CN102968818B - Geometrical and biomechanical hybrid hand muscle deformation method - Google Patents

Abstract

The invention provides a geometrical and biomechanical hybrid hand muscle deformation method. the method includes: gesture deformation prediction is performed on hand muscles from a geometrical aspect, for deformed gesture results, tendon distribution corresponding to a gesture is calculated from a biomechanical aspect, secondary deformation is performed on the deformed gesture and a calculated tendon by adopting an overlaying mode, and finally a more vivid effect is achieved. The method combines a geometrical method and knowledge of the field of biomechanics, achieves a data-driven unified deformation framework with geometrical and biomechanical characteristics, makes full use of simplicity of surface calculation and advantages of the biomechanics in simulation of human body muscle deformation, trains and learns muscle activation level at a pre-processing stage, and then performs corresponding prediction at a given novel geometric position.

Description

The hand muscle deformation method that a kind of geometry mixes with biomechanics

Technical field

The invention belongs to virtual reality technology and computer graphics techniques field, the specifically hand muscle deformation method that mixes with biomechanics of a kind of geometry, first from geometric aspects, posture deforming prediction is carried out to hand muscle, for distortion attitude result again from the angle calculation of biomechanics to should tendon distribution attitude, adopt the mode of superposition to carry out secondary deformation on distortion attitude and the tendon calculated, finally reach effect more true to nature.

Background technology

Staff is as one of the vitals of human body, its interior tissue runs far deeper than skin and bone, when hands movement, tendon and the muscle superficial skin of induced effect simultaneously that to move accordingly under skin surface forms certain visual effect, and these effects are being comprehensively mutually related with its concrete mode of motion and the various power suffered by inside.Such as, face shaping and the hand of the muscle on the back of the hand be how movement and to be applied in great power relevant.

Some biomechanics analogy methods in the past, it is the simulation that linear force or solid mechanics model all well can not be applicable to staff, because the motion of staff is relatively flexible, its multiple constraint condition adds the muscle tendon movement difficulty in simulation staff.

In linear force model, the surface of outermost layer parcel is used to the moving line of the muscle tendon being described in juxtra-articular approx, but these surfaces only have impact on kinematics and are not applied to the dynamic moving of muscle tendon.

In solid mechanics model, the 3 D deformation of muscle can be calculated fully, but it is often more difficult and also larger by the performance cost of its simulation distortion to build this class model.In addition, this attribute of meat fiber does not here embody intuitively.Generally speaking above method all can not the dynamic motion of muscle tendon under Simulation of Complex constraint, here we propose a kind of method based on chain muscle, can the coupled motions of effective simulate muscular tendon and bone when various different kinematic constraint.

Consider that Spline Model has the advantage of mass-spring model, and it is steady smooth (such as cubic B-spline in essence, it has two demi continuities on each tie point), current Spline Model is also used to cable, the simulation of yarn and muscle.In addition, based on the Muscle Simulation of Spline Model, effectively can add the constraints such as slip and enter.

There have been some papers to use the thin various phenomenon of physics chain microstructure modeling before, as document 1:Q IN, H., ANDT ERZ OP O UL O S, D.1996.D-NURBS:A Physics-Based Framework for Geometric Design.IEEETransactions on Visualization and Computer Graphics 2,1,85 – 96.Document 2:BERTAILS, F., AUDOLY, B., CANI, M.-P., Q UERLEUX, B., L EROY, F., ANDL ' EV QU E, J.-L.2006.Super-helices for pre-dicting the dynamics of natural hair.ACM Trans.Graph. (Proc.SIGGRAPH) 25, 3, 1180 – 1187. and the present invention extends the way of restraint and active mode, the modeling of the muscle parts of whole simulation just adopts the chain muscle model based on Spline Model, wherein come tendon under simulated skin top layer and muscle with batten, chain muscle is adopted also to be the anatomical structure that with reference to real musculature, because comprise meat fiber in muscle, meat fiber under stressing conditions can bend in space, meat fiber composition muscle package, the contraction that meat fiber is corresponding when muscle is activated, the power of shrinking also is transmitted along meat fiber, therefore chain muscle can more directly simulate this behavior.

The distortion of pure method of geometry, although have meticulous resurfacing ability and quick computing power, but geometry deformation is not owing to considering the biocomponents characteristics such as the muscle tendon of staff inside, lack the ability of the subcutaneous tendon motion of dynamic reconstruction, so the method that the present invention adopts geometry to mix with biomechanics is out of shape to simulate staff.

Summary of the invention

The technical problem to be solved in the present invention is: the deficiency overcoming existing pure geometry deformation technology, combine method of geometry and biomechanics domain knowledge, achieving one with data is the geometry of driving and the unified distortion framework of biomechanics characteristic, the simplicity that the surface making full use of geometry deformation calculates and the advantage of biomechanics in simulated humanbody muscle deformation, and provide the hand muscle deformation method that a kind of geometry mixes with biomechanics, it utilizes the thinking of secondary Superposed Deformation, convenient collocation different skin surface deformation algorithm, namely the process of muscle deformation simulation can independent of the distortion of skin surface.

The technical scheme that the present invention solves the problems of the technologies described above employing is: the hand muscle deformation method that a kind of geometry mixes with biomechanics, and its feature is that step is as follows:

After step (1), spatial digitizer obtain hand model, what obtain model by the method for tri patch cluster acts on behalf of bone;

Step (2), choose geometry reference mark by graphical interfaces, record geometry reference mark coordinate, the CCA algorithm of employing standard, off-line carries out maximum correlation analysis to the matrix acting on behalf of bone rotational transform and translation transformation obtained in geometry reference mark and step S101, namely the form that obtains is the correlation analysis form of AB=C, B is matrix corresponding to geometry reference mark, and C is the matrix of the correspondence acting on behalf of bone rotational transform and translation transformation, and A is maximal correlation matrix;

Step (3), given new reference mark predict corresponding hand distortion attitude;

The biocomponents of step (4), reference staff inside arranges the arrangement of initial tendon;

Step (5), use cubic B-spline are as the abstract mathematical model of muscle tendon, and pretreatment stage calculates the quality at all reference mark of all battens;

Step (6), each frame is calculated respectively to the gravity of spline control points, active force, by power and damping force, then calculate making a concerted effort of above four kinds of power;

Step (7), the spline control points calculated according to step (6) make a concerted effort to calculate acceleration, according to the speed of acceleration calculation spline control points, and then can calculate the position of present frame of spline control points;

Step (8), gone out by the position calculation of spline control points whole tendon locus distribution;

Step (9), based on step (3) hand distortion attitude and step (8) tendon locus distribution carry out last superposition to reach the secondary deformation of superficial skin.

In described step (1), the bone of acting on behalf of being obtained model by the method for tri patch cluster is specially: the tri patch according to triangle grid model each in sample rotates similarity, calculate the cost function of adjacent two tri patchs distortion, choose the diabolo that corresponding cost function value is minimum, be polymerized to a class, iteration like this, stops iteration after cost function meets threshold requirement, complete cluster process, namely a class is one and acts on behalf of bone.

In described step (3), given new reference mark predicts that corresponding hand distortion attitude can be specifically: new geometry reference mark is stored as linear vector form, and maximum correlation matrix in utilizing step (2), only need to carry out maximum correlation matrix and new geometry reference mark to be stored as linear vector multiplication and can to obtain acting on behalf of the new conversion of bone, and the coordinate after adopting SSD (the Subspace Skeleton Deformation) algorithm of standard to calculate triangle grid model vertex deformation.

In described step (4), the method of structure installation initial tendon arrangement is: with reference to the inner actual biological structure of staff to arrange tendon position, because by the mathematical model of cubic B-spline as tendon etc., so that is to say the initial distribution position that batten is set.

In described step (5), the method calculating the quality at reference mark is: for the cubic B-spline having n reference mark, first its long measureization is arrived s ∈ (0,1), then n-3 section is divided into, each section of correspondence four basis functions, calculate the mass matrix M of n × n, wherein M further according to the mutual relationship between basis function _ilcorresponding i-th reference mark and l reference mark.

The present invention's advantage is compared with prior art:

(1) method of geometry and biomechanics domain knowledge is combined, achieving one with data is the geometry of driving and unified distortion framework, the simplicity that the surface making full use of geometry deformation calculates and the advantage of biomechanics in simulated humanbody muscle deformation of biomechanics characteristic.

(2) with reference to the anatomical structure of real musculature, adopt chain Muscle Simulation staff muscle deformation, because chain muscle can the distortion of more direct simulate muscular fiber when stressed.And with the abstract mathematical model of cubic B-spline as chain muscle, avoiding the shortcoming of linear model effect less than muscle tendon dynamic moving, the calculation cost of simultaneously simulating distortion does not have the large of solid mechanics model yet, has taken into account both advantages simultaneously.

(3) provide a kind of thinking of secondary Superposed Deformation, convenient collocation different skin surface deformation algorithm, i.e. the process of muscle deformation simulation can independent of the distortion of skin surface.

Accompanying drawing explanation

Fig. 1 is the hand muscle deformation method process flow diagram that a kind of geometry of the present invention mixes with biomechanics.

Embodiment

Fig. 1 is algorithm flow chart of the present invention, and as shown in Figure 1, specific implementation step of the present invention is as follows:

Step S101, in step S101, initial sample is the triangle grid model set of the different attitude of same real-world object obtained by spatial digitizer, and the triangle grid model in set has identical number of vertex and topological structure, but geological information is different.Iterative initial state using each triangle as a class, and the cost function calculated between often pair of adjacent triangle, basis is the amplitude that adjacent triangle is out of shape between different model, two triangles amplitude of deformation between two different attitude modes is similar, then cost function value is little, otherwise then large.Each iteration, a minimum value is chosen from cost function value, it is a class that one diabolo of its correspondence gathers, until after minimum cost function value equals or exceeds threshold value, stop iteration, obtain all classes, a class is one and acts on behalf of bone, and calculates and eachly act on behalf of the rotational transform of bone and the matrix of translation transformation.

In step s 102, geometry reference mark is chosen by graphical interfaces, record geometry reference mark coordinate, CCA (the Canonical Correlation Analysis) algorithm of employing standard, off-line carries out maximum correlation analysis to the matrix acting on behalf of bone rotational transform and translation transformation obtained in geometry reference mark and step S101, namely the form that obtains is the correlation analysis form of AB=C, B is matrix corresponding to geometry reference mark, C is the matrix of the correspondence acting on behalf of bone rotational transform and translation transformation, and A is maximal correlation matrix.

In step s 103, giving a set of new geometry reference mark coordinate D in deformation process, by being multiplied with A, namely obtaining in deformation process, acting on behalf of the new conversion of bone, then adopt standard SSD method, new conversion is mixed, calculates the deformation coordinate on geometry summit.

In step S104, the method of structure installation initial tendon arrangement is: with reference to the inner actual biological structure of staff to arrange tendon position, because by the mathematical model of cubic B-spline as tendon etc., so that is to say the initial distribution position arranging batten, the invention provides an operation friendly, efficient visual editor realizes the work of initialization editor batten.The biocomponents with reference to staff inside is needed to set the arrangement of initial tendon, because the active force in deformation simulation process and being calculated relative to the tendon of initial frame by the deformation present frame tendon in power, so initial tendon position can directly have influence on after the result of calculation of each frame, also therefore need to carry out the setting of tendon initial placement with reference to the actual biological structure of staff, better close to actual staff.

In step S105, the method calculating the quality at reference mark is: for the cubic B-spline having n reference mark, first by its long measureization to s ∈ (0,1), one section, four reference mark, ns section altogether, M is the mass matrix of n × n, wherein M _ijthe element of corresponding i-th row and l row.The calculating of this Metzler matrix you can realize in the following way:

$M_{\mathrm{il}}=\underset{j\∈[0,\mathrm{ns}]}{\mathrm{\Σ}}\underset{0}{\overset{1}{\∫}}{p}_j\left(s\right)b_l^i\left(s\right)b_i^j\left(s\right)\mathrm{ds}$

Wherein j represents jth section, represent jth Duan Zhong l basis function.

With the abstract mathematical model of cubic B-spline as muscle tendon, mainly consider that Spline Model has the advantage of mass-spring model, and be steadily smooth in essence, chain muscle is built as mathematical model with it, also can better tendon under simulated skin top layer and muscle, spline control points quality is seeing, so just calculate the quality at all reference mark of all battens at pretreatment stage of not changing with simulation process.

In step s 106, force analysis is done to spline control points and can draw it altogether by the effect of four power, gravity respectively, active force, by power and damping force, so will calculate respectively its four power, wherein biomechanics is embodied in active force and by the calculating of power, and calculate the state of activation collection that active force needs first to calculate muscle, can as training sample after state of activation collection calculates, to predict the state of activation of the correspondence under new attitude, the calculating of damping force needs making a concerted effort based on above three.

About the method for making a concerted effort calculating spline control points be: muscle active force f is calculated respectively to spline control points _a, muscle is by power f _p, gravity f _gwith damping force f _ddeng four component, then obtain and make a concerted effort.For active force f _a, can be understood as linear activation level, matrix can be expressed as and seize the opportunity form f with vectorial _a=Aa, wherein a is a vector, represents muscle activation state set, and what an element in a was corresponding is the degree that one piece of muscle is bending in distortion, and data area is (0,1), and wherein 0 expression does not activate completely, and 1 expression activates completely.A is the activation transition matrix of (#DoF × #Muscles) dimension, and line number is DoF nodes, the corresponding muscle masses number of columns, using state of activation collection a as input, and the power in each dimension in each reference mark of o spline.F _acan adopt following account form:

$f_a=\left(f_0\mathrm{FV}\left(\stackrel{\·}{\mathrm{\ϵ}}\right)A_{\mathrm{CS}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{\∫}_0^1{\mathrm{FL}}_a\left(\mathrm{\ϵ}\right){b^{\′}}_i\frac{x^{\′}}{\left|\right|x^{\′}\left|\right|}\mathrm{ds}\right)a\⇐\⇒f_a=\mathrm{Aa}$

The computing method of state of activation collection a are by kinetics equation $M{\stackrel{\·}{q}}^{(k+1)}={M\stackrel{\·}{q}}^{\left(k\right)}+h(f_d+f_g+f_p+f_a)-G^T\mathrm{\λ}$ First be converted into KKT form, finally problem being converted into is that the least squares formalism of a belt restraining solves.KKT form is specific as follows:

$\left(\begin{array}{cc}M& G^T\\ G& 0\end{array}\right)\left(\begin{array}{c}{\mathrm{\φ}}^{(k+1)}\\ \mathrm{\λ}\end{array}\right)=\left(\begin{array}{c}{\mathrm{M\φ}}^{\left(k\right)}+\mathrm{hf}+\mathrm{hAa}\\ -\mathrm{\μg}+0\end{array}\right)\⇐\⇒\tilde{M}\widetilde{\mathrm{\φ}}=\tilde{f}+\tilde{A}a$

Wherein M is the quality that gross mass matrix contains all reference mark of batten and all rigid bodies, G is constraint matrix, and φ is the speed that speed queue contains all rigid bodies and spline control points, and h is time step, f is by comprising gravity, by power and damping force strong the making a concerted effort except active force.Wherein the constraint of constraint matrix G comprises surface restraint and constraint of sliding, and surface restraint formula is:

$\stackrel{\·}{g}={\stackrel{\→}{n}}^T(\stackrel{\·}{p}-{\stackrel{\·}{p}}_0),$ Sliding constraint formulations ${\stackrel{\·}{g}}_1={\stackrel{\→}{n}}_1^T(\stackrel{\·}{p}-{\stackrel{\·}{p}}_0),{\stackrel{\·}{g}}_2={\stackrel{\→}{n}}_2^T(\stackrel{\·}{p}-{\stackrel{\·}{p}}_0)$

The least squares equation of final belt restraining is as follows, solves this equation following and just can obtain state of activation collection a:

$\begin{array}{cccc}\underset{a}{\min }& w_a{a}^{T}a+w_x{\left|\right|H_{x}a-(v_x-v_f)\left|\right|}^2+w_d{(a-a^0)}^T(a-a^0)& s.t.& a\∈\left[\mathrm{0,1}\right]\end{array}$

For by power f _pthe correspondence of direct calculating by the FL function of power, and then calculates f further _p.Concrete mode is:

$\begin{array}{c}{f}_p=-\frac{\∂V}{{\∂q}_i}\\ =-A\underset{j=0}{\overset{n-4}{\mathrm{\Σ}}}{\∫}_0^1\frac{\∂}{{\∂q}_i}[\∫\mathrm{\σ}\left(\mathrm{\ϵ}\right)\mathrm{d\ϵ}]\left|\right|{p^{\′}}_0\left|\right|\mathrm{ds}\\ =-A\underset{j=0}{\overset{n-4}{\mathrm{\Σ}}}{\∫}_0^1\frac{\∂}{\∂\mathrm{\ϵ}}[\∫\mathrm{\σ}\left(\mathrm{\ϵ}\right)\mathrm{d\ϵ}]\frac{\∂\mathrm{\ϵ}}{{\∂q}_i}\left|\right|{p^{\′}}_0\left|\right|\mathrm{ds}\\ =-A\underset{j=0}{\overset{n-4}{\mathrm{\Σ}}}{\∫}_0^1\mathrm{\σ}\left(\mathrm{\ϵ}\right)\frac{\∂}{{\∂q}_i}\left(\frac{\left|\right|p^{\′}\left|\right|}{\left|\right|{p^{\′}}_0\left|\right|}\right)\left|\right|{p^{\′}}_0\left|\right|\mathrm{ds}\\ =-A\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{\∫}_0^1\mathrm{\σ}\left(\mathrm{\ϵ}\right){b^{\′}}_{i-j}\frac{p^{\′}}{\left|\right|p^{\′}\left|\right|}\mathrm{ds}\end{array}$

Wherein V is the gross energy of chain muscle, and computing formula is q _iit is the position at i-th reference mark.It is also spline deformation speed and stressed mapping function that σ (ε) is FV, and A is batten cross-sectional area in addition, can be considered as a constant.Gravity f _gcalculating carry out at pretreatment stage, because gravity is unaffected in deformation process.Gravity is specifically by obtaining as follows:

$f_g=-\underset{j\∈[0,\mathrm{ns}]}{\mathrm{\Σ}}\underset{0}{\overset{1}{\∫}}{p}_j(s,t)b_i^j\left(s\right)\mathrm{ds}$

Wherein p _jthe density that (s, t) is batten, can be considered as constant. for jth section i-th basis function of cubic B-spline.The occlusometer of last basis three power above calculates damping force f _das follows:

$f_d=-A\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{\∫}_0^1\frac{{b^{\′}}_{i-j}{b^{\′}}_{k-j}}{{\left|\right|p^{\′}\left|\right|}^2}[(\frac{{\mathrm{\σ}}^{\′}\left(\mathrm{\ϵ}\right)}{\left|\right|{p^{\′}}_0\left|\right|}-\frac{\mathrm{\σ}\left(\mathrm{\ϵ}\right)}{\left|\right|p^{\′}\left|\right|})p^{,}{p}^{,T}+f\left(\mathrm{\ϵ}\right)|\left|p^{\′}\right|\left|I\right]\mathrm{ds}$

In step s 107, the method calculating the reposition of present frame spline control points is: by the acceleration first calculating spline control points with joint efforts of step 6, then reference mark speed is calculated further, finally in conjunction with position and the current speed of previous frame, in regular hour step-length, the new position of present frame spline control points can be obtained.

In step S108, the method calculating the locus distribution of whole tendon is: according to the position of the batten spline control points of step 7, substitute into cubic B-spline formula finally can obtain the locus of whole batten, also namely calculate the reposition of present frame tendon.Four basis functions wherein in spline formula are:

b ₀(s)＝(-s ³+3s ²-3s+1)/6

b ₁(s)＝(3s ³-6s ²+4)/6

b ₂(s)＝(-3s ³+3s ²+3s+1)/6

b ₃(s)＝s ³/6

Wherein q _it () is the position of t i-th spline control points, b _is () is i-th spline base function, (i ∈ [0,3]).The coordinate (s ∈ [0,1]) that p (s, t) is the batten point on t s position.Owing to being that cubic B-spline all has four basis functions.Although can there be a reference mark (being at least 4) arbitrarily in batten, a concrete batten point is at most only by the impact at 4 reference mark.

$\stackrel{\·}{p}(s,t)\≡\frac{\mathrm{dp}}{\mathrm{dt}}=\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{b}_i\left(s\right){\stackrel{\·}{q}}_i\left(t\right)$

$p^{,}(s,t)\≡\frac{\∂p}{\∂s}=\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{b_i}^{\′}\left(s\right)q_i\left(t\right)$

The corresponding t of formula above, the speed of batten point p (s, t) of s position and tangent vector.Can be derived in t by spline formula, the expression-form being in the strain of s position batten point and strain rate is as follows:

$\mathrm{\ϵ}(s,t)\≡\underset{l\→0}{\lim }\frac{\mathrm{\δl}}{l}=\frac{\left|\right|p^{\′}(s,t)\left|\right|}{\left|\right|{p_0}^{\′}\left(s\right)\left|\right|}-1$

$\stackrel{\·}{\mathrm{\ϵ}}(s,t)\≡\underset{l\→0}{\lim }\frac{\mathrm{\δl}}{l}=\frac{\left|\right|{\stackrel{\·}{p}}^{\′}(s,t)\left|\right|}{\left|\right|{p_0}^{\′}\left(s\right)\left|\right|}$

Wherein p ₀' (s)=p ₀' (s, 0), the initial frame moment of t=0.ε (s) is the strain of the batten point of batten s position.

In step S109, final superficial skin secondary Superposed Deformation method is: step 3 and step 8 have obtained staff distortion attitude and the distribution of corresponding tendon respectively, point from its nearest tendon batten is calculated to all dough sheet points of current staff attitude mode, then the point of each tri patch in model is calculated to the point of the nearest tendon of its correspondence, calculate the weighing factor of each dough sheet point, decrement factor again, finally calculate the double offset amount that each dough sheet point is corresponding.Superposition algorithm is as follows:

d＝p _s-p _v

h＝max(d·n+c,0)

$f=\mathrm{aexp}\left(\frac{-{\left|\right|d-(d\·n)n\left|\right|}^2}{{2b}^2}\right)$

p _v＝p _v+(w·h·f)n

A weighing factor is provided, so that the degree of controlling distortion to each facilities network lattice point on skin.In each frame, the batten point nearest apart from the point on given skin is confirmable seeing, kdtree can be adopted to search for nearest batten point.Here n is to should the normal vector of skin points, and parameter a controls the height of skew, and parameter b is horizontal decay factor, and c controls the degrees of offset that it answers normal vector direction, the w i.e. weighing factor of this skin points.Therefore, each skin vertex does once corresponding double offset according to it to the distance from its nearest batten point along its normal direction, the degree of distortion can be controlled by factor of influence w, can finely tune deformation effect in addition by adjustment offset height and decay factor.In described step (9), last superposition is carried out to reach the secondary deformation of superficial skin based on the staff distortion attitude of step 3 and the tendon muscle distribution of step 8, this provide a kind of thinking of secondary Superposed Deformation, the skin surface deformation algorithm that convenient collocation is different, hand muscle deformation can to carry out effect integrated with given skin surface, i.e. the process of muscle deformation simulation can independent of the distortion of skin surface.

Claims (5)

1. the hand muscle deformation method that mixes with biomechanics of geometry, is characterized in that: the method step is as follows:

Step (1), obtain hand model by spatial digitizer after, what obtain model by the method for tri patch cluster acts on behalf of bone, and calculates each rotational transform and the translation transformation of acting on behalf of bone;

Step (2), choose geometry reference mark by graphical interfaces, record geometry reference mark coordinate, the CCA algorithm of employing standard, off-line carries out maximum correlation analysis to the matrix acting on behalf of bone rotational transform and translation transformation obtained in geometry reference mark and step (1), namely the form that obtains is the correlation analysis form of AB=C, B is matrix corresponding to geometry reference mark, and C is the matrix of the correspondence acting on behalf of bone rotational transform and translation transformation, and A is maximal correlation matrix;

Step (3), given new geometry reference mark predict corresponding hand distortion attitude;

The biocomponents of step (4), reference staff inside arranges the arrangement of initial tendon;

Step (5), use cubic B-spline are as the abstract mathematical model of muscle tendon, and pretreatment stage calculates the quality at all reference mark of all battens;

Step (6), each frame is calculated respectively to the gravity f of spline control points _g, muscle active force f _a, muscle is by power f _pand damping force f _d, then calculate making a concerted effort of above four kinds of power;

Gravity f _gaccount form as follows:

$f_g=-\underset{j\∈[0,\mathrm{ns}]}{\mathrm{\Σ}}\underset{0}{\overset{1}{\∫}}{p}_j(s,t)b_i^j\left(s\right)\mathrm{ds}$

Wherein p _jthe density that (s, t) is batten, can be considered as constant, for jth section i-th basis function of cubic B-spline, active force f _aaccount form as follows:

$f_a=\left(f_0\mathrm{FV}\left(\stackrel{\·}{\mathrm{\ϵ}}\right)A_{\mathrm{CS}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{\∫}_0^1{\mathrm{FL}}_a\left(\mathrm{\ϵ}\right){b^{\′}}_i\frac{x^{\′}}{\left|\right|x^{\′}\left|\right|}\mathrm{ds}\right)a\⇐\⇒f_a=\mathrm{Aa}$

Wherein A is the activation transition matrix of (#DoF × #Muscles) dimension, and line number is DoF nodes, row

The corresponding muscle masses number of number, using state of activation collection a as input, the power in each dimension in each reference mark of o spline, by power f _paccount form as follows:

$f_p=-\frac{\∂V}{\∂q_i}=-A\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{\∫}_0^1\mathrm{\σ}\left(\mathrm{\ϵ}\right){b^{\′}}_{i-j}\frac{p^{\′}}{\left|\right|p^{\′}\left|\right|}\mathrm{ds}$

Wherein V is the gross energy of chain muscle, and computing formula is q _ibe the position at i-th reference mark, it is also spline deformation speed and stressed mapping function that σ (ε) is FV, and A is batten cross-sectional area in addition, can be considered as a constant,

Damping force f _daccount form as follows:

$f_d=-A\underset{j=i-3}{\overset{i}{\mathrm{\Σ}}}{\∫}_0^1\frac{{b^{\′}}_{i-j}{b^{\′}}_{k-j}}{{\left|\right|p^{\′}\left|\right|}^2}[(\frac{{\mathrm{\σ}}^{\′}\left(\mathrm{\ϵ}\right)}{\left|\right|{p^{\′}}_0\left|\right|}-\frac{\mathrm{\σ}\left(\mathrm{\ϵ}\right)}{\left|\right|p^{\′}\left|\right|})p^{\′}{p}^{\′T}+f\left(\mathrm{\ϵ}\right)|\left|p^{\′}\right|\left|I\right]\mathrm{ds}$

Step (7), the spline control points calculated according to step (6) make a concerted effort to calculate acceleration, according to the speed of acceleration calculation spline control points, and then can calculate the position of present frame spline control points;

Step (8), gone out by the position calculation of spline control points whole tendon locus distribution;

Step (9), based on step (3) hand distortion attitude and step (8) tendon locus distribution carry out last superposition to reach the secondary deformation of superficial skin.

2. the hand muscle deformation method that mixes with biomechanics of geometry according to claim 1, it is characterized in that: in described step (1), the bone of acting on behalf of being obtained model by the method for tri patch cluster is specially: the tri patch according to triangle grid model each in sample rotates similarity, calculate the cost function of adjacent two tri patchs distortion, choose the diabolo that corresponding cost function value is minimum, be polymerized to a class, iteration like this, iteration is stopped after cost function meets threshold requirement, complete cluster process, namely a class is one and acts on behalf of bone.

3. the hand muscle deformation method that mixes with biomechanics of geometry according to claim 1, it is characterized in that: in described step (3), given new reference mark predicts that corresponding hand distortion attitude can be specifically: new geometry reference mark is stored as linear vector form, and maximum correlation matrix in utilizing step (2), only need to carry out maximum correlation matrix and new geometry reference mark to be stored as linear vector multiplication and can to obtain acting on behalf of the new conversion of bone, and the coordinate after adopting the SSD algorithm of standard to calculate triangle grid model vertex deformation.

4. the hand muscle deformation method that mixes with biomechanics of geometry according to claim 1, it is characterized in that: in described step (4), the method arranging the arrangement of initial tendon is: with reference to the inner actual biological structure of staff to arrange tendon position, because by the mathematical model of cubic B-spline as tendon etc., so that is to say the initial distribution position that batten is set.

5. the hand muscle deformation method that mixes with biomechanics of geometry according to claim 1, it is characterized in that: in described step (5), the method calculating the quality at reference mark is: for the cubic B-spline having n reference mark, first its long measureization is arrived s ∈ (0,1), n-3 section is then divided into, each section of correspondence four basis functions, the mass matrix M of n × n is calculated further, wherein M according to the mutual relationship between basis function _ilcorresponding i-th row l column element.