CN100583160C - A physical distortion method based on details coding and reconstruction - Google Patents

Abstract

A physical deformation method based on detail coding and reconstruction includes: (1) at the pre-treating stage, self adaptive predigestion is carried out on an original fine gridding model so as to build a basic gridding expression; the generated basic gridding is used for the calculation of physical deformation during operation; (2) detail coding is carried out based on the position and the normal vector of the basic gridding to the top point of fine gridding; (3) at the operation stage, physical deformation calculation is carried out on the basic gridding model; (4) the fine gridding model is reconstructed according to the basic gridding model and the detail coding after deformation and finally realistic drafting is carried out. By adopting the physical deformation method based on detail coding and reconstruction of the invention, the user can interactively simulate the elastic deformation process of a complex object only by simply appointing the material parameters of the object; the geometrical detail of the surface of the object can be better maintained under the premise of ensuring the deformation quality of the object.

Description

A kind of physical deformation method based on details coding and reconstruct

Technical field

The invention belongs in computer virtual reality and the computer graphics techniques field, particularly computer animation deformation of body technology based on physics.

Background technology

For a long time, deformation of body is the research focus of field of Computer Graphics all the time, it is soft, deformable that many objects are arranged in the real world, so the simulation of deformation of body all has a wide range of applications in fields such as computer animation, computer-aided design (CAD), video-game and operation emulation.

In field of Computer Graphics, the method for existing realization deformation of body mainly is divided into two classes: methods based on how much and based on the method for physics.To control the target location of point set or differential attribute as constraint condition based on how much method, object will be adjusted into the attitude or the shape of anticipation by geometric operation.By handling control framework object is deformed as traditional Free Transform technology, its basic ideas are that the object that will be out of shape embeds in the control framework linearly, and hypothesis object and control framework are made by commaterial, mobile control vertex makes control framework produce distortion, and object also produces distortion thereupon.The Free Transform technology is very directly perceived, the efficiency of algorithm height, but it can not keep the geometric detail of body surface well.In order to address this problem better, scholars have proposed the multi-resolution grid editing technique.This technology is decomposed into a model sequence with master pattern, and each model in the sequence is all represented the version under the different frequency of master pattern, and master pattern just can be expressed as a basic model and additional a series of details codings like this.The user can carry out by reconstruction technique details coding being rebuild on the model of the lower frequency after the distortion alternately on the model of lower frequency, can obtain final deformation effect.Gridding edition technology based on the differential attribute is the gridding edition method of nearest 2 years comparative heats, and it is converted into manipulation to object lattice local geometric differential attribute with the problem of traditional change object space coordinate.Based on the method, the efficient editor that the user only need adopt editing operation seldom can realize grid avoids the necessary model disintegration of multiresolution technology, and can keep the surface geometry details preferably in deformation process.On the whole, the methods based on how much are often according to physics principle, and the deviser changes the shape of object according to the visual sense to the actual physical world, though this makes that its computing velocity is fast, fidelity is not high, needs the deviser to adjust repeatedly.

Follow objective physics law based on the method for physics object is carried out The deformation calculation, easier the distortion object is reasonably controlled strong sense of reality, but calculation cost is high, is applied to fields such as animation, video-game and virtual operation more.The physical deformation method that extensively adopts is that deformable bodies is considered as the continuity solid at present, adopts its constitutive equation of finite element method (finite elementmethod) numerical solution.Finite element method more meets real physics law, yet calculation cost is high, generally can only real time modelling on up-to-date consumer level graphic hardware has the deformation of body of a hundreds of unit.People such as Pentland are (referring to A Penland, J Williams.Good vibrations:model dynamics for graphics and animation.In:Procof the 16th annual conference on Computer graphics and interactive techniques.New York:ACM Press, 1989,215-222) modal analysis method of Yin Ruing (modal analysis) has been simplified amount of calculation significantly.It utilizes the thinking of similar frequency-domain analysis, by precomputation and store the natural mode of vibration of object, differential equation group is converted to one group of equation that is not coupled mutually, calculates the modal coordinate of each mode in real time, utilizes the method for linear superposition to obtain displacement of joint.But the shortcoming of method is: real-time is poor, is difficult for keeping the elasticity of complex object.

Generally speaking, fast based on how much deformation method computing velocity, be fit to real-time, interactive and use, but fidelity is not enough; Based on the method for physics, finite element method fidelity height particularly, but calculation cost is high, distortion that still can't the real time modelling complex object on present consumer level graphic hardware.

Summary of the invention

Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, a kind of physical deformation method based on details coding and reconstruct real-time, that can keep the complex object geometric detail is provided, this method user only needs the material parameter of simple specified object, get final product the elastic deformation process of interactive simulation complex object, under the prerequisite of the texturing quality that guarantees object, keep the geometric detail of body surface preferably.

The technical solution used in the present invention is: a kind of physical deformation method based on details coding and reconstruct, and its characteristics are:

(1) at pretreatment stage, original fine grid blocks model is carried out adaptive simplification represents to set up its base net lattice, the base net lattice of generation for when operation physical deformation calculate and use;

(2) based on the base net lattice position and the normal vector on fine grid blocks summit carried out details coding;

(3) in the stage when operation, the base net lattice model is carried out physical deformation calculate;

(4), carry out the sense of reality at last and draw according to base net lattice model and details coding reconstruct fine grid blocks model after the distortion.

Principle of the present invention: at pretreatment stage, the present invention uses adaptive Mesh simplification algorithm that original fine grid blocks model is simplified, thereby obtains the base net lattice model.

In order fully to keep the local detail feature of original mesh model surface and to recover after distortion, the present invention has provided a kind of details coding method, and this method is divided into vertex position coding and vertex scheme vector coding two parts:

(1) vertex position coding. for the arbitrary summit p on the fine grid blocks model, the details coding of its position can be made of following tlv triple: (q, N _q, h), wherein q is the corresponding point of summit p on the base net lattice, N _qThe normal vector of representing q to order, and h represents p and q distance between two points.Annotate: for the stability consideration, the vector length of common hope record local feature is short as far as possible, and therefore requirement is positioned at the normal vector direction sensing p point of the corresponding point q of base net lattice.

Based on above-mentioned definition, the position that p is ordered can be expressed as p=q+hN _q

(2) vertex scheme vector coding. for the arbitrary summit p on the fine grid blocks model, the details coding of its normal vector can be made of following tlv triple: (q, R _q, N _Local), wherein q is the corresponding point of summit p on the base net lattice, R _qRepresent the transformation matrix of the local space at q point place, N to world space _LocalRepresent the normal vector direction of p point, as shown in Figure 2 at this local space.

Here the normal vector that p is ordered is mapped to the local space at q point place, and supposes that this normal vector remains unchanged in local space in deformation process, is designated as N _Local, this value can be tried to achieve in precomputation process; R _qBe the transformation matrix of the local space at q point place to world space, normal vector N, tangent vector T and the secondary normal vector B of being ordered by q determine, are shown below:

$R=\left[\begin{array}{ccc}{T}_x& B_x& N_x\\ T_y& B_y& N_y\\ T_z& B_z& N_z\end{array}\right]$

The present invention needed that at first the base net lattice model is carried out physical deformation and calculates in the operation phase, had used modal analysis method to carry out physical deformation, and the user can suitably adjust according to demand.The essence of modal analysis method is exactly that kinetic equation to the elastomeric objects anamorphotic system carries out the decoupling zero operation, makes it become one group of independent equation of describing with modal coordinate and modal parameter, so that obtain the modal coordinate and even the displacement of joint of system.In the deformation simulative process, only need to handle the tangible mode of those deformation effect and get final product, in general, want more real represented object deformation effect, probably need about 50 mode, so modal analysis method can reduce calculated amount effectively.

The present invention tries to achieve the modal matrix and the corresponding eigenwert of object at first in advance and stores when utilizing modal analysis method to calculate deformation of body; At deformation stage, find the solution the modal coordinate of object, the displacement that calculates each node of object afterwards gets final product.When carrying out the reconstruct of fine grid blocks model based on the base net lattice model after the distortion, for fine grid blocks summit p, reposition after its base net lattice corresponding point q distortion and new normal vector all are easy to calculate, and are designated as q ' and N respectively _{Q '}Owing to suppose in deformation process h in the details coding and N _LocalRemain constantly, the reposition p ' that therefore puts after the p distortion can pass through formula p '=q '+hN _{Q '}Obtain; New normal vector N after the some p distortion _{P '}Can pass through formula N _{P '}=R _{Q '}N _LocalObtain.

The present invention's advantage compared with prior art is: the deformation of body method calculation cost based on physics is high, even adopt at present modal analysis method to quicken the deformation process that finding the solution still of physical equation can't real time modelling complex geometry object; On the other hand, in applications such as computer animation, video-games, people do not pay close attention to accurate mechanics simulation result, realize that deformation effect true to nature as far as possible is only key satisfying under the real-time prerequisite.The present invention is divided into comparatively simple base net lattice model and details coding two parts with original fine grid blocks model, thereby make the bulk deformation effect of object meet the actual physical rule by the base net lattice model being carried out accurate physical deformation calculating, the effect nature; Utilize details coding to be reconstructed, recovered the object surfaces minutia preferably, make this method be fit to be applied to the complex geometry object being out of shape back object surfaces details.Generally speaking, deformation velocity of the present invention is fast, can satisfy real-time needs fully for the distortion of complex geometry object.The deformation calculation meets the actual physical rule, the effect nature.

Description of drawings

Fig. 1 keeps the main process flow diagram of deformation method for details of the present invention;

Fig. 2 is the synoptic diagram of normal vector coding of the present invention;

Fig. 3 is the original bunny fine grid blocks model of example of the present invention;

Fig. 4 is the bunny base net lattice model of the embodiment of the invention after simplifying;

Fig. 5 is the bunny base net lattice model after the embodiment of the invention distortion;

Fig. 6 is the bunny fine grid blocks model after the embodiment of the invention distortion.

Embodiment

The present invention is described in detail below in conjunction with embodiment.

Embodiment: the bunny model that Stanford university is provided carries out the The deformation calculation that details keeps.As shown in Figure 3, Bunny original mesh model vertices number is 35022.

As Fig. 1, the present invention includes pretreatment stage and when operation stage two parts totally four steps, specific as follows:

The first step: the base net lattice generate.

The present invention requires that original fine grid blocks model is carried out adaptive simplification and represents to set up its base net lattice, the base net lattice of generation during for operation physical deformation calculate use.The present invention adopts M Garland, P S Heckbert.Surface simplification usingquadric error metric.In:Proc of the 24th Annual Conference on Computer Graphics and interactiveTechniques International Conference on Computer Graphics and Interactive Techniques.New York:ACM Press, 1997, the Mesh simplification algorithm that provides among the 209-216 is simplified the fine grid blocks model, Fig. 4 has provided the base net lattice model that obtains after the original bunny model simplification, and its number of vertex is 2981.

Second step: the position and the normal vector on fine grid blocks summit carried out details coding based on the base net lattice.

As shown in Figure 2, the process of carrying out details coding of the arbitrary summit p on the fine grid blocks is as follows:

(1) searches the corresponding triangle of a p on the base net lattice.According to putting leg-of-mutton minimal distance principle, promptly calculation level p is to all leg-of-mutton distances of base net lattice, with its middle distance reckling as corresponding triangle.

(2) at corresponding triangle internal searching corresponding point q.Because require the normal vector direction of corresponding point q to point to some p, therefore putting q should satisfy (p-q) * N _q=0.Wherein q point position and normal vector can be obtained by leg-of-mutton each vertex position of correspondence and normal vector bilinear interpolation respectively.Adopt the multidimensional process of iteration in delta-shaped region, to search (p-q) * N during concrete calculating _qMinimum value in the hope of corresponding point q.

(3) measuring point q position, the normal vector N of some q _qAnd p and q distance between two points h carry out the position details coding; The local space at record q point place is to the transformation matrix R of world space _q, some p is at the normal vector direction N of this local space _LocalCarry out the normal vector details coding.

Repeat above-mentioned steps (1)-(3), until details coding is all finished on all summits on the fine grid blocks.

The 3rd step: the base net lattice model is carried out physical deformation calculate.

Use the detailed process of modal analysis method computational physics distortion as follows:

(1) the elastomeric objects kinetic equation can be expressed as: $M\stackrel{..}{u}+C\stackrel{.}{u}+\mathrm{Ku}=F,$ Wherein u,

With ü be respectively motion vector, velocity vector and the vector acceleration of system's node; F is suffered the importing and the outer force vector of generation such as collision or user of system; M, C and K are respectively mass matrix, damping matrix and the stiffness matrix of system.According to the finite element grid of base net lattice model, calculate the oeverall quality matrix M and the stiffness matrix K of object, damping matrix C=c ₁K+c ₂M, wherein c ₁And c ₂Be the Rayleigh damping constant; The oeverall quality matrix M of object can be calculated by relevant finite element analysis software with stiffness matrix K.

(2) specify the original state of determining system by the user, as the initial position u on each summit ₀And initial velocity

(3) according to formula M Φ Λ=K Φ gross mass matrix M and stiffness matrix K are carried out characteristic value decomposition, calculate corresponding mode, eigenwert Φ and eigenvalue matrix Λ, remove the excessive mode of eigenwert.Use the matrix computations storehouse of mathematical tool or specialty to calculate, calculate as in Matlab, using the eigs order.

(4) make z=Φ ^-1U, g=Φ ^TF, then the kinetic equation of elastomeric objects can be reduced to the diagonal angle equation: $\mathrm{\Λ}\·z+({\mathrm{\α}}_1\mathrm{\Λ}+{\mathrm{\α}}_{2}I)\·\stackrel{.}{z}+\stackrel{..}{z}=g,$ Here z regards the value of representing as in modal coordinate, and F is suffered the importing and the outer force vector of generation such as collision or user of system, and I is a unit matrix, and u is a vertex position.

(5) every frame is by the second differential equation in the numerical solution step 4 $\mathrm{\Λ}\·z+({\mathrm{\α}}_1\mathrm{\Λ}+{\mathrm{\α}}_{2}I)\·\stackrel{.}{z}+\stackrel{..}{z}=g,$ The new value of compute mode coordinate z.

(6) according to u=u ₀+ Φ z upgrades each top displacement u, if simulation is not finished as yet, then returns step 5, otherwise finishes.Fig. 5 has provided the physical deformation effect of bunny base net lattice model, the mouth of being executed in this example of making a concerted effort to be positioned at bunny, and the mode number that is kept is 24, the base net lattice are out of shape and are about 5ms required computing time.

The 4th step: according to base net lattice model and the details coding reconstruct fine grid blocks model after the distortion.

The process that fine grid blocks summit p carries out details reconstruct is as follows:

(1) according to the base net lattice model behind the physical deformation calculate after the base net lattice corresponding point q distortion reposition and

(2) new normal vector is designated as q ' and N respectively _{Q '}, q '=α a '+β b '+γ c ' and N wherein _{Q '}=α N _{A '}+ β N _{B '}+ γ N _{C '}, a ', b ' and the c ' reposition after by the vertex deformation of some p corresponding Atria wherein, N _{A '}, N _{B '}And N _{C '}Be the new normal vector after three vertex deformation, all can calculate by physical deformation.

(3) by formula p '=q '+hN _{Q '}Reposition p ' after the calculation level p distortion; H is the range coding in the details coding.

(4) by formula N _{P '}=R _{Q '}N _LocalNew normal vector N after the calculation level p distortion _{P '}R wherein _q' being to obtain the new transformation matrix after the distortion by the normal vector and the tangent vector of distortion back q ' point, concrete formula is R ' _q=[T ' _qB ' _qN ' _q], T ' _q=a '-b ', N _{Q '}Shown in step 2, calculate B ' _q=T ' _q* N ' _q, Nlocal is the normal vector encoded radio in the details coding.

(5) repeat above-mentioned steps,, subsequently information such as the vertex position of fine grid blocks model and normal vector are sent into frame buffer and carried out the sense of reality and draw until all summits that reconstruct on the fine grid blocks.

Fig. 6 has provided the bunny fine grid blocks modelling effect figure after the distortion, comparison diagram 3 and Fig. 5 as can be seen, the minutia that details coding that this paper proposes and reconstructing method have recovered body surface preferably.Bunny distortion and required T.T. of reconstruct are 21.5ms, play up frame per second and reach 46.7fps, can satisfy real-time needs fully.

Claims (4)

1, a kind of physical deformation method based on details coding and reconstruct is characterized in that:

(1) at pretreatment stage, original fine grid blocks model is simplified generation base net lattice model, the base net lattice model of generation calculates for the operation phase physical deformation and uses;

(2) based on the base net lattice model position and the normal vector on fine grid blocks summit carried out details coding;

Described process of carrying out details coding is as follows:

A. search the corresponding triangle of arbitrary summit p on the base net lattice on the base net lattice model, calculation level p is to all leg-of-mutton distances of base net lattice, with its middle distance reckling as corresponding triangle;

B. at described corresponding triangle internal searching corresponding point q, require the normal vector direction of corresponding point q to point to arbitrary summit p, corresponding point q satisfies (p-q) * N _q=0, wherein: N _qBe normal vector, the position of corresponding point q and normal vector N _qObtain by leg-of-mutton each vertex position of correspondence and normal vector bilinear interpolation respectively;

C. write down the position of corresponding point q, make the normal vector N of these corresponding point q _qAnd arbitrary summit p and corresponding point q distance between two points h carry out the position details coding, and the local space at record corresponding point q place is to the transformation matrix R of world space _q, to the normal vector direction N of arbitrary summit p at this local space _LocalCarry out the normal vector details coding;

D. repeat above-mentioned a-c step, until details coding is all finished on all summits on the fine grid blocks;

(3) stage when operation, adopt modal analysis method to carry out physical deformation to the base net lattice model and calculate;

(4), carry out the sense of reality at last and draw according to the details coding reconstruct fine grid blocks model in base net lattice model behind the physical deformation in the step (3) and the step (2).

2, the physical deformation method based on details coding and reconstruct according to claim 1 is characterized in that: the employing modal analysis method in the described step (3) carries out the performing step that physical deformation calculates:

(1), calculates the oeverall quality matrix M and the stiffness matrix K of object, damping matrix C=α according to the finite element grid of base net lattice model ₁K+ α ₂M, wherein α ₁And α ₂Be the Rayleigh damping constant;

(2) determine the original state of system, comprising: the initial position u on each summit ₀And initial velocity

(3) according to formula M Φ Λ=K Φ gross mass matrix M and stiffness matrix K are carried out characteristic value decomposition, calculate corresponding mode, eigenwert Φ and eigenvalue matrix Λ, remove the mode of eigenwert greater than the given threshold range of user;

(4) make z=Φ ^-1U, g=Φ ^TF, $\mathrm{\Λ}\·z+({\mathrm{\α}}_1\mathrm{\Λ}+{\mathrm{\α}}_{2}I)\·\stackrel{\·}{z}+\stackrel{\·\·}{z}=g,$ The value of z in modal coordinate, representing, F is suffered the importing and the outer force vector of generation such as collision or user of system, and I is a unit matrix, and u is a vertex position;

(5) every frame is by the second differential equation in the numerical solution step (4) $\mathrm{\Λ}\·z+({\mathrm{\α}}_1\mathrm{\Λ}+{\mathrm{\α}}_{2}I)\·\stackrel{\·}{z}+\stackrel{\·\·}{z}=g,$ The new value of compute mode coordinate z;

(6) according to u=u ₀+ Φ z upgrades each top displacement u, does not finish as yet if physical deformation calculates, and then returns step (5), otherwise finishes.

3, the physical deformation method based on details coding and reconstruct according to claim 1 is characterized in that: the method for the reconstruct of fine grid blocks model in the described step (4) is as follows:

(1) according to reposition and new normal vector after the calculating of the base net lattice model behind the physical deformation base net lattice corresponding point q distortion, is designated as q ' and N respectively _{Q '}, wherein: q '=α a '+β b '+γ c ' and N _{Q '}=α N _{A '}+ β N _{B '}+ γ N _{C '}, a ', b ' and the c ' reposition after by the vertex deformation of some p corresponding Atria, N _{A '}, N _{B '}And N _{C '}It is the new normal vector after three vertex deformation;

(2) by formula p '=q '+hN _{Q '}Reposition p ' after the arbitrary summit p distortion of calculation level, h is the range coding in the details coding;

(3) by formula N _{P '}=R _{Q '}N _LocalNew normal vector N after the calculation level p distortion _{P '}, wherein: R _{Q '}Be the new transformation matrix after the distortion, can obtain that formula is R ' by the normal vector and the tangent vector of distortion back q ' point _q=[T ' _qB ' _qN ' _q], T ' _q=a '-b ', N _{Q '}Shown in step (2), calculate, $B_q^{/}=T_q^{\′}\×N_q^{\′},$ N _LocalBe the normal vector encoded radio in the details coding;

(4) repeat above-mentioned steps (1)-(3), until all summits that reconstruct on the fine grid blocks.

4, the physical deformation method based on details coding and reconstruct according to claim 2 is characterized in that: described method of searching corresponding point q is: suppose that the corresponding triangle of p point is that (c), its vertex scheme vector is respectively N to Δ for a, b _a, N _bAnd N _c, then triangle is inner a bit can be expressed as arbitrarily: q=α a+ β b+ γ c, and alpha+beta+γ=1 wherein, corresponding normal vector can be expressed as: N _q=α N _a+ β N _b+ γ N _c, the normal vector direction of the corresponding point q on the base net lattice is pointed to arbitrary summit p, so corresponding point q point satisfies following formula: and (p-q) * N _q=0, adopt the multidimensional process of iteration in delta-shaped region, to search (p-q) * N when specifically calculating _qMinimum value in the hope of corresponding point q.

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