CN104616338B - The consistent speed change interpolating method of space-time based on 2 D animation - Google Patents
The consistent speed change interpolating method of space-time based on 2 D animation Download PDFInfo
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Abstract
The invention discloses a kind of consistent speed change interpolating method of space-time based on 2 D animation, including：Set the time shaft of role movement, calculate the position of interpolation intermediate frame on a timeline according to the basic law of variable motion, or by the way that middle frame position is manually specified, then according to interval different on time shaft, corresponding intermediate frame is obtained by key frame interpolation, variable motion in 2 D animation automatically generated so as to realize.Through the above way, the consistent speed change interpolating method of space-time of the invention based on 2 D animation, for the problem of action change and time are separated present in two-dimension cartoon making interpolation process, in order to improve producing efficiency and quality of animation, by the way of being combined using time, space, with time shaft serve as theme guiding action change interpolation process, solve the problems, such as that current computer interpolation animation can not handle variable motion.
Description
Technical field
The present invention relates to animation interpolating method field, more particularly to a kind of consistent speed change of space-time based on 2 D animation
Interpolating method.
Background technology
2 D animation is the simulation and exaggeration process to real world, and real action changing rule is its premise,
It is basis.Therefore, during two-dimension cartoon making, the action of role is kept to change that to meet in general rule be to 2 D animation
The basic demand of producer.In traditional Freehandhand-drawing 2 D animation, the simulation to real rule is required for relying on animation teacher's root
Animation frame is first produced according to its own experience, is then put it on time shaft, forms animation process.In this mode,
The quality of one role animation is just often closely related with animation teacher's experience, and is moved when multiple animation Shi Hezuo complete a scene
When making, due between animation teacher to role action understanding and experience difference, allow for animation quality become be more difficult to control
System.
Currently, most of cartoon making enterprise all using two-dimension cartoon making software carry out key frame interpolating operations, this
Largely solve because of interpolation animation style inconsistence problems caused by the difference between animation teacher, but in interpolation
Interval（Time series variation）With corresponding action change（The role locus corresponding with some timing node）Both
Between consistency problem still still exist, ought particularly run into acceleration or variable motion situation, current 2 D animation
Software often can not Direct interpolation generation intermediate frame, key frame can only be added, this just virtually add animation Shi Renwei because
The influence of element, causes the situation of role action inconsequent to occur.
With constantly promoting the use of for digital two-dimension cartoon making technology, intermediate frame is automatically derived by key frame interpolation
Have become the major way of cartoon making.At present, intermediate frame master is obtained by key frame interpolation during two-dimension cartoon making
Two methods are used to carry out;First, using computer animation software, divide interpolation according to locus etc. by key frame
Mode obtain intermediate frame, the animation so obtained must be uniform motion in motion state；Second, in it can not carry out
When inserting（Such as cartoon role variable motion, three-dimensional perspective or when the reason such as block and interpolation can not be carried out）, adopt
The mode drawn frame by frame by hand obtains intermediate frame.
It is the method that current main flow animation soft all generally uses by key frame etc. point interpolation animation frame, but passes through
The application and research of long period is crossed, especially for the making of the scene such as existing variable motion during two-dimension cartoon making
Practice, it is believed that the defects of following several respects also be present only for the decile interpolating method of key frame locus at present：
1st, space etc. divides interpolating method enforceable the change of role action locus is set as uniform motion, also
To say after key frame is set, the action variable quantity of cartoon role and time must be it is synchronous, can not be to the speed change of role
Motion carries out animation description（Because variable motion actually means that the action variable quantity of role is different and different with the time,
For example belong to accelerated motion when under role set placement in height, then when time shaft is closer to the key frame on ground, it acts variable quantity
Just should be bigger）.
2nd, the change that interpolating method only accounts for role locus in interpolation process is divided in space etc., without consider when
Between the influence of change is acted to it, lacked time dimension on space-time latitude, this allow for the 2 D animation made often and
Difference be present in the actual characteristics of motion, particularly when the variable motion to role carries out interpolation, the intermediate frame and reality of generation
Rule differs greatly, and it is difficult to cause the sympathetic response of people to cause animation product, and this is also to cause China's animation production to a certain extent
The reason for product vitality is not strong.
3rd, variable motion is described well because space etc. point interpolation can not be realized, therefore is facing such field
Jing Shi, producer have to draw intermediate frame using the method for manual drawing, and this just inevitably causes production efficiency
Decline, and the reason because producer lacks experience etc., the not smooth and jitter phenomenon for also easily causing action to change, seriously
Influence the quality of animation product.
The content of the invention
The present invention solves the technical problem of provide a kind of space-time based on 2 D animation consistent speed change interpolation side
Method, have the advantages that unfailing performance height, registration, quality of animation are high, while in the application and popularization of animation interpolating method
There are extensive market prospects.
In order to solve the above technical problems, one aspect of the present invention is：
There is provided a kind of space-time based on 2 D animation consistent speed change interpolating method, its step includes：
1) key frame is drawn：Change for role action, draw out the several keys that can show the change of role's main actions
Frame；
2) time shaft is set：According to role action change time, setting time shaft length, i.e., according to role action when
Between length, draw a time axis process, axial length be role action change time length；
3) calculating or given intermediate frame：The position of intermediate frame is calculated using physical equation or manually sets the position of intermediate frame
Put, the physical equation calculates middle frame position, refers to based on the basic physical principle such as variable motion, by one with the time
The variable motion situation of object is described for the physical equation of parameter, and the position of each intermediate frame is obtained according to interpolation frame number；
4) interpolation intermediate frame：Using the computational methods of linear interpolation, according to the intermediate frame node interpolation set on time shaft
Obtain corresponding intermediate animation.
In a preferred embodiment of the present invention, the method that middle frame position is calculated using physical equation includes decile
Interpolation computational methods and random motion interpolation computational methods.
In a preferred embodiment of the present invention, the physical equation calculates middle frame position, and its specific steps includes：
Given interpolation frame number, sets key frame and interpolation frame number as n；
Set the motion state descriptive equation of role；
When the motion state of role is acceleration mode, the sports immunology equation of role is：1-, 0<θ<Pi/2,
Then for n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
,j=1,2,…,n
Wherein, Δ t is the time difference between two key frames, and t1 is initial time；
When the motion state of role is deceleration regime, the sports immunology equation of role is：
Sin θ, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
, j=1,2 ..., n, Δ t is the time difference between two key frames, and t1 is initial
Time；
When role motion state for plus-deceleration admixture when, the sports immunology equation of role is：
1/2（1-）, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame calculates
It is as follows：
, j=1,2 ..., n, the time difference of Δ t two key frames of expression.
In a preferred embodiment of the present invention, the specific steps of the interpolation intermediate frame include：
（1）If starting polygon is A=[A0, A1 ... An], target polygon is B=[B0, B1 ... Bn] in starting polygon
I-th of summit Ai is taken in shape A（I=0,1 ... n）, then make straight line from the origin of coordinates to Ai, obtain vectorial s, then use
Same method, corresponding match point Bj is taken in target polygon B, and (j=1,2 ... n), obtains vectorial d；
（2）By vector calculation, the angle between s and d is obtained, is set to θ, when θ≤90 °, using linear interpolation,
Interpolation formula is as follows：
C (t)=(1-t) * s+t*d, t ∈ [0,1]
Wherein, c (t) as solves the top of obtained middle polygon (setting middle polygon as V=[V0, V1 ... Vn])
Point Vk vector, the starting polygon summit corresponding with result polygon, it is corresponding with Vk；
（3）Work as θ>At 90 °, more vectorial s and d length, if | s>D ∣, then m=d is made, otherwise m=s, calculate line segment A0B0
Perpendicular bisector and m where straight line intersection point, note intersection point is O（X0, y0）；
（4）Then using point O as the center of circle, using line segment OS as radius, it is circle (x- x0) 2+ (y- x0) 2=r2；
（5）The intersection point of straight line and circle where finally calculating vectorial c (t), the intersection point are corresponding on middle polygon
Summit Vk；
（6）After above-mentioned algorithm n+1 times is called in repetition, you can obtain intermediate interpolated polygon V=[V0, V1 ... Vn] top
Point sequence V0, V1 ... Vn, obtains intermediate animation.
The beneficial effects of the invention are as follows：Mutually taken off with the time for action change present in two-dimension cartoon making interpolation process
From the problem of, in order to improve producing efficiency and quality of animation, by the way of being combined using time, space, served as theme with time shaft
The interpolation process of guiding action change, solves the problems, such as that current computer interpolation animation can not handle variable motion.
Brief description of the drawings
Technical scheme in order to illustrate the embodiments of the present invention more clearly, make required in being described below to embodiment
Accompanying drawing is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the present invention, for
For those of ordinary skill in the art, on the premise of not paying creative work, it can also be obtained according to these accompanying drawings other
Accompanying drawing, wherein：
Fig. 1 is that the flow of the consistent preferred embodiment of speed change interpolating method one of the space-time based on 2 D animation of the present invention is shown
It is intended to；
Fig. 2 is the structural representation of triangle acceleration function when interpolation frame is 5 in the present invention；
Fig. 3 is the structural representation at interpolation interval when interpolation frame is 5 in the present invention；
Fig. 4 is the structural representation of three angular deceleration functions when interpolation frame is 5 in the present invention；
Fig. 5 is the structural representation of the reduction degree of time interval when interpolation frame is 5 in the present invention；
Fig. 6 be in the present invention when role motion state for plus triangle acceleration-deceleration during-deceleration admixture
The structural representation of function；
Fig. 7 is when the motion state of role is plus-interpolation the interval of deceleration admixture constantly in the present invention
Structural representation.
Embodiment
The technical scheme in the embodiment of the present invention will be clearly and completely described below, it is clear that described implementation
Example is only the part of the embodiment of the present invention, rather than whole embodiments.It is common based on the embodiment in the present invention, this area
All other embodiment that technical staff is obtained under the premise of creative work is not made, belong to the model that the present invention protects
Enclose.
Fig. 1-7 are referred to, the embodiment of the present invention includes：
A kind of consistent speed change interpolating method of space-time based on 2 D animation, the mainly time by setting role movement
Axle, calculates the position of interpolation intermediate frame according to the basic law of variable motion on a timeline, or by being manually specified in
Between frame position, then according to interval different on time shaft, corresponding intermediate frame is obtained by key frame interpolation, so as to realize to two
Variable motion automatically generates in dimension animation, and step includes：
1) key frame is drawn：Change for role action, draw out the several keys that can show the change of role's main actions
Frame；
2) time shaft is set：According to role action change time, setting time shaft length, i.e., according to role action when
Between length, draw a time axis process, axial length be role action change time length, its process mainly calculate
The drawing process of machine graphics；
3) calculating or given intermediate frame：The position of intermediate frame is calculated using physical equation or manually sets the position of intermediate frame
Put, the physical equation calculates middle frame position, refers to based on the basic physical principle such as variable motion, by one with the time
The variable motion situation of object is described for the physical equation of parameter, and the position of each intermediate frame is obtained according to interpolation frame number；
4) interpolation intermediate frame：Using the computational methods of linear interpolation, according to the intermediate frame node interpolation set on time shaft
Obtain corresponding intermediate animation.
2nd, the consistent speed change interpolating method of the space-time according to claim 1 based on 2 D animation, it is characterised in that
The method that middle frame position is calculated using physical equation includes decile interpolation computational methods and random motion interpolation calculating side
Method.
3rd, the consistent speed change interpolating method of the space-time according to claim 2 based on 2 D animation, it is characterised in that
Described to calculate middle frame position using physical equation, its specific steps includes：
Given interpolation frame number, sets key frame and interpolation frame number as n；
Set the motion state descriptive equation of role；
In order to simulation accelerated（Positive acceleration）, to allow the time interval of interframe to increase, so that adding in object movement
There is larger change in location when fast, when the motion state of role is acceleration mode, between the time for increasing interframe, the motion of role
Descriptive equation is：1-, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame calculates such as
Under：
,j=1,2,…,n
Wherein, Δ t is the time difference between two key frames, and t1 is initial time；
When the motion state of role is deceleration regime, the sports immunology equation of role is：
Sin θ, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
, j=1,2 ..., n, Δ t is the time difference between two key frames, and t1 is initial
Time；
Motion is often comprising acceleration（Startup stage）And deceleration（Ending phase）, can be by first increasing interpolation time interval after
The method pair for reducing the interval adds --- and deceleration carries out hybrid modeling, when the motion state of role is to add-deceleration admixture
When, the sports immunology equation of role is：
1/2（1-）, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame calculates
It is as follows：
, j=1,2 ..., n, the time difference of Δ t two key frames of expression.
4th, the consistent speed change interpolating method of the space-time according to claim 1 based on 2 D animation, it is characterised in that
The specific steps of the interpolation intermediate frame include：
（1）If starting polygon is A=[A0, A1 ... An], target polygon is B=[B0, B1 ... Bn] in starting polygon
I-th of summit Ai is taken in shape A（I=0,1 ... n）, then make straight line from the origin of coordinates to Ai, obtain vectorial s, then use
Same method, corresponding match point Bj is taken in target polygon B, and (j=1,2 ... n), obtains vectorial d；
（2）By vector calculation, the angle between s and d is obtained, is set to θ, when θ≤90 °, using linear interpolation,
Interpolation formula is as follows：
C (t)=(1-t) * s+t*d, t ∈ [0,1]
Wherein, c (t) as solves obtained middle polygon (setting middle polygon as V=[V0, V1 ... Vn]) summit Vk
Vector, the starting polygon summit corresponding with result polygon, be corresponding with Vk；
（3）Work as θ>At 90 °, more vectorial s and d length, if | s>D ∣, then m=d is made, otherwise m=s, calculate line segment A0B0
Perpendicular bisector and m where straight line intersection point, note intersection point is O（X0, y0）；
（4）Then using point O as the center of circle, using line segment OS as radius, it is circle (x- x0) 2+ (y- x0) 2=r2；
（5）The intersection point of straight line and circle where finally calculating vectorial c (t), the intersection point are corresponding on middle polygon
Summit Vk；
（6）After above-mentioned algorithm n+1 times is called in repetition, you can obtain intermediate interpolated polygon V=[V0, V1 ... Vn] top
Point sequence V0, V1 ... Vn, obtains intermediate animation.
The beneficial effect of the consistent speed change interpolating method of the space-time based on 2 D animation of the invention is：Retouched by the present invention
The speed change interpolation results that the method stated obtains substantially conform to the characteristics of motion under reality, enhance the performance shape of 2 D animation
Formula, improve quality of animation.Meanwhile we have also drawn some encouraging data and conclusion below：
（1）Effectively increase the efficiency of cartoon making variable motion process
In the two-dimension cartoon making software currently generally used, because the making of variable motion process can not adopt
Solved with the technological means of interpolation, therefore still need cartoon making personnel by the method for manual drawing to complete centre
The making of frame animation.This blank has then been filled up using technical scheme, has passed through in general animation personnel simple
Operation can produces the variable motion process animation being consistent with reality, avoids traditional manual work, efficiency
Improve clearly.
（2）It is effectively saved the cost of manufacture of moving scene
After technical scheme, the efficiency of variable motion process animation making is not only increased, and
Realize and animation is substituted by computer graphics disposal technologies such as interpolations completely in moving scene manufacturing process
Making experience, so that original painting producer of a high price can suitably be reduced by making enterprise, then engaged with relatively low cost
With primary cartoon making personnel, that is, be advantageous to the culture of enterprise's talent system, can effectively save human cost again.
（3）Effectively increase the role animation quality under motion state
The variable motion effect under reality is simulated using computational methods, the result for making to finally obtain more accords with
The universal law in reality is closed, has met or exceeded the effect of Freehandhand-drawing to a certain extent, and using calculating
Method also effectively avoids different personnel because being moved caused by different to motion process understanding to realize variable motion effect
The different situation of effect is drawn, or even occurs shaking and acting phenomena such as not smooth, more conforms to the motion process of making
Real rule.
These data and experience have shown that, the speed change interpolating method that proposes is based on basic physics law, fusion in the present invention
Computer graphics disposal technology, the automatic interpolation process of variable motion is realized, solve digital two-dimension cartoon making process
Present in variable motion can not interpolation the problem of, there is stronger application prospect.
Embodiments of the invention are the foregoing is only, are not intended to limit the scope of the invention, it is every to utilize this hair
The equivalent structure or equivalent flow conversion that bright description is made, or directly or indirectly it is used in other related technology necks
Domain, it is included within the scope of the present invention.
Claims (3)
1. the consistent speed change interpolating method of a kind of space-time based on 2 D animation, it is characterised in that step includes：
1) key frame is drawn：Change for role action, draw out the multiple key frames that can show role action change；
2) time shaft is set：The time changed according to role action, setting time shaft length, i.e., grown according to the time of role action
It is short, the process of a time axis is drawn, axial length is the time length of role action change；
3) calculating or given intermediate frame：The position of intermediate frame is calculated using physical equation or manually sets the position of intermediate frame,
The physical equation calculates middle frame position, refers to the physical principle based on variable motion, by one using the time as parameter
Physical equation obtains the position of each intermediate frame to describe the variable motion situation of object according to interpolation frame number；
Specific steps include：
Given interpolation frame number, sets key frame and interpolation frame number as n；
Set the motion state descriptive equation of role；
When the motion state of role is acceleration mode, the sports immunology equation of role is：1-cos θ, 0<θ<Pi/2, then for
For n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
,j=1,2,…,n
Wherein, Δ t is the time difference between two key frames, and t1 is initial time, and any point is to original on the contour line of role
The line of point and the angle of x-axis are θ；
When the motion state of role is deceleration regime, the sports immunology equation of role is：
Sin θ, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
, j=1,2 ..., n, Δ t is the time difference between two key frames, and t1 is initial
Time；
When role motion state for plus-deceleration admixture when, the sports immunology equation of role is：
1/2（1- cos θ）, 0<θ<Pi/2, then for n interpolation frame, the time location of j-th of interpolation frame is calculated as follows：
, j=1,2 ..., n, the time difference of Δ t two key frames of expression；
4) interpolation intermediate frame：Using the computational methods of linear interpolation, obtained according to the intermediate frame node interpolation set on time shaft
Corresponding intermediate animation.
2. the consistent speed change interpolating method of the space-time according to claim 1 based on 2 D animation, it is characterised in that described
The method of middle frame position is calculated using physical equation includes decile interpolation computational methods and random motion interpolation computational methods.
3. the consistent speed change interpolating method of the space-time according to claim 1 based on 2 D animation, it is characterised in that described
The specific steps of interpolation intermediate frame include：
（1）If starting polygon is A=[A0, A1 ... An], target polygon is B=[B0, B1 ... Bn], in starting polygon A
In take i-th of summit Ai（I=0,1 ... n）If middle polygon is V=[V0, V1 ... Vn], then from the origin of coordinates to Ai
Make straight line, obtain vectorial s, then using same method, taken in target polygon B corresponding match point Bj (j=1,2 ...
N), vectorial d is obtained；
（2）By vector calculation, the angle between s and d is obtained, is set to β, when β≤90 °, using linear interpolation, interpolation
Formula is as follows：
C (t)=(1-t) * s+t*d, t ∈ [0,1]
Wherein, c (t) as solves obtained middle polygon V summit Vk vector, starting polygon and result polygon phase
Corresponding summit, it is corresponding with Vk；
（3）Work as β>At 90 °, more vectorial s and d length, if m is a variable for being used to represent vectorial s or d, if | s>D ∣,
M=d is then made, otherwise m=s, the intersection point of straight line where calculating line segment A0B0 perpendicular bisector and m, note intersection point is O（X0, y0）；
（4）Then using point O as the center of circle, using line segment OS as radius, circle (x- x0) is done2+(y- x0)2=r2, wherein, r is radius OS
Length, center of circle O coordinate is（X0, x0）；
（5）The intersection point of straight line and circle where finally calculating vectorial c (t), the intersection point are summit corresponding on middle polygon
Vk；
（6）Repeat to call n+1 above-mentioned steps（1）-（5）Afterwards, you can obtain intermediate interpolated polygon V=[V0, V1 ... Vn's]
Vertex sequence V0, V1 ... Vn, obtains intermediate animation.
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| CN101436310A (en) * | 2008-11-28 | 2009-05-20 | 牡丹江新闻传媒集团有限公司 | Method for automatically generating middle frame during two-dimension cartoon making process |
| CN102609969A (en) * | 2012-02-17 | 2012-07-25 | 上海交通大学 | Method for processing face and speech synchronous animation based on Chinese text drive |
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| CN101436310A (en) * | 2008-11-28 | 2009-05-20 | 牡丹江新闻传媒集团有限公司 | Method for automatically generating middle frame during two-dimension cartoon making process |
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