CN104463934B - A kind of point-based surface Automatic Generation of Computer Animation method of " mass spring " system drive - Google Patents
A kind of point-based surface Automatic Generation of Computer Animation method of " mass spring " system drive Download PDFInfo
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Abstract
The present invention discloses a kind of point-based surface Automatic Generation of Computer Animation method by " mass spring " system drive.Method reads point-based surface data first, scales it to specify size, and calculate the coordinate axial direction bounding box of model after scaling；Then " mass spring " system is set up by subdivision bounding box, while determining the incidence relation of spring grid and each point in point-based surface；Primary condition and motion philosophy according to setting, analyze the stressing conditions of " mass spring " system, drive point to concentrate the location updating of each point by spring system.In a collection changing process, point set curved surface is built by current time point-based surface, and point set curved surface is carried out into gridding treatment, then the present frame of animation is generated by drawing grid model；The spring system Determines of the subsequent frame of animation subsequent time determined by kinetics equation.This method only needs the original state of initialization system just can to automatically generate point-based surface motion animation.
Description
Technical field
The present invention discloses a kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, and the party is owned by France
In Computer Animated Graph field, more particularly to point set Automatic Generation of Computer Animation technical method.
Background technology
In computer animation field, the method for generating animation mainly has following three kinds：Method, key frame method and bone frame by frame
Animation.Frame refers to the single width image frame of least unit in animation, soft in animation equivalent to each lattice camera lens on cinefilm
Frame shows as a lattice on the time shaft of part.
Method is exactly that the content of each frame is edited and drawn one by one frame by frame, then plays shape successively sequentially in time
Into animation.Such method is mainly used in the making of traditional animation.Its advantage is：Good simulation, the free degree is high, can simulate various pictures
Face changes；It is disadvantageous in that：Animation work is very cumbersome, and labour intensity is huge.
Key frame method refers to that in the manufacturing process of animation, designer is only responsible for the key picture of design animation, by
Computer generates middle transition frames by interpolation calculation, and then completes the making of animation.Relative to method frame by frame, such method shows
Reduce the workload of animation personnel with writing, reduce the cost of cartoon making；Its weak point is：It is more multiple processing
During miscellaneous motion process, it is still necessary to draw the sense of reality effect that substantial amounts of key frame just can guarantee that cartoon picture；If Partial key
It is improper that frame is set, and also generation can act the phenomenons such as distortion in animation.
Skeleton cartoon (referring to：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 that represented with hierarchical structure is
Row bone (i.e. skeleton), each bone contains the animation data of its own；Another part is the skin covered on skeleton
(i.e. grid model), for providing geometrical model and texture and material information required for animation is drawn etc..Carried out by skeleton
Animation simulation, recycles bone control skin to be generated as skeleton cartoon effect.Relative to key-frame animation, the method is in generation
During animation, bone (bone number is relatively fewer) data of each frame need to be only stored, thus it is smaller to take up room, and multiple skins
Skin can share identical bone to generate different animations；It is disadvantageous in that：More, bone is taken in skeleton cartoon render process
Movement relation between marrow and skin is difficult to hold.
The content of the invention
The present invention in view of the shortcomings of the prior art, proposes a kind of point-based surface animation of " Mass-spring " system drive certainly
Dynamic generation method.The method is based on point-based surface and physical motion rule, by setting the primary condition that animation is moved, quickly,
Automatically generate the model sport and curved surface deformation effect for meeting nature physics law.Relative to key-frame animation, this method without
Key frame need to be drawn, so as to reduce the workload of designer, the cost of cartoon making has been saved；Relative to skeleton cartoon,
This method need not define the movement locus of bone, render refresh rate soon, be easy to animation personnel simply and quickly to enter action
Draw and make.
The present invention uses following technical scheme：
A kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, its step is：
A. point-based surface pretreatment：Point-based surface data are read, the data are to determine a series of three dimensions under coordinate system
The coordinate on summit；Apex coordinate maximum and minimum value in the x, y, z-directions in point-based surface is chosen respectively, and according to these
Value builds axial bounding box B of each rib each parallel to reference axis1；To bounding box B1Point set equal proportion scaling with bounding box, makes
Its longest edge side is L, forms normalization point-based surface and bounding box B2；By Standardized Model and its bounding box B2Move to coordinate
It is the disposable position in space；
B. " Mass-spring " system is set up：By bounding box B2In be split into N parallel to each bar rib of x, y, z axle1、N2、N3
Part, every part of length is called Duan Yuan, forms size for N1×N2×N3Space lattice structure, it is by bounding box B2It is split into one
The small grid cell of series；Choose bounding box B28 summits in coordinate components reckling be designated as p, calculate other vertex rasters
Relative to the section unit number that point p deviates, each vertex raster coordinate is obtained；It is the particle of M that quality is placed at vertex raster, will be every
One particle is adjacent thereto or the adjacent particle in interval uses stiffness coefficient to be connected for the spring of K, obtains " Mass-spring " system；
C. correlation model summit and spring grid：Set up each point v ∈ P and the " particle-bullet where it in point-based surface
The incidence relation between space lattice unit is determined in spring " system：First determine the index of grid where any point in point-based surface
Number and point v residing in grid local relative position；According to grid where model points v relative to the first number of section that point p deviates,
The call number of computation grid；Any in grid where selected point v sets up the relativeness of point v and basic point b as basic point b；
D. active force is applied in spring system：Particle movement original state, such as mass M of spring, initial speed V are set
Etc. parameter, some or all particles in " Mass-spring " system are applied with active force, change its motion state；
E. the stressing conditions of spring system are analyzed, and updates point set coordinate：Each matter in detection " Mass-spring " system
Point, particle stressing conditions are analyzed according to spring annexation：Calculate it and be subject to making a concerted effort for spring inner power, damping, gravity etc.；So
The information such as acceleration, speed, the displacement of each particle are solved according to Newton's law afterwards and it sits in the position of subsequent time
Mark；
F. the corresponding point set curved surface of point-based surface is built：According to the locus of each point in current point-based surface, with song
The implicit surface that face approximating method constructs current point-based surface is represented；
G. gridding point set curved surface：It is the set of small cubes (Cubes) by the uniformly subdivision where implicit surface, uses
Marching Cubes methods based on uniformly subdivision, are carried out at trigonometric ratio to part of the implicit surface in each small cubes
Reason, 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 grid model of generation is rendered to the present frame of animation, and determined by kinetics equation
The next frame of the spring system Determines animation of subsequent time, iterates and (returns to e steps, iterative analysis spring system
Stressing conditions, update point set coordinate, rebuild grid model), untill the animation frame series needed for generation.This is a series of
Successive frame realizes automatically generating for animation.
The inventive method has the following advantages that relative to prior art：
(1) while being applied to 2D, 3D animation field, can be used for the various generations based on physics law animation；
(2) original state need only be given, follow-up object moving state is produced by " Mass-spring " system automatic Iterative,
Without considering complicated intermediate link, the workload of designer is greatly simplified；
(3) quality, the stiffness factor of spring, damping, acceleration of gravity according to parameter setting particle etc., by different
Combination can produce different animation effects.
Brief description of the drawings
Fig. 1 is the flow chart 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 scaling：Wherein (a) is the bounding box before scaling, and (b) is after scaling
Bounding box；
Fig. 3 is that the bounding box example after rasterizing (takes N1=4, N2=3, N3=2)；
Fig. 4 is the first number schematic diagram of p sections of vertex raster deviation point；
Fig. 5 is the example of " Mass-spring " system under the conditions of 2D：A () is " Mass-spring " system summary structure, (b) is knot
Structure spring, (c) is shear spring, and (d) is flexural spring；
Fig. 6 be model points in grid relative to the schematic diagram of basic point present position；
Fig. 7 is the schematic diagram that part of the implicit surface in a small cubes can be approached with triangle；
Fig. 8 is 15 kinds of simplified situations of small cubes summit distinct symbols configuration.
Specific embodiment
With reference to the accompanying 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 specific reality
Apply step as follows：
The point-based surface data and the primary condition of setting read according to user：Scale lengths L, part of bounding box decile
Number N1、N2、N3, the initial length L of spring0(L0Be spring connection two particles between distance), the stiffness coefficient K of spring (K=α/
L0, in this example, α=15.0), the mass M of particle, damped coefficient CdDeng realizing automatically generating for point-based surface animation.
1. the pretreatment of point-based surface：This example builds the axial bounding box B of cuboid to the point-based surface for reading in1, determine L
With bounding box B1The longest edge side between ratio, according to this ratio to point-based surface and cuboid bounding box B1Carry out proportional
Scaling treatment, and move the geometric center of the two to the origin of coordinates.Specific practice is：
A) point-based surface data are read to internal memory by file, sets up one-dimension array storage point set, and define vertex data knot
Structure, comprising x, tri- components of y, z deposit the coordinate value of point set.At the same time, x, the minimum value x on tri- directions of y, z are recorded1,
y1,z1With maximum x2,y2,z2.Then 8 apex coordinates of cuboid bounding box are (x1,y1,z1)、(x1,y1,z2)、(x1,y2,z1)、
(x1,y2,z2)、(x2,y1,z1)、(x2,y1,z2)、(x2,y2,z1)、(x2,y2,z2), you can determine cuboid bounding box B1It is big
It is small, refer to accompanying drawing 2 (a).
B) cuboid bounding box B1Length, width and height be respectively in W, H, D, this example, scale lengths L=2, then scaling ratio
For：
μ=max (W, H, D)/L
According to μ to point-based surface and cuboid bounding box B1Proportional scaling treatment is carried out, normalization point-based surface is formed
With bounding box B2, refer to the attached drawing 2 (b), and move the geometric center of the two to the origin of coordinates.
2. " Mass-spring " system is set up：In this example, by cuboid bounding box B2Parallel to x, y, each bar rib of z-axis
It is divided into N1、N2、N3Part (takes N1=6, N2=6, N3=6), and every part is called Duan Yuan；Formation size is N1×N2×N3Space
Lattice structure, it is by bounding box B2Subdivision is a series of small space lattice units, and accompanying drawing 3 is 4 × 3 × 2 space lattice knot
Structure schematic diagram.Setting bounding box B28 summits in x, y, z value be respectively less than 0 point be p (refer to the attached drawing 4), if Dx、Dy、DzIt is
Relative to the section unit number that mesh point p is deviateed, the coordinate (i, j, k) of point q can be represented arbitrary mess point q in space lattice structure
For：
I=(Dx-N1/2)×W/(μ×N1)
J=(Dy-N2/2)×H/(μ×N2)
K=(Dz-N3/2)×D/(μ×N3)
And then at vertex raster place particle, each particle it is adjacent thereto or interval particle between be using stiffness factor
The spring of K is attached, and refers to accompanying drawing 5.
A) structure spring:Structure spring is connected by a particle and with the particle that it is joined directly together, and refers to accompanying drawing 5
(b)。
B) shear spring：Shear spring is to be connected a particle and the particle diagonal with it, refers to accompanying drawing 5 (c).
C) flexure spring：With its interval particle be connected one particle across a particle by flexure spring, refers to attached
Fig. 5 (d).
For cuboid grid screen, each particle has 6 structure springs, 6 flexure springs, 12 shearing bullets
Spring, needs special consideration at boundary point.After to all particles addition spring, " Mass-spring " system is finally obtained.
3. correlation model summit and spring grid：In this example, each point in spring grid and point-based surface is set up
Incidence relation mainly includes two steps：The call number and point v of grid where solving model point v location in grid.Specifically
Way is as follows：
A) from step 2, grid where model points v is relative to section unit's number respectively D that mesh point p is deviateedx、Dy、
Dz, in other words Dx、Dy、DzThe x of grid where respectively point v, y, the call number on z-axis direction is translated into one-dimensional shape
Formula, i.e.,：
Index=Dx+Dy×N1+Dz×N1×N2
Wherein Dx∈[0,N1-1],Dy∈[0,N2-1],Dz∈[0,N3-1].Index is point v in cuboid bounding box in formula
B2In corresponding grid.
B) using the geometric center point of each small grid in " Mass-spring " system as the origin of coordinates, build local empty
Between coordinate system, its coordinate axially is consistent with global coordinate system.By x, y in 8 summits of small grid, z coordinate value is all in seat
The point of the negative axle of mark system is used as basic point b (bx, by, bz), basic point and three adjacent length on summit are calculated, R is designated as respectivelyx、Ry、
Rz.And then record each model points v (vx, vy vz) on three components with the distance (referring to accompanying drawing 6) of basic point, and calculate
Proportion Px、Py、Pz, i.e., the ratio value in point-based surface is：
Px=(vx-bx)/Rx；
Py=(vy-by)/Ry；
Pz=(vz-bz)/Rz。
4. active force is applied in spring system：Particle movement original state, such as mass M=0.01 ginseng of particle are set
Number, active force is applied to the part particle in " Mass-spring " system, changes its motion state.
5. the stressing conditions of spring system are analyzed, and updates point set coordinate：In this example, the side by progressively scanning
Method, detects that each particle is subject to making a concerted effort for spring inner power, damping, gravity etc.；Then according to Newton's law and dominant Euler product
Point-score solves position coordinates of each particle in subsequent time, realizes the whole updating of " Mass-spring " system；
And then the location updating of each point in point-based surface is driven by spring system.It is broadly divided into following 3 step：
A) particle in detection " Mass-spring " system, by the method for progressively scanning, detects the stress of each particle
Situation.We make a concrete analysis of with regard to its stress below：
First, each particle is all subject to spring system inside power, uses fijRepresent the spring effect between particle i and particle j
Power on particle i, spring here follows Hooke laws, then have:
kijIt is the elastic coefficient between particle i and particle j, xiAnd xjTwo positions of particle are represented respectively,Generation
The initial length of table spring.K in this exampleij、The initial length L of stiffness factor K respectively mentioned above and spring0。
Therefore particle i total forces can just be expressed as：
Secondly, this example is also adopted by damper model, specific as follows：
fd=-Cd(vi-vj)
Here fdIt is damping force of the spring effect between connection particle i and particle j on particle i, CdIt is damped coefficient,
vi, vjIt is the movement velocity of two particles, C in this exampled=0.001.The total damping force acted on so on particle is represented by：
Additionally, each particle possesses identical mass M in particle spring system.These particles are received due to earth attraction
The power for arriving is directly proportional we term it gravity, the size of the gravity with the quality of particle, then any particle i is subject to gravity fgiFor：
fgi=mig
Wherein, fgiIt is particle i in the gravity suffered by moment t；miIt is the quality of particle i, is M mentioned above；G is gravity
Acceleration, is a constant value.According to Newton interpolation algorithm, then make a concerted effort fs of the particle i in the power suffered by ti CloseFor：
fi Close=fi+fi d+fgi
B) after the completion of force analysis, using dominant euler integration scheme, speed, the displacement equivalence, tool at moment after Δ t are obtained
Body formula is as follows：
ai=fi Close/mi
The two formula, show that each particle needs to store two attributes, speed and position.Elapsed time step delta t
Afterwards, the new speed and coordinate of subsequent time can be calculated using above formula.
C) after the completion of above step, the position of each particle there occurs change, realize " Mass-spring " system
Whole updating, and by each point v (v in " Mass-spring " system drive point-based surfacex, vy vz) location updating.Specifically such as
Under：
vx=Px×Rx+bx
vy=Py×Ry+by
vz=Pz×Rz+bz
Here (bx, by, bz) it is coordinate (attention, the base of each grid cell of basic point in the grid cell of model points place
Point coordinates is different), Px、Py、PzIt is the proportionality coefficient for having calculated, Rx、Ry、RzIt is spring system basic point and phase after updating
The distance of adjoint point.Finally, the coordinate value after point-based surface updates is calculated.
6. the corresponding point set curved surface of point-based surface is built：According to the spatial positional information of each point in current point-based surface, fortune
With the curve reestablishing technology based on approximating method, the implicit surface for constructing current point-based surface is represented.Herein using " multi-level single
Position subdivision implicit surface reconstructing method " obtains the implicit surface approximating function of current point-based surface, and specific method is referring to (Ohtake
Y, Belyaev A, Alexa M, wait .Multi-level partition of unity implicits.ACM
Transaction of Graphics,2003,22(3):463-470).If the implicit surface function for constructing is f (x, y, z),
Then for any point p ∈ R in three dimensions3, have：
7. gridding point set curved surface：It is one group of set of small cubes (Cubes) by the uniformly subdivision where implicit surface,
Using the Marching Cubes methods based on uniformly subdivision, trigonometric ratio is carried out to part of the implicit surface in each small cubes
Treatment.For each small cubes, the implicit surface functional value on its 8 summits is first sought；The top on each bar side of small cubes is judged again
Point implicit surface functional value whether contrary sign；The side necessarily and surface intersection, can be in the hope of phase using dichotomy if contrary sign
Answer the approximation of intersection point.As shown in Figure 7, part of the curved surface inside a small cubes can be approached with triangle, and three
Angular summit is the intersection point of curved surface and small cubes side.28 kinds of situation (roots of the symbol configuration according to 8 summits of small cubes
According to symmetry, 28 kinds of situations can be reduced to 15 kinds of situations as shown in Figure 8), can be by curved surface inside each small cubes
Part triangularization；Triangularization results set in all small cubes is got up, the triangulation network of implicit surface is just obtained
Lattice approximate model.
8. animation producing：The grid model of generation is rendered to the present frame of animation, and determined by kinetics equation
The next frame of the spring system Determines animation of subsequent time, iterates and (returns to the 5th step, iterative analysis spring system
Stressing conditions, update point set coordinate, rebuild grid model).Due to the presence for damping, the kinetic energy meeting of " Mass-spring " system
Progressively weaken, until whole spring system remains static, now, this series of successive frame realizes the automatic life of animation
Into.
Claims (1)
1. a kind of point-based surface Automatic Generation of Computer Animation method of " Mass-spring " system drive, its step is：
A. point-based surface pretreatment：Point-based surface data are read, the data are to determine a series of three dimensions summits under coordinate system
Coordinate；Apex coordinate maximum and minimum value in the x, y, z-directions in point-based surface is chosen respectively, and according to these value structures
Build axial bounding box B of each rib each parallel to reference axis1；To bounding box B1Point set equal proportion scaling with bounding box, makes it most
Longitudinal edge is L, forms normalization point-based surface and bounding box B2；By Standardized Model and its bounding box B2Move to coordinate system empty
Between in disposable position；
B. " Mass-spring " system is set up：By bounding box B2Subdivision is carried out, space lattice structure is formed；Placed at vertex raster
Quality is the particle of M, each particle is adjacent thereto or be spaced adjacent particle and use stiffness coefficient to be connected for the spring of K, is obtained
" Mass-spring " system；
C. correlation model summit and spring grid：In space lattice in " Mass-spring " system and point-based surface each
The position distribution relation on summit, determines the grid corresponding to each summit in point-based surface, sets up association therebetween；
D. active force is applied in spring system：Particle movement original state is set, to the part in " Mass-spring " system or institute
There is particle to apply active force, change its motion state；
E. the stressing conditions of spring system are analyzed, and updates point set coordinate：Each particle in detection " Mass-spring " system,
Particle stressing conditions are analyzed according to spring annexation：Calculate that it is subject to makes a concerted effort；Then each matter is solved according to the law of motion
Point acceleration, speed, displacement and its subsequent time position coordinates；
F. the corresponding point set curved surface of point-based surface is built：According to the locus of each point in current point-based surface, intend with curved surface
The implicit surface for closing the current point-based surface of method construct is represented；
G. gridding point set curved surface：Using the Marching Cubes methods based on uniformly subdivision, implicit surface is converted into three
Angle grid model；
H. animation producing：The grid model of generation is rendered to the present frame of animation, and it is next determined by kinetics equation
The next frame of the spring system Determines animation at moment；Iterate, untill the animation frame series needed for generation.
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