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 physical deformation method based on detail encoding and reconstruction

technical field

The invention belongs to the technical field of computer virtual reality and computer graphics, in particular to the physics-based object deformation technology in computer animation.

Background technique

For a long time, object deformation has always been a research hotspot in the field of computer graphics. In the real world, many objects are soft and deformable. Therefore, the simulation of object deformation is widely used in computer animation, computer-aided design, video games and surgical simulation. Has a wide range of applications.

In the field of computer graphics, existing methods for realizing object deformation are mainly divided into two categories: geometry-based methods and physics-based methods. Geometry-based methods take the target position or differential properties of the control point set as constraints, and adjust the object to the expected pose or shape through geometric operations. For example, the traditional free deformation technology deforms the object by manipulating the control frame. The basic idea is to embed the object to be deformed into the control frame linearly, and assume that the object and the control frame are made of the same material, and move the control vertices to make the control frame Deformation occurs, and the object deforms accordingly. The free-form deformation technique is very intuitive and the algorithm is efficient, but it cannot preserve the geometric details of the object surface very well. In order to better solve this problem, scholars have proposed multi-resolution grid editing technology. This technique decomposes the original model into a model sequence, each model in the sequence represents a version of the original model at a different frequency, so that the original model can be expressed as a basic model and an additional series of detail codes. Users can interact on the lower frequency model, and the details are encoded on the deformed lower frequency model by reconstruction technology to reconstruct the final deformation effect. The mesh editing technology based on differential attributes is a relatively hot mesh editing method in the past two years, which transforms the traditional problem of changing the spatial coordinates of objects into the manipulation of local geometric differential attributes of object meshes. Based on this method, users only need to use few editing operations to realize efficient mesh editing, avoid model decomposition work necessary for multi-resolution technology, and better maintain surface geometric details during deformation. Generally speaking, the geometry-based method is often not based on the principles of physics. The designer changes the shape of the object according to the intuitive feeling of the real physical world, which makes it fast in calculation, but the fidelity is not high, requiring repeated adjustments by the designer. .

The physics-based method follows the objective physical laws to calculate the deformation of the object, which makes it easier to control the deformed object reasonably, and has a strong sense of reality, but the calculation cost is high, and it is mostly used in animation, video games and virtual surgery and other fields. The physical deformation method widely used at present is to treat the deformable object as a continuous solid, and use the finite element method (finite element method) to numerically solve its constitutive equation. The finite element method is more in line with the real physical laws, but the calculation cost is high. On the latest consumer graphics hardware, it can generally only simulate the deformation of objects with hundreds of elements in real time. The model introduced by Pentland et al. (see 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) The modal analysis greatly simplifies the computational workload. It uses an idea similar to frequency domain analysis to convert the differential equations into a set of uncoupled equations by pre-calculating and storing the natural modes of the object, and calculates the modal coordinates of each mode in real time, using the method of linear superposition Get the node displacement. But the disadvantage of the method is: the real-time performance is poor, and it is not easy to preserve the elasticity of complex objects.

In general, the geometry-based deformation method has fast calculation speed and is more suitable for real-time interactive applications, but its fidelity is not enough; the physics-based method, especially the finite element method, has high fidelity, but the calculation cost is high. It is not yet possible to simulate the deformation of complex objects in real time on hardware.

Contents of the invention

The technical problem of the present invention is to overcome the deficiencies of the prior art and provide a real-time physical deformation method based on detail coding and reconstruction that can retain the geometric details of complex objects. In this method, the user only needs to simply specify the material parameters of the object. It can interactively simulate the elastic deformation process of complex objects, and better maintain the geometric details of the object surface under the premise of ensuring the deformation quality of the object.

The technical solution adopted in the present invention is: a physical deformation method based on detail coding and reconstruction, which is characterized in that:

(1) In the preprocessing stage, the original fine mesh model is adaptively simplified to establish its base grid representation, and the generated base grid is used for runtime physical deformation calculations;

(2) Encode the position and normal vector of the vertices of the fine grid based on the base grid;

(3) In the runtime stage, perform physical deformation calculation on the base grid model;

(4) Reconstruct the fine mesh model according to the deformed base mesh model and detail coding, and finally perform realistic rendering.

Principle of the present invention: In the preprocessing stage, the present invention uses an adaptive grid simplification algorithm to simplify the original fine grid model, thereby obtaining the base grid model.

In order to fully preserve the local detail features of the original mesh model surface and restore them after deformation, the present invention provides a detail encoding method, which is divided into two parts: vertex position encoding and vertex normal vector encoding:

(1) Vertex position coding. For any vertex p on the fine grid model, the detailed coding of its position can be composed of the following triples: (q, N _q , h), where q is the vertex p on the base grid The corresponding point of , N _q represents the normal vector of point q, and h represents the distance between two points p and q. Note: For the sake of stability, it is usually hoped that the length of the vector recording local features is as short as possible, so the normal vector direction of the corresponding point q located in the base grid is required to point to point p.

Based on the above definition, the position of point p can be expressed as p=q+h·N _q .

(2) Vertex normal vector encoding. For any vertex p on the fine grid model, the detailed encoding of its normal vector can be composed of the following triples: (q, R _q , N _local ), where q is the vertex p in the base For the corresponding point on the grid, R _q represents the transformation matrix from the local space where point q is located to world space, and N _local represents the normal vector direction of point p in the local space, as shown in Figure 2.

Here, the normal vector of point p is mapped to the local space where point q is located, and it is assumed that the normal vector remains unchanged in the local space during the deformation process, denoted as N _local , and this value can be obtained during the pre-computation process; R _q is the transformation matrix from the local space where the q point is located to the world space, which is determined by the normal vector N, the tangent vector T and the subnormal vector B of the q point, as shown in the following formula:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}& {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}& {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}& {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}& {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\end{array}\right]$

In the running stage of the present invention, it is first necessary to calculate the physical deformation of the base grid model, using the modal analysis method for physical deformation, and the user can make appropriate adjustments according to requirements. The essence of the modal analysis method is to decouple the dynamic equation of the elastic object deformation system, making it a set of independent equations described by modal coordinates and modal parameters, in order to obtain the modal coordinates and even the node displacement of the system . In the process of deformation simulation, it is only necessary to deal with the modes with obvious deformation effects. Generally speaking, about 50 modes are needed to show the deformation effect of objects more realistically, so the modal analysis method can effectively reduce the Calculations.

When using the modal analysis method to calculate the deformation of the object, the present invention first obtains the modal matrix and corresponding eigenvalues of the object in advance and stores them; in the deformation stage, the modal coordinates of the object are calculated, and then the Just move. When the fine grid model is reconstructed based on the deformed base grid model, for the fine grid vertex p, the new position and new normal vector of the corresponding point q of the base grid after deformation are easy to calculate, denoted as q ' and N _q' . Since it is assumed that h and N _local in detail coding remain unchanged during the deformation process, the new position p′ after point p deformation can be obtained by the formula p′=q′+h·N _q′ ; after point p deformation The new normal vector N _p' of can be obtained by the formula N _p' = R _q' N _local .

Compared with the prior art, the present invention has the advantages that: the calculation cost of the physics-based object deformation method is high, and even if the modal analysis method is used to accelerate the solution of the physical equation, it is still unable to simulate the deformation process of complex geometric objects in real time; on the other hand, In computer animation, video games and other application fields, people do not pay attention to accurate mechanical simulation results, and the key is to achieve as realistic deformation effects as possible under the premise of satisfying real-time. The invention divides the original fine grid model into two parts, the relatively simple base grid model and the detail code, and performs accurate physical deformation calculation on the base grid model so that the overall deformation effect of the object conforms to the real physical law, and the effect is natural ; Using detail coding to reconstruct the surface details of the deformed object, the surface detail features of the object are better restored, making this method suitable for complex geometric objects. In a word, the deformation speed of the present invention is fast, and the deformation of complex geometric objects can fully meet the real-time requirements. The deformation calculation conforms to the real physical law, and the effect is natural.

Description of drawings

Fig. 1 is the main flowchart of the present invention's details keeping deformation method;

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

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

Fig. 4 is the simplified bunny base grid model of the embodiment of the present invention;

Fig. 5 is the deformed bunny base grid model of the embodiment of the present invention;

FIG. 6 is a deformed bunny fine mesh model according to an embodiment of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with examples.

Example: Perform detail-preserving deformation calculation on the bunny model provided by Stanford University. As shown in Figure 3, the number of vertices in Bunny's original mesh model is 35022.

As shown in Fig. 1, the present invention comprises four steps in total of two parts of preprocessing stage and runtime stage, specifically as follows:

The first step: base grid generation.

The present invention requires adaptive simplification of the original fine grid model to establish its base grid representation, and the generated base grid is used for runtime physical deformation calculation. The present invention adopts M Garland, P S Heckbert. Surface simplification using quadric error metric. In: Proc of the 24th Annual Conference on Computer Graphics and interactive Techniques International Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 1997, 6 The mesh simplification algorithm provided simplifies the fine mesh model. Figure 4 shows the base mesh model obtained after simplifying the original bunny model, and its number of vertices is 2981.

Step 2: Based on the base grid, the position and normal vector of the vertices of the fine grid are encoded in detail.

As shown in Figure 2, the process of detail encoding for any vertex p on the fine grid is as follows:

(1) Find the corresponding triangle of point p on the base grid. According to the principle of the minimum distance from point to triangle, that is, calculate the distance from point p to all triangles in the base grid, and take the one with the smallest distance as the corresponding triangle.

(2) Find the corresponding point q inside the corresponding triangle. Since the direction of the normal vector corresponding to the point q is required to point to the point p, the point q should satisfy (pq)×N _q =0. Wherein, the position and normal vector of point q can be obtained by bilinear interpolation of each vertex position and normal vector of the corresponding triangle respectively. In the specific calculation, the multidimensional iterative method is used to find the minimum value of (pq)×N _q in the triangular area to obtain the corresponding point q.

(3) Record the position of point q, the normal vector N _q of point q, and the distance h between two points p and q for position detail encoding; record the transformation matrix R _q from the local space where point q is located to world space, and point p is in this local The normal vector direction N _local of the space encodes the normal vector details.

Repeat the above steps (1)-(3) until all vertices on the fine mesh are encoded with details.

Step 3: Perform physical deformation calculation on the base grid model.

The specific process of calculating the physical deformation using the modal analysis method is as follows:

和ü分别是系统结点的位移向量、速度向量和加速度向量；F是系统所受的诸如碰撞或用户输入而产生的外力向量；M、C和K分别是系统的质量矩阵、阻尼矩阵和刚度矩阵。根据基网格模型的有限元网格，计算物体的总体质量矩阵M和刚度矩阵K，阻尼矩阵C＝c₁K+c₂M，其中c₁和c₂为Rayleigh阻尼常数；物体的总体质量矩阵M和刚度矩阵K可由相关的有限元分析软件计算得到。(1) The dynamic equation of an elastic object can be expressed as: $m\stackrel{..}{u}+C\stackrel{.}{u}+\mathrm{Ku}=f,$ where u,

and ü are the displacement vector, velocity vector and acceleration vector of the system nodes respectively; F is the external force vector generated by the system such as collision or user input; M, C and K are the mass matrix, damping matrix and stiffness of the system respectively matrix. According to the finite element grid of the base grid model, calculate the overall mass matrix M and stiffness matrix K of the object, and the damping matrix C=c ₁ K+c ₂ M, where c ₁ and c ₂ are Rayleigh damping constants; the overall mass of the object Matrix M and stiffness matrix K can be calculated by relevant finite element analysis software.

(2) The initial state of the system is specified by the user, such as the initial position u ₀ and initial velocity of each vertex

(3) Decompose the eigenvalues of the total mass matrix M and stiffness matrix K according to the formula MΦΛ=KΦ, calculate the corresponding modes, eigenvalues Φ and eigenvalue matrix Λ, and remove the modes with too large eigenvalues. Use mathematical tools or a professional matrix calculation library to perform calculations, such as using the eigs command in Matlab to calculate.

(4) Let z=Φ ^-1 ·u, g=Φ ^T ·F, then the dynamic equation of the elastic object can be simplified into a diagonal equation: $\mathrm{\&Lambda;}\&CenterDot;z+({\mathrm{\&alpha;}}_1\mathrm{\&Lambda;}+{\mathrm{\&alpha;}}_{2}I)\&CenterDot;\stackrel{.}{z}+\stackrel{..}{z}=g,$ Here z is regarded as the value expressed in the modal coordinates, F is the external force vector generated by the system such as collision or user input, I is the identity matrix, and u is the position of the vertex.

(5) Each frame numerically solves the quadratic differential equation in step 4 $\mathrm{\&Lambda;}\&CenterDot;z+({\mathrm{\&alpha;}}_1\mathrm{\&Lambda;}+{\mathrm{\&alpha;}}_{2}I)\&Center\; Dot;\stackrel{.}{z}+\stackrel{..}{z}=g,$ Computes a new value for the modal coordinate z.

(6) Update the displacement u of each vertex according to u=u ₀ +Φ·z, if the simulation has not been completed, return to step 5, otherwise end. Figure 5 shows the physical deformation effect of the bunny base grid model. In this example, the resultant force applied is located at the mouth of the bunny, and the number of retained modes is 24. The calculation time required for base grid deformation is about 5ms.

Step 4: Reconstruct the fine mesh model based on the deformed base mesh model and detail codes.

The process of detailed reconstruction of fine mesh vertex p is as follows:

(1) According to the base grid model after physical deformation, calculate the new position and

(2) New normal vectors, denoted as q′ and N _q′ respectively, where q′=αa′+βb′+γc′ and N _q′ =αN _a′ +βN _b′ +γN _c′ , where a′, b ' and c' are the new deformed positions of the three vertices of the triangle corresponding to point p, and N _a' , N _b' and N _c' are the new normal vectors of the three vertices after deformation, all of which can be obtained through physical deformation calculation.

(3) Calculate the new position p' of the point p after deformation by the formula p'=q'+h·N _q' ; h is the distance code in the detail code.

(4) Calculate the new normal vector N _p' after deformation of point p through the formula N _p' = R _q' N _local ; where R _q ' is the new transformation matrix after deformation, and the normal vector and tangent of point q' after deformation can be calculated The vector is obtained, the specific formula is R' _q = [T' _q B' _q N' _q ], T' _q = a'-b', N _q' is calculated as shown in step 2, B' _q = T' _q × N′ _q , Nlocal is the normal vector encoding value in detail encoding.

(5) Repeat the above steps until all vertices on the fine mesh are reconstructed, and then send information such as vertex positions and normal vectors of the fine mesh model to the frame buffer for realistic rendering.

Figure 6 shows the rendering of the deformed bunny fine mesh model. Comparing Figure 3 and Figure 5, it can be seen that the detailed encoding and reconstruction method proposed in this paper can better restore the detailed features of the object surface. The total time required for Bunny's deformation and reconstruction is 21.5ms, and the rendering frame rate reaches 46.7fps, which can fully meet the real-time needs.

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, $\mathrm{\&Lambda;}\&CenterDot;z+({\mathrm{\&alpha;}}_1\mathrm{\&Lambda;}+{\mathrm{\&alpha;}}_{2}I)\&CenterDot;\stackrel{\&CenterDot;}{z}+\stackrel{\&CenterDot;\&CenterDot;}{z}=g,$ 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) $\mathrm{\&Lambda;}\&CenterDot;z+({\mathrm{\&alpha;}}_1\mathrm{\&Lambda;}+{\mathrm{\&alpha;}}_{2}I)\&CenterDot;\stackrel{\&CenterDot;}{z}+\stackrel{\&CenterDot;\&CenterDot;}{z}=g,$ 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, $B_q^{/}=T_q^{\&prime;}\&times;N_q^{\&prime;},$ 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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