CN105261056A - Object deformation sequence completion method based on modal space subdivision strategy - Google Patents

Abstract

The invention provides an object deformation sequence completion method based on a modal space subdivision strategy. The method takes a key model for performing sparse sampling on a time axis as input to quickly complete the whole deformation sequence of the model. The method comprises: performing modal analysis for the key model; describing the deformation of object by taking the obtained modal as group of basis; and in the modal space of the model, utilizing a recursion subdivision strategy to iteratively generate intermediate models for the two continuous key models continuously, and taking the generated intermediate modes as the key models so as to generate more intermediate modes so as to achieve the aim for completing the whole deformation sequence. As the modal space cannot cover the local micro deformation of the models, the details are processed individually in addition. During the modal analysis process, the obtained modal is related with the data, and the deformation of the input models are preferably described; the model has certain physical reliability; the dimensions of data are greatly reduced; and the result is provided with an analytical expression so that real-time interaction can be realized.

Description

A kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy

Technical field

The present invention relates to a kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy, belong to Computer Animated Graph field.

Background technology

Along with the development of computer hardware technique, the acquisition of high-quality static model becomes more and more convenient.In the middle of the practical applications such as computer animation, usually utilize grid model to describe the action of personage, and require that it constantly changed along with the time, and be required to meet certain action constraint in the process of change, figure action is linked up, and wherein still there is a lot of technical matters in this.

First, the more common method of current use is physically-based deformation method, and it, by solving the constrained kinetics equation of band, drives object of which movement to meet the constraint of given key operations.But this method must ensure numerical stability and convergence, therefore need to solve complicated Equations of Mathematical Physics, and the method calculated amount of traditional implicit integration is very huge.And, if when model has different material distributions, this method will become more complicated and uncontrollable, mainly because the constitutive relation of model can be nonlinearities change along with the time.

Secondly, main method of geometry, by generating a curve by the higher-dimension of key model to achieve the goal at shape space, be similar to common curve, and namely key model is the key point of curve.This method realizes simple, is convenient to understand, and therefore gets a lot of applications.But the rationality of this method power shortage and physical reality, therefore can produce in some cases as self intersection or the factitious mistake such as excessively.And want to reach more real effect, just need more more intensive key models, and this is impossible often in actual applications.

Again, no matter be the method for physically based deformation or the method based on geometry, be all difficult to realize Real-time Feedback.On the one hand, the simplification of physical law is difficult to the accuracy ensureing modeling, and user is difficult to self-defined physics and is out of shape really.On the other hand, the method for simple curve be difficult to when user gets involved to ensure in model some characteristic.So need to develop a kind of new method, can get up by the method for physically based deformation with based on the methods combining of geometry.

In order to solve the problem, the invention provides a kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy, the method with the key model of sparse sampling on a timeline for input, can the whole Deformation Series of generation model fast.

Summary of the invention

The technical matters that the present invention solves is: the deficiency overcoming existing physically based deformation and the Deformation Series method of reducing based on geometry, provides a kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy.

The technical solution used in the present invention is: a kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy.Comprise the following steps:

Step (1), (key model is translated by key-model or key-frame of English and is come to calculate key model, represent in cartoon making, the model inputted by user, this be in field generally acknowledge call) linear normal modes: the key model of sparse sampling is input model first on a timeline, the surface mesh of input model is carried out volume mesh division, calculate the stiffness matrix of input model, input model is carried out to the feature decomposition of broad sense, obtain the body linear normal modes of input model, then the surface body linear normal modes obtained being mapped to input model obtains surface linear mode,

The Modal Space of step (2), key model is set up: the body linear normal modes obtained in step (1) is formed one group of orthonormal basis, utilize this group orthonormal basis by the Modal Space of the deformation space transforming of object to object, significantly reduce the dimension of expression and certain physics confidence level of maintenance simultaneously;

The segmentation of step (3), iteration solves mid-module: in the Modal Space that step (2) obtains, find two key models of arbitrary neighborhood, set up majorized function, solve and find mid-module, then mid-module is added to new key model, repeat this step, until the closeness of the input model sequence obtained meets the demands, thus reach the object of the whole Deformation Series of completion.

The process of the distortion details of step (4) is carried out again after described step (3), because Modal Space cannot cover the miniature deformation of model local, therefore the mid-module obtained in step (3) lost distortion details, need the position may with miniature deformation to split, separately distortion details is processed.

In described step (1), the surface mesh of input model is carried out tetrahedral grid division, adopt As-Rigid-As-Possible strain energy of distortion again, and the body linear normal modes of model is obtained using the gloomy matrix in the sea of energy as stiffness matrix, then body linear normal modes is mapped to model surface and obtains surface linear mode, to reduce computation complexity.

Orthonormal basis in described step (2) is obtained by the gloomy matrix in the sea of generalized singular value decomposition strain energy of distortion, and form projection matrix by this group orthonormal basis, solution room is reduced to hundreds of dimension by tens thousand of dimension, keeps physics confidence level simultaneously.

Iteration segmentation solution strategies in described step (3) is in Modal Space, and solve the mid-module of adjacent key model iteratively, its solution procedure is realized by optimization object function.

Separately distortion details is processed in described step (4), after iteration segmentation has solved, utilize existing shape interpolation technology, detail section is processed separately, disposal route: first utilize a kind of mesh segmentation method based on model analysis, input model is divided into multiple pieces, then those blocks with microdeformation are found out, then existing gridding interpolation technology is utilized to carry out interpolation to these fritters, obtain new deformation, thus complete the process of distortion details.

Principle of the present invention is: the invention provides a kind of deformation of body sequence complementing method based on Modal Space segmentation Strategy, the method with the key model of sparse sampling on a timeline for input, can the whole Deformation Series of generation model fast.First model analysis is carried out to key model, using the mode obtained as one group of base to describe the deformation of object.Then in the Modal Space obtained, take a kind of strategy of recursion, constantly the mid-module of grey iterative generation two continuous key models, and the mid-module generated is used as key model, to generate more mid-module, thus reach the object of the whole Deformation Series of completion.In model analysis process, institute's mode that obtains is associated with the data, and can describe the distortion of input model well, there is certain physics confidence level, significantly reduce again the dimension of data, and result has analytical expression, can realize Real-time Feedback simultaneously.Content of the present invention mainly includes following four aspects:

(1) model analysis of key model.Model analysis is a kind of method in modern age of research object structures characteristic, is the application of system identification method in Engineering Vibration field.In computer realm, model analysis is applied to the physical simulation of extensive deformable model, because in fact mode can be regarded as object being subject to a kind of tendentious response under External Force Acting, just can describe object distortion under external force by mode.Model analysis is applied to tetrahedral grid by the present invention, the second order of the energy be defined on volume mesh is utilized to lead the stiffness matrix replaced in kinetics equation, and generalized singular value decomposition is carried out to stiffness matrix obtain body linear normal modes, then body linear normal modes is mapped to again on the surface to reduce the summit quantity participating in calculating, reduces the complexity calculated.

(2) Modal Space iteration segmentation Strategy.Due to the characteristic of mode, the linear combination of the distortion of model with primary modal can be represented, so just the shape space of original tens thousand of dimension can being reduced in the Modal Space only having the even tens of dimension of hundreds of dimension, drastically increasing counting yield when not too damaging effect.Meanwhile, this just makes it possible to, in relatively little Modal Space, segment iteratively to input model sequence, constantly solves the mid-module of adjacent key model, thus reaches the object of the whole Deformation Series of quick completion.

(3) the solving of mid-module.In Modal Space, the deformation linear normal modes of object carries out linear expression, therefore an objective function can be built with these linear expressions, this objective function defines the difference of mid-module and two key models, a model is found by optimizing, it must meet almost identical with the difference of two key models and they with minimum, Here it is required mid-module.

(4) process of details distortion.Due to the introducing of model analysis, inevitably cause all dimension reduction methods all must faced by problem, that is exactly that linear normal modes cannot cover whole deformation space completely, especially for those high frequencies, the deformation of details, some areas that the mid-module therefore solved has microdeformation can have problems.So, after trying to achieve mid-module, also need to utilize existing interpolation technique again to process details.

The present invention's being a little compared with prior art:

(1) modal analysis method of the present invention's proposition, the second order of the energy that use is defined on volume mesh leads the stiffness matrix in alternate power equation, and generalized singular value decomposition is carried out to obtain linear normal modes to it, the second order due to energy is led has analytical expression, calculates simple efficient.

(2) linear normal modes that calculated by volume mesh of the present invention, can avoid the problem because kinetics equation linearization brings preferably, can avoid introducing the larger nonlinear analog-circuit of calculated amount.

(3) dimensionality reduction of model analysis of the present invention and the independent process of details, balance the performance of method and the quality of result well, can produce high-quality result high efficiency while.

(4) data are correlated with: the mode that the present invention obtains obtains according to the key model of input, depends on data, describe the internal characteristics of key model, can well the distortion of descriptive model.

5, physics is true: the present invention is the physical energy based on describing deformation of body, and the result obtained is all meet that physics is true and physics is believable.

6, Real-time Feedback: due to high efficiency realization, the present invention can also accomplish that user adjusts parameter, and is fed back in real time.

Accompanying drawing explanation

Fig. 1 is the deformation of body sequence complementing method process flow diagram based on Modal Space segmentation Strategy;

Fig. 2 be based on surface energy linear normal modes (on) and physical efficiency linear normal modes (under) contrast;

Fig. 3 is the schematic diagram carrying out iteration segmentation in Modal Space;

Fig. 4 is the schematic diagram finding mid-module in Modal Space;

Fig. 5 is the schematic diagram for the treatment of of details, and the left side is the result of model segmentation, and the right is the result with or without treatment of details;

Fig. 6 is the result that mid-module generates, and outermost end two models are input model, and middle is generation model;

Fig. 7 is the contrast of method of the present invention (right side) and simple linear interpolation method (left side);

Fig. 8 be method of the present invention (on) with a kind of contrast of existing method (under), wherein dashed rectangle is that details is amplified, the left side be the inventive method, the right be existing method.

Embodiment

Fig. 1 gives the overall process flow of the deformation of body sequence complementing method based on Modal Space segmentation Strategy, further illustrates the present invention below in conjunction with other the drawings and the specific embodiments.

The invention provides the deformation of body sequence complementing method based on Modal Space segmentation Strategy, key step is described below:

1, the model analysis of key model

After reading input model, be first that model analysis is carried out to model.First the model surface grid of input is carried out tetrahedral grid division, according to the strain energy of distortion be defined on model grid, the gloomy matrix in the sea of energy is utilized to carry out alternative stiffness matrix, it is carried out to the feature decomposition of broad sense, obtain the body linear normal modes of model, the surface then body linear normal modes being mapped to object obtains surface linear mode.

1) energy definition

The present invention adopts As-Rigid-As-Possible (ARAP) energy, and it is a kind of strain energy of distortion of classics, requires that, in the process of distortion, the local of object will keep rigid body characteristic as much as possible:

$E_P\left(u\right)=\underset{p_i\∈P}{\Σ}\underset{c_i}{\min }\underset{j\∈N_i}{\Σ}{w}_{ij}\left|\right|c_i\×(p_i-p_j)-u_i+u_j|{|}^2$

Wherein, P represents the vertex set of model, and u represents the deformation of model, N _irepresent the adjacent vertex quantity on i-th summit, c _i× (p _i-p _j) be around axle c _irotate || c _i|| the first approximation of the distortion of radian.Weight w _ijreflect the sampling density of grid, classical cosine weight can be used.The second derivative of this energy can obtain explicit expression formula by certain shifting onto, can easily calculate rapidly.

2) linear normal modes

Hypothesized model grid is the rope of a free vibration, and namely the mode of low frequency be cause the elastic energy of rope to change minimum deformation direction, and this phenomenon also exists in three-dimensional body.And this mode can obtain by solving following generalized eigenvalue problem:

Kφ＝λMφ

Wherein, eigenvalue λ _irepresent vibration frequency, because the λ in equation has multiple solution, so distinguish with subscript, proper vector φ _i, be namely mode of oscillation (k=1,2 ..., n), n is the summit quantity of model, namely aforementioned said linear normal modes, K, M are rigidity and the mass matrix of model respectively, and stiffness matrix is obtained by the second derivative of calculating strain energy of distortion here.Because energy is defined in tetrahedral grid, the linear normal modes obtained also is body, due to the support of inner structure, the mode occurring model inter collapse can be avoided to occur, as shown in Figure 2.Then part from the teeth outwards in a retention body mode, participates in the quantity on the summit calculated after can reducing like this, reduce the complexity calculated, and result remains unchanged.

2, Modal Space iteration segmentation Strategy

The linear normal modes obtained by above-mentioned steps can form one group of orthonormal basis, utilizes this group base that the deformation of object is projected to from spatial domain the object that frequency field (Modal Space) reaches dimensionality reduction.And in Modal Space, solve the mid-module of adjacent two key models iteratively, and using mid-module as new key model, so to iterate, finally generate level and smooth, a dense Deformation Series.

1) dimensionality reduction

In the deformation of body emulation of physically based deformation, displacement meet the following differential equation:

$M\stackrel{\·\·}{u}+D\stackrel{\·}{u}+Ku=f$

Wherein, M, D, K represent the quality of model, damping and stiffness matrix respectively, and f is the external force that object is subject to.Now the summit quantity of the dimension of this system to be 3n, n be model meshes, usually can reach tens thousand of, be unfavorable for calculating.R in above-mentioned formula is real number set, and the meaning is here u is the vector that 3n is.

The linear normal modes that therefore said process can be obtained as one group of base, and carries out linear expression by this group base to the deformation of object:

$x=\stackrel{\‾}{x}+\underset{i=1}{\overset{k}{\Σ}}{a}_i{\mathrm{\φ}}_i$

Wherein for reference model, be namely here key model, φ _ifor linear normal modes (said that namely proper vector is linear normal modes above, one is the name inside math equation, and one is the name in physical application), a _ifor the coefficient of its correspondence.Usually, that k linear normal modes only selecting character pair value minimum just enough expresses major part distortion (usual k<<3n) of a model.

2) iteration segmentation

More given sparse points in the planes, want generation one by smooth curve a little, the most direct method be exactly find iteratively two points intermediate point and ensure that the flexional of curve is minimum, Here it is traditional divided method.

The present invention by this application of policies in the Modal Space of model.Similarly, each key model is expressed as a point in Modal Space, find a continuous print Deformation Series just to become and ask for so high dimension curve, it is by each key point in Modal Space, ensure that the strain energy of distortion of model is minimum simultaneously, as shown in Figure 3, wherein V represents Modal Space for the point that key model is corresponding in Modal Space.

3, the solving of mid-module

1) definition of objective function

After selected two key models, in their respective Modal Spaces, choose an agent model x respectively ₁, x ₂, require them identical relative to the strain energy of distortion of respective key model, and these two models are as far as possible similar, as shown in Figure 4, d ₂describe agent model x ₁, x ₂between deformation difference, it drive two agent models draw close toward centre; d ₁, d ₃respectively describe agent model x ₁, x ₂with they respective key models between strain energy of distortion, they ensure that agent model can ensure respective shape in the process of drawing close to centre simultaneously.So objective function is defined as:

$\underset{a}{min}{d}_1+{\mathrm{\&mu;d}}_2+d_3$

Wherein a is two agent model linear expressions separately (coefficient that linear normal modes is corresponding), d here ₁, d ₃what adopt is that the method being similar to shell energy defines:

$d(\stackrel{\&OverBar;}{x},x)=\mathrm{\&alpha;}\underset{e\&Element;\mathrm{\&epsiv;}}{\&Sigma;}{({\stackrel{\&OverBar;}{l}}_e-l_e)}^2\frac{1}{{\stackrel{\&OverBar;}{l}}_e^2}+\mathrm{\&beta;}\underset{e\&Element;\mathrm{\&epsiv;}}{\&Sigma;}{({\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_e-{\mathrm{\&theta;}}_e)}^2\frac{{\stackrel{\&OverBar;}{l}}_e^2}{{\stackrel{\&OverBar;}{A}}_e}+\mathrm{\&gamma;}{(\stackrel{\&OverBar;}{v}-v)}^2\frac{1}{{\stackrel{\&OverBar;}{v}}^2}$

Wherein, l _ewhat represent is the a certain bar limit length of side of x, θ _erepresent corresponding dihedral angle, what v represented is the volume of x, represent in adjacent two the leg-of-mutton area sums of a certain bar limit e.

D ₂direct employing Euclidean distance defines:

d(x ₁,x ₂)＝||x ₁-x ₂|| ²

Majorized function is above the non-linear least square problem of a standard, and traditional gauss-newton method can be used to carry out iterative, greatly reduces, so solution efficiency is very high because model analysis will solve dimension.

Optimize and obtain two agent models final mid-module can be obtained by these two agent models average simply $X_{mid}=0.5*(x_1^{*}+x_2^{*}).$

2) process of details

Due to the introducing of model analysis, the efficiency of the calculating improved on the one hand, also inevitably brings a problem on the other hand: can not be covered by linear normal modes at the small deformation of model local, cause the mistake of net result.On the basis of therefore superincumbent result, also need to process details distortion.

First a kind of mesh segmentation method based on model analysis is utilized, input model is divided into multiple pieces, then find out those blocks with microdeformation and (usually all appear at the outshot of model, as water chestnut), then utilize existing gridding interpolation technology to carry out interpolation to these fritters, obtain new deformation.Because these blocks are smaller, the number of grid comprised is less, even if use existing method, also can calculate soon.Be illustrated in figure 5 the segmentation result (a) of grid and generate result (b) with or without the mid-module for the treatment of of details.

Fig. 6 is a complete segmentation result, and ragged edge two models are input model, and middle model is the result that method of the present invention generates, its deformation process nature, coherent.Fig. 7 is the contrast of a simple linear interpolation method and the inventive method, simple linear interpolation, can cause the pilot process distortion of being out of shape.Fig. 8 be the inventive method (on) with existing method (under) contrast, dashed rectangle is the amplification display of water chestnut part, the left side is method of the present invention, the right be existing method, can see that method of the present invention can keep the details in model deformation process well significantly.

The technology contents that the present invention does not elaborate belongs to the known technology of those skilled in the art.

Although be described the illustrative embodiment of the present invention above; so that the technician of this technology neck understands the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various change to limit and in the spirit and scope of the present invention determined, these changes are apparent, and all innovation and creation utilizing the present invention to conceive are all at the row of protection in appended claim.

Claims (6)

1., based on a deformation of body sequence complementing method for Modal Space segmentation Strategy, it is characterized in that comprising following four steps:

The linear normal modes of step (1), calculating key model: the key model of sparse sampling is input model first on a timeline, the surface mesh of input model is carried out volume mesh division, calculate the stiffness matrix of input model, input model is carried out to the feature decomposition of broad sense, obtain the body linear normal modes of input model, the surface then the body linear normal modes obtained being mapped to input model obtains linear normal modes;

The Modal Space of step (2), key model is set up: the body linear normal modes obtained in step (1) is formed one group of orthonormal basis, utilize this group orthonormal basis by the Modal Space of the deformation space transforming of object to object, significantly reduce the dimension of expression and certain physics confidence level of maintenance simultaneously;

The segmentation of step (3), iteration solves mid-module: in the Modal Space that step (2) obtains, find two key models of arbitrary neighborhood, set up majorized function, solve and find mid-module, then mid-module is added to new key model, repeat this step, until the closeness of the input model sequence obtained meets the demands, thus reach the object of the whole Deformation Series of completion.

2. the deformation of body sequence complementing method based on Modal Space segmentation Strategy according to claim 1, it is characterized in that: the process carrying out the distortion details of step (4) after described step (3) again, because Modal Space cannot cover the miniature deformation of model local, therefore the mid-module obtained in step (3) lost distortion details, need the position may with miniature deformation to split, separately distortion details is processed.

3. the deformation of body sequence complementing method based on Modal Space segmentation Strategy according to claim 1, it is characterized in that: in described step (1), the surface mesh of input model is carried out tetrahedral grid division, adopt As-Rigid-As-Possible strain energy of distortion again, and the body linear normal modes of model is obtained using the gloomy matrix in the sea of energy as stiffness matrix, then body linear normal modes is mapped to model surface and obtains surface linear mode, to reduce computation complexity.

4. the deformation of body sequence complementing method based on Modal Space segmentation Strategy according to claim 1, it is characterized in that: the orthonormal basis in described step (2) is obtained by the gloomy matrix in the sea of generalized singular value decomposition strain energy of distortion, and form projection matrix by this group orthonormal basis, solution room is reduced to hundreds of dimension by tens thousand of dimension, keeps physics confidence level simultaneously.

5. the deformation of body sequence complementing method based on Modal Space segmentation Strategy according to claim 1, it is characterized in that: the iteration segmentation solution strategies described in step (3) is in Modal Space, solve the mid-module of adjacent key model iteratively, its solution procedure is realized by optimization object function.

6. the deformation of body sequence complementing method based on Modal Space segmentation Strategy according to claim 2, it is characterized in that: separately distortion details is processed in described step (4), after iteration segmentation has solved, utilize existing shape interpolation technology, detail section is processed separately, disposal route: first utilize a kind of mesh segmentation method based on model analysis, input model is divided into multiple pieces, then those blocks with microdeformation are found out, then existing gridding interpolation technology is utilized to carry out interpolation to these fritters, obtain new deformation, thus complete the process of distortion details.