CN103914872A - Tree animation simulation method based on simplification modal analytical method - Google Patents

Abstract

The invention relates to a tree animation simulation method based on a simplification modal analytical method. According to the simulation method, modal analysis is carried out on independent leaves and leaf stalks but not on a whole tree, then a dynamical model of the broad leaves is combined, and a new dynamical model of the tree is set up through matrix transformation according to the hierarchical structure of the tree. The method comprises the specific steps: a dynamical model of a three-dimensional bending cantilever beam is set up, dynamical equations of the bending beam are respectively expressed as a time domain equation and a space domain equation by adopting a variable separation method, an air dynamical model is set up to determine the sum of the external force applied on branches, the dynamical model of the leaves is set up to solve the sum of the external force applied on blades, and a tree model and the dynamical model of the whole tree are set up. The tree animation simulation method can be used for developing three-dimensional tree animation simulation engines, serves as a support for development of virtual reality, game and three-dimensional animation core technologies, and has the important application prospect.

Description

A kind of tree animation simulation method based on simplifying modal analysis method

Technical field

The present invention relates to field of Computer Graphics, relate in particular to a kind of tree animation simulation method based on simplifying modal analysis method.

Background technology

Tree animation simulation technology based on the computer graphics value that has a wide range of applications in fields such as three-dimensional animation, video display special efficacy, battlefield virtual reality, landscape design and agriculture and forestry informationizations.In three-dimensional animation and video display special efficacy, introducing dynamic tree model can greatly increase the sense of reality of scene; In the reality environment of battlefield, the dynamic model of tree is applied in military simulated training, can strengthen the feeling of immersion of simulation; At landscape architecture and architecture field, can be landscape design and Environmental Decision-making supports; In IT application to agriculture field, the tree animation that generates by computing machine can intuitively represent the complex model in agri-scientific research work to layman, also can be agricultural extension and agricultural education provides effective means.

Existing investigative technique is broadly divided into three types: " based on the simulation of physics ", " based on the simulation of process " and " based on the simulation of data-driven ".

Wherein, " based on the analogue technique of physics " mainly adopts modal analysis method to solve the kinetics equation of tree, can embody the Li Saru curve of branch motion, but exist solving complexity high, ignore high frequency vibrating dynamic model and cause the problem of the aspect such as details motion loss of leaf and sprig part; " based on the analogue technique of process " reckons without influencing each other of moving between the branch under generalized coordinate, for branch independently, motion can not truly show the dynamics of branch motion, the Li Saru curve of branch motion cannot be embodied, and the Interactive control to tree can not be realized.The animation that " based on the analogue technique of data-driven " generates is confined to specific input data, fails to carry out effective combination with " based on the analogue technique of physics " and " based on the analogue technique of process ".

In view of above-mentioned defect, creator of the present invention has obtained this creation finally through long research and practice.

Summary of the invention

The object of the present invention is to provide a kind of tree animation simulation method based on simplifying modal analysis method, in order to overcome above-mentioned technological deficiency.

For achieving the above object, the invention provides a kind of tree animation simulation method based on simplifying modal analysis method,

By to independent leaf and petiole but not whole tree carries out model analysis, then in conjunction with the kinetic model of broad-leaved, and set up new tree kinetic model according to the hierarchical structure relation of tree by matrixing; This detailed process is:

Step a, sets up the kinetic model of three-dimensional bending semi-girder, domain equation and spatial domain equation when the kinetics equation of curved beam adopts separation of variables to be expressed as;

Step b, sets up Aerodynamics Model, determines the suffered external force sum of branch;

Step c, sets up the kinetic model of leaf, solves the external force sum acting on blade;

Steps d, sets up the kinetic model of tree-model and whole tree.

Further, the process of above-mentioned steps a is:

Step a1, supposes that curved beam is by joint P ₀, P ₁..., P _nbe formed by connecting, and be subject to External Force Acting L (t) under local coordinate (u, v, w);

Step a2, adopts three mode of vibration that are dominant to represent to every branch, determines three time domain equations that the mode of vibration that is dominant is corresponding;

Step a3, is converted into three static balancing power L ' by three of the every branch mode of vibration displacements that are dominant _u(t), L ' _vand L ' (t) _w(t);

${L^{\′}}_u\left(t\right)={4\mathrm{\π}}^2{f}_u^2{q}_u\left(t\right)$

${L^{\′}}_v\left(t\right)={4\mathrm{\π}}^2{f}_v^2{q}_v\left(t\right)$

${L^{\′}}_w\left(t\right)={4\mathrm{\π}}^2{f}_w^2{q}_w\left(t\right)$

In formula, f _u, f _v, f _wcorresponding every branch adopts the free-running frequency of three mode of vibration that are dominant respectively; _u(t), q _vand q (t) _w(t) represent that every branch adopts the displacement of three mode of vibration that are dominant;

Step a4, utilize static balancing power F (t)=(L ' _u(t), L ' _v(t), L ' _w(t)) solve the spatial domain equation of above-mentioned three mode of vibration that are dominant, solve curved beam static balancing position under external force.

Further, the time domain equation of above-mentioned steps a2 is:

${\stackrel{\·\·}{q}}_u\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_u{f}_u{\stackrel{\·}{q}}_u\left(t\right)+{4\mathrm{\π}}^2{f}_u^2{q}_u\left(t\right)=\left|L_w\left(t\right)\right|/m$

${\stackrel{\·\·}{q}}_v\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_v{f}_v{\stackrel{\·}{q}}_v\left(t\right)+{4\mathrm{\π}}^2{f}_v^2{q}_v\left(t\right)=r\left|L_w\left(t\right)\right|/m,r=u\·P_0{P}_n$

${\stackrel{\·\·}{q}}_w\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_w{f}_w{\stackrel{\·}{q}}_w\left(t\right)+{4\mathrm{\π}}^2{f}_w^2{q}_w\left(t\right)=\left|L_u\left(t\right)\right|/m$

In formula, f _u, f _v, f _wand ζ _u, ζ _v, ζ _wcorresponding every branch adopts free-running frequency and the ratio of damping of three mode of vibration that are dominant respectively; _u(t), q _vand q (t) _w(t) represent that every branch adopts the displacement of three mode of vibration that are dominant.

Further, in above-mentioned steps a4, while solving static balancing position,

According to moment of flexure and elasticity coefficient k _ibetween proportionate relationship can try to achieve bending angle

$k_i={\mathrm{EI}}_{\max }{[1-(1-\frac{D_t}{D_r})\frac{i+1}{n}]}^3$

In formula, F _i(t) be that static balancing power F (t) mean allocation is to sections P _ip _i+1on power, EI _maxbe the maximum elastance that user sets, Dt and Dr represent respectively cylindricality branch end face and bottom surface diameter.

Further, in above-mentioned steps b,

Suppose that branch is the skeleton of the normal vector supporting plane that is n, the wind velocity vector acting in this plane is v _wind, tangent vector t=v _wind× n, along normal vector n and vector n × t Directional Decomposition v _windcan obtain v _y, v _xz; Vector v _windand v _xzangle be angle of attack θ,

Based on aerodynamics, act on the pulling force v on this branch _dragwith lift v _liftcan be expressed as:

v _drag=0.5c _d(θ)ρv _wind

$v_{\mathrm{lift}}=0.5c_l\left(\mathrm{\θ}\right)\mathrm{\ρ}\left|\right|v_{\mathrm{wind}}\left|\right|\frac{t\×v_{\mathrm{wind}}}{\left|\right|t\×v_{\mathrm{wind}}\left|\right|}$

In formula, c _d(θ) and c _l(θ) be tension coefficient and lift coefficient, ρ is atmospheric density,

The suffered external force sum of branch can be expressed as L (t)=v _drag(t)+v _lift(t)+G, G is gravity.

Further, in the process of above-mentioned steps c be:

Step c1 sets up kinetic model under leaf local coordinate;

Suppose that blade is the curved surface that comprises vein and leaf film, sets up following kinetic model under leaf local coordinate:

$\frac{\∂}{\∂t}\left(\mathrm{\μ}\left(a\right)\frac{\∂r(a,t)}{\∂t}\right)+\mathrm{\γ}\left(a\right)\frac{\∂r(a,t)}{\∂t}+\frac{\∂\mathrm{\ϵ}\left(r(a,t)\right)}{\∂r(a,t)}=f\left(r(a,t)\right)$

Wherein, r (a, t) be the position of node a at moment t, the mass density that μ (a) is node a place, γ (a) is the damping density at node a place, ε (r) is the potential energy of blade deformation, and f (r, t) is for acting on the external force sum on blade;

Step c2, sets up the potential energy formula of blade deformation.

Further, above-mentioned steps c2, for the distortion of curved surface, the potential energy of blade deformation intends adopting formula:

$\mathrm{\ϵ}\left(r(a,t)\right)={\∫}_{\mathrm{\Ω}}{\left|\right|G-G^0\left|\right|}_{\mathrm{\α}}^2+{\left|\right|B-B^0\left|\right|}_{\mathrm{\β}}^2{\mathrm{da}}_1{\mathrm{da}}_2$

Wherein, G and B represent respectively elasticity energy (stretching energy) and bending energy (bending energy), G ⁰and B ⁰represent elasticity energy and bending energy under original state.

Further, in above-mentioned steps d, also comprise,

Step e, sets up wind-field model; The present invention, for setting up dimensional wind model, adopts following frequency spectrum function (1/f ^βnoise function) set up wind-field model:

$S(\mathrm{\β},f_1,f_2,...,f_n)=\frac{1}{{\sqrt{f_1^2+f_2^2+...+f_n^2}}^{(\mathrm{\β}+n-1)/2}}$

Wherein n is wind field dimension, and β represents the unordered degree of wind field, f _irepresent the frequency of i dimension, a complete wind-field model need comprise four-dimensional information, for further simplified model, formula is carried out after invert fast fourier transformation (IFFT), adopt Taylor's wind field freezing technology three-dimensional matrice information can be converted into four-dimensional wind field information w (x, y, z, t).

Beneficial effect of the present invention is compared with prior art: the present invention is based on the tree animation simulation method of simplifying modal analysis method,

(1) can embody the Li Saru curve that needs " based on the analogue technique of physics " the real world branches and leaves that could show to move;

(2) simplify modal analysis method and be only applied to independent branches and leaves part, and the motion simulation of whole tree is adopted to " based on the analogue technique of process ", therefore calculate real-time high, can avoid " based on the analogue technique of physics " problem that solving complexity is high;

(3) compared with " based on the analogue technique of data-driven ", the method does not rely on particular data, while consider free-running frequency and the ratio of damping of tree, can generate alternately Various Seasonal, different large small-scale tree animation.

The present invention is based on and simplify the tree animation simulation method of modal analysis method and also can be the plant animation that research has complex branches structure new method is provided, simultaneously, the present invention can be applicable to develop three-dimensional tree dynamic simulated engine, support for the exploitation of virtual reality, game, three-dimensional animation core technology, there is important application prospect.

Brief description of the drawings

Fig. 1 is the process flow diagram that the present invention is based on the tree animation simulation method of simplifying modal analysis method;

Fig. 2 is the schematic diagram of three mode of vibration that are dominant of bent beam of the present invention;

Fig. 3 is the model schematic diagram solving of static balancing of the present invention position;

Fig. 4 is the Aerodynamics Model schematic diagram of branch of the present invention;

Fig. 5 is blade node and the link information schematic diagram after triangularization of the present invention;

Fig. 6 is tree-model of the present invention and hierarchical structure schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, technical characterictic and the advantage with other above-mentioned to the present invention are described in more detail.

The present invention is based on the tree animation simulation method of simplifying modal analysis method, by to independent leaf and petiole but not whole tree carries out model analysis, then set up new tree kinetic model in conjunction with the kinetic model of broad-leaved, and according to the hierarchical structure relation of tree by matrixing.

Refer to shown in Fig. 1, it is the process flow diagram that the present invention is based on the tree animation simulation method of simplifying modal analysis method, and this detailed process is:

Step a, sets up the kinetic model of three-dimensional bending semi-girder; According to the thought of modal analysis method, domain equation and spatial domain equation when the kinetics equation of curved beam adopts separation of variables to be expressed as.

Step a1, supposes that curved beam is by joint P ₀, P ₁..., P _nbe formed by connecting, and be subject to External Force Acting L (t) under local coordinate (u, v, w); Refer to shown in Fig. 2 the schematic diagram of its three mode of vibration that are dominant that are bent beam of the present invention.

Step a2, adopts three mode of vibration that are dominant to represent to every branch, determines three time domain equations that the mode of vibration that is dominant is corresponding.

In the present embodiment time, domain equation is respectively shown in following (1)-(3),

${\stackrel{\·\·}{q}}_u\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_u{f}_u{\stackrel{\·}{q}}_u\left(t\right)+{4\mathrm{\π}}^2{f}_u^2{q}_u\left(t\right)=\left|L_w\left(t\right)\right|/m---\left(1\right)$

${\stackrel{\·\·}{q}}_v\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_v{f}_v{\stackrel{\·}{q}}_v\left(t\right)+{4\mathrm{\π}}^2{f}_v^2{q}_v\left(t\right)=r\left|L_w\left(t\right)\right|/m,r=u\·P_0{P}_n---\left(2\right)$

${\stackrel{\·\·}{q}}_w\left(t\right)+4\mathrm{\π}{\mathrm{\ζ}}_w{f}_w{\stackrel{\·}{q}}_w\left(t\right)+{4\mathrm{\π}}^2{f}_w^2{q}_w\left(t\right)=\left|L_u\left(t\right)\right|/m---\left(3\right)$

In formula, f _u, f _v, f _wand ζ _u, ζ _v, ζ _wcorresponding every branch adopts free-running frequency and the ratio of damping of three mode of vibration that are dominant respectively; _u(t), q _vand q (t) _w(t) represent that every branch adopts the displacement of three mode of vibration that are dominant.

Step a3, is converted into three static balancing power L ' by three of the every branch mode of vibration displacements that are dominant _u(t), L ' _vand L ' (t) _w(t);

${L^{\′}}_u\left(t\right)={4\mathrm{\π}}^2{f}_u^2{q}_u\left(t\right)$

${L^{\′}}_v\left(t\right)={4\mathrm{\π}}^2{f}_v^2{q}_v\left(t\right)---\left(4\right)$

${L^{\′}}_w\left(t\right)={4\mathrm{\π}}^2{f}_w^2{q}_w\left(t\right)$

Step a4, utilize static balancing power F (t)=(L ' _u(t), L ' _v(t), L ' _w(t)) solve the spatial domain equation of above-mentioned three mode of vibration that are dominant, solve curved beam static balancing position under external force.

Refer to shown in Fig. 3 its model schematic diagram solving that is static balancing of the present invention position; In the time solving the equipoise of bent beam,

According to moment of flexure and elasticity coefficient k _ibetween proportionate relationship can try to achieve bending angle

$k_i={\mathrm{EI}}_{\max }{[1-(1-\frac{D_t}{D_r})\frac{i+1}{n}]}^3---\left(6\right)$

In formula, F _i(t) be that static balancing power F (t) mean allocation is to sections P _ip _i+1on power, EI _maxbe the maximum elastance that user sets, Dt and Dr represent respectively cylindricality branch end face and bottom surface diameter.

Step b, sets up Aerodynamics Model, determines the suffered external force sum of branch; Refer to shown in Fig. 4, its Aerodynamics Model schematic diagram that is branch of the present invention,

Suppose that branch is the skeleton of the normal vector supporting plane that is n, the wind velocity vector acting in this plane is v _wind, tangent vector t=v _wind× n, along normal vector n and vector n × t Directional Decomposition v _windcan obtain v _y, v _xz; Vector v _windand v _xzangle be angle of attack θ.

Based on aerodynamics, act on the pulling force v on this branch _dragwith lift v _liftcan be expressed as:

v _drag=0.5c _d(θ)ρv _wind

$v_{\mathrm{lift}}=0.5c_l\left(\mathrm{\θ}\right)\mathrm{\ρ}\left|\right|v_{\mathrm{wind}}\left|\right|\frac{t\×v_{\mathrm{wind}}}{\left|\right|t\×v_{\mathrm{wind}}\left|\right|}---\left(7\right)$

In formula, c _d(θ) and c _l(θ) be tension coefficient and lift coefficient, ρ is atmospheric density.

The suffered external force sum of branch can be expressed as L (t)=v _drag(t)+v _lift(t)+G, G is gravity.

Step c, sets up the kinetic model of leaf, solves the external force sum acting on blade; Refer to shown in Fig. 5, it is blade node and link information schematic diagram after triangularization of the present invention;

Step c1 sets up kinetic model under leaf local coordinate;

Suppose that blade is the curved surface that comprises vein and leaf film, sets up following kinetic model under leaf local coordinate:

$\frac{\∂}{\∂t}\left(\mathrm{\μ}\left(a\right)\frac{\∂r(a,t)}{\∂t}\right)+\mathrm{\γ}\left(a\right)\frac{\∂r(a,t)}{\∂t}+\frac{\∂\mathrm{\ϵ}\left(r(a,t)\right)}{\∂r(a,t)}=f\left(r(a,t)\right)---\left(8\right)$

Wherein, r (a, t) be the position of node a at moment t, the mass density that μ (a) is node a place, γ (a) is the damping density at node a place, ε (r) is the potential energy of blade deformation, and f (r, t) is for acting on the external force sum on blade.

Step c2, sets up the potential energy formula of blade deformation;

For the distortion of curved surface, the potential energy of blade deformation intends adopting formula:

$\mathrm{\ϵ}\left(r(a,t)\right)={\∫}_{\mathrm{\Ω}}{\left|\right|G-G^0\left|\right|}_{\mathrm{\α}}^2+{\left|\right|B-B^0\left|\right|}_{\mathrm{\β}}^2{\mathrm{da}}_1{\mathrm{da}}_2---\left(9\right)$

Wherein, G and B represent respectively elasticity energy (stretching energy) and bending energy (bending energy), G ⁰and B ⁰represent elasticity energy and bending energy under original state.

Vein is harder than leaf film as skeleton, and in formula (9), corresponding vein summit can arrange larger counter-bending coefficient and stretch-proof coefficient.Consider aerodynamic impact, the suffered external force f of blade (r, t) can adopt formula (7) to calculate.

Step c3, adopts method of conjugate gradient to solve formula (8) and (9), solves the external force sum that acts on blade and the potential energy of blade deformation.

Steps d, sets up the kinetic model of tree-model and whole tree; Refer to shown in Fig. 6, it is tree-model of the present invention and hierarchical structure schematic diagram; For ease of building the kinetic model of whole tree, the tree geometric model of reconstruction all has hierarchical structure clearly.

From trunk to branch, successively time carry out matrixing to leaf again, and in conjunction with the transformation law between local coordinate and world coordinates, make branch at all levels and leaf can embody the independence of its motion, can embody again the globality of its motion, set up the kinetic model of whole tree.

This model and the method based on physics will be set as a bulk treatment different, but adopt pure mechanics method to simulate the motion of independent branch and leaf part, be a kind of brand-new tree dynamics simulation technology.

Step e, sets up wind-field model; The present invention, for setting up dimensional wind model, adopts following frequency spectrum function (1/f ^βnoise function) set up wind-field model:

$S(\mathrm{\β},f_1,f_2,...,f_n)=\frac{1}{{\sqrt{f_1^2+f_2^2+...+f_n^2}}^{(\mathrm{\β}+n-1)/2}}---\left(10\right)$

Wherein n is wind field dimension, and β represents the unordered degree of wind field, f _irepresent the frequency of i dimension.A complete wind-field model need comprise four-dimensional information, for further simplified model, formula (10) is carried out after invert fast fourier transformation (IFFT), adopt Taylor's wind field freezing technology three-dimensional matrice information can be converted into four-dimensional wind field information w (x, y, z, t).

The present invention is based on the tree animation simulation method of simplifying modal analysis method,

(1) can embody the Li Saru curve that needs " based on the analogue technique of physics " the real world branches and leaves that could show to move;

(2) simplify modal analysis method and be only applied to independent branches and leaves part, and the motion simulation of whole tree is adopted to " based on the analogue technique of process ", therefore calculate real-time high, can avoid " based on the analogue technique of physics " problem that solving complexity is high;

(3) compared with " based on the analogue technique of data-driven ", the method does not rely on particular data, while consider free-running frequency and the ratio of damping of tree, can generate alternately Various Seasonal, different large small-scale tree animation.

The present invention is based on and simplify the tree animation simulation method of modal analysis method and can be the plant animation that research has complex branches structure new method is provided, simultaneously, the present invention can be applicable to develop three-dimensional tree dynamic simulated engine, support for the exploitation of virtual reality, game, three-dimensional animation core technology, there is important application prospect.

The foregoing is only preferred embodiment of the present invention, is only illustrative for invention, and nonrestrictive.Those skilled in the art is understood, and in the spirit and scope that limit, can carry out many changes to it in invention claim, amendment, and even equivalence, but all will fall within the scope of protection of the present invention.

Claims (8)

1. the tree animation simulation method based on simplifying modal analysis method, it is characterized in that, by to independent leaf and petiole but not whole tree carries out model analysis, then in conjunction with the kinetic model of broad-leaved, and set up new tree kinetic model according to the hierarchical structure relation of tree by matrixing; This detailed process is:

Step a, sets up the kinetic model of three-dimensional bending semi-girder, domain equation and spatial domain equation when the kinetics equation of curved beam adopts separation of variables to be expressed as;

Step b, sets up Aerodynamics Model, determines the suffered external force sum of branch;

Step c, sets up the kinetic model of leaf, solves the external force sum acting on blade;

Steps d, sets up the kinetic model of tree-model and whole tree.

2. the tree animation simulation method based on simplifying modal analysis method according to claim 1, is characterized in that, the process of above-mentioned steps a is:

Step a1, supposes that curved beam is by joint P ₀, P ₁..., P _nbe formed by connecting, and be subject to External Force Acting L (t) under local coordinate (u, v, w);

Step a2, adopts three mode of vibration that are dominant to represent to every branch, determines three time domain equations that the mode of vibration that is dominant is corresponding;

Step a3, is converted into three static balancing power L ' by three of the every branch mode of vibration displacements that are dominant _u(t), L ' _vand L ' (t) _w(t);

In formula, f _u, f _v, f _wcorresponding every branch adopts the free-running frequency of three mode of vibration that are dominant respectively; _u(t), q _vand q (t) _w(t) represent that every branch adopts the displacement of three mode of vibration that are dominant;

Step a4, utilize static balancing power F (t)=(L ' _u(t), L ' _v(t), L ' _w(t)) solve the spatial domain equation of above-mentioned three mode of vibration that are dominant, solve curved beam static balancing position under external force.

3. the tree animation simulation method based on simplifying modal analysis method according to claim 2, is characterized in that, the time domain equation of above-mentioned steps a2 is:

In formula, f _u, f _v, f _wand ζ _u, ζ _v, ζ _wcorresponding every branch adopts free-running frequency and the ratio of damping of three mode of vibration that are dominant respectively; U (t), q _vand q (t) _w(t) represent that every branch adopts the displacement of three mode of vibration that are dominant.

4. according to the tree animation simulation method based on simplifying modal analysis method described in claim 2 or 3, it is characterized in that, in above-mentioned steps a4, while solving static balancing position,

According to moment of flexure and elasticity coefficient k _ibetween proportionate relationship can try to achieve bending angle

In formula, F _i(t) be that static balancing power F (t) mean allocation is to sections P _ip _i+1on power, EI _maxbe the maximum elastance that user sets, Dt and Dr represent respectively cylindricality branch end face and bottom surface diameter.

5. the tree animation simulation method based on simplifying modal analysis method according to claim 1 and 2, is characterized in that, in above-mentioned steps b,

Suppose that branch is the skeleton of the normal vector supporting plane that is n, the wind velocity vector acting in this plane is v _wind, tangent vector t=v _wind× n, along normal vector n and vector n × t Directional Decomposition v _windcan obtain v _y, v _xz; Vector v _windand v _xzangle be angle of attack θ,

Based on aerodynamics, act on the pulling force v on this branch _dragwith lift v _liftcan be expressed as:

v _drag＝0.5c _d(θ)ρv _wind

In formula, c _d(θ) and c _l(θ) be tension coefficient and lift coefficient, ρ is atmospheric density,

The suffered external force sum of branch can be expressed as L (t)=v _drag(t)+v _lift(t)+G, G is gravity.

6. the tree animation simulation method based on simplifying modal analysis method according to claim 1 and 2, is characterized in that, in the process of above-mentioned steps c is:

Step c1 sets up kinetic model under leaf local coordinate;

Suppose that blade is the curved surface that comprises vein and leaf film, sets up following kinetic model under leaf local coordinate:

Wherein, r (a, t) be the position of node a at moment t, the mass density that μ (a) is node a place, γ (a) is the damping density at node a place, ε (r) is the potential energy of blade deformation, and f (r, t) is for acting on the external force sum on blade;

Step c2, sets up the potential energy formula of blade deformation.

7. the tree animation simulation method based on simplifying modal analysis method according to claim 6, is characterized in that, above-mentioned steps c2, and for the distortion of curved surface, the potential energy of blade deformation intends adopting formula:

Wherein, G and B represent respectively elasticity energy (stretching energy) and bending energy (bending energy), G ⁰and B ⁰represent elasticity energy and bending energy under original state.

8. the tree animation simulation method based on simplifying modal analysis method according to claim 1, is characterized in that, in above-mentioned steps d, also comprise,

Step e, sets up wind-field model; The present invention, for setting up dimensional wind model, adopts following frequency spectrum function (1/f ^βnoise function) set up wind-field model:

Wherein n is wind field dimension, and β represents the unordered degree of wind field, f _irepresent the frequency of i dimension, a complete wind-field model need comprise four-dimensional information, for further simplified model, formula is carried out after invert fast fourier transformation (IFFT), adopt Taylor's wind field freezing technology three-dimensional matrice information can be converted into four-dimensional wind field information w (x, y, z, t).