CN105677950A - Fabric deformation simulation method - Google Patents

Abstract

The invention discloses a fabric deformation simulation method which, based on the classic spring-mass model, introduces the concept of a semi-rigid spline, and takes into full consideration of stretching property, compressing property, cutting property, bending property and surface roughness of the fabric, and effectively addresses the problem of anisotropy and superelasticity in fabric deformation simulation, and increases real sense of fabric deformation simulation. In aspect of numerical integration, compared with traditional explicit euler method and implicit euler method which have defects of slow solution speed, the method of the invention Verlet integration method which has substantial increase in velocity and computing stability. In aspect of collision treatment, the method further simplifies a collision model, and only considers collisions of "top pint-triangle" type and "edge-edge" type that occur in large amount in fabric simulation, which effectively reduces times for collision treatment and accelerates computing velocity.

Description

A kind of method of cloth modeling

Technical field

The present invention relates to a kind of method of cloth modeling.

Background technology

Since the 80's of last century, the simulation emulation of fabric distortion is the research focus of in field of Computer Graphics always. Spring proton model is because its principle is simple, be easy to realization, textile simulating obtains and applies more widely, but this kind of model only considered the isotropic physical property of fabric, and easily superelastic phenomena occurs in simulation process, cause emulation result distortion. The numerical integration that textile simulating relates to the equation of motion calculates and a large amount of hit-treatments, and these often become the performance bottleneck of emulation. In numerical integration, there is the slower shortcoming of solving speed in traditional explicit Euler, implicit expression Euler.

Summary of the invention

It is an object of the invention to for the deficiencies in the prior art, it is provided that a kind of method of cloth modeling.

It is an object of the invention to be achieved through the following technical solutions: a kind of method of cloth modeling, comprises the steps:

Step 1: according to the semi-rigid batten parameter k of fabric, set up the proton grid model of anisotropy fabric, comprise insert semi-rigid batten spring structure (through the structure spring between, broadwise adjacent protons, along textile plane direction shear spring and along the flexural spring in the outer direction of textile plane). Described semi-rigid batten parameter K, is used for describing these battens when there is not tensile deformation, it is possible to bending compression occurs, in simulation process, shows as the fold of fabric. And when these battens are opened completely, it is possible to there is tensile deformation, show the character of spring. But by mechanical model, the deformation of batten is constrained within certain threshold value by we, it is possible to the restriction fabric superelastic phenomena when emulating.

Step 2: the structural models of consideration fabric, gravity model, wind force model, artificially external force model and damper model, all protons of traversal fabric grid, carry out analyzing by power, calculate it with joint efforts suffered, set up the equation of motion.

Step 3: use Verlet numerical integration method to be solved by the equation of motion of textile simulating, calculate the coordinate of subsequent time fabric grid proton.

Whether step 4: consideration " summit trilateral " and " limit, limit " two class collision, detect and have collision to occur in this simulation time slice.If systems axiol-ogy is to collision, then recording and return the relevant informations such as collision moment, fabric grid model will, from collision moment, be carried out analyzing by power by collision response process again, and use Verlet method again to carry out numerical solution, calculate the new coordinate of fabric grid proton.

Step 5: after whole hit-treatment end of processing, according to the spatiality of the new coordinate renew fabric of fabric grid proton. Now, if simulation time not yet terminates, then enter future time sheet, transfer step 2 to. Otherwise, whole simulation process terminates.

Described step 1: the model in the method is on the spring proton model basis of classics, introduce the concept of semi-rigid batten, fully consider the stretchiness of fabric, compressibility, shearing, bendability and surfaceness, efficiently solve the problem of every opposite sex and super-elasticity aspect in textile simulating, it is to increase the true sense of textile simulating.

Further, the spring structure of the semi-rigid batten of described insertion, three kinds of situations are adopted to retrain: proton M (i, j) and proton M (i+1, j), proton M (i, j) Yu between proton M (i, j+1) structure spring is adopted, and according to fabric model type, in broadwise or through inserting the semi-rigid batten of k section between adjacent protons, the stretchiness of simulate fabric, compressibility and flexible fold;

For preventing fabric excessive deformation in own layer, proton M (i, j) and proton M (i+1, j+1), adopt shear spring between proton M (i+1, j) Yu proton M (i, j+1), thus gives fabric shear rigidity;

For preventing fabric in the outer overbending of own layer, proton M (i, j) and proton M (i+2, j), adopt flexural spring between proton M (i, j) Yu proton M (i, j+2), thus gives fabric bending rigidity.

Further, described structure spring comprises broadwise spring and through to spring;

The formula of broadwise structure spring is as follows:

${\stackrel{\&RightArrow;}{f}}_{struct}^{weft}<r_{i,j}>=\left\{\begin{array}{c}\begin{array}{cc}\stackrel{\&RightArrow;}{0,}& r_{i,j}\&le;{\mathrm{\&delta;}}_1\end{array}\\ k_{s0}^{weft}(r_{i,j}-{\mathrm{\&delta;}}_1)\stackrel{\&RightArrow;}{n},\\ \begin{array}{cc}{k}_{s1}^{weft}{(r_{i,j}-{\mathrm{\&delta;}}_2)}^5\stackrel{\&RightArrow;}{n},& r_{i,j}>{\mathrm{\&delta;}}_2\end{array}\end{array}\right.,{\mathrm{\&delta;}}_1<r_{i,j}\&le;{\mathrm{\&delta;}}_2$ Formula (1 1)

Proton i points to the vector of proton j, i and j is broadwise adjacent protons herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of broadwise structure spring power, here, we only consider tensile properties, for proton i,For proton j,

δ₁: the distance of equilibrium state between proton i and proton j, the i.e. overall length of the semi-rigid batten of k section.

δ₂: broadwise structure spring stretching threshold value, in engineering, the tensile deformation of general fabrics is no more than 10% usually, and we get δ₂=(1+10%) δ₁。

Broadwise structure spring stiffness coefficient.

In formula (1 1),

Work as r_i,j≤δ₁Time, representing weft yams compression, Interproton Distance is from being less than equilibrium state. It is considered that yarn is incompressible, the energy that compression produces is dissipated by damping corresponding in the deformation of the semi-rigid batten of k section and proton movement process. And the deformation of the semi-rigid batten of k section will show multi-form fabric crease, embody the flexible characteristic of anisotropy fabric.

Work as δ₁< r_i,j≤δ₂Time, represent that yarn is in normal deformation range. This is that the semi-rigid batten of k section will be opened completely, produces tensile deformation, is suitable for Hook's law, linear by power and deformation, produces an elastic force in opposite directions between proton i and proton j.

Work as r_i,j≥δ₂Time, represent yarn excessive tensile, namely may cause superelastic phenomena. This adopts constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, and uses bigger spring stiffness coefficientLimit excessive deformation.

Through as follows to structure spring formula:

${\stackrel{\&RightArrow;}{f}}_{struct}^{warp}\left(r_{i,j}\right)=\left\{\begin{array}{cc}{k}_{s0}^{warp}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& \mathrm{\&delta;}-\mathrm{\&epsiv;}\&le;r_{i,j}\&le;\mathrm{\&delta;}+\mathrm{\&epsiv;}\\ k_{s1}^{warp}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{u,j}\&le;\mathrm{\&delta;}-\mathrm{\&epsiv;}\left|\right|r_{i,j}>\mathrm{\&delta;}+\mathrm{\&epsiv;}\end{array}\right.$ Formula (1 2)

Proton i points to the vector of proton j, i and j is through to adjacent protons herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of radial structure spring power, for proton i, r_i,jDuring > δ,r_i,jDuring≤δ,For proton j, r_i,jDuring > δ,r_i,jDuring≤δ,

δ: the distance of equilibrium state between proton i and proton j, namely through to adjacent protons spacing.

ε: radial structure spring stretching threshold value, in engineering, the tensile deformation of general fabrics is no more than 10% usually, and we get ε=(1+10%) δ.

Radial structure spring stiffness coefficient.

Owing to broadwise inserting semi-rigid batten, can produce the bending position of fold more than through to, it is believed that weft yams is incompressible. Through upwards, it is believed that yarn has compression characteristic, meanwhile, but the spring structure that we have employed constrained strain is to limit superelastic phenomena.

As δ-ε≤r_i,jDuring≤δ+ε, represent that yarn is in normal deformation range. Produce stretching, compressive set, it is suitable for Hook's law, linear by power and deformation quantity, produce an elastic force in opposite directions between proton i and proton j.

Work as r_i,j< δ ε | | r_i,jDuring > δ+ε, represent yarn excessive tensile, compression, namely may cause superelastic phenomena. At this moment our constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, and the spring stiffness coefficient that use is biggerLimit excessive deformation.

Shear spring deformation formula is as follows:

${\stackrel{\&RightArrow;}{f}}_{shear}\left(r_{i,j}\right)=\left\{\begin{array}{cc}\stackrel{\&RightArrow;}{0,}& {\mathrm{\&delta;}}_1\&le;r_{i,j}\&le;{\mathrm{\&delta;}}_2\\ k_{sh0}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& {\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\&le;r_{i,j}<{\mathrm{\&delta;}}_1\left|\right|{\mathrm{\&delta;}}_2<r_{i,j}\&le;{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\\ k_{sh1}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{i,j}<{\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\left|\right|r_{i,j}>{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\right.$

Formula (1 3)

Proton i points to the vector of proton j, i and j is two protons on diagonal lines in a proton unit rectangular node herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of shear spring power, for proton i, r_i,j> δ₂Time,r_i,j< δ₁Time,For proton j, r_i,j> δ₂Time,r_1,j≤δ₁Time,

δ₁: the semi-rigid batten of broadwise K section is in original state, not yet opens, δ₁For the hypotenuse length of the right-angle triangle that broadwise adjacent protons spacing and radially adjoining Interproton Distance are formed.

δ₂: the semi-rigid batten of broadwise K section is opened completely, δ₂For the hypotenuse length of the right-angle triangle that overall length and the radially adjoining Interproton Distance of the semi-rigid batten of k section are formed.

δ: r_i,j< δ₁Time, δ=δ₁, r_i,j> δ₂Time, δ=δ₂。

ε₁、ε₂: shear spring compression, stretching threshold value, the tensile deformation that we get general fabrics in engineering here is no more than 10% usually, and we get ε₁=10% δ₁, ε₂=10% δ₂。

k_sh0、k_sh1: shear spring stiffness coefficient.

Shear spring simulation proton M (i, j) and proton M (i+1, j+1), the shear property between proton M (i+1, j) and proton M (i, j+1), prevents fabric excessive deformation in own layer.

Work as δ₁-ε₁≤r_i,j< δ₁||δ₂< r_i,j≤δ₂+ε₂Time, represent that normal compression, tensile deformation occur shear spring, it is suitable for Hook's law, linear by power and deformation, produce an elastic force in opposite directions between proton i and proton j.

Work as r_i,j< δ₁-ε₁||r_i,j> δ₂+ε₂Time, represent shear spring excessive tensile, compression, namely may cause superelastic phenomena. At this moment our constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, limit excessive deformation.

When four angles of a proton unit rectangular node all keep right angle, shear spring reaches equilibrium state. δ₁≤r_i,j≤δ₂,

Flexural spring comprises broadwise flexural spring and radially bends spring,

The formula of broadwise flexural spring is as follows:

${\stackrel{\&RightArrow;}{f}}_{bend}^{weft}\left(r_{i,j}\right)=\left\{\begin{array}{cc}\stackrel{\&RightArrow;}{0,}& {\mathrm{\&delta;}}_1\&le;r_{i,j}\&le;{\mathrm{\&delta;}}_2\\ k_{n0}^{weft}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& {\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\&le;r_{i,j}<{\mathrm{\&delta;}}_1\left|\right|{\mathrm{\&delta;}}_2<r_{i,j}\&le;{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\\ k_{b1}^{weft}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{i,j}<{\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\left|\right|r_{i,j}>{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\right.,$

Formula (1 4)

Proton i points to the vector of proton j, i and j is broadwise two proton separately herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of broadwise flexural spring power, for proton i, r_i,j> δ₂Time,

r_i,j< δ₁Time,For proton j, r_i,j> δ₂Time,

r_i,j< δ₁Time,

δ₁: the semi-rigid batten of broadwise k section is in original state, not yet opens, δ₁For broadwise two Interproton Distance separately.

δ₂: the semi-rigid batten of broadwise K section is opened completely, δ₂For the overall length of the semi-rigid batten of 2k section.

δ: r_i,j< δ₁Time, δ=δ₁, r_i,j> δ₂Time, δ=δ₂。

ε₁、ε₂: flexural spring compression, stretching threshold value, the tensile deformation that we get general fabrics in engineering here is no more than 10% usually, and we get ε₁=10% δ₁, ε₂=10% δ₂。

Broadwise flexural spring stiffness coefficient.

Radially bend spring formula as follows:

${\stackrel{\&RightArrow;}{f}}_{bend}^{warp}\left(r_{i,j}\right)=\left\{\begin{array}{cc}{k}_{b0}^{warp}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& \mathrm{\&delta;}-\mathrm{\&epsiv;}\&le;r_{i,j}\&le;\mathrm{\&delta;}+\mathrm{\&epsiv;}\\ k_{b1}^{warp}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{i,j}<\mathrm{\&delta;}-\mathrm{\&epsiv;}\&le;r_{i,j}\&le;\mathrm{\&delta;}+\mathrm{\&epsiv;}\end{array}\right.$ Formula (1 5)

Proton i points to the vector of proton j, i and j is through to two proton separately herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

Radially bend the direction vector of spring power, for proton i, r_i,jDuring > δ,r_i,jDuring≤δ,

For proton j, r_i,jDuring > δ,r_i,jDuring≤δ,

δ: the distance of equilibrium state between proton i and proton j, namely through to two Interproton Distance separately.

ε: radially bend spring stretching threshold value, in engineering, the tensile deformation of general fabrics is no more than 10% usually, and we get ε=10% δ.

Radially bend spring stiffness coefficient.

Flexural spring simulation proton M (i, j) and proton M (i+2, j), the curved characteristic between proton M (i, j) and proton M (i, j+2), prevents fabric from excessively naturally not bending outside own layer. Identical with structure spring, we consider the stress model that parallel and warp two directions are different, and when excessive deformation occurs flexural spring, adopt the Hook's law restriction superelastic phenomena of distortion.

Two adjacent rectangle grids in units of a proton are in same plane, and namely when its normal line vector angle is zero, flexural spring reaches equilibrium state. Now,Time,

The structural models of described fabric, gravity model, wind force model, artificially external force model and damper model, all protons of traversal fabric grid, carry out analyzing by power, calculate it with joint efforts suffered, set up the equation of motion. It is specially:

Proton M (i, j) is suffered makes a concerted effortFor:

${\stackrel{\&RightArrow;}{F}}_{i,j}={\stackrel{\&RightArrow;}{F}}_{i,j}^{grav}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{struct}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{shear}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{bend}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{wind}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{human}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{damp}$ Formula (3 1)

${\stackrel{\&RightArrow;}{F}}_{i,j}^{grav}=m_{i,j}\stackrel{\&RightArrow;}{g}$ Formula (3 2)

${\stackrel{\&RightArrow;}{F}}_{i,j}^{struct}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{weft}+\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{warp}$ Formula (3 3)

${\stackrel{\&RightArrow;}{F}}_{i,j}^{shear}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{shear}$ Formula (3 4)

${\stackrel{\&RightArrow;}{F}}_{i,j}^{bend}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{bend}^{weft}+\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{bend}^{warp}$ Formula (3 5)

For universal gravity constant,Gravity suffered by proton,

For in fabric grid, the reactive force produced from the radial structure spring formed with adjacent protons and broadwise structure spring that proton M (i, j) is subject to,

The shear spring power that unit grids residing for proton M (i, j) produces,

The spring power that radially bends that unit grids and adjacent cells grid residing for proton M (i, j) produce and broadwise spring power,

${\stackrel{\&RightArrow;}{F}}_{i,j}^{wind}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{wind}$ Formula (3 6)

It is the summation of each face sheet wind-force, whereinFor the wind-force of single sheet,

${\stackrel{\&RightArrow;}{F}}_{i,j}^{human}=-k_h\stackrel{\&RightArrow;}{h}$ Formula (3 7)

Simulation manpower, pulls fabric with mouse, wherein k_h: artificial outer force coefficient is a permanent amount,Outer force vector, shows as vector between mouse coordinates and proton coordinate.

${\stackrel{\&RightArrow;}{f}}_{i,j}^{damp}=-k_d\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{v}}_{i,j}$ Formula (3 8)

Simulate and consider linear damping for spring structure, wind force model and external force model. Wherein, k_dFor ratio of damping, it is certain constant,For the relative velocity vector of proton M (i, j).

${\stackrel{\&RightArrow;}{F}}_{i,j}^{damp}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{damp}$ Formula (3 9)

Damping suffered by proton M (i, j) is above every summation.

Described numerical integration aspect, the shortcoming slower compared to traditional explicit Euler, implicit expression Euler's solving speed, it may also be useful to Verlet integrative approach, is enhanced in speed and computational stability.

Method is when solving proton subsequent time coordinate, it is not necessary to explicitly solves the movement velocity of proton current time, and only needs the coordinate of proton current time and previous moment.

We add a coefficient entry ε in systems in which, it is to increase the stability in integral process, and improve integrating rate. Its calculation formula is as follows:

${\stackrel{\&RightArrow;}{X}}_{t+1}={\stackrel{\&RightArrow;}{X}}_t+\mathrm{\&epsiv;}({\stackrel{\&RightArrow;}{X}}_t-{\stackrel{\&RightArrow;}{X}}_{t-1})+\stackrel{\&RightArrow;}{\mathrm{\&alpha;}}{\mathrm{\&Delta;t}}^2$ Formula (4 1)

Represent the coordinate vector P of proton M (i, j) subsequent time_i,j∈R³。

Represent the coordinate vector of the current t of proton.

The coordinate vector of proton previous moment.

ε: Verlet coefficient entry so that numerical evaluation is more stable, usual 0 < ε≤1.

The power acceleration of proton M (i, j)

Δ t: fixing integration step-length.

During system realizes, we are at each moment t, and traversal fabric grid proton, calculates it with joint efforts sufferedUse Newton interpolation algorithmSolve the power acceleration of proton M (i, j)Then choose specific Verlet coefficient ε, bring formula (4 1) into. Formula maintains Two Variables,WithOnce solve by calculatingAfter, namely renewableForUpgradeForAll fabric grid proton coordinatesAfter all being upgraded, enter next time slice and calculate.

Described hit-treatment aspect, collision model has been done further simplification by the present invention, only considered a large amount of collision occurred in textile simulating of " summit trilateral ", " limit, limit " this two class, effectively reduces the quantity of hit-treatment, accelerate computing velocity.

Further, the formula of described summit trilateral collision is as follows:

For the collision described between motion summit and trilateral grid, proton movement the Representation Equation is by we:

$P\left(t\right)=P\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_P$ Formula (5 1)

P (t): proton P at the coordinate of t, t ∈ [t₀,t₀+ Δ t],

P(t₀): proton P is in initial moment t₀Coordinate,

Proton is from initial moment t₀Movement velocity in this Δ t time slice started is steady state value.

Definition M (t) is motion summit, and the summit that A (t), B (t), C (t) are trilateral grid, can be obtained by formula (5 1):

$M\left(t\right)=M\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_M$ Formula (5 2)

$A\left(t\right)=A\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_A$ Formula (5 3)

$B\left(t\right)=B\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_B$ Formula (5 4)

$C\left(t\right)=C\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_C$ Formula (5 5)

At t₀In the Δ t time slice that moment starts, motion summit and trilateral grid collide, and so summit M (t) will be positioned at trilateral ABC (t) inside:

$\&Exists;t\&Element;\&lsqb;t_0,t_0+\mathrm{\&Delta;}t\&rsqb;,\&Exists;u,v\&Element;\&lsqb;0,1\&rsqb;,u+v\&le;1,\stackrel{\&RightArrow;}{AM}\left(t\right)=u\stackrel{\&RightArrow;}{AM}\left(t\right)+v\stackrel{\&RightArrow;}{AC}\left(t\right)$ Formula (5 6)

Obtain the normal line vector on summit:

$\stackrel{\&RightArrow;}{N}\left(t\right)=\stackrel{\&RightArrow;}{AB}\left(t\right)+\stackrel{\&RightArrow;}{AC}\left(t\right)$ Formula (5 7)

Therefore, summit M (t) of moving will be positioned at triangle interior and can represent and be:

$\stackrel{\&RightArrow;}{AM}\left(t\right)\&CenterDot;\stackrel{\&RightArrow;}{N}\left(t\right)=0$ Formula (5 8)

Solve formula (5 8) this about the simple cubic equation of time variable t, solve three values, when solving value, to meet formula (5 6) be possible value, if there are many groups of (t, u, v) make formula (5 6) set up, get the solution in t minimum value moment for " summit trilateral " collision moment.

The formula of limit, described limit collision is as follows:

$\&Exists;t\&Element;\&lsqb;t_0,t_0+\mathrm{\&Delta;}t\&rsqb;,\&Exists;u,v\&Element;\&lsqb;0,1\&rsqb;,u\stackrel{\&RightArrow;}{AB}\left(t\right)=v\stackrel{\&RightArrow;}{CD}\left(t\right)$ Formula (5 9)

When a collision occurs, four summits on two limits collided are positioned at same plane, therefore:

$\left(\stackrel{\&RightArrow;}{AB}\right(t)\&times;\stackrel{\&RightArrow;}{CD}(t\left)\right)\&CenterDot;\stackrel{\&RightArrow;}{AC}\left(t\right)=0$ Formula (5 10)

For limitWithDetermined the normal line vector of plane.

By solving formula (5 10), obtain three values of t, get the minimal solution meeting formula (5 10), be namely the moment that the collision of limit, limit occurs.

After collision occurs, collision moment t will be returned. Collision response considers the sliding friction power produced when collision occurs and collision elastic force, obtains following formula:

${\stackrel{\&RightArrow;}{F}}_{i,j}^{,}=\left\{\begin{array}{cc}{\stackrel{\&RightArrow;}{F}}_T-k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\frac{{\stackrel{\&RightArrow;}{F}}_T}{\left|\right|F_T\left|\right|}-k_n{\stackrel{\&RightArrow;}{F}}_N,& \left|\right|{\stackrel{\&RightArrow;}{F}}_T\left|\right|\&GreaterEqual;k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\\ -k_n{\stackrel{\&RightArrow;}{F}}_N,& \left|\right|{\stackrel{\&RightArrow;}{F}}_T\left|\right|<k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\end{array}\right.$ Formula (5 11)

Proton M (i, j) is in time slice initial moment t₀In time, suffered makes a concerted effort.

Proton M (i, j) is suffered making a concerted effort when collision moment t.

Along a component of point of contact H place normal direction,

Along a component of point of contact H place normal direction,

k_f: the coefficient of sliding friction, shows as the physical property that fabric face is coarse.

k_n: non-perfect elastic collision waste of energy parameter, 0≤k_n≤1。

In collision detection, at most put trilateral " collide and " limit, limit " collision. When collision response, we make different regulations by the normal line vector N of its contact surface. In " summit trilateral " collides, N gets trilateral normal line vector, and in " limit, limit " collides, N gets the vector cross product on two overlapping limits.

Analyze by power by collision moment fabric grid proton is re-started, solve and make a concerted effortAfter, we can upgrade the coordinate of proton in numerical evaluation, and enters future time sheet.

Compared with prior art, the technical program has the following advantages:

The method of cloth modeling of the present invention, the method is on the spring proton model basis of classics, introduce the concept of semi-rigid batten, fully consider the stretchiness of fabric, compressibility, shearing, bendability and surfaceness, efficiently solve the problem of every opposite sex and super-elasticity aspect in textile simulating, it is to increase the true sense of textile simulating.

In numerical integration, the shortcoming slower compared to traditional explicit Euler, implicit expression Euler's solving speed, it may also be useful to Verlet integrative approach, is enhanced in speed and computational stability.

In hit-treatment, collision model is done further simplification, only considered a large amount of collision occurred in textile simulating of " summit trilateral ", " limit, limit " this two class, effectively reduce the quantity of hit-treatment, accelerate computing velocity.

Accompanying drawing explanation

Fig. 1 is the method flow of the cloth modeling of the embodiment of the present invention.

Embodiment

Owing to the method for existing cloth modeling exists super-elasticity problem, and the shortcoming such as computing velocity is slow, inconvenience may be produced, therefore, embodiments provide a kind of method of cloth modeling, this model is on the spring proton model basis of classics, introduce the concept of semi-rigid batten, fully consider the stretchiness of fabric, compressibility, shearing, bendability and surfaceness, efficiently solve the problem of every opposite sex and super-elasticity aspect in textile simulating, it is to increase the true sense of textile simulating.

The inventive method is in numerical integration, and the shortcoming slower compared to traditional explicit Euler, implicit expression Euler's solving speed, it may also be useful to Verlet integrative approach, is enhanced in speed and computational stability.

The inventive method is in hit-treatment, collision model has been done further simplification, only considered a large amount of collision occurred in textile simulating of " summit trilateral ", " limit, limit " this two class, effectively reduce the quantity of hit-treatment, accelerate computing velocity.

Below in conjunction with accompanying drawing, by specific embodiment, the technical scheme of the present invention is carried out clear, complete description.

As shown in Figure 1, to give a kind of anisotropy textile simulating prototype system algorithm flow as follows in the present invention:

Step 1: according to the semi-rigid batten parameter k of fabric, set up the proton grid model of anisotropy fabric, comprise insert semi-rigid batten spring structure (through the structure spring between, broadwise adjacent protons, along textile plane direction shear spring and along the flexural spring in the outer direction of textile plane).

Step 2: the structural models of consideration fabric, gravity model, wind force model, artificially external force model and damper model, all protons of traversal fabric grid, carry out analyzing by power, calculate it with joint efforts suffered, set up the equation of motion.

Step 3: use Verlet numerical integration method to be solved by the equation of motion of textile simulating, calculate the coordinate of subsequent time fabric grid proton.

Whether step 4: consideration " summit trilateral " and " limit, limit " two class collision, detect and have collision to occur in this simulation time slice. If systems axiol-ogy is to collision, then recording and return the relevant informations such as collision moment, fabric grid model will, from collision moment, be carried out analyzing by power by collision response process again, and use Verlet method again to carry out numerical solution, calculate the new coordinate of fabric grid proton.

Step 5: after whole hit-treatment end of processing, according to the spatiality of the new coordinate renew fabric of fabric grid proton. Now, if simulation time not yet terminates, then enter future time sheet, transfer step 2 to. Otherwise, whole simulation process terminates.

The present invention uses anisotropy fabric stress model and speed-up computation method to achieve a textile simulating prototype system. The dynamic effect of this systems simulation curtain under wind effect and tablecloth naturally drooping on desk, effectively simulate the physical property such as anisotropy and fold of fabric.

In anisotropy textile simulating process, first we load a secondary real two-dimensional scene photo by system peripherals framework, then adds our fabric model in scene and dynamically emulates. Emulating according to the method for the present invention, we are by the specific fabric parameter of input and simulation parameter, generate the anisotropy fabric model of differing materials, different physical property. Then, by arranging the correlation parameter of external force model, we can simulate the emulation effect of fabric under different gravity, wind-force and artificial external force.

We add a curtain model in real scene, and simulate the dynamic effect of curtain under wind effect. In addition, curtain is also applied with artificial pulling by us. From effect, we can very clearly see the flexible fold of fabric, and effectiveness comparison is true.

In another experiment, first we be loaded with the three-dimensional model of desk in scene, then uses soft fabric and heavy weight fabric, simulates the effect that the tablecloth of differing materials naturally droops on desk. Analogue system has processed the collision between fabric and three-dimensional body well, embodies the verity of textile simulating.

In the present embodiment, we simulate the dynamic effect of curtain under wind effect, and tablecloth naturally drooping on desk, embody the physical propertys such as the anisotropy of fabric, fold well, and improve the superelastic phenomena of spring proton model structure preferably.

Although the present invention is with better embodiment openly as above; but it is not for limiting the present invention; any those skilled in the art are without departing from the spirit and scope of the present invention; can utilize the Method and Technology content of above-mentioned announcement that technical solution of the present invention is made possible variation and amendment; therefore; every content not departing from technical solution of the present invention; any simple modification, equivalent variations and the modification above embodiment done according to the technical spirit of the present invention, all belongs to the protection domain of technical solution of the present invention.

Claims (5)

1. the method for a cloth modeling, it is characterised in that, comprise the steps:

Step 1: according to the semi-rigid batten parameter k of fabric, set up the proton grid model of anisotropy fabric, comprise the spring structure inserting semi-rigid batten;

Described spring structure comprises through the structure spring between, broadwise adjacent protons, along textile plane direction shear spring and along the flexural spring in the outer direction of textile plane.

Described semi-rigid batten parameter K is used for describing these battens when there is not tensile deformation, it is possible to bending compression occurs, in simulation process, shows as the fold of fabric. And when these battens are opened completely, it is possible to there is tensile deformation, show the character of spring.

Step 2: the structural models of consideration fabric, gravity model, wind force model, artificially external force model and damper model, all protons of traversal fabric grid, carry out analyzing by power, calculate it with joint efforts suffered, set up the equation of motion.

Step 3: use Verlet numerical integration method to be solved by the equation of motion of textile simulating, calculate the coordinate of subsequent time fabric grid proton.

Whether step 4: consideration " summit trilateral " and " limit, limit " two class collision, detect and have collision to occur in this simulation time slice. If systems axiol-ogy is to collision, then recording and return collision moment information, fabric grid model will, from collision moment, be carried out analyzing by power by collision response process again, and use Verlet method again to carry out numerical solution, calculate the new coordinate of fabric grid proton.

Step 5: after whole hit-treatment end of processing, according to the spatiality of the new coordinate renew fabric of fabric grid proton. Now, if simulation time not yet terminates, then enter future time sheet, transfer step 2 to. Otherwise, whole simulation process terminates.

2. the method for a kind of cloth modeling as claimed in claim 1, it is characterised in that, in described step 1, the spring structure of the semi-rigid batten of described insertion, adopts three kinds of situations to retrain:

Proton M (i, j) with proton M (i+1, j), proton M (i, j) Yu between proton M (i, j+1) structure spring is adopted, and according to fabric model type, in broadwise or through inserting the semi-rigid batten of k section between adjacent protons, the stretchiness of simulate fabric, compressibility and flexible fold;

For preventing fabric excessive deformation in own layer, proton M (i, j) and proton M (i+1, j+1), adopt shear spring between proton M (i+1, j) Yu proton M (i, j+1), thus gives fabric shear rigidity;

For preventing fabric in the outer overbending of own layer, proton M (i, j) and proton M (i+2, j), adopt flexural spring between proton M (i, j) Yu proton M (i, j+2), thus gives fabric bending rigidity.

Described structure spring comprises broadwise spring and through to spring;

The formula of broadwise structure spring is as follows:

${\stackrel{\&RightArrow;}{f}}_{struct}^{weft}\left(r_{i,j}\right)=\left\{\begin{array}{c}\begin{array}{cc}\stackrel{\&RightArrow;}{0},& r_{i,j}\&le;{\mathrm{\&delta;}}_1\end{array}\\ k_{s0}^{weft}\left(r_{i,j}-{\mathrm{\&delta;}}_1\right)\stackrel{\&RightArrow;}{n}\\ \begin{array}{cc}{k}_{s1}^{weft}{\left(r_{i,j}-{\mathrm{\&delta;}}_2\right)}^5\stackrel{\&RightArrow;}{n},& r_{i,j}>{\mathrm{\&delta;}}_2\end{array}\end{array}\right.,{\mathrm{\&delta;}}_1<r_{i,j}\&le;{\mathrm{\&delta;}}_2---(1-1)$

Proton i points to the vector of proton j, i and j is broadwise adjacent protons herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of broadwise structure spring power, only considers tensile properties here, for proton i,For proton j,

δ₁: the distance of equilibrium state between proton i and proton j, the i.e. overall length of the semi-rigid batten of k section.

δ₂: broadwise structure spring stretching threshold value, get δ₂=(1+10%) δ₁。

Broadwise structure spring stiffness coefficient.

In formula (1 1),

Work as r_i,j≤δ₁Time, representing weft yams compression, Interproton Distance is from being less than equilibrium state, and the energy that compression produces is dissipated by damping corresponding in the deformation of the semi-rigid batten of k section and proton movement process. And the deformation of the semi-rigid batten of k section will show multi-form fabric crease, embody the flexible characteristic of anisotropy fabric.

Work as δ₁< r_i,j≤δ₂Time, represent that yarn is in normal deformation range. This is that the semi-rigid batten of k section will be opened completely, produces tensile deformation, is suitable for Hook's law, linear by power and deformation, produces an elastic force in opposite directions between proton i and proton j.

Work as r_i,j≥δ₂Time, represent yarn excessive tensile, namely may cause superelastic phenomena. This adopts constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, and uses bigger spring stiffness coefficientLimit excessive deformation.

Through as follows to structure spring formula:

${\stackrel{\&RightArrow;}{f}}_{struct}^{warp}\left(r_{i,j}\right)=\left\{\begin{array}{c}{k}_{s0}^{warp}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},\mathrm{\&delta;}-\mathrm{\&epsiv;}\&le;r_{i,j}\&le;\mathrm{\&delta;}+\mathrm{\&epsiv;}\\ k_{s1}^{warp}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},r_{i,j}\&le;\mathrm{\&delta;}-\mathrm{\&epsiv;}\left|\right|r_{i,j}>\mathrm{\&delta;}+\mathrm{\&epsiv;}\end{array}\right.---(1-2)$

Proton i points to the vector of proton j, i and j is through to adjacent protons herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of radial structure spring power, for proton i, r_i,jDuring > δ,r_i,jDuring≤δ,For proton j, r_i,jDuring > δ,r_i,jDuring≤δ,

δ: the distance of equilibrium state between proton i and proton j, namely through to adjacent protons spacing.

ε: radial structure spring stretching threshold value, gets ε=(1+10%) δ.

Radial structure spring stiffness coefficient.

Owing to broadwise inserting semi-rigid batten, can produce the bending position of fold more than through to, therefore think that weft yams is incompressible. But yarn has compression characteristic diametrically, the spring structure of constrained strain is adopted to limit superelastic phenomena.

As δ-ε≤r_i,jDuring≤δ+ε, represent that yarn is in normal deformation range. Produce stretching, compressive set, it is suitable for Hook's law, linear by power and deformation quantity, produce an elastic force in opposite directions between proton i and proton j.

Work as r_i,j< δ ε | | r_i,jDuring > δ+ε, represent yarn excessive tensile, compression, namely may cause superelastic phenomena. At this moment constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, and uses bigger spring stiffness coefficientLimit excessive deformation.

Shear spring deformation formula is as follows:

${\stackrel{\&RightArrow;}{f}}_{shear}\left(r_{i,j}\right)=\left\{\begin{array}{c}\begin{array}{cc}\stackrel{\&RightArrow;}{0},& {\mathrm{\&delta;}}_1\&le;r_{i,j}\&le;{\mathrm{\&delta;}}_2\end{array}\\ \begin{array}{cc}{k}_{sh0}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& {\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\&le;r_{i,j}<{\mathrm{\&delta;}}_1\left|\right|{\mathrm{\&delta;}}_2<r_{i,j}\&le;{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\\ \begin{array}{cc}{k}_{sh1}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{i,j}<{\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\left|\right|r_{i,j}>{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\end{array}\right.---(1-3)$

Proton i points to the vector of proton j, i and j is two protons on diagonal lines in a proton unit rectangular node herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of shear spring power, for proton i, r_i,j> δ₂Time,r_i,j< δ₁Time,For proton j, r_i,j> δ₂Time,r_i,j≤δ₁Time,

δ₁: the semi-rigid batten of broadwise K section is in original state, not yet opens, δ₁For the hypotenuse length of the right-angle triangle that broadwise adjacent protons spacing and radially adjoining Interproton Distance are formed.

δ₂: the semi-rigid batten of broadwise K section is opened completely, δ₂For the hypotenuse length of the right-angle triangle that overall length and the radially adjoining Interproton Distance of the semi-rigid batten of k section are formed.

δ: r_i,j< δ₁Time, δ=δ₁, r_i,j> δ₂Time, δ=δ₂。

ε₁、ε₂: shear spring compression, stretching threshold value, get ε₁=10% δ₁, ε₂=10% δ₂。

k_sh0、k_sh1: shear spring stiffness coefficient.

Shear spring simulation proton M (i, j) and proton M (i+1, j+1), the shear property between proton M (i+1, j) and proton M (i, j+1), prevents fabric excessive deformation in own layer.

Work as δ₁-ε₁≤r_i,j< δ₁||δ₂< r_i,j≤δ₂+ε₂Time, represent that normal compression, tensile deformation occur shear spring, it is suitable for Hook's law, linear by power and deformation, produce an elastic force in opposite directions between proton i and proton j.

Work as r_i,j< δ₁-ε₁||r_i,j> δ₂+ε₂Time, represent shear spring excessive tensile, compression, namely may cause superelastic phenomena. At this moment constrained strain, adopts the Hook's law of distortion, is directly proportional to five powers of deformation quantity by power, limit excessive deformation.

When four angles of a proton unit rectangular node all keep right angle, shear spring reaches equilibrium state. δ₁≤r_i,j≤δ₂, ${\stackrel{\&RightArrow;}{f}}_{shear}\left(r_{i,j}\right)=\stackrel{\&RightArrow;}{0}.$

Flexural spring comprises broadwise flexural spring and radially bends spring,

The formula of broadwise flexural spring is as follows:

${\stackrel{\&RightArrow;}{f}}_{bend}^{weft}\left(r_{i,j}\right)=\left\{\begin{array}{c}\begin{array}{cc}\stackrel{\&RightArrow;}{0},& {\mathrm{\&delta;}}_1\&le;r_{i,j}\&le;{\mathrm{\&delta;}}_2\end{array}\\ \begin{array}{cc}{k}_{b0}^{weft}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},& {\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\&le;r_{i,j}<{\mathrm{\&delta;}}_1\left|\right|{\mathrm{\&delta;}}_2<r_{i,j}\&le;{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\\ \begin{array}{cc}{k}_{b1}^{weft}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},& r_{i,j}<{\mathrm{\&delta;}}_1-{\mathrm{\&epsiv;}}_1\left|\right|r_{i,j}>{\mathrm{\&delta;}}_2+{\mathrm{\&epsiv;}}_2\end{array}\end{array}\right.,---(1-4)$

Proton i points to the vector of proton j, i and j is broadwise two proton separately herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

The direction vector of broadwise flexural spring power, for proton i, r_i,j> δ₂Time,r_i,j< δ₁Time, For proton j, r_i,j> δ₂Time,r_i,j< δ₁Time,

δ₁: the semi-rigid batten of broadwise k section is in original state, not yet opens, δ₁For broadwise two Interproton Distance separately.

δ₂: the semi-rigid batten of broadwise K section is opened completely, δ₂For the overall length of the semi-rigid batten of 2k section.

δ: r_i,j< δ₁Time, δ=δ₁, r_i,j> δ₂Time, δ=δ₂。

ε₁、ε₂: flexural spring compression, stretching threshold value, get ε₁=10% δ₁, ε₂=10% δ₂。

Broadwise flexural spring stiffness coefficient.

Radially bend spring formula as follows:

${\stackrel{\&RightArrow;}{f}}_{bend}^{warp}\left(r_{i,j}\right)=\left\{\begin{array}{c}{k}_{b0}^{warp}\left|r_{i,j}-\mathrm{\&delta;}\right|\stackrel{\&RightArrow;}{n},\mathrm{\&delta;}-\mathrm{\&epsiv;}\&le;r_{i,j}\&le;\mathrm{\&delta;}+\mathrm{\&epsiv;}\\ k_{b1}^{warp}{\left|r_{i,j}-\mathrm{\&delta;}\right|}^5\stackrel{\&RightArrow;}{n},r_{i,j}<\mathrm{\&delta;}-\mathrm{\&epsiv;}\left|\right|r_{i,j}>\mathrm{\&delta;}+\mathrm{\&epsiv;}\end{array}\right.---\left(1-5\right)$

Proton i points to the vector of proton j, i and j is through to two proton separately herein.

r_i,j: vectorMould, i.e. the distance of current time between proton i and proton j.

Radially bend the direction vector of spring power, for proton i, r_i,jDuring > δ,r_i,jDuring≤δ,For proton j, r_i,jDuring > δ,r_i,jDuring≤δ,

δ: the distance of equilibrium state between proton i and proton j, namely through to two Interproton Distance separately.

ε: radially bend spring stretching threshold value, get ε=10% δ.

Radially bend spring stiffness coefficient.

Flexural spring simulation proton M (i, j) and proton M (i+2, j), the curved characteristic between proton M (i, j) and proton M (i, j+2), prevents fabric from excessively naturally not bending outside own layer.

Identical with structure spring, it is contemplated that the stress model that parallel and warp two directions are different, and when excessive deformation occurs flexural spring, adopt the Hook's law restriction superelastic phenomena of distortion.

Two adjacent rectangle grids in units of a proton are in same plane, and namely when its normal line vector angle is zero, flexural spring reaches equilibrium state. Now,Time,

3. the method for a kind of cloth modeling as claimed in claim 1, it is characterised in that, described step 2 is specific as follows:

Proton M (i, j) is suffered makes a concerted effortFor:

${\stackrel{\&RightArrow;}{F}}_{i,j}={\stackrel{\&RightArrow;}{F}}_{i,j}^{grav}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{strucu}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{shear}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{bend}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{wind}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{human}+{\stackrel{\&RightArrow;}{F}}_{i,j}^{damp}---\left(3-1\right)$

${\stackrel{\&RightArrow;}{F}}_{i,j}^{grav}=m_{i,j}\stackrel{\&RightArrow;}{g}---(3-2)$

${\stackrel{\&RightArrow;}{F}}_{i,j}^{struct}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{weft}+\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{warp}---(3-3)$

${\stackrel{\&RightArrow;}{F}}_{i,j}^{shear}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{shear}---(3-4)$

${\stackrel{\&RightArrow;}{F}}_{i,j}^{bend}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{bend}^{weft}+\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{bend}^{warp}---(3-5)$

For universal gravity constant,Gravity suffered by proton, m_i,jFor the quality of proton;

For in fabric grid, the reactive force produced from the radial structure spring formed with adjacent protons and broadwise structure spring that proton M (i, j) is subject to,

The shear spring power that unit grids residing for proton M (i, j) produces,

The spring power that radially bends that unit grids and adjacent cells grid residing for proton M (i, j) produce and broadwise spring power,

${\stackrel{\&RightArrow;}{F}}_{i,j}^{wind}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{wind}---(3-6)$

It is the summation of each face sheet wind-force, whereinFor the wind-force of single sheet,

${\stackrel{\&RightArrow;}{F}}_{i,j}^{human}=-k_h\stackrel{\&RightArrow;}{h}---(3-7)$

Simulation manpower, pulls fabric with mouse, wherein k_h: artificial outer force coefficient is a permanent amount,

Outer force vector, shows as vector between mouse coordinates and proton coordinate.

${\stackrel{\&RightArrow;}{f}}_{i,j}^{damp}=-k_d\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{v}}_{i,j}---(3-8)$

Simulate and consider linear damping for spring structure, wind force model and external force model. Wherein, k_dFor ratio of damping, it is certain constant,For the relative velocity vector of proton M (i, j).

${\stackrel{\&RightArrow;}{F}}_{i,j}^{damp}=\mathrm{\&Sigma;}{\stackrel{\&RightArrow;}{f}}_{i,j}^{damp}---(3-9)$

Damping suffered by proton M (i, j) is above every summation.

4. the method for a kind of cloth modeling as claimed in claim 1, it is characterised in that, in described step 3, described Verlet numerical integration method, adds a coefficient entry ε in systems in which, and its calculation formula is as follows:

${\stackrel{\&RightArrow;}{X}}_{t+1}={\stackrel{\&RightArrow;}{X}}_t+\mathrm{\&epsiv;}({\stackrel{\&RightArrow;}{X}}_t-{\stackrel{\&RightArrow;}{X}}_{t-1})+\stackrel{\&RightArrow;}{\mathrm{\&alpha;}}{\mathrm{\&Delta;t}}^2---(4-1)$

Represent the coordinate vector P of proton M (i, j) subsequent time_i,j∈R³。

Represent the coordinate vector of the current t of proton.

The coordinate vector of proton previous moment.

ε: Verlet coefficient entry, 0 < ε≤1.

The power acceleration of proton M (i, j)

Δ t: fixing integration step-length.

During system realizes, at each moment t, traversal fabric grid proton, calculates it with joint efforts sufferedUse Newton interpolation algorithmSolve the power acceleration of proton M (i, j)Then choose specific Verlet coefficient ε, bring formula (4 1) into. Formula maintains Two Variables,WithOnce solve by calculatingAfter, namely renewableForUpgradeForAll fabric grid proton coordinatesAfter all being upgraded, enter next time slice and calculate.

5. the method for a kind of cloth modeling as claimed in claim 1, it is characterised in that, described step 4 is specially:

The formula of described summit trilateral collision is as follows:

By proton movement the Representation Equation it is:

$P\left(t\right)=P\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_P---(5-1)$

P (t): proton P at the coordinate of t, t ∈ [t₀,t₀+ Δ t],

P(t₀): proton P is in initial moment t₀Coordinate,

Proton is from initial moment t₀Movement velocity in this Δ t time slice started is steady state value.

Definition M (t) is motion summit, and the summit that A (t), B (t), C (t) are trilateral grid, can be obtained by formula (5 1):

$M\left(t\right)=M\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_M---(5-2)$

$A\left(t\right)=A\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_A---(5-3)$

$B\left(t\right)=B\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_B---(5-4)$

$C\left(t\right)=C\left(t_0\right)+t{\stackrel{\&RightArrow;}{V}}_C---(5-5)$

At t₀In the Δ t time slice that moment starts, motion summit and trilateral grid collide, and so summit M (t) will be positioned at trilateral ABC (t) inside:

$\&Exists;t\&Element;\&lsqb;t_0,t_0+\mathrm{\&Delta;}t\&rsqb;,\&Exists;u,v\&Element;\&lsqb;0,1\&rsqb;,u+v\&le;1,\stackrel{\&RightArrow;}{AM}\left(t\right)=u\stackrel{\&RightArrow;}{AM}\left(t\right)+v\stackrel{\&RightArrow;}{AC}\left(t\right)---(5-6)$

Obtain the normal line vector on summit:

$\stackrel{\&RightArrow;}{N}\left(t\right)=\stackrel{\&RightArrow;}{AB}\left(t\right)+\stackrel{\&RightArrow;}{AC}\left(t\right)---(5-7)$

Therefore, summit M (t) of moving will be positioned at triangle interior and can represent and be:

$\stackrel{\&RightArrow;}{AM}\left(t\right)\&CenterDot;\stackrel{\&RightArrow;}{N}\left(t\right)=0---(5-8)$

Solve formula (5 8) this about the simple cubic equation of time variable t, solve three values, when solving value, to meet formula (5 6) be possible value, if there are many groups of (t, u, v) make formula (5 6) set up, get the solution in t minimum value moment for " summit trilateral " collision moment.

The formula of limit, limit collision is as follows:

$\&Exists;t\&Element;\&lsqb;t_0,t_0+\mathrm{\&Delta;}t\&rsqb;,\&Exists;u,v\&Element;\&lsqb;0,1\&rsqb;,u\stackrel{\&RightArrow;}{AB}\left(t\right)=v\stackrel{\&RightArrow;}{CD}\left(t\right)---(5-9)$

When a collision occurs, four summits on two limits collided are positioned at same plane:

$\left(\stackrel{\&RightArrow;}{AB}\right(t)\&times;\stackrel{\&RightArrow;}{CD}(t\left)\right)\&CenterDot;\stackrel{\&RightArrow;}{AC}\left(t\right)=0---(5-10)$

For limitWithDetermined the normal line vector of plane.

By solving formula (5 10), obtain three values of t, get the minimal solution meeting formula (5 10), be namely the moment that the collision of limit, limit occurs.

After collision occurs, collision moment t will be returned. Collision response considers the sliding friction power produced when collision occurs and collision elastic force, obtains following formula:

${\stackrel{\&RightArrow;}{F}}_{i,j}^{,}=\left\{\begin{array}{c}{\stackrel{\&RightArrow;}{F}}_T-k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\frac{{\stackrel{\&RightArrow;}{F}}_T}{\left|\right|F_T\left|\right|}-k_n{\stackrel{\&RightArrow;}{F}}_N,\left|\right|{\stackrel{\&RightArrow;}{F}}_T\left|\right|\&GreaterEqual;k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\\ -k_n{\stackrel{\&RightArrow;}{F}}_N,\left|\right|{\stackrel{\&RightArrow;}{F}}_T\left|\right|<k_f\left|\right|{\stackrel{\&RightArrow;}{F}}_N\left|\right|\end{array}\right.---(5-11)$

Proton M (i, j) is in time slice initial moment t₀In time, suffered makes a concerted effort.

Proton M (i, j) is suffered making a concerted effort when collision moment t.

Along a component of point of contact H place normal direction,

Along a component of point of contact H place normal direction,

k_f: the coefficient of sliding friction, shows as the physical property that fabric face is coarse.

k_n: non-perfect elastic collision waste of energy parameter, 0≤k_n≤1。

In collision detection, " summit trilateral " collision and " limit, limit " collision. When collision response, the normal line vector N of its contact surface is made different regulations. In " summit trilateral " collides, N gets trilateral normal line vector, and in " limit, limit " collides, N gets the vector cross product on two overlapping limits. Analyze by power by collision moment fabric grid proton is re-started, solve and make a concerted effortAfter, numerical evaluation upgrades the coordinate of proton, and enters future time sheet.