CN107993275A - Method and system for the dynamic sampling of the slow-action curve of animation - Google Patents
Method and system for the dynamic sampling of the slow-action curve of animation Download PDFInfo
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T13/00—Animation
- G06T13/80—2D [Two Dimensional] animation, e.g. using sprites
Abstract
The present invention relates to a kind of method and system of the dynamic sampling of the slow-action curve for animation.The described method includes：Obtain the local extremum of the slow-action curve；By the local extremum by the slow-action curve segmentation into section；Calculate the sampling interval of the slow-action curve；Uniform sampling is carried out in each section using the sampling interval, to obtain sampled point；The sampled point is screened by deviation.Using the method and system of the present invention, the fidelity of sampling is substantially increased.By the combination of local extremum and uniform sampling, the high fidelity sampling for the slow-action curve for being suitable for animation is realized.
Description
Technical field
This patent disclosure relates generally to computer animation, and the more particularly, to sampling of the slow-action curve of animation.
Background technology
Computer animation or CGI animations, are for the processing by using computer graphical generation animated image.Computer
Animation can be translation, rotation, scaling, the change of color, the change of opacity or any other analog.In recent years
Come, slow-action function is used in many animation libraries.
Slow-action function is the function of the time of reflection progress percent value.Progress can include it is following any one change
Become：Displacement, shape, color, opacity, motion state etc..Slow-action function can be plotted as slow-action curve, wherein, x-axis table
Show the time, and y-axis represents the percentage of the progress of animation.
In general, slow-action curve includes：One or more line segments and/or one or more Bezier (Bezier) are bent
Line.In order to improve the performance of computer animation, the sampling of slow-action curve is carried out.And in order to reduce the calculating in run time,
It is right that slow-action curve can be sampled as a series of (t, v (t)).As shown in Figure 1A, Figure 1A is illustrated according to the prior art 1
The figure of uniform sampling exemplary, with fixed intervals sampling, wherein, black color dots are sampled points, and Grey Point is slow-action curve
Local extremum.Local extremum is maximum and minimum value in given range.
As shown in fig. 1b, there are two kinds of slow-action curves.One kind is design slow-action curve (bold portion in Figure 1B),
That is, the slow-action curve of the actual play of computer animation, this is for the uniform sampling of fixed intervals according to its method of sampling
Sampled point and formed.Another kind is actual play curve (dotted portion in Figure 1B).Actual play curve and design slow-action
Curve is different.As it is known to the person skilled in the art, extreme value is particularly significant in slow-action curve.But if in this way,
Then possibly it can not sample these points.In addition, drawn from Figure 1B, if the duration long enough of animation, animation
With design slow-action curve it is significantly different play out.
(author is Tatiana Surazhsky and Vitaly Surazhsky to the meeting paper announced in 2004, paper
Topic is " using sample plane curve (the Sampling Planar Curve Using of the shape analysis based on curvature
Curvature-Based Shape Analysis) ") prior art 2 is used as, describe the sampling using the shape based on curvature
Plane curve.The method of sampling according to this paper is according to curvature signature function (curvature signature function)
Size the method for sampling.
But many defects are also had according to this method of the prior art 2.For example, for slow-action curve, it is too neighbouring
Sampled point is nonsensical.In another example, local extremum is particularly significant to slow-action curve.But if bent curvature of a curve
Very small, then the local extremum of reference point is almost nil, i.e. since bent curvature of a curve is small, local extremum may be not big enough
And it cannot be sampled.But if matching somebody with somebody the threshold value set low for curvature, there is the too many sampled point to be obtained.
In general, the duration of animation is longer, it is necessary to better fidelity.According to the method for the prior art 2 not
Consider this point.
Based on the above, it is expected to propose a kind of new method and system of the dynamic sampling of the slow-action curve for animation.
The content of the invention
At least one of in view of the above problems, propose the present invention.
An aspect of of the present present invention provides a kind of method of sampling of slow-action curve for animation, the described method includes：Obtain
The local extremum of the slow-action curve；By the local extremum by the slow-action curve segmentation into section；It is bent to calculate the slow-action
The sampling interval of line；Uniform sampling is carried out in each section using the sampling interval, to obtain sampled point；Institute is screened by deviation
State sampled point.
Using the method and system of the present invention, the fidelity of sampling is greatly improved.Pass through local extremum and uniform sampling
With reference to realization is suitable for the high fidelity sampling of the slow-action curve of animation.
It will be clear by the description to exemplary embodiment, further characteristic of the invention referring to the drawings.
Brief description of the drawings
Be incorporated in the description and constitution instruction a part attached drawing exemplified with the embodiment of the present invention, and with explanation
Book principle used to explain the present invention together.
Examples of the Figure 1A and Figure 1B exemplified with the prior art 1.Figure 1A is to illustrate the uniform sampling sampled with fixed intervals
Figure, for Figure 1B exemplified with the slow-action curve of the actual play for computer animation, this is shape according to the sampled point with reference to Figure 1A
Into.
Fig. 2A is that by the embodiment of the present invention, schematic block diagram according to the first exemplary system architecture.
Fig. 2 B are that by the embodiment of the present invention, schematic block diagram according to the second exemplary system architecture.
Fig. 3 is the block diagram of the exemplary hardware configuration of the computing device 220 in diagrammatic illustration 2A and Fig. 2 B.
Fig. 4 A and Fig. 4 B are the samplings for illustrating exemplary embodiment, the slow-action curve being made of line segment according to the present invention
Schematic diagram.
Fig. 5 A, Fig. 5 B and Fig. 5 C are illustration exemplary embodiments according to the present invention, are delayed by what Bezier was formed
The schematic diagram of the sampling of moving curve.
Fig. 6 A, Fig. 6 B and Fig. 6 C are spring (bounce-in) slow-action songs for illustrating exemplary embodiment according to the present invention
The schematic diagram of the sampling of line.
Fig. 7 A, Fig. 7 B and Fig. 7 C are showing for the sampling for the elastic slow-action curve for illustrating exemplary embodiment according to the present invention
It is intended to.
Fig. 8 be exemplary embodiment according to the present invention, for animation slow-action curve the method for sampling flow chart.
Fig. 9 be exemplary embodiment according to the present invention, for animation slow-action curve the method for sampling detailed stream
Cheng Tu.
Figure 10 be exemplary embodiment according to the present invention, for animation slow-action curve sampling system block diagram.
Embodiment
Now, the various exemplary embodiments of the present invention be will be described in detail with reference to the accompanying drawings.It should be noted that in these embodiments
Component and the positioned opposite of step of middle elaboration, numerical expression and numerical value are not limit the scope of the invention, unless otherwise tool
Body explanation.
Being described below at least one exemplary embodiment is substantially merely illustrative and is in no way intended to limit this
Invention, its application or purposes.
Technology, method and apparatus may not be discussed in detail as known to those of ordinary skill in the related art, but
It should be the part of this specification when appropriate.
Herein illustrate and discuss all examples in, any occurrence should be construed as merely it is illustrative rather than
Restricted.Therefore, other examples of exemplary embodiment can have different values.
It note that similar reference numeral and the alphabetical similar terms referred in attached drawing, therefore, once in an attached drawing
Define project, it becomes possible to it is discussed further following attached drawing need not to be directed to.
Fig. 2A is that by the embodiment of the present invention, schematic block diagram according to the first exemplary system architecture.Shooting
Equipment 20 includes the computing device 220 of camera sensor 210 and connection.Camera sensor 210 obtains video or image sequence
Row.The method that computing device 220 realizes the boundary point for tracking object in video.Computing device 220 can be with integrated circuit
The form of chip, this is compact and is easy to be embedded into picture pick-up device 20.For example, picture pick-up device 20 can be hand-held photograph
Machine, web camera or the mobile phone with camera.
Fig. 2 B are that by the embodiment of the present invention, schematic block diagram according to the second exemplary system architecture.Photograph
Machine sensor 210 is used to obtain video or image sequence.These videos or image sequence are sent to meter by computer network 230
Calculate equipment 220.The method that computing device 220 realizes the boundary point for tracking object in video.Computing device 220 can be with this
The form of ground personal computer, remote server or work station.
Fig. 3 is the block diagram of the exemplary hardware configuration of the computing device 220 in diagrammatic illustration 2A and Fig. 2 B.
Facilitated by input/output (I/O) interface 310 from camera sensor 210 to the image of computing device 220
Send, input/output (I/O) interface 310 can be met Universal Serial Bus (USB) standard and have a corresponding USB connections
The universal serial bus of device.The video for including image sequence, 240 energy of local memory device can also be downloaded from local memory device 240
Enough include SIM card, SD card and USB memory card etc..
Image is obtained by I/O interfaces 310, and is sent to memory 340.Processor 320 is arranged to retrieval and deposits
The software program of the disclosed method of storage in a memory 340.In one embodiment, processor 320 is also arranged to carry
Take, decode and perform all steps (for example, the flow chart illustrated in Fig. 8 and Fig. 9) according to disclosed method.Processor
320 use system bus 330, and the result from each operation recorded memory 340.In addition to memory 340, may be used also
Via I/O interfaces 370, output is more muchly stored in storage device 240.Alternatively, it can also use sound
Frequently/video interface 360, display output is watched for people on monitor 250.
Computing device 220 can be various forms, such as the processing system of embedded picture pick-up device in fig. 2, or Fig. 2 B
In independent computer, may have the unnecessary component of one or more removals, or add with one or more
The additional component added.
Next, describe the exemplary embodiment of the method for the boundary point for tracking object in video in detail.
As previously mentioned, slow-action curve generally includes one or more line segments and/or one or more Beziers.
In the simple examples embodiment of the present invention, slow-action curve is only made of multiple line segments.Wherein, the slow-action being made of line segment is bent
The function of line is as follows：
Then, according to the function for the slow-action curve being made of multiple line segments, i.e. formula 1, the step of being sampled to slow-action curve, will
Come into question as follows：
First, the first derivative of all the points on line segment S1, S2 and S3 is calculated.If the first derivative at a little is not determined
Justice, then the value of the point be confirmed as local extremum.By it for example for formula 1, first derivative is not defined in point P1 and point P2, institute
It is the local extremum of slow-action curve with P1 and P2.
Secondly, by local extremum by slow-action curve segmentation into section.According to local extremum P1 and P2, by whole slow-action curve
Three sections are divided into, respectively S1, S2 and S3, as shown in Figure 4 A.Wherein, point Ps is origin, point P1 be line segment S1 terminal and
The starting point of line segment S2；Similarly, point P2 is the terminal of line segment S2 and the starting point of line segment S3, and point Pe is the terminal of line segment S3.
Next, calculate the sampling interval for the uniform sampling of slow-action curve.By animation play parameter (such as animation it is lasting when
Between or system in minimum redraw the time), to calculate the sampling interval.How long is the duration control animation broadcasting of animation.It is minimum
Redraw the time reflection system redraw how soon.The formula for calculating the interval (interval) for uniform sampling is as follows：
Wherein, k is predefined coefficient；Min_repaint_time refers to the minimum for redrawing the time in run time
Value；And animation_duration refers to the duration of animation.
It is concluded that min_repaint_time is smaller, the sampling interval is smaller.Similarly, animation_
Duration is longer, and the sampling interval is smaller.
In some embodiments of the invention, the value of animation_duration is arranged to 1000ms, min_
The value of repaint_time is arranged to 100ms, and the value of k is arranged to 1.
Based on above-mentioned value and formula 2, the sampling interval is calculated as：
Sampling interval=100/1000=0.1.
Then, uniform sampling is carried out using the sampling interval 0.1 calculated.In figure 4b exemplified with sample graph, wherein, it is black
Color dot is sampled point, such as point 401, point 402.
Then, the deviation for each sampled point is calculated.In this step, at same time point slow-action curve reality
Do and deviate between value and linear interpolation.Because in the present embodiment of the present invention, slow-action curve is made of multiple line segments, respectively
A line segment is straight line.Therefore, the deviation of all the points is 0.
Next, remove the sampled point that deviation is less than threshold value.It is nonsensical that the sampled point too small to deviation, which carries out sampling,
's.Therefore, when the deviation of all sampled points created using uniform sampling is 0, all these points are removed.
Finally, final sampled point is obtained.Based on previous step, final sampled point is Ps, P1, P2, Pe.
It is well known that Bezier is the parameter curve frequently used in computer graphical and association area.At this
In the exemplary embodiment of invention, slow-action curve is only made of a Bezier.
In general, the function of Bezier is as follows：
Wherein, t is the run time of animation；Point P0 refers to the starting point of Bezier；Point P3 refers to Bezier
Terminal.P1 and P2 refers to the control point for being directed to beginning and end respectively.As shown in Figure 5 A, Fig. 5 A are the curves that function is formula 3
Figure, wherein, line L1 is tangent lines of the curve S1 at point P0, and line L2 is tangent lines of the curve S3 at point P3.On the online L1 of point P1, point
On the online L2 of P3.
Then, according to the function for the slow-action curve being made of a Bezier, i.e. formula 3, to the sampling of slow-action curve
Step will come into question as follows：
First, the first derivative to all the points on Bezier is calculated, and obtains local extremum.According to formula 3, to shellfish
The formula of the first derivative of all the points on Sai Er curves is as follows：
In some embodiments of the invention, take a little as follows：
P0 (0,0),
P1 (0.27,1.26),
P2 (0.76,0.03),
P3(1,1)。
Based on the above-mentioned parameterized function to Bezier, the first derivative for finding point Pe1 and Pe2 is 0 (such as Fig. 5 A
Shown in), and the symbol of the derivative of the left point of point Pe1 and Pe2/right point is opposite.Therefore, Pe1 and Pe2 is extreme point.Then,
Can be derived that, if a little at first derivative be zero, and the first derivative of its left point and right point symbol on the contrary,
The point is confirmed as local extremum.
Secondly, by local extremum by slow-action curve segmentation into section.In this step, according to Local Extremum Pe1 and
Pe2, whole slow-action curve are divided into three sections, respectively S1, S2 and S3, as shown in Figure 5 A.Wherein, curve S1 is from point P0
To the curve of point Pe1, curve S2 is the curve from point Pe1 to point Pe2, and curve S3 is the curve from point Pe2 to P3.
3rd, calculate the sampling interval of the uniform sampling for slow-action curve.Uniformly adopted by animation play parameter to calculate
The sampling interval of sample.The formula for calculating the sampling interval for uniform sampling is as follows：
Similar with the implication of formula (2), min_repaint_time represents the minimum value for redrawing the time in run time；
Animation_duration represents the duration of animation.
In some embodiments of the invention, the value of animation_duration is arranged to 1000ms；min_
The value of repaint_time is arranged to 100ms.
Based on above-mentioned value and formula 5, the sampling interval is calculated as：
Sampling interval=100/1000=0.1
Then, uniform sampling is carried out using the sampling interval 0.1 calculated.Next, calculate for each sampled point
Deviation.In some embodiments of the invention, the formula of the deviation (deviation) of sampled point P1 is calculated according to Bezier such as
Under：
Exemplified with the implication of the deviation for the point P1 on curve in Fig. 5 B.
The step of with the preceding embodiment of the present invention, is similar, removes the sampled point that deviation is less than threshold value.
In some embodiments of the invention, it is 0.01 to take threshold value.
Finally, final sampled point is obtained.As shown in Figure 5 C, Fig. 5 C show the figure of the result of final sampled point.
The slow-action curve for including multiple line segments and/or including a Bezier above is introduced, in showing for the present invention
In example property embodiment, slow-action curve includes multiple Beziers, such as spring curve.
Fig. 6 A are the spring slow-action curves for animation.Similarly, based on the figure, the step of to spring slow-action curve sampling
It will come into question as follows：
First, the local extremum of slow-action curve is obtained.Using the similar method of sampling as previously mentioned, example in fig. 6
The Local Extremum on curve is shown.As shown in FIG, for example, point 601 and point 602 are local extremums.
Second, by local extremum by slow-action curve segmentation into section.Since spring slow-action curve includes multiple Bezier song
Line, therefore for the purpose of simplifying the description, using only one section of curve as an example, as shown in fig. 6b, only leaves the right side of curve
Part, as example.
Using similar method as previously mentioned, the uniform sampling of section is carried out, as depicted in figure 6b；For example, point 603 to
Point 606 is sampled point.Then, the deviation of sampled point as previously mentioned is calculated, and in next step only when the deviation of sampled point is big
When threshold value, just retain sampled point.As shown in figure 6c, since the deviation of point 603 and point 604 is not more than threshold value, then 605 are only put
It is left with point 606.
Elastic slow-action curve is the classical curve for computer animation.In an exemplary embodiment of the present invention, slow-action
Curve can be elastic slow-action curve.
Fig. 7 A are the elastic slow-action curves for animation.Similarly, based on the figure, the step of sampling to elastic slow-action curve
It will come into question as follows：
As previously mentioned, first, the local extremum of slow-action curve is obtained.Use sampling side similar as previously mentioned
Method, in fig. 7 exemplified with the Local Extremum on curve, such as point 701, point 702.
Secondly, by local extremum by slow-action curve segmentation into section.Similarly, since elastic slow-action curve is also including multiple
Bezier, therefore for the purpose of simplifying the description, it is using only one section of curve as an example, as shown in fig. 7b, only leave song
The left part of line, as example.
Using method similar as previously mentioned, the uniform sampling of section is carried out to obtain sampled point, as shown in fig.7b；
For example, point 703 to point 706 is sampled point.Then, the similar deviation as previously mentioned of sampled point is calculated；And in next step
Only when the deviation of sampled point is more than threshold value, just retain sampled point, as shown in fig. 7c；Due to the deviation of point 705 and point 706 not
More than threshold value, therefore only point 703 and point 704 is left.
Fig. 8 is the flow chart of the method for sampling of the slow-action curve for animation of exemplary embodiment according to the present invention.
Fig. 9 is the detail flowchart of the method for sampling of the slow-action curve for animation of exemplary embodiment according to the present invention.Figure 10
It is the block diagram of the sampling system 100 of the slow-action curve for animation of exemplary embodiment according to the present invention.Next, will be
Hereinafter by referring to Fig. 8, Fig. 9 and Figure 10, to describe the operation principle of system 100 in detail.
As shown in Figure 10, system 100 generally comprises five modules：Extreme value computing module 1001, segmentation module 1002, adopt
Sample interval calculation module 1003, uniform sampling module 1004 and sampling screening module 1005.Modules carry out corresponding work(
Energy.
The general work flow chart of system 100 is illustrated as follows in fig. 8：
In step S801, extreme value computing module 1001 obtains the local extremum of slow-action curve, for example, the side before use
Method (for example, using First derivative spectrograply), to obtain the local extremum of slow-action curve.In this step, if the single order of any is led
Number is zero, and the symbol of the first derivative of its left point and right point is on the contrary, then the point is considered as local extremum.If any
First derivative is not defined, then it is considered as local extremum.
In step S802, extreme value computing module 1001 stores the qualified point of local extremum, as sampled point.Root
The qualified point of local extremum is obtained according to following two conditions：
First derivative such as fruit dot is zero, and the symbol of the first derivative of its left point and right point is on the contrary, then it is determined
For local extremum；First derivative such as fruit dot is not defined, then it is confirmed as local extremum.
In step S803, segmentation module 1002 is by local extremum by slow-action curve segmentation into section.
Then, in step S804, total duration and target of the sampling interval computing module 1003 based on animation are set
Minimum in standby redraws the time, to calculate the sampling interval of uniform sampling.
In step S805, in each section, uniform sampling module 1004 is uniformly adopted using the sampling interval calculated
Sample, to obtain sampled point.Then go to step S806.
In step S806, screening sample module 1005 calculates deviation for all sampled points, and by deviation screening sampling
Point.If the deviation of cut-point is less than threshold value, it is poor small between the value that is obtained according to linear interpolation to mean actual value.Cause
This, it being capable of interior carry out linear interpolation at runtime.It will be removed from sampled point.
Similarly, the detailed operational flow diagrams of system 100 are illustrated as follows in fig.9：
In step S901, extreme value computing module 1001 calculates the first derivative of the point in slow-action curve, then step
S902 is the processing of Rule of judgment.If first derivative is calculated as 0, step S903 is gone to；If it is not, then go to step
S905.Step S903 is also the processing of Rule of judgment.If the first derivative of left point/right point symbol on the contrary, if go to step
S904。
In step S904, extreme value computing module 1001 stores local extremum as sampled point, then goes to step S906.
Step S905 is the processing of Rule of judgment.If the calculating of first derivative is not defined, then goes to step S904；If no
It is then to go to step S906.
The processing of step S906 also Rule of judgment.If all the points are processed, step S907 is gone to；If it is not, then
Back to step S901.In step s 907, segmentation module 1002 by local extremum by slow-action curve segmentation into section, Ran Houzhuan
To step S908.
In step S908, sampling interval computing module 1003 calculates the sampling interval of uniform sampling, then goes to step
S909.In step S909, uniform sampling module 1004 carries out uniform sampling to obtain sampled point for each section, then goes to step
Rapid S910.
In step S910, extreme value computing module 1001 calculates the deviation of sampled point, then goes to step S911.Step
S911 is the processing of Rule of judgment.If the calculating of deviation is more than default threshold value, step S913 is gone to；If it is not, then
Go to S912.The processing that step S912 is to skip.
In step S913, extreme value computing module 1001 stores qualified point and is used as sampled point.
According to method as previously mentioned, in some embodiments of the invention, function module can be configured to carry out
Corresponding to the function of method as previously mentioned.It note that the purpose for this discussion, term " module " is appreciated that bag
Include software, firmware and hardware (such as one or more circuits, microchip or equipment or any combination of them) and they
At least one of any combinations.However, it should be understood that in physical device, modules can include one or
More than one component, and all parts for forming a part for the module can cooperate in or independently of formation module
A part any other component and work.
Using the method and system of the present invention, the fidelity of sampling is substantially increased.Pass through local extremum and uniform sampling
Combination, realize be suitable for animation slow-action curve high fidelity sampling.
It can implement the method and system of the present invention in many ways.For example, can by software, hardware, firmware or
Its any combinations come implement the present invention method and system.The said sequence of the step of this method is only intended to be illustrative, and
And the step of of the invention method is not limited to the order of above-mentioned specific descriptions, unless otherwise expressly specified.In addition, in some realities
Apply in example, the present invention can also be embodied as recording program in the recording medium, it includes being used for realization according to the present invention
The machine readable instructions of method.
Although some specific embodiments of the present invention have been shown in detail using example, those skilled in the art should manage
Solution, above-mentioned example, which is meant only to, to be illustrative but not to limit the scope of the invention.It should be understood by those skilled in the art that
, above-described embodiment can be changed without departing from the scope and spirit of the present invention.The scope of the present invention is by appended
Claim limit.
Claims (22)
1. a kind of method of the dynamic sampling of slow-action curve for animation, described method includes following steps：
(1) local extremum of the slow-action curve is obtained；
(2) by the local extremum by the slow-action curve segmentation into section；
(3) sampling interval of the slow-action curve is calculated；
(4) uniform sampling is carried out in each section using the sampling interval, to obtain sampled point；
(5) sampled point is screened by deviation.
2. according to the method described in claim 1, wherein, obtained by calculating the first derivative of the point on the slow-action curve
The local extremum.
3. according to the method described in claim 2, wherein, it is described by calculate the first derivative of the point on the slow-action curve come
The step of obtaining the local extremum further includes：
If the first derivative of any is undefined, which is confirmed as local extremum.
4. according to the method described in claim 2, wherein, it is described by calculate the first derivative of the point on the slow-action curve come
The step of obtaining local extremum further includes：
At the first derivative be zero, and the opposite situation of symbol of the first derivative of the left point of the point and right point
Under, which is confirmed as the local extremum.
5. according to the method described in claim 1, wherein, the sampling interval is calculated by animation play parameter, it is described dynamic
It is that the duration of animation or the minimum of system redraw the time to draw play parameter.
6. according to the method described in claim 5, wherein, the sampling interval depends on the duration of the animation.
7. according to the method described in claim 6, wherein, the duration of the animation is longer, the sampling interval is smaller.
8. according to the method described in claim 5, wherein, the sampling interval depends on redrawing the minimum value of time.
9. according to the method described in claim 8, wherein, it is described redraw the time minimum value it is smaller, the sampling interval is smaller.
10. according to the method described in claim 1, wherein, the reality of deviation slow-action curve at same time point
Between value and the linear interpolation of slow-action curve.
11. according to the method described in claim 1, wherein, when the deviation of any is less than threshold value, then the point is left sampling
Point.
12. a kind of system of the dynamic sampling of slow-action curve for animation, the system comprises：
Extreme value computing module, it is configured to be responsible for the local extremum for obtaining the slow-action curve；
Segmentation module, it is configured to the slow-action curve segmentation by the local extremum into section；
Sampling interval computing module, it is configured to the sampling interval for calculating the slow-action curve；
Uniform sampling module, it is configured to carry out uniform sampling in each section using the sampling interval, to be sampled
Point；
Screening module is sampled, it is configured to screen the sampled point by deviation.
13. system according to claim 12, wherein, the extreme value computing module further includes：
The local extremum is obtained by calculating the first derivative of the point on the slow-action curve.
14. system according to claim 13, wherein, asked by calculating the first derivative of the point on the slow-action curve
Go out local extremum to further include：
At the first derivative be not defined in the case of, which is confirmed as the local extremum.
15. system according to claim 13, wherein, asked by calculating the first derivative of the point on the slow-action curve
Go out local extremum to further include：
At the first derivative be zero, and the opposite situation of symbol of the first derivative of the left point of the point and right point
Under, which is confirmed as the local extremum.
16. system according to claim 12, wherein, the sampling interval is calculated by animation play parameter, it is described
Animation play parameter is that the duration of animation or the minimum of system redraw the time.
17. system according to claim 16, wherein, the sampling interval depends on the duration of the animation.
18. system according to claim 17, wherein, the duration of the animation is longer, and the sampling interval is smaller.
19. system according to claim 16, wherein, the sampling interval depends on redrawing the minimum value of time.
20. system according to claim 19, wherein, it is described redraw the time minimum value it is smaller, the sampling interval gets over
It is small.
21. system according to claim 12, wherein, the reality of deviation slow-action curve at same time point
Between value and the linear interpolation of slow-action curve.
22. system according to claim 12, wherein, in the case where being less than threshold value for the deviation of point, the point
It is left the sampled point.
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