CN102222353A - Curve drawing method based on secondary B spline iteration - Google Patents

Curve drawing method based on secondary B spline iteration Download PDF

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CN102222353A
CN102222353A CN2011101340685A CN201110134068A CN102222353A CN 102222353 A CN102222353 A CN 102222353A CN 2011101340685 A CN2011101340685 A CN 2011101340685A CN 201110134068 A CN201110134068 A CN 201110134068A CN 102222353 A CN102222353 A CN 102222353A
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curve
vector
individual
coordinate
iteration
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Inventor
蒋勇
王介付
李玉梅
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Nanjing University of Information Science and Technology
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a curve drawing method based on secondary B spline iteration. In the method, a curve passing through each coordinate point is drawn by using a computer according to a given periodic coordinate point. The method comprises the following steps of: inputting a super vector of the given periodic coordinate point; performing boundary supplementation on the super vector with a boundary supplementation method to obtain a new super vector; computing an approximate B spline curve by taking the new super vector as an initial control point; recording a coordinate value on the approximate B spline curve; and computing an error super vector and judging whether next iteration is needed according to the condition of whether the error super vector meets a given accuracy requirement. Compared with the prior art, the method has the advantages of high convergence rate of a drawn curve, high convergence accuracy, convenience for local modification and the like.

Description

A kind of curve plotting method based on the Quadric Spline iteration
Technical field
The present invention relates to a kind of method of utilizing computing machine to carry out curve plotting, relate in particular to a kind of curve plotting method based on the Quadric Spline iteration.
Background technology
So-called curve approach rendering technique be exactly with computer realization to needing the drafting of curve, make it approach actual required curve as far as possible.The key problem that the realization curve approaches rendering technique is to find a kind of algorithm with high efficiency and accuracy, makes it can draw out curve required in the actual production easily and fast.Curve not only has a wide range of applications in Precision Machinery Designs such as aircraft, steamer, automobile, aerospace flight vehicle, and the important research content in it still is computational mathematics fields such as data are approached, numerical differentiation, Numerical solution of partial defferential equatio, computational geometry, computer graphics.Enter the nineties in 20th century, the research that develops into curve soft, hardware of computing machine provides powerful expulsive force.Develop into now, curve approach, the theory of aspects such as interpolation, match has been very perfect, and successfully be used in the industrial and agricultural production.But also formed simultaneously the matured product of large quantities of curve plottings in the world, as AUTOCAD, 3DMax, corelDraw, Photoshop etc., the domestic well-known software such as CAD of hoping in also having.Realize at present the several different methods of having approached of curve, existing curve approaches, fitting algorithm is generally based on interpolating spline or approach batten, and the drafting of carrying out curve based on SPL has become a kind of trend of curve plotting technology.During concrete enforcement, very crucial to the selection of SPL.In " Computer-aided Geometric Design and non-uniform rational B-spline " (Higher Education Publishing House) and " numeric representation of curve curve and approach " (Shanghai science tech publishing house), multiple interpolation method and approach method have been introduced.But because all there are certain shortcoming in these two kinds of battens, such as interpolating spline can not carry out local modification, and the degree of accuracy of approaching batten is not high.So in actual applications, if require product both to have good degree of accuracy and slickness, can conveniently carry out local modification again, existing algorithm just can not meet the demands.Therefore, how to overcome the limitation of prior art, propose a kind of new curve and approach rendering technique, make new rendering technique under the prerequisite that keeps the prior art advantage, overcome the defective of prior art, just become the focus of scholar's concern of association area.
Summary of the invention
Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, and a kind of curve plotting method based on the Quadric Spline iteration is provided, and this method both can make curve have higher degree of accuracy and slickness, was convenient to carry out local modification again.
The present invention is specifically by the following technical solutions:
A kind of curve plotting method based on the Quadric Spline iteration according to given periodicity coordinate points, utilizes the curve of computer drawing through each coordinate points, may further comprise the steps:
The super vector of steps A, the given periodicity coordinate points of input
Figure 172149DEST_PATH_IMAGE001
, super vector
Figure 740796DEST_PATH_IMAGE001
Expression formula as follows,
Figure 365681DEST_PATH_IMAGE002
，
In the formula,
Figure 723982DEST_PATH_IMAGE003
Be respectively the 1st, the 2nd ..., NThe coordinate vector of individual given periodicity coordinate points, NBe the number of given periodicity coordinate points,
Figure 825580DEST_PATH_IMAGE004
,
Figure 860401DEST_PATH_IMAGE005
,
Figure 723314DEST_PATH_IMAGE006
Represent respectively
Figure 2011101340685100002DEST_PATH_IMAGE007
Individual
Figure 760672DEST_PATH_IMAGE008
Axle,
Figure 710917DEST_PATH_IMAGE009
Axle,
Figure 932951DEST_PATH_IMAGE010
Coordinate components on the axle,
Figure 470111DEST_PATH_IMAGE011
Step B, usefulness border replenishment are to super vector
Figure 920946DEST_PATH_IMAGE001
Carrying out the border replenishes and to obtain new super vector
Figure 40212DEST_PATH_IMAGE012
Step C, with coordinate points
Figure 620098DEST_PATH_IMAGE012
As initial control point, calculate approximate B-spline curves according to following formula
Figure 222985DEST_PATH_IMAGE013
,
Figure 726779DEST_PATH_IMAGE014
Wherein
Figure 887501DEST_PATH_IMAGE015
，
Figure 202070DEST_PATH_IMAGE016
，
Figure 526872DEST_PATH_IMAGE017
，
Figure 755728DEST_PATH_IMAGE018
Be given
Figure 535072DEST_PATH_IMAGE007
Individual some process
Figure 519078DEST_PATH_IMAGE019
The curve of approximation that obtains after the inferior iteration;
Figure 65597DEST_PATH_IMAGE020
Be given
Figure 865188DEST_PATH_IMAGE021
Individual some process
Figure 62820DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Figure 968459DEST_PATH_IMAGE022
Be given
Figure 693619DEST_PATH_IMAGE007
Individual some process
Figure 326595DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Figure 395045DEST_PATH_IMAGE023
Be given Individual some process
Figure 615865DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Figure 553997DEST_PATH_IMAGE025
Be
Figure 601587DEST_PATH_IMAGE007
The curve of approximation of individual point;
Figure 590972DEST_PATH_IMAGE026
Be
Figure 599379DEST_PATH_IMAGE007
Individual Parameter coordinate on the axle;
Figure 305615DEST_PATH_IMAGE027
Be
Figure 723958DEST_PATH_IMAGE007
Individual Parameter coordinate on the axle;
Figure 683617DEST_PATH_IMAGE029
Be Individual Parameter coordinate on the axle;
Figure 825513DEST_PATH_IMAGE030
Be
Figure 158406DEST_PATH_IMAGE021
Individual some process
Figure 894149DEST_PATH_IMAGE019
After the inferior iteration Component of a vector on the axle;
Figure 815936DEST_PATH_IMAGE031
Be Individual some process
Figure 542769DEST_PATH_IMAGE019
After the inferior iteration
Figure 490128DEST_PATH_IMAGE028
Component of a vector on the axle;
Figure 916561DEST_PATH_IMAGE032
Be
Figure 43786DEST_PATH_IMAGE021
Individual some process
Figure 252657DEST_PATH_IMAGE019
After the inferior iteration Component of a vector on the axle;
Figure 783181DEST_PATH_IMAGE033
,
Figure 261567DEST_PATH_IMAGE034
,
Figure 327874DEST_PATH_IMAGE035
,
Figure 53254DEST_PATH_IMAGE036
, ,
Figure 439420DEST_PATH_IMAGE038
Implication by that analogy;
Step D, usefulness
Figure 124348DEST_PATH_IMAGE039
The approximate B-spline curves of record
Figure 568099DEST_PATH_IMAGE040
Go up corresponding to
Figure 410415DEST_PATH_IMAGE041
Coordinate figure;
Step e, error of calculation super vector
Figure 479871DEST_PATH_IMAGE042
, and whether error in judgement reach given accuracy requirement, if then stop algorithm and curve of output; If not, then change step F;
Step F, pass through
Figure 455524DEST_PATH_IMAGE043
Calculate new reference mark
Figure 70176DEST_PATH_IMAGE044
, use
Figure 695062DEST_PATH_IMAGE045
The approximate B-spline curves of record
Figure 7356DEST_PATH_IMAGE046
Go up corresponding to
Figure 152030DEST_PATH_IMAGE047
Coordinate figure, pass through then
Figure 390113DEST_PATH_IMAGE048
Error of calculation super vector carries out iteration successively once more, up to reaching default accuracy requirement, curve of output.
Preferably, described in the step B to super vector
Figure 6689DEST_PATH_IMAGE001
Carry out the additional interpolation end-point data that is meant in border
Figure 168680DEST_PATH_IMAGE049
,
Figure 682707DEST_PATH_IMAGE050
, obtain new super vector then
Figure 593156DEST_PATH_IMAGE051
, wherein
Figure 677787DEST_PATH_IMAGE052
, wherein NNumber for given periodicity coordinate points.
Preferably, the specific implementation method of step D is as follows:
With
Figure 892737DEST_PATH_IMAGE053
Write down approximate B-spline curves
Figure 697488DEST_PATH_IMAGE040
Go up corresponding to
Figure 90423DEST_PATH_IMAGE041
Coordinate figure; Wherein
Figure 177197DEST_PATH_IMAGE054
And
Figure 369406DEST_PATH_IMAGE055
,
Figure 343178DEST_PATH_IMAGE056
,
Figure 156283DEST_PATH_IMAGE057
NNumber for given periodicity coordinate points.
Preferably, error super vector in the step e
Figure 895132DEST_PATH_IMAGE042
Obtain according to following formula:
Figure 202616DEST_PATH_IMAGE058
The present invention is by improving on the basis of existing curve approximate algorithm, overcome that the prior art precision is not high, the defective of curve local modification inconvenience.Compared to existing technology, the present invention has advantages such as institute's curve plotting fast convergence rate, convergence precision height and local modification convenience.
Description of drawings
Fig. 1 is the principle schematic of the inventive method;
The curve that Fig. 2 draws for coordinate points given in advance;
The function of Fig. 3 for adopting the inventive method to draw
Figure 545742DEST_PATH_IMAGE059
Curve;
The function of Fig. 4 for adopting the inventive method to draw
Figure 968895DEST_PATH_IMAGE060
Curve;
The function of Fig. 5 for adopting the inventive method to draw
Figure 515414DEST_PATH_IMAGE061
Curve;
The fabric fibre structure of Fig. 6 for adopting the inventive method to draw.
Embodiment
Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:
Curve plotting method based on the Quadric Spline iteration of the present invention, its principle specifically may further comprise the steps as shown in Figure 1:
The super vector of steps A, the given periodicity coordinate points of input Super vector herein
Figure 244128DEST_PATH_IMAGE001
Refer in the space given in advance with x, y, z axle to be a series of coordinate points of coordinate, these coordinate points all need on the curve of being drawn, super vector
Figure 149768DEST_PATH_IMAGE001
Expression formula as follows,
Figure 432850DEST_PATH_IMAGE002
，
In the formula,
Figure 82137DEST_PATH_IMAGE003
Be respectively the 1st, the 2nd ..., NThe coordinate vector of individual given periodicity coordinate points, NBe the number of given periodicity coordinate points,
Figure 901320DEST_PATH_IMAGE004
,
Figure 977860DEST_PATH_IMAGE005
,
Figure 420343DEST_PATH_IMAGE006
Represent respectively
Figure 626983DEST_PATH_IMAGE007
Individual Axle,
Figure 46649DEST_PATH_IMAGE009
Axle,
Figure 789477DEST_PATH_IMAGE010
Coordinate components on the axle,
Figure 531299DEST_PATH_IMAGE011
7 coordinate points given in advance in the present embodiment are as follows:
Figure 308762DEST_PATH_IMAGE062
；
Step B, usefulness border replenishment are to super vector
Figure 914056DEST_PATH_IMAGE001
Carrying out the border replenishes and to obtain new super vector
Figure 157562DEST_PATH_IMAGE012
Specifically be meant the interpolation end-point data
Figure 686764DEST_PATH_IMAGE049
,
Figure 833580DEST_PATH_IMAGE050
, obtain new super vector then
Figure 422825DEST_PATH_IMAGE051
, wherein
Figure 890977DEST_PATH_IMAGE052
, wherein NNumber for given periodicity coordinate points;
Step C, with coordinate points
Figure 223870DEST_PATH_IMAGE012
As initial control point, calculate approximate B-spline curves according to following formula
Figure 162876DEST_PATH_IMAGE013
,
Wherein
，
Figure 278969DEST_PATH_IMAGE016
，
Figure 885531DEST_PATH_IMAGE017
，
Be given
Figure 446274DEST_PATH_IMAGE063
Individual some process
Figure 72034DEST_PATH_IMAGE019
The curve of approximation that obtains after the inferior iteration;
Figure 533102DEST_PATH_IMAGE020
Be given
Figure 884318DEST_PATH_IMAGE021
Individual some process
Figure 63626DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Be given
Figure 608319DEST_PATH_IMAGE007
Individual some process
Figure 396016DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Figure 797041DEST_PATH_IMAGE023
Be given Individual some process
Figure 2861DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Be
Figure 538196DEST_PATH_IMAGE007
The curve of approximation of individual point;
Figure 358385DEST_PATH_IMAGE026
Be
Figure 897819DEST_PATH_IMAGE007
Individual
Figure 778051DEST_PATH_IMAGE008
Parameter coordinate on the axle;
Figure 901471DEST_PATH_IMAGE027
Be Individual
Figure 287333DEST_PATH_IMAGE028
Parameter coordinate on the axle;
Be
Figure 388331DEST_PATH_IMAGE007
Individual Parameter coordinate on the axle;
Figure 752764DEST_PATH_IMAGE030
Be
Figure 709219DEST_PATH_IMAGE021
Individual some process
Figure 807231DEST_PATH_IMAGE019
After the inferior iteration
Figure 959864DEST_PATH_IMAGE008
Component of a vector on the axle;
Figure 79130DEST_PATH_IMAGE031
Be Individual some process
Figure 794724DEST_PATH_IMAGE019
After the inferior iteration
Figure 547785DEST_PATH_IMAGE028
Component of a vector on the axle;
Figure 787137DEST_PATH_IMAGE032
Be
Figure 104635DEST_PATH_IMAGE021
Individual some process
Figure 350809DEST_PATH_IMAGE019
After the inferior iteration
Figure 658293DEST_PATH_IMAGE010
Component of a vector on the axle;
Figure 502884DEST_PATH_IMAGE033
,
Figure 237622DEST_PATH_IMAGE034
, ,
Figure 879004DEST_PATH_IMAGE036
,
Figure 575172DEST_PATH_IMAGE037
, Implication by that analogy;
Step D, usefulness
Figure 701577DEST_PATH_IMAGE039
The approximate B-spline curves of record
Figure 101596DEST_PATH_IMAGE040
Go up corresponding to Coordinate figure; Specifically can adopt following method: use Write down approximate B-spline curves
Figure 751386DEST_PATH_IMAGE040
Go up corresponding to
Figure 782245DEST_PATH_IMAGE041
Coordinate figure; Wherein And
Figure 936332DEST_PATH_IMAGE055
,
Figure 633155DEST_PATH_IMAGE056
,
Figure 624244DEST_PATH_IMAGE057
NNumber for given periodicity coordinate points;
Step e, error of calculation super vector
Figure 650975DEST_PATH_IMAGE042
, and whether error in judgement reach given accuracy requirement, if then stop algorithm and curve of output; If not, then change step F; Wherein, error super vector
Figure 69318DEST_PATH_IMAGE042
Obtain according to following formula:
Figure 312824DEST_PATH_IMAGE058
Step F, pass through
Figure 28976DEST_PATH_IMAGE043
Calculate new reference mark
Figure 660946DEST_PATH_IMAGE044
, use
Figure 266502DEST_PATH_IMAGE045
The approximate B-spline curves of record
Figure 983922DEST_PATH_IMAGE046
Go up corresponding to
Figure 566082DEST_PATH_IMAGE047
Coordinate figure, pass through then
Figure 318138DEST_PATH_IMAGE048
Error of calculation super vector carries out iteration successively once more, up to reaching default accuracy requirement, curve of output; In the present embodiment, the numerical value approximate procedure data variation in the curve plotting process is as shown in table 1 below, and wherein, k represents iterations.
Table 1
? i=0 i=1 i=2 i=3 i=4 i=5 i=6 i=7 I=8
k=1 -4.25 4.25 3.75 1.125 4.125 2.375 -3.375 -4.25 4.25
k=2 -5.4219 5.375 4.0156 0.42188 4.7188 2.875 -3.9844 -5.4219 5.375
k=3 -5.7793 5.7695 4.0293 0.13867 4.8926 3.002 -4.0527 -5.7793 5.7695
k=4 -5.9094 5.9111 4.0188 0.044434 4.9556 3.0205 -4.041 -5.9094 5.9111
k=5 -5.9611 5.9641 4.0103 0.014313 4.9808 3.0158 -4.0241 -5.9611 5.9641
k=6 -5.9828 5.9849 4.0053 0.0046997 4.9914 3.0094 -4.0129 -5.9828 5.9849
k=7 -5.9922 5.9934 4.0026 0.0015888 4.9961 3.005 -4.0065 -5.9922 5.9934
k=8 -5.9964 5.9971 4.0013 0.00055784 4.9982 3.0026 -4.0032 -5.9964 5.9971
k=9 -5.9983 5.9987 4.0006 0.00020481 4.9992 3.0013 -4.0016 -5.9983 5.9987
k=10 -5.9992 5.9994 4.0003 7.8903e-005 4.9996 3.0006 -4.0008 -5.9992 5.9994
k=11 -5.9996 5.9997 4.0001 3.1865e-005 4.9998 3.0003 -4.0004 -5.9996 5.9997
k=12 -5.9998 5.9999 4.0001 1.3422e-005 4.9999 3.0001 -4.0002 -5.9998 5.9999
k=13 -5.9999 5.9999 4 5.8523e-006 5 3.0001 -4.0001 -5.9999 5.9999
k=14 -6 6 4 2.6204e-006 5 3 -4 -6 6
k=15 -6 6 4 1.1962e-006 5 3 -4 -6 6
The reference mark -6.00 6.00 4.00 0.00 5.00 3.00 -4.00 -6.00 6.00
Resulting curve passes through after the iteration 15 times as shown in Figure 2 as we can see from the figure during iteration 15 times, and the curve of being drawn has approached actual required curve very much; And by table 1 as can be seen, the curve plotting precision of this moment is unusual height, and 15 operations on computers of iteration are very fast, and this speed that this method operation is described is very fast also.
Fig. 3-Fig. 5 is the curve that adopts the common mathematical function that the inventive method draws, and wherein, Fig. 3 is a function
Figure 831945DEST_PATH_IMAGE059
Curve, Fig. 4 is a function
Figure 36662DEST_PATH_IMAGE060
Curve, Fig. 5 is a function
Figure 422513DEST_PATH_IMAGE061
Curve.Concrete drawing process is identical with a last embodiment, repeats no more herein.
The inventive method can be write out corresponding computer programs easily according to actual conditions, thereby can be widely used in the middle of the industrial design, the fibrous structure chart of a cloth that Fig. 6 draws for the software that is used for textile industry that adopts the inventive method to write.

Claims (4)

1. the curve plotting method based on the Quadric Spline iteration according to given periodicity coordinate points, utilizes the curve of computer drawing through each coordinate points, it is characterized in that, may further comprise the steps:
The super vector of steps A, the given periodicity coordinate points of input
Figure 280127DEST_PATH_IMAGE001
, super vector
Figure 83611DEST_PATH_IMAGE001
Expression formula as follows,
Figure 962574DEST_PATH_IMAGE002
，
In the formula,
Figure 325684DEST_PATH_IMAGE003
Be respectively the 1st, the 2nd ..., NThe coordinate vector of individual given periodicity coordinate points, NBe the number of given periodicity coordinate points,
Figure 786753DEST_PATH_IMAGE004
,
Figure 403548DEST_PATH_IMAGE005
,
Figure 582856DEST_PATH_IMAGE006
Represent respectively
Figure 2011101340685100001DEST_PATH_IMAGE007
Individual
Figure 599923DEST_PATH_IMAGE008
Axle,
Figure 931810DEST_PATH_IMAGE009
Axle,
Figure 204659DEST_PATH_IMAGE010
Coordinate components on the axle,
Step B, usefulness border replenishment are to super vector
Figure 822515DEST_PATH_IMAGE001
Carrying out the border replenishes and to obtain new super vector
Step C, with coordinate points
Figure 216773DEST_PATH_IMAGE012
As initial control point, calculate approximate B-spline curves according to following formula
Figure 793510DEST_PATH_IMAGE013
,
Figure 613698DEST_PATH_IMAGE014
Wherein
Figure 153133DEST_PATH_IMAGE015
， ，
Figure 100327DEST_PATH_IMAGE017
，
Figure 707895DEST_PATH_IMAGE018
Be given
Figure 806563DEST_PATH_IMAGE007
Individual some process
Figure 857696DEST_PATH_IMAGE019
The curve of approximation that obtains after the inferior iteration;
Be given Individual some process The vector that obtains after the inferior iteration;
Figure 287836DEST_PATH_IMAGE022
Be given
Figure 326461DEST_PATH_IMAGE007
Individual some process The vector that obtains after the inferior iteration;
Figure 660676DEST_PATH_IMAGE023
Be given
Figure 788032DEST_PATH_IMAGE024
Individual some process
Figure 328602DEST_PATH_IMAGE019
The vector that obtains after the inferior iteration;
Figure 81664DEST_PATH_IMAGE025
Be
Figure 321015DEST_PATH_IMAGE007
The curve of approximation of individual point;
Be
Figure 881758DEST_PATH_IMAGE007
Individual
Figure 189242DEST_PATH_IMAGE008
Parameter coordinate on the axle;
Figure 765324DEST_PATH_IMAGE027
Be
Figure 687012DEST_PATH_IMAGE007
Individual
Figure 233531DEST_PATH_IMAGE028
Parameter coordinate on the axle;
Figure 95439DEST_PATH_IMAGE029
Be
Figure 230754DEST_PATH_IMAGE007
Individual
Figure 136393DEST_PATH_IMAGE010
Parameter coordinate on the axle;
Figure 923870DEST_PATH_IMAGE030
Be
Figure 573158DEST_PATH_IMAGE021
Individual some process
Figure 625296DEST_PATH_IMAGE019
After the inferior iteration
Figure 701836DEST_PATH_IMAGE008
Component of a vector on the axle;
Figure 911363DEST_PATH_IMAGE031
Be
Figure 348030DEST_PATH_IMAGE021
Individual some process After the inferior iteration
Figure 266231DEST_PATH_IMAGE028
Component of a vector on the axle;
Figure 461589DEST_PATH_IMAGE032
Be
Figure 452678DEST_PATH_IMAGE021
Individual some process
Figure 980874DEST_PATH_IMAGE019
After the inferior iteration
Figure 399217DEST_PATH_IMAGE010
Component of a vector on the axle;
Figure 878609DEST_PATH_IMAGE033
,
Figure 353016DEST_PATH_IMAGE034
,
Figure 984986DEST_PATH_IMAGE035
,
Figure 823497DEST_PATH_IMAGE036
,
Figure 494912DEST_PATH_IMAGE037
,
Figure 14755DEST_PATH_IMAGE038
Implication by that analogy;
Step D, usefulness
Figure 501232DEST_PATH_IMAGE039
The approximate B-spline curves of record
Figure 274759DEST_PATH_IMAGE040
Go up corresponding to Coordinate figure;
Step e, error of calculation super vector
Figure 803010DEST_PATH_IMAGE042
, and whether error in judgement reach given accuracy requirement, if then stop algorithm and curve of output; If not, then change step F;
Step F, pass through
Figure 894725DEST_PATH_IMAGE043
Calculate new reference mark
Figure 91351DEST_PATH_IMAGE044
, use The approximate B-spline curves of record
Figure 398671DEST_PATH_IMAGE046
Go up corresponding to
Figure 859739DEST_PATH_IMAGE047
Coordinate figure, pass through then
Figure 414217DEST_PATH_IMAGE048
Error of calculation super vector carries out iteration successively once more, up to reaching default accuracy requirement, curve of output.
2. according to claim 1 based on the curve plotting method of Quadric Spline iteration, it is characterized in that, described in the step B to super vector
Figure 78679DEST_PATH_IMAGE001
Carry out the additional interpolation end-point data that is meant in border
Figure 557065DEST_PATH_IMAGE049
,
Figure 325170DEST_PATH_IMAGE050
, obtain new super vector then
Figure 345822DEST_PATH_IMAGE051
, wherein
Figure 12427DEST_PATH_IMAGE052
, wherein NNumber for given periodicity coordinate points.
3. according to claim 1 based on the curve plotting method of Quadric Spline iteration, it is characterized in that the specific implementation method of step D is as follows:
With
Figure 215875DEST_PATH_IMAGE053
Write down approximate B-spline curves
Figure 402268DEST_PATH_IMAGE040
Go up corresponding to
Figure 846019DEST_PATH_IMAGE041
Coordinate figure; Wherein
Figure 249187DEST_PATH_IMAGE054
And
Figure 772439DEST_PATH_IMAGE055
,
Figure 62607DEST_PATH_IMAGE056
, NNumber for given periodicity coordinate points.
4. according to claim 1 based on the curve plotting method of Quadric Spline iteration, it is characterized in that error super vector in the step e
Figure 256139DEST_PATH_IMAGE042
Obtain according to following formula:
Figure 614439DEST_PATH_IMAGE058
CN2011101340685A 2011-05-24 2011-05-24 Curve drawing method based on secondary B spline iteration Pending CN102222353A (en)

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CN109614574A (en) * 2018-11-23 2019-04-12 成都景中教育软件有限公司 The implementation method of iteration in a kind of dynamic geometry software
CN110097613A (en) * 2019-05-08 2019-08-06 广西大学 A kind of B-spline curves generation method and system based on probability calculation
CN111325815A (en) * 2020-03-05 2020-06-23 成都威爱新经济技术研究院有限公司 Editing method of multi-level B-spline curve

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Publication number Priority date Publication date Assignee Title
CN103680177A (en) * 2013-12-03 2014-03-26 上海交通大学 Intelligent vehicle speed prompting driving system based on mobile phone
CN103680177B (en) * 2013-12-03 2016-06-01 上海交通大学 Based on the intelligent vehicle speed prompting driving system of mobile phone
CN103676786A (en) * 2013-12-23 2014-03-26 北京航空航天大学 Curve fairing method based on accelerated speed principle
CN103676786B (en) * 2013-12-23 2016-05-25 北京航空航天大学 A kind of curve smoothing method based on acceleration principle
CN104931362A (en) * 2015-06-09 2015-09-23 中华人民共和国昆山出入境检验检疫局 Drop height fitting method
CN104931362B (en) * 2015-06-09 2018-02-02 中华人民共和国昆山出入境检验检疫局 Falling height approximating method
CN109614574A (en) * 2018-11-23 2019-04-12 成都景中教育软件有限公司 The implementation method of iteration in a kind of dynamic geometry software
CN110097613A (en) * 2019-05-08 2019-08-06 广西大学 A kind of B-spline curves generation method and system based on probability calculation
CN110097613B (en) * 2019-05-08 2023-08-25 广西大学 B spline curve generation method and system based on probability calculation
CN111325815A (en) * 2020-03-05 2020-06-23 成都威爱新经济技术研究院有限公司 Editing method of multi-level B-spline curve
CN111325815B (en) * 2020-03-05 2023-05-02 成都威爱新经济技术研究院有限公司 Editing method of multi-level B spline curve

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Application publication date: 20111019