of algorithm.In addition to this, it can be also used for effectively reconstructed mesh model, this is at the place of Laplacian curved surface
It is generally existing in reason mode.
In the model containing hole, the loss of learning of patch and side at hole, and there is no any mechanism to compensate table
Face tension.
Therefore, it at for hole border vertices, by equation (2), is calculated with the method for cotangent weight
In Laplacian vector, there are the tangent ingredients of larger proportion.
In order to overcome this problem, using the method for Wang et al., concrete processing procedure is as follows:
By each border vertices viWith its a ring neighbor point vj, j ∈ N (i) projects on its normal plane, obtains pair
The subpoint v answeredi' and v‘ j, j ∈ N (i), wherein N (i) indicates vertex viA ring neighbor point；
Laplacian vector is calculated on normal plane:Wherein ωijIt is calculated by equation (2)
It obtains.
The Laplacian vector calculated by this method is parallel to the normal vector of corresponding border vertices, and eliminates
Tangent ingredient in original vector.
One-dimensional EEMD is decomposed and is applied on three-dimension curved surface, extracts Finite Number from the function being defined on three-dimensional surface
Accumulate mode function IMFs in amount, these functions have reacted the basic model in data.
Function g:M → the R, M being defined on triangle grid model surface indicate that grid model, R indicate real number set, EEMD
Decomposable process it is as follows:
Wherein, fkIndicate that k-th IMFs, k=1 ..., N, N indicate IMFs sum, rNIndicate corresponding signal margin；
For function g, if g (vi) meet: g (vi)≥g(vj), j ∈ N (i) or g (vi)≤g(vj), j ∈ N (i) then claims
viFor the maximum point or minimum point of g；
In the decomposable process of EEMD, extension of the biharmonic function as three-dimension curved surface cubic spline interpolation can be used for counting
Calculate the upper lower envelope on threedimensional model surface.Give a function being defined on the M of threedimensional model surfaceIt again may be by double
Harmonic function minimizes functionThin-plate energy,
The Euler-Lagrange equation of corresponding above formula are as follows:
Wherein, ΔMIndicate the Laplace-Beltrami operator on three-dimension curved surface M.
When given interpolation point and corresponding value { (vi, g (vi), i ∈ C) }, the linear equation of the following n × n of solution can be passed through
Group calculates interpolating function
L2φ=0, s.t., φ (vi)=g (vi),i∈C, (8)
Wherein, C is the interpolation point set of scalar function g, and L is the discrete Laplacian Matrix of n × n, and element representation is as follows:
ω1=10.0 (9)
Wherein,Indicate cotangent average weight, αijWith two angles correspond to side (i,
J), AiFor vertex ViDimension promise area.
The convergence of iteration screening process is in order to judge whether be every time interior to accumulate mode letter by the obtained function of screening
Number IMF, it is determined that the convergence of screening process: for all vertex, step sizing result h twicejAnd hj-1Standard deviation it is small
In specific threshold, then just stopping screening, determine that current results are an IMF.The calculating of standard deviation such as following formula:
Wherein, SD indicates the standard deviation between adjacent signal value twice, hjAnd hj-1Indicate the adjacent letter iterated to calculate twice
Number value.
As one-dimensional EEMD decomposition, usual threshold value is only in [0.1,0.3] this section, and threshold value is smaller, IMFs's
Quantity is more, and vice versa.The preferred default threshold of the application is 0.1.
It is decomposed according to the EEMD that description above can be carried out model surface signal, decomposable process are as follows: setting is initial
Signal margin is the average curvature of triangle grid model, calculates the Local Extremum of current surplus every time, and to all extreme points
Interpolation is carried out, the average value of lower envelope is calculated, the result that current surplus subtracts average value is updated to new surplus, until before
The difference of surplus is less than defined threshold value or beyond until maximum number of iterations twice afterwards；In the process, adjacent surplus twice
Difference be different scale IMFs, last surplus be final signal margin.
Grid model reconstruct is carried out according to average curvature
It is several IMFs, Ke Yigen by the model surface signal decomposition based on average curvature based on above content
According to needing to adjust them, to obtain new signal.Proposed adoption of the present invention integrates minimum of the V as constraint condition using model original vertices
Square law realizes mesh reconstruction.This method is widely used for Laplce's field of surface treatment, following secondary by making
Energy minimum is calculated:
Above-mentioned energy equation can deform are as follows:
Obviously, corresponding system of linear equations AV '=b is
Wherein, L indicates discrete Laplacian Matrix；N indicates that the normal direction moment matrix on vertex, μ are original vertices position
It is 0.1, I that weight factor, which is default value of the present invention,n×nFor the unit matrix of n × n, s ' is the new signal of model surface, and V is original
Point set, the new vertex set after v ' reconstruct.The present invention can find out that EEMD decomposition can not only extract well model not from Fig. 2
With the geological information of scale, while if when filtering out high-level IMF information, moreover it is possible to play the role of smoothing model.
In step (2), the relevant demographic information of correlation model damaged area contiguous structure feature describe sub-definite with
And similitude patch is chosen, and is the geometric detail information and signal margin that model different scale is obtained by step (1), then
Mesh reconstruction is carried out to signal margin, obtains a smooth model, carries out the initial repairing of hole on this model.At this time
Model is the absence of the model of geometric detail information, needs the detailed information of Restoration model, and the present invention uses the side of similarity measurement
Method defines patch description, then searches the source patch most like with target patch description, and its geometric detail information is moved
It moves on target patch, to realize the reparation of geometric detail.
Contiguous structure feature relevant demographic information description in model damaged area passes through the heat on descriptive model surface
Change as the time spreads, to reflect the internal characteristics of grid vertex, so as to be used as description of apex feature.?
Moment t=0 gives unit a heat source x, heat kernel function ht(x, y) indicates moment t, and the total amount of heat of point y is traveled to from point x.If
Only consider the field of point x, heat kernel function will be deformed into ht(x,x).Therefore, the calorific value in different time time domain can provide one
The effective full range feature of kind, and the anisotropy information for describing to joined patch in subprocess is being constructed, it can preferably take
It is engaged in Model Matching.
A Riemann manifold M is given, the heat in moment t certain point is f (x, t), then the heat diffusion on M passes through as follows
The control of thermodynamics diffusion equation:
Wherein, T (x) is the initial temperature being defined on M, and Δ is Laplace-Beltrami operator.When manifold includes side
When boundary, borderline point is needed additionally to meet f (x, 0)=0,In addition after giving M, there are following equatioies:
Wherein, HTFor thermodynamics operator, htWhen (x, y) is considered as moment t, from the heat of point x to y transmitting.
Feature decomposition is carried out to thermonuclear, it can be deduced that contiguous structure feature relevant demographic information in model damaged area is retouched
State son:
Wherein, λ itAnd ΩiRespectively the corresponding characteristic value of anisotropy Laplace-Beltrami operator and with feature letter
Number, meets equation: Δ M Ωi=λ itΩi.From formula above it can easily be seen that anisotropy heat transfer relation reflects on model
The geometrical characteristic of a certain vertex different scale, while part and global geological information and partial structurtes are also reflected respectively to different
Property information.
Description sub-definite based on point is extended on patch by the definition of description, defines patch using statistical method
Description son:
Wherein, [0,1] indicates to be normalized to section [0,1].Description contains the heat transmitting on all vertex on patch
Relationship average value and variance, and in order to make description can be adapted for different models, select the description of three time domains
Son, that is to say, that corresponding three descriptions of each patch is respectively as follows: entire time domain, 3/4 time domain, 1/2 time domain.In the present invention
Time domainHeat transfer relation weight vectors of 100 time points of middle sampling as a point.
It calculates patch using the standard of Euclidean distance according to the description of definition and describes the distance between son, for each
Target patch selects k apart from nearest, most like source patch, as candidate patches.
Wherein, the default value of k is the 0.1% of vertex sum, from similar patch Candidate Set, needs to select most like benefit
Fourth carries out details migration.The matching error defined between patch is as follows:
Wherein, NTFor the patch number in target patch set T, S indicates source patch set, D (Ti,Sj) indicate target patch
TiWith source patch SjBetween, pass through the error after Rigid Registration, S (Ti) indicate target patch TiCorresponding similar source patch is candidate
Collection.It is to be noted that during Rigid Registration being closed by searching for the anisotropic thermal transmitting of the entire time domain of vertex correspondence
Most similar point is to as with punctual matching double points in set occurrence.
By finding the description of process to description sub-definite and similar patch above, similitude as shown in Figure 3 can be obtained
Matching result.In Fig. 3, the culminating point of patch is illustrated only, and correspond to target perforated with dash area in left figure,
Dash area is the corresponding Similarity matching region obtained by similitude matching primitives in right figure.From figure 3, it can be seen that fixed
The available good similitude matching result of description of justice.
The geometric detail of different scale level migrates and model full range editor is after searching out similar source patch, need by
Its geometric detail information transfer is to target patch.Method of the invention is had been described above in upper, does not need to replicate and paste source patch
Operation, but by means of EEMD decomposition algorithm carry out details migration.In step (1), EEMD decomposition has been done to model,
And geological information (IMFs) and signal margin under model different scale have been obtained, therefore it may only be necessary to by the IMFs of source patch
Then information transfer carries out resurfacing according to the new surface signal formed after migration, to realize geometry to target patch
The migration of details.Meanwhile during IMFs migration, by controlling the weight of each scale IMF, to realize full range boundary
Effect.The present invention will be described in detail the migration for how realizing geometric detail and full range editor.
The formula that EEMD is decomposed from step (1), the available EEMD being defined on target patch are decomposed:
Wherein, gTIndicate the function being defined on target patch, i.e. signal；T indicates target patch.It is obtained according to step (2)
The similitude matching result arrived, the IMFs of source patch is migrated to target patch, then will obtain being defined on model surface
New signal:
Wherein,For the new signal of formation, fk SFor the IMF information of similar source patch, ωkFor corresponding dimensional information
Weight.
It will be detailed below, using the method introduced in step (1) section, carrying out reconstructed mesh model according to new signal.But
During reconstruct, the dimension of Laplacian Matrix, IMFS and signal margin is consistent with model vertices number, before this
Through having carried out initial repairing to model, number of vertex has changed, the IMFs decomposed in step (1) by EEMD, more than signal
Amount and Laplacian Matrix needs reconfigure, and keep it consistent with "current" model.For the relevant information of model internal vertex,
It still remains unchanged, it is only necessary to which the information for increasing vertex correspondence newly to border vertices and hole repair reconfigures.
Define LNFor new Laplacian Matrix after initially repairing,For in matrix it is corresponding with model internal vertex at
Point,For ingredient corresponding with border vertices,For the ingredient for increasing vertex correspondence newly, there is following formula,
Construct new Laplacian MatrixFor initial Laplacian Matrix and model internal vertex pair
The ingredient answered.According to the signal of neotectonics, surface weight is carried out with the Laplce's energy minimization method introduced in step (1)
It builds, while the weight by changing IMF, to realize the editable effect of full range.Fig. 4 and Fig. 5 is illustrated from archetype to first
Begin repairing, then to geometric detail migration after as a result, wherein (a), (b), (c), (d) respectively indicating archetype, model hole
Smooth repairing, the reparation result after geometric detail migration are initially repaired in hole.Fig. 6 illustrates the effect of full range editor, wherein (a)
Indicate that initial model, (b)~(f) respectively indicate the corresponding weights omega of three IMF1,ω2, ω3Corresponding difference when taking different value
Repairing effect.
As shown in the table, it is shown that bunny model difference editor repairs result respective weights assignment situation.
| As a result weight | ω1 | ω2 | ω3 |
| b | 1.0 | 1.0 | 1.0 |
| c | 2.0 | 3.0 | 14.0 |
| d | 3.0 | 3.0 | 3.0 |
| e | 3.0 | 10.0 | 10.0 |
| f | 10.0 | 3.0 | 3.0 |
From the above table it can be clearly seen that b, c, d, five kinds of differences of e, f are repaired as a result, respectively corresponding different in Fig. 6
ω1,ω2, ω3Weight combination, is apparent from by adjusting weight size, can obtain diversified repairing effect, make triangle gridding mould
The reparation of type can be edited according to different demands.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (5)
1. a kind of geometrical model full range details restorative procedure, it is characterised in that: it include following implementation steps,
Step (1) geometrical model full range details catabolic phase, using average curvature as the adaptive decomposition of triangle grid model
Input signal decomposes this signal, obtains including the full range geometric detail letter for accumulateing mode function and signal margin in one group
Breath；
Step (2) Patch model Optimum Matching stage is based on model damaged area contiguous structure feature, in different time time domain
Anisotropy heat transfer relation weighted value determine full range feature carry out Model Matching；It is closed on by Definition Model damaged area
Relevant demographic information description of structure feature, describes son for anisotropy and describes the description that son extends to patch by vertex
Son, effectively search with the most matched similitude patch of target patch, and save matching result；
Step (3), geometry information transmitting and model full range repairing phase will be walked according to the matching result that step (2) obtains
Suddenly (1) obtains full range geometric detail information, is migrated by similitude patch to target patch；During migration, adjust different
The weight for accumulateing mode function in scale obtains different signals；The reconstruction for carrying out grid model for each signal respectively, obtains
Different geometric detail reparations are as a result, to make model editable.
2. according to geometrical model full range details restorative procedure described in patent requirements 1, it is characterised in that: in the step (1)
In, the adaptive decomposition input signal of triangle grid model is decomposed based on set empirical mode decomposition (EEMD)；
Function g:M → the R, M being defined on triangle grid model surface indicate that grid model, R indicate real number set,
Wherein, fkIt indicates k-th IMFs, k=1 ..., N, mode function sum, r is accumulate in N expressionNIt indicates more than corresponding signal
Amount；
Decomposable process is as follows,
Firstly, the definition of extreme point, for function g, if g (vi) meet: g (vi)≥g(vj), j ∈ N (i) or g (vi)≤g
(vj), j ∈ N (i) then claims viFor the maximum point or minimum point of g；
Secondly, defining according to the extreme point in upper step, extreme point is searched out, with extreme point structurally lower envelope, the solution of envelope
It is to use biharmonic interpolation calculation, it was minimum triangle gridding that biharmonic interpolation, which is extension of the spline interpolation in three-dimension curved surface,
Model potential manifold surface M on the energy function that defines realize,
∫M(ΔMφ)2dV.
Corresponding Lagrange's equation isWherein ΔMIt is the Laplace-Beltrami operator of curved surface M, specifically,
For given interpolation point and corresponding value { (vi,g(vi)), i ∈ C }, interpolating function φ=(φ (v1),φ(v2),...,
φ(vn)) can be acquired by solving following n × n linear system:
L2φ=0, s.t., φ (vi)=g (vi),i∈C,
Wherein, C is interpolation set, and L is n × n Laplacian Matrix for triangle grid model；
Finally, the convergence of iteration screening process, calculated and (deletes the word?) on after lower envelope, by envelope come really
Accumulate mode function in front of settled；The convergence of screening, which is exactly whether interior the signal after determining screening is, accumulates mode function；
End process is to see whether standard variance SD is less than given threshold value, and standard variance SD is using two adjacent the selection result meters
It calculates, standard variance SD formula is as follows,
3. according to geometrical model full range details restorative procedure described in patent requirements 1, it is characterised in that: in the step (2)
In, son is described by the relevant demographic information of Definition Model damaged area contiguous structure feature, to obtain the phase for being used for patch
Like property matching result；
After giving potential manifold surface M, there are following equatioies:
Wherein, HTFor thermodynamics operator, htWhen (x, y) regards moment t as, from the heat of point x to y transmitting；
Matching process is as follows,
Firstly, carrying out feature decomposition to thermonuclear, the relevant demographic information description of model damaged area contiguous structure feature is obtained
Son:
Wherein, λ itAnd ΩiRespectively one Marco Beltrami of Laplce (Laplace-Beltramioperator) operator is corresponding
Characteristic value and and characteristic function, meet equation DELTA M Ωi=λ itΩi, partial structurtes information is added to Laplacian Matrix structure
In building；
Secondly, according to the anisotropy heat transfer relation weighted value that vertex is calculated in previous step, Definition Model damaged area
Relevant demographic information description of contiguous structure feature is as follows,
Wherein, [0,1] indicates to be normalized to section [0,1], selects description of multiple time domains, i.e., each patch corresponds to multiple retouch
State son；In time domainAnisotropy heat transfer relation power of 100 time points of middle sampling as a point
Weight vector；
Finally, describing son according to the relevant demographic information of defined model damaged area contiguous structure feature, calculates and mend
Matching result between fourth is calculated patch and describes the distance between son, each target is mended using the standard of Euclidean distance
Fourth selects k apart from nearest, most like source patch, as candidate patches；
Define patch between matching error formula be,
Wherein, NTFor the patch number in target patch set T, D (Ti,Sj) indicate target patch TiWith source patch SjBetween by rigid
Property registration after error；
According to above formula, from candidate patches, the smallest patch of matching error is selected as matching result.
4. geometrical model full range details restorative procedure according to claim 1, it is characterised in that: in the step (3)
In, it is transferred to corresponding target patch by the way that mode function information will be accumulate in similitude patch, to realize the biography of geometric detail
It passs；Accumulate the weight of mode function by adjusting in different levels simultaneously with implementation model full range reparation；
The set empirical mode decomposition being defined on target patch decomposes equation,
Wherein, gTIndicate the function being defined on target patch, i.e. signal；T indicates target patch；
Including following implementation steps,
Firstly, accumulateing mode function information according to obtained in the matching result of step (2) and step (1), by source patch
Inside accumulate mode function to migrate to target patch, obtains the new signal for being defined on model surface；
Wherein,For the new signal of formation, fk STo accumulate mode function information, ω in similar source patchkFor corresponding scale letter
The weight of breath, rN TFor the signal margin of target patch；
Secondly, Laplacian Matrix reconfigures while previous step generates new signal, L is definedNAfter initially repairing
New Laplacian Matrix,For ingredient corresponding with model internal vertex in matrix,For ingredient corresponding with border vertices,For increase newly vertex correspondence ingredient, i.e.,The new Laplacian Matrix constructedFor original LaPlacian matrix ingredient corresponding with model internal vertex；
Finally, according to the signal of neotectonics and new Laplacian Matrix, the method that energy is minimized using Laplce, weight
Structure three-dimensional grid model obtains different repairing effects, that is, the editor of model by accumulateing the weight of mode function in adjusting
Effect.
5. according to geometrical model full range details restorative procedure described in patent requirements 2, it is characterised in that: the threshold value is 0.1.
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| CN110070096A (en) * | 2019-05-31 | 2019-07-30 | 中国科学院自动化研究所 | Sub- generation method and device are described for the matched local frequency domain of non-rigid shape |
| CN110363759A (en) * | 2019-07-22 | 2019-10-22 | 国家超级计算天津中心 | Three-dimensional mould tuning parameter determines method and device |
| CN110889893A (en) * | 2019-10-25 | 2020-03-17 | 中国科学院计算技术研究所 | Three-dimensional model representation method and system for expressing geometric details and complex topology |
| CN118003031A (en) * | 2024-04-09 | 2024-05-10 | 中国长江电力股份有限公司 | Self-adaptive machining method for material-adding repairing bearing bush |
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