CN104463934A - Automatic generation method for point set model animation driven by mass point-spring system - Google Patents

Automatic generation method for point set model animation driven by mass point-spring system Download PDF

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CN104463934A
CN104463934A CN201410617737.8A CN201410617737A CN104463934A CN 104463934 A CN104463934 A CN 104463934A CN 201410617737 A CN201410617737 A CN 201410617737A CN 104463934 A CN104463934 A CN 104463934A
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point set
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CN104463934B (en
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祁彬斌
庞明勇
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Nanjing Normal University
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T13/00—Animation

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Abstract

The invention discloses an automatic generation method for a point set model animation driven by a mass point-spring system. The method includes the steps that firstly, point set model data are read, the point set model data are zoomed to the designated size, and an axial coordinate bounding box of a zoomed model is calculated; the mass point-spring system is set up by partitioning the bounding box, and the incidence relation of a spring grid and all points in the point set model is determined; the stress condition of the mass point-spring system is analyzed according to the set initial conditions and the basic movement law, and updating of the positions of the points in a point set is driven by the spring system. In the point set changing process, a point set curved surface is constructed by the point set model at the current moment, gridding processing is conducted on the point set curved surface, and a current frame of the animation is generated by drawing a grid model; a follow-up frame of the animation is determined by the spring system state determined by a kinetic equation at the next moment. According to the automatic generation method, the motion animation of the point set model can be automatically generated simply by setting the initial state of the system.

Description

A kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive
Technical field
The point-based surface Automatic Generation of Computer Animation method of open a kind of " Mass-spring " system drive of the present invention, the method belongs to Computer Animated Graph field, particularly relates to the technical method of point set Automatic Generation of Computer Animation.
Background technology
In computer animation field, the method generating animation mainly contains following three kinds: method, key frame method and skeleton cartoon frame by frame.Frame refers to the single width image frame of least unit in animation, and be equivalent to each the lattice camera lens on cinefilm, on the time shaft of animation software, frame shows as lattice.
Method is exactly edit one by one the content of each frame and draw frame by frame, then plays formation animation successively according to time sequencing.These class methods are mainly used in the making of traditional animation.Its advantage is: good simulation, and degree of freedom is high, can simulate the change of various picture; Weak point is: animation work is very loaded down with trivial details, and labour intensity is huge.
Key frame method refers in the manufacturing process of animation, and designer is only responsible for the key picture of design animation, generates middle transition frames, and then complete the making of animation by computing machine by interpolation calculation.Relative to method frame by frame, these class methods significantly reduce the workload of animation personnel, reduce the cost of cartoon making; Its weak point is: when processing comparatively complicated motion process, still needs the sense of reality effect of drawing a large amount of key frame guarantee cartoon pictures; If it is improper that Partial key frame is arranged, also the phenomenons such as action distortion can be produced in animation.
Skeleton cartoon (see: Qi Jun, patent " a kind of implementation method of skeleton cartoon ", application number: CN201110362515.2) in technology, animation model is represented by two parts: a part is a series of bones (i.e. skeleton) represented by hierarchical structure, and each bone contains himself animation data; Another part covers skin (i.e. grid model) on skeleton, for providing the geometric model of animate and texture and material information etc.By carrying out animation simulation to skeleton, recycling bone controls skin and just generates skeleton cartoon effect.Relative to key-frame animation, the method, when generating animation, only need store bone (bone number the is relatively less) data of each frame, thus take up room less, and multiple skin can share identical bone to generate different animations; Weak point is: consuming time more in skeleton cartoon render process, the kinematic relation between marrow and skin is not easily held.
Summary of the invention
The present invention is directed to the deficiencies in the prior art, propose a kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive.The method, based on point-based surface and physical motion rule, by the starting condition of setting animation motion, generates the model sport and the surf deform effect that meet nature physics law quickly and automatically.Relative to key-frame animation, this method without the need to drawing key frame, thus decreases the workload of designer, has saved the cost of cartoon making; Relative to skeleton cartoon, this method, without the need to defining the movement locus of bone, is played up refresh rate fast, is convenient to animation personnel and simply, quickly carries out cartoon making.
The present invention is by the following technical solutions:
A kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, the steps include:
A. point-based surface pre-service: read point-based surface data, these data are the coordinates on a series of three dimensions summit under determining coordinate system; Choose the maximal value in the x, y, z-directions of apex coordinate in point-based surface and minimum value respectively, and build according to these values the axial bounding box B that each rib is all parallel to coordinate axis 1; To bounding box B 1with the point set equal proportion convergent-divergent in bounding box, make its longest edge limit be L, form normalization point-based surface and bounding box B 2; By Standardized Model and bounding box B thereof 2move to the easy process position in coordinate system space;
B. " Mass-spring " system is set up: by bounding box B 2in be parallel to x, y, z axle each bar rib be split into N 1, N 2, N 3part, claim the length of every part to be Duan Yuan, formation size is N 1× N 2× N 3space lattice structure, it is by bounding box B 2be split into a series of little grid cell; Choose bounding box B 28 summits in coordinate components reckling be designated as p, calculate the section unit number that other vertex raster departs from relative to a p, obtain each vertex raster coordinate; Placing quality at vertex raster place is the particle of M, is adjacent by each particle or the adjacent particle in interval adopts stiffness coefficient to be that the spring of K is connected, and obtains " Mass-spring " system;
C. correlation model summit and spring graticule mesh: set up in " Mass-spring " system at each some v ∈ P and its place in point-based surface the incidence relation determined between space lattice unit: call number and the local relative position of some v residing in grid of first determining any point place grid in point-based surface; According to the section unit number that model points v place grid departs from relative to a p, the call number of computation grid; Any in the grid of selected point v place, as basic point b, sets up the relativeness of some v and basic point b;
D. apply acting force in spring system: particle movement original state is set, as parameters such as the mass M of spring, initial speed V, acting force is applied to the some or all particles in " Mass-spring " system, changes its motion state;
E. analyze the stressing conditions of spring system, and upgrade point set coordinate: detect each particle in " Mass-spring " system, analyze particle stressing conditions according to spring annexation: calculate it and be subject to making a concerted effort of spring inner power, damping, gravity etc.; Then information and its position coordinates at subsequent time such as acceleration, speed, displacement of each particle is solved according to Newton's law;
F. build point-based surface corresponding point set curved surface: according to the locus of each point in current point-based surface, the implicit surface using curved surface fitting method to construct current point-based surface represents;
G. gridding point set curved surface: the set by the uniformly subdivision at implicit surface place being small cubes (Cubes), adopt the Marching Cubes method based on uniformly subdivision, trigonometric ratio process is carried out to the part of implicit surface in each small cubes, and the trigonometric ratio results set in all small cubes is got up, implicit surface is converted into triangle grid model;
H. animation producing: the present frame grid model of generation being played up animation, and the next frame of spring system Determines animation by the determined subsequent time of kinetics equation, iterate and (namely get back to e step, the stressing conditions of iterative analysis spring system, renewal point set coordinate, reconstruction grid model), until the animation frame series needed for generating.This series of successive frame achieves the automatic generation of animation.
The inventive method is relative to prior art, and tool has the following advantages:
(1) be applicable to 2D, 3D animation field simultaneously, can be used for the generation of various physically based deformation rule animation;
(2) need only given original state, follow-up object moving state is produced by " Mass-spring " system automatic Iterative, without the need to considering complicated intermediate link, greatly simplifies the workload of designer;
(3) according to the quality of setting parameter particle, the stiffness factor, damping, acceleration of gravity etc. of spring, different animation effects can be produced by different array modes.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the inventive method and the change situation of related data;
Fig. 2 is the bounding box example of point-based surface before and after convergent-divergent: wherein (a) is the bounding box before convergent-divergent, and (b) is the bounding box after convergent-divergent;
Fig. 3 is that the bounding box example after rasterizing (gets N 1=4, N 2=3, N 3=2);
Fig. 4 is vertex raster deviation point p section unit number schematic diagram;
Fig. 5 is the example of " Mass-spring " system under 2D condition: (a) is " Mass-spring " system summary structure, and (b) is structure spring, and (c) is shear spring, and (d) is flexural spring;
Fig. 6 is model points schematic diagram relative to basic point present position in grid;
Fig. 7 is the schematic diagram that the part of implicit surface in a small cubes can be approached with triangle;
Fig. 8 is 15 kinds of simplification situations of small cubes summit distinct symbols configuration.
Embodiment
Below in conjunction with drawings and Examples, the present invention is elaborated.
As shown in Figure 1, a kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, its concrete implementation step is as follows:
The point-based surface data read according to user and the starting condition of setting: scale lengths L, the number N of bounding box decile 1, N 2, N 3, the initial length L of spring 0(L 0be spring connect two particles between distance), the stiffness coefficient K (K=α/L of spring 0, in this example, α=15.0), the mass M of particle, ratio of damping C ddeng, realize the automatic generation of point-based surface animation.
1. the pre-service of point-based surface: this example builds the axial bounding box B of rectangular parallelepiped to the point-based surface read in 1, determine L and bounding box B 1the longest edge limit between ratio, according to this ratio to point-based surface and rectangular parallelepiped bounding box B 1carry out proportional convergent-divergent process, and the geometric center both moving is to true origin.Specific practice is:
A) read point-based surface data to internal memory by file, set up one-dimension array and deposit point set, and define vertex data structure, comprise x, y, z tri-components, deposit the coordinate figure of point set.Meanwhile, the minimum value x on x, y, z tri-directions is recorded 1, y 1, z 1with maximal value x 2, y 2, z 2.Then rectangular parallelepiped bounding box 8 apex coordinates are (x 1, y 1, z 1), (x 1, y 1, z 2), (x 1, y 2, z 1), (x 1, y 2, z 2), (x 2, y 1, z 1), (x 2, y 1, z 2), (x 2, y 2, z 1), (x 2, y 2, z 2), rectangular parallelepiped bounding box B can be determined 1size, can with reference to accompanying drawing 2 (a).
B) rectangular parallelepiped bounding box B 1length, width and height be respectively W, H, D, in this example, scale lengths L=2, then scaling ratio is:
μ＝max(W,H,D)/L
According to μ to point-based surface and rectangular parallelepiped bounding box B 1carry out proportional convergent-divergent process, form normalization point-based surface and bounding box B 2, with reference to accompanying drawing 2 (b), and the geometric center both moving is to true origin.
2. set up " Mass-spring " system: in this example, by rectangular parallelepiped bounding box B 2be parallel to x, y, each bar rib of z-axis is divided into N 1, N 2, N 3part (gets N 1=6, N 2=6, N 3, and claim every part for Duan Yuan=6); Formation size is N 1× N 2× N 3space lattice structure, it is by bounding box B 2subdivision is a series of little space lattice unit, and accompanying drawing 3 is the space lattice structural representation of 4 × 3 × 2.Setting bounding box B 28 summits in x, y, the z value point that is all less than 0 be p (with reference to accompanying drawing 4), if D x, D y, D zbe the section unit number that in space lattice structure, arbitrary mess point q departs from relative to net point p, the coordinate (i, j, k) of some q can be expressed as:
i＝(D x-N 1/2)×W/(μ×N 1)
j＝(D y-N 2/2)×H/(μ×N 2)
k＝(D z-N 3/2)×D/(μ×N 3)
And then place particle at vertex raster place, each particle is adjacent or uses between the particle of interval the spring that stiffness factor is K to connect, can with reference to accompanying drawing 5.
A) structure spring: structure spring is connected by a particle with the particle that it is directly connected, can with reference to accompanying drawing 5 (b).
B) shear spring: shear spring is by a particle and is connected with the particle at its diagonal angle, can with reference to accompanying drawing 5 (c).
C) flexure spring: flexure spring strides across a particle, is connected a particle and its interval particle, can with reference to accompanying drawing 5 (d).
For rectangular parallelepiped grid screen, each particle has 6 structure springs, 6 flexure springs, 12 shear springs, and frontier point place needs special consideration.After spring is added to all particles, finally obtain " Mass-spring " system.
3. correlation model summit and spring graticule mesh: in this example, the incidence relation setting up each point in spring graticule mesh and point-based surface mainly comprises two steps: the call number of solving model point v place grid and the position of some v residing in grid.Specific practice is as follows:
A) from step 2, the section unit number that model points v place grid departs from relative to net point p is respectively D x, D y, D z, in other words D x, D y, D zbe respectively some x of v place grid, a y, the call number on z-axis direction, is translated into one dimension form, that is:
index＝D x+D y×N 1+D z×N 1×N 2
Wherein D x∈ [0, N 1-1], D y∈ [0, N 2-1], D z∈ [0, N 3-1].In formula, index is that a v is at rectangular parallelepiped bounding box B 2in corresponding grid.
B) using the geometric center point of each little grid in " Mass-spring " system as true origin, build local spatial coordinate system, its coordinate axis is consistent to global coordinate system.By x, y in little grid 8 summits, z coordinate value is all in coordinate system and bears the point of axle as basic point b (b x, b y, b z), calculate the length on basic point and adjacent three summits, be designated as R respectively x, R y, R z.And then record each model points v (v x, v yv z) on three components with the distance of basic point (can with reference to accompanying drawing 6), and calculate proportion P x, P y, P z, the ratio value namely in point-based surface is:
P x＝(v x-b x)/R x；
P y＝(v y-b y)/R y；
P z＝(v z-b z)/R z。
4. apply acting force in spring system: particle movement original state is set, as the parameter such as mass M=0.01 of particle, acting force is applied to the part particle in " Mass-spring " system, changes its motion state.
5. analyze the stressing conditions of spring system, and upgrade point set coordinate: in this example, by the method for lining by line scan, detect each particle and be subject to making a concerted effort of spring inner power, damping, gravity etc.; Then solve the position coordinates of each particle at subsequent time according to Newton's law and dominant euler integration scheme, realize the whole updating of " Mass-spring " system;
And then the location updating of each point in point-based surface is driven by spring system.Mainly be divided into following 3 steps:
A) detect the particle in " Mass-spring " system, by the way of lining by line scan, detect the stressing conditions of each particle.We stressedly to make a concrete analysis of with regard to it below:
First, each particle is all subject to spring system internal forces, uses f ijrepresent the power of spring action on particle i between particle i and particle j, Hooke law followed by spring here, then have:
f ij = k ij ( | | x j - x i | | - l ij 0 ) × x j - x i | | x j - x i | |
K ijfor the elastic coefficient between particle i and particle j, x iand x jrepresent the position of two particles respectively, represent the initial length of spring.K in this example ij, be respectively the initial length L of stiffness factor K mentioned above and spring 0.
Therefore particle i total force just can be expressed as:
f i = Σ ( i , j ∈ E ) f ij = Σ ( i , j ∈ E ) k ij ( | | x j - x i | | - l ij 0 ) × x j - x i | | x j - x i | |
Secondly, this example also adopts damper model, specific as follows:
f d＝-C d(v i-v j)
Here f dconnect the damping force of spring action on particle i between particle i and particle j, C dratio of damping, v i, v jthe movement velocity of two particles, C in this example d=0.001.Total damping force that such particle acts on can be expressed as:
f i d = - C d Σ ( i , j ∈ E ) ( v i - v j )
In addition, in particle spring system, each particle has identical mass M.The power that these particles are subject to due to earth attraction we be referred to as gravity, the size of this gravity is directly proportional with the quality of particle, then arbitrary particle i is subject to gravity f gifor:
f gi＝m ig
Wherein, f gifor the gravity of particle i suffered by moment t; m ifor the quality of particle i, be M mentioned above; G is acceleration of gravity, is a constant value.According to Newton interpolation algorithm, then the f that makes a concerted effort of the power of particle i suffered by t i closefor:
F i close=f i+ f i d+ f gi
B) after force analysis completes, use dominant euler integration scheme, obtain the speed in moment after Δ t, displacement is equivalent, concrete formula is as follows:
A i=f i close/ m i
v i n + 1 = v i n + Δt × a i
x i n + 1 = x i n + Δt × v i n
These two formula, show that each particle needs storage two attributes, speed and positions.After elapsed time step delta t, utilize above formula can calculate new speed and the coordinate of subsequent time.
C) after above step completes, the position of each particle there occurs change, realizes the whole updating of " Mass-spring " system, and by each point v (v in " Mass-spring " system drive point-based surface x, v yv z) location updating.Specific as follows:
v x＝P x×R x+b x
v y＝P y×R y+b y
v z＝P z×R z+b z
Here (b x, b y, b z) be the coordinate (note, the basic point coordinate of each grid cell is different) of basic point in the grid cell of model points place, P x, P y, P zthe scale-up factor calculated, R x, R y, R zit is the distance upgrading rear spring system basic point and consecutive point.Finally, the coordinate figure after point-based surface renewal is calculated.
6. build point-based surface corresponding point set curved surface: according to the spatial positional information of each point in current point-based surface, use the curve reestablishing technology based on approximating method, the implicit surface constructing current point-based surface represents." multi-level unit subdivision implicit surface reconstructing method " is adopted to obtain the implicit surface approximating function of current point-based surface herein, concrete grammar is see (Ohtake Y, Belyaev A, Alexa M, Deng .Multi-level partition of unity implicits.ACMTransaction of Graphics, 2003,22 (3): 463-470).If the implicit surface function constructed is f (x, y, z), then for any point p ∈ R in three dimensions 3, have:
7. gridding point set curved surface: the set by the uniformly subdivision at implicit surface place being one group of small cubes (Cubes), adopt the Marching Cubes method based on uniformly subdivision, trigonometric ratio process is carried out to the part of implicit surface in each small cubes.For each small cubes, first ask the implicit surface functional value on its 8 summits; Judge the implicit surface functional value whether contrary sign on the summit on each bar limit of small cubes again; If contrary sign, the certain and surface intersection in this limit, adopts dichotomy can in the hope of the approximate value of respective quadrature point.As shown in Figure 7, the part of curved surface a small cubes inside can be approached with triangle, and vertex of a triangle is the intersection point on curved surface and small cubes limit.28 kinds of situations configuring according to the symbol on small cubes 8 summits (according to symmetry, 28 kinds of situations can be reduced to 15 kinds of situations as shown in Figure 8), can by the part triangularization of curved surface in each small cubes inside; Triangularization results set in all small cubes is got up, just obtains the triangle gridding approximate model of implicit surface.
8. animation producing: the present frame grid model of generation being played up animation, and the next frame of spring system Determines animation by the determined subsequent time of kinetics equation, iterate and (namely get back to the 5th step, the stressing conditions of iterative analysis spring system, upgrade point set coordinate, rebuild grid model).Due to the existence of damping, the kinetic energy of " Mass-spring " system can progressively weaken, until whole spring system remains static, now, this series of successive frame achieves the automatic generation of animation.

Claims (1)

1. the point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, the steps include:
A. point-based surface pre-service: read point-based surface data, these data are the coordinates on a series of three dimensions summit under determining coordinate system; Choose the maximal value in the x, y, z-directions of apex coordinate in point-based surface and minimum value respectively, and build according to these values the axial bounding box B that each rib is all parallel to coordinate axis 1; To bounding box B 1with the point set equal proportion convergent-divergent in bounding box, make its longest edge limit be L, form normalization point-based surface and bounding box B 2; By Standardized Model and bounding box B thereof 2move to the easy process position in coordinate system space;
B. " Mass-spring " system is set up: by bounding box B 2carry out subdivision, form space lattice structure; Placing quality at vertex raster place is the particle of M, is adjacent by each particle or the adjacent particle in interval adopts stiffness coefficient to be that the spring of K is connected, and obtains " Mass-spring " system;
C. correlation model summit and spring graticule mesh: according to the position distribution relation on each summit in the space lattice in " Mass-spring " system and point-based surface, determine the grid corresponding to each summit in point-based surface, sets up association therebetween;
D. apply acting force in spring system: particle movement original state is set, acting force is applied to the some or all particles in " Mass-spring " system, changes its motion state;
E. analyze the stressing conditions of spring system, and upgrade point set coordinate: detect each particle in " Mass-spring " system, analyze particle stressing conditions according to spring annexation: calculate it and be subject to spring inner power, damping, the making a concerted effort of gravity and other power; Then the acceleration of each particle, speed, displacement and other information and its position coordinates at subsequent time is solved according to the law of motion;
F. build point-based surface corresponding point set curved surface: according to the locus of each point in current point-based surface, the implicit surface using curved surface fitting method to construct current point-based surface represents;
G. gridding point set curved surface: adopt the Marching Cubes method based on uniformly subdivision, implicit surface is converted into triangle grid model;
H. animation producing: the present frame grid model of generation being played up animation, and the next frame of spring system Determines animation by the determined subsequent time of kinetics equation; Iterate, until the animation frame series needed for generating.
CN201410617737.8A 2014-11-05 2014-11-05 A kind of point-based surface Automatic Generation of Computer Animation method of " mass spring " system drive Expired - Fee Related CN104463934B (en)

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CN112057854A (en) * 2020-09-10 2020-12-11 网易（杭州）网络有限公司 Game object processing method and device, electronic equipment and computer readable medium
CN112528522A (en) * 2020-12-29 2021-03-19 福州智永信息科技有限公司 Lightweight flexible body effect realization method and terminal
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