Cong nghe CAD-CAM (merged file).pdf

8/13/2019 Cong nghe CAD-CAM (merged file).pdf

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CAD/CAM/CNCCAD/CAM/CNC

G CAD

CAD (C D)Thit k c s tr gip ca my tnh

Thit k y c hiu l v chi tithoc sn phm bng my vi tnh didng 2D hoc m hnh ha dng 3D

CAD

C (CAD), cn c hiul (CADD) l vic s dng my tnh ( )

Thit k c s tr gip ca my tnh l qutrnh to ra cc bn v k thut bng cch sdng cc phn mm my tnh.

C D D

CAD Technology = Design Techniques +Computers (HWare+SWare)

M hnh hahnh hc

hamy tnh

Thit k kthut

CAD Systems

A CAD system consists of three major parts:

1. Hardware: computer and input/output devices.

2. Operating system software.

3. Application software: CAD package.

Application

software

Graphics

utility

Devices

drivers

Input-output

devices

User

interface

Database

(CAD

model)

Basic structure of a CAD system


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K CAD

Sn phm hay cn gi l u ra ca CAD s l ccfile bn v in t cha cc d liu v hnh hc phc v cho vic in n bn v hoc phc v victo ra d liu cho qu trnh gia cng ch to

CAD khng ch bao gm vn m t hnh hc.Tng t nh cc bn v k thut v bng tay, ura ca CAD cn phi chuyn ti thm cc thng tinkhc nh vt liu, kch thc v dung sai

L CAD1. Tng nng sut thit k,

Automation of repeated tasks

Insert standard parts (e.g. fasteners) from database

2. Htrvic sa i thit kddng

3. Nng cao cht lng v chnh xc bn v

4. Ci hin vic trao i thng tin,

Gia cc nhm (ks) thit k, chto v nh cungcp

Vi cc ng dng khc nhCAM, FEM, CAE

Marketting, trnh by sn phm

5. To ra csdliu phc vcho qu trnh gia cng chto sau ny.

CAD

1. CAD c s dng rng khp trongnhiu lnh vc cng nghip, bao gm , , , , , .

2. CAD cng c s dng sn xuthot hnh hoc cc hiu ng t bittrong phim nh v qung co.

V d v mt bn v CAD 2D

V d v cc m hnh 3D

C

CAD 1981:

Solid modelling packages Romulus(ShapeData) and UniSolid (Unigraphics)

Surface modeler CATIA(Dassault Systemes)

1982

Autodesk was founded 1982 by John Walker, which led tothe 2D system AutoCAD.

1988

Featurebased modeling methods and parametric linkingof the parameters of features Pro/ENGINEER

Midrange packages such as SolidWorksin 1995, Solid Edge(then Intergraph) in 1996 and Autodesk Inventorin 1999.


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Cc cng cCAD htrqu trnh thit k

Giai on (pha) thit k Cc cng cCAD yu cu

Thit k tng (phc tho) Geometric modeling techniques;Graphics aids; manipulations; and

visualization

M hnh ha v m phng Same as above; animation; assemblies;special modeling packages.

Phn tch Analysis packages; customized

programs and packages.

Ti u Customized applications; structuraloptimization.

nh gi, thm tra Dimensioning; tolerances; BOM; NC.

Lp ti liu (hs) thit k Drafting and detailing

CAD

G ( ) CAM CAM (Computeraided Manufacturing) Gia cng,

ch to, sn xut c s tr gip ca my tnh

v thng dng nht, CAM l s dngmy tnh iu khin my cng c v cc my mc clin quan nhm gia cng cc chi tit.

, CAM l s s dng h thng mytnh lp k hoch sn xut, qun l, v iu khinhot ng ca mt nh my SX bng cch trc tiphoc gin tip tc ng ln cc trang thit b my mctrong nh my

CAM

Nu theo ngha hp, CAM l mt qu trnhtip ni sau CAD v i khi l CAE,

khi m sn phm to ra t CAD c phn tch,tnh ton, kim tra ri nhp vo cc phnmm CAM,

sau iu khin my cng c CNC gia cng

C CAM

(theo ngha rng)M hnh ha hnh hc

Trao i d liu

Lp k hoch sn xut

Chng trnh gia cng

Kim tra

Lp rp ng gi

Mt ng dng ca CAM:

T m hnh CAD n sn phm trong cng nghkhun mu

M CAD

CAMG

CNC


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C CAM 10 2010

1. Cimatron (4.1%) with GibbsCAM

2. CNC Software (3.3%) with Mastercam

3. C&G Systems (3.7%)

4. Dassault Systmes (18%) with CATIA

5. Delcam(7.5%) with PowerMILL

6. Open Mind (3.8%) with HyperMill

7. Planit (6.3%) with Edgecam

8. PTC (4.6%) with Pro/E

9. Siemens PLM Software (12.1%) with NX

10. Tebis AG (4.4%) with Tebis

11. : ://..//.=99

CAD/CAM

Thit k v ch to c s trgip ca my tnh CADCAMthng c gn lin vinhau (tch hp)

The CAM Process is a subsetof Manufacturing Process

Integration of CAD and CAMleads to automation

nh ngha CAD/CAM da vo cu thnh

Mfg tools

Networking

Design tools

Geometric

modeling

Computer

graphics

concepts

CAD/CAM

tools M hnh ha

hnh hc

Cng cthit k

hamy tnh

Mng truynthng

Cng cch to

The Product Cycle and CAD/CAM

hiu r hn v phm ving dng vnh ngha ca CAD/CAM trong mitrng k thut, ng thi xc nh cccng c c lin quan

ta cn nghin cu mt chu k sn xutin hnh (Product cycle)

The Manufacturing Process

The Design Process

SynthesisAnalysis The CAD Process

The CAM Process

Design

needs

Design

definitions,

specifications,

and requirements

Collecting

relevant design

information and

feasibility study

Design

conceptualization

Design

modeling and

simulation

Design

analysis

Design

optimization

Design

evaluation

Design

documentation and

communication

Process

planning

Order

materials

Design and

procurement of

new tools

Production

planning

NC, CNC, DNC

programming

ProductionQuality

control

Packaging

Marketing

Shipping

Typical Product Life Cycle Minh ha Qu trnh thit k


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Implementation of a Typical CAD Process on a

CAD/CAM system

Phc ha hnhdng

Chuyni phcha

M hnh hnh hc

Phn tch

Bn vchi tit

Ti liu thit k

To CAM Process

Trao i dliuv giao tip gia

cc m-un

Thay i thit k

Implementation of a Typical CAM Process on a

CAD/CAM system

M hnh hnh hc

Trao i dliuv gia tip

Lp k hoch sn xut

Kim tra

Lp rp

ng gp

Giao hngn thtrng

NC programs

u im ca cc hthng CAD/CAM

1. Linh hot hn

2. Rt n gn thi gian thit k+ chun bsn xut + snxut (lead time)

3. Gim chi ph u t

4. Tng nng sut

5. Ci thin dch vkhchhng

6. Tngcht lng SP

7. Ci thin mi giao tipvi nh cung cp phtng

8. Thit kSP tt hn9. iu khin sn xut

tt hn10. H trtch hp11. Gim gi thnh12. Gim slng my

cng c13. Gim khng gian nh

xng

Gii thiu v sn xut Sn xut l bin cc chi tit c thit kthnh sn phm

vt l (sn phm tht) Mt stiu ch nh gi qu trnh sn xut:

Cht lng C p ng yu cu kthut khng?

Nng sut Bao nhiu sn phm c sn xut trong mt n vthi gian?

Gi thnh

Gi ca mi sn phm Stin u tcho my mc v trang thit bdng c?

linh hot Chng ta c thsn xut sn phm no khc vi trang thit b

hin c? Mt bao nhiu thi gian ti ccu li quy trnh sn xut?


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HA I NH HA I NH

Computer graphics

Khi nim

1. ha my tnh (Computer Graphics ) l hac to bi my tnh, ni cch khc l s thaotc v biu din d liu nh bng my tnh

2. ha my tnh l mt khoa hc lin ngnhmy tnh v cc k thut khc cung cp mtphng thc tng tc gia con ngi v mytnh thng qua mn hnh.

3. ha my tnh lin quan n vic to cc mhnh 2 chiu, 3 chiu, phi cnh v t bng mang li s biu din trc quan cc vt th,phong cnh, hot hnh, m phng v thc t o.

Cc k thut ha

ha vct (vector graphics)

ha mnh (raster graphics)

ha vct ha vector s dng cc i tng hnh hc

c bn nh im, ng thng, ng conghoc a gic, ng trn, elip da vo cccng thc ton hc biu din hnh hc.

ha vector da trn cc hnh nh c tobi cc vector (cn c gi l cc nghoc nt) c nh ngha bng cc im iukhin. Mi im u c ta x v y trn mtphng lm vic v hng ca vector (cn gi ltrack). Mi track c th c gn c mu sc,hnh dng, dy nt v nn t bn tronghnh.

ha vct

nh vector khi zoom to khng b ntnt hoc nhe v khng nh hngn kch thc ca file d liu bi vcc thng tin c lu di dngcu trc ch khng phi im nhnh ha mnh (raster graphics)

Khi in n, cc file ha vector cin di dng nh bitmap sau khichuyn t dng vector sang bitmap.

Cc phn mm CAD u dng havector

V d v thng tin v hnh trn

For example, consider a circleof radius. The mainpieces of information a programneeds in order todraw this circle are

1. an indication that what is to be drawn is a circle

2. the radius

3. the locationof the center point of the circle

4. stroke line style and color (possibly transparent)

5. fill style and color (possibly transparent)


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ha mnh (raster graphics)

nh ha mnh, cn gi l nh bitmap,

l tp hp mt ma trn im biu dintrong khung li pixel hay cn gi v ccim nh trong mt hnh ch nht. nhny c th nhn thy c thng qua ccthit b nh mn hnh, giy hoc ccphng tin biu din hnh nh khc.

nh vector cha trong cc file nh vi rtnhiu nh dng khc nhau nh bmp,

jpeg, tga, tiff, png Thut ng raster xut pht t ting La

tinh c ngha l qut, c ngun gc pdng cho cch qut nh ca ng phngin t CRT ca mn hnh CRT. nh cv bng cch qut tng ng thng ccchm in t iu khin (li) bng ttrng.

u im ca ha vector so vi ha mnh

1. Dung lng ca file nh vector nh hn dung lngca file nh bitmap.

2. Khi zoomto nh vi t l rt ln, nt v trn truca cc i tng nh ng thng, cung trn vnc gi nguyn. dy nt ca cc ng khngtng ln mt cch t l khi zoom to

3. Cc tham s ca i tng nh c th chnh sa sauny (d dng thc hin cc thao tc di chuyn, t l,xoay v t mu)

4. Vi nh phi cnh 3D, t bng bng nh vector chohnh nh chn thc hn

Thut ton ha DDA(D )

Trong ha my tnh, phn cng hoc phnmm thc hin php phn tch vi phn s DDAc dng ni suy tuyn tnh v biu dinon thng cho bi im u v im cui.

Cch n gin nht ca thut ton DDA ni suy

tuyn tnh cc gi tr trong khong [(xstart, ystart),(xend, yend)] bng cch tnh xitrong phng trnh xi= xi1+1/m, yi= yi1+ m, trong x = xend xstartand y = yend ystartv m = y/x

Thut ton DDA

X

Y

Pend

Pstart

Xstart Xend

Ystart

Yend

X

Y

Mt ng thng c th biu din bngphng trnh:y = mx + c (1)Trong h s gc (2)

V hng s c = ys mxs (3)Trong thc t ni suy s dng phn cng,ngi ta khng dng 3 phng trnh trn mdng thut ton DDA. Thut ton phn tch viphn s DDA cho php tc tnh ton rtnhanh

se

se

xx

yym

=

Vi phn phng trnh (1) ta c:dy = m dx, thut ton DDA nh sau:Xt ng thng c h s gc m dng v m1, o ngc vai tr ca x thnh y, chn dy=1, khi xk+1= xk+1/mKhi tnh ton, cc gi tr ca x v y c lm trn thnh s nguyn v ta pixelkhng th l s l thp phn.

V d DDA Ni suy mt on thng c:

im bt u (10,20)mm

im kt thc (100,80) mm

Biu din on thng ny trn mt mn hnh c kch thc 300x250mm c phngii l 640x480 pixel

G:

Tnh h s phng i (hoc thu nh) theo phng x v y:

xs= 640/300 = 2.133 pixel/mm

ys= 480/250 = 1.920 pixel/mm

biu din c ton b ng thng trong mn hnh, chn phng i b 1.920pixel/mm

Chuyn ta im u v im cui ca on thng thnh ta pixel

im u: (10*1.92,20*1.92) = (19,38)

im cui: (100*1.92,80*1.92) = (192,154)

Tnhx = 192 19 =173

Tnhy = 154 38 = 116

Tnh m =y/x = 116/173 = 0.671

V m < 1 nn chn gia s dx =1 v p dng cng thc yk+1= yk+m

(Ta c th lp bng tnh, cho x ln lt tng 1 n v v tnh ln lt yk


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V d tnh tonx y tnh ton y lm trn

19 38.671 3920 39.341 39

21 40.012 40

22 40.682 41

23 41.353 41

24 42.023 42

25 42.694 43

26 43.364 43

43

42

41

40

39

19 20 21 22 23 24 25 26

Li pixelon thng c biu

din (on u)

Cc thut ton ha khc thay thcho DDA

Bresenham's line algorithmis an algorithm forline rendering.

Xiaolin Wu's line algorithmis an algorithm forline antialiasing

Hiu ng bc thang

Cc thut ton ni suy v im ha tnh ton v tr cc pixel theo cch lmtrn thnh s nguyn. Do cc ng nghing s b hiu ng bc thang.

.

.

Hin th ng thng theo pixel gy nn hin tng mt on thng cchiu di bng nhau c th biu din bng s pixel khch nhau, hoc ngcli, vi cng mt s lng pixel c th biu din cc on thng c chiu dikhc nhau ty theo gc nghing ca chng

Cch kh hiu ng bc thang

Nu so snh din mo ca mt ng thngnh nhau v trn AutoCAD v v trn MSWord hoc Power point th chng hon tonkhc hn v hiu ng bc thang.

lm gim hiu ng bc thang ngi ta da

vo l thuyt ly mu v lm m mt s pixel vng bin tip gip gia mu nn v muca ng.

AA Gi s khi zoom to mt on thng,

rng ca nt cng thay i. Hnhdng l tng ca on thng l mthnh ch nht hp nm nghing nhhnh v. Cc pixel no nm trong hnhch nht y s c mu m, ct hnhch nht s b lm nht mu (thay i transparent) v ngoi hnh ch nhtth khng c mu (trng mu nn)

Lm gim hiu ng bc thang i hivic tnh ton nhiu hn.

,

, ?


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C s d liu quan h

D liu biu din quan h c lu tr trong

cc file truy xut dng tun t.V d i tng trn hnh bn c m t bng ba quan

h: im (biu din ta cc nh) ng (ch ra nhng nh l im cui ca ng) Mt (ch ra cc cnh gii hn mt mt)

C s d liu phn cp

L cu trc dng cy gm nhiu phn t c th bc

gi l nt. nh cy gi l nt gc, s phn cp tnh t nt ny

tr xung to thnh cc mc khc nhau

C s d liu mng

C mi quan h manytomany gia cc phnt. Phn t mc di c th lin kt vinhiu phn t mc trn

Cu trc d liu c s cho ha

1. Cc mng tnh (static aray)

2. Cc dng d liu c cu trc (struct ca C,record ca pascal)

3. Con tr (pointer)

4. Danh sch lin kt (cu trc d liu ng chophp pht trin ln thm hoc thu nh)

5. Cu trc cy: cy tng qut, cy nh phn, cyt phn

V d v cu trc cy nh phn trong m t

hnh hc khi rn cu trc CSG


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C Graphics Standards

C rt nhiu tiu chun ha c s dng.Vn s dng tiu chun no ph thuc votnh tin li v s c lp ca thit b.

1. BGI(Borland graphics interface, 1987)2. GKS (graphics kernel system, the first ISO standard for lowlevel

computer graphics, introduced in 1977)3. PHIGS (' H I G ) is an API

standard for rendering 3D computer graphics, at one time considered to bethe 3D graphics standard for the 1990s)

4. OpenGL(O Graphics Library developed by SiliconGraphics Inc. in 1992 and is widely used in CAD, virtualreality, scientific visualization, information visualization,flight simulation, and video games)

Tiu chun trao i d liugraphics data exchange

cc phn mm CAD khc nhau c th giao tipv trao i d liu hnh hc ln nhau, vic ny ihi phi s dng cc chng trnh bin dch giacc phn mm vi nhau s phc tp

Cc phn mm CAD hin nay s dng ccchng trnh tin x l (preprocessor) chuynd liu CAD ca mnh thnh cc file trung ha(neural file) v ngc li cng c th chuyn ccfile trung ha thnh dng d liu CAD ca mnh

IGE

The I G E (IGE)(pronounced) is a file formatwhich defines a vendor neutral data formatthat allows the digital exchangeof information among Computeraided design(CAD) systems.

The official title of IGES is , first published inJanuary, 1980 by the U.S. National Bureau of Standardsas NBI801978. Many documents (like early versions of the DefenseStandardsMILPRF28000[1] and MILSTD1840[2]) referred to it asAME14.26M, the designation of the ANSIcommittee thatapproved IGES Version 1.0.

Using IGES, a CAD user can exchange product data models in theform of circuit diagrams, wireframe, freeform surfaceor solidmodeling representations. Applications supported by IGES includetraditional engineering drawings, models for analysis, and othermanufacturingfunctions.

History

The IGES project was started in 1979 by a groupof CAD users and vendors, including Boeing,General Electric, Xerox, Computervision andApplicon, with the support of the NationalBureau of Standards (now known as NIST) andthe U.S. Department of Defense(DoD). The namewas carefully chosen to avoid any suggestion of adatabase standard that would compete with theproprietary databases then used by the differentCAD vendors.

F

An IGES file is composed of 80character ASCIIrecords,a record length derived from the punched cardera.Text strings are represented in "Hollerith" format, thenumber of characters in the string, followed by theletter "H", followed by the text string, .., "4HSLOT"(this is the text string format used in early versions ofthe Fortranlanguage). Early IGES translators hadproblems with IBM mainframe computersbecause themainframes used EBCDICencoding for text, and someEBCDICASCII translators would either substitute thewrong character, or improperly set the Parity bit,causing a misread.


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The file is divided into 5 sections: Start, Global,Directory Entry, Parameter Data, and Terminateindicated by the characters S, G, D, P, or T incolumn 73. The characteristics and geometricinformation for an entity is split between twosections; one in a two record, fixedlength format(the Directory Entry, or DE Section), the other in amultiple record, comma delimited format (theParameter Data, or PD Section), as can be seen ina more humanreadable representation of thefile.[

STEP (IO 10303)

IO 10303is an ISOstandard for thecomputerinterpretable representationandexchangeof product manufacturinginformation. Its official title is:A

. It is knowninformally as "STEP", which stands for"Standard for the Exchange of Product modeldata". IO 10303can represent 3D objects.

The International standard's objective is to provide a mechanismthat is capable of describing product data throughout the life cycleof a product, independent from any particular system. The natureof this description makes it suitable not only for neutral fileexchange, but also as a basis for implementing and sharing productdatabases and archiving.

Typically STEP can be used to exchange databetween CAD,Computeraided manufacturing, Computeraided engineering,Product Data Management/EDMand other CAxsystems. STEP isaddressing product data from mechanical and electrical design,Geometric dimensioning and tolerancing, analysis andmanufacturing, with additional information specific to variousindustries such as automotive, aerospace, building construction,ship, oiland gas, process plants and others.

History of STEP

The evolution of STEP can be divided into four release phases. Thedevelopment of STEP started in 1984 as a successor of IGES, SETand VDAFS.[1] The initial plan was that "STEP shall be based on onesingle, complete, implementationindependent Product InformationModel, which shall be the Master Record of the integrated topicaland application information models".[2] But because of thecomplexity, the standard had to be broken up into smaller partsthat can be developed, balloted and approved separately.[3] In1994/95 ISO published the of STEP as internationalstandards (IS) with the parts 1, 11, 21, 31, 41, 42, 43, 44, 46, 101,AP 201 and AP 203.[4] Today AP 203 C 3Dis still one of the most important parts of STEP andsupported by many CAD systems for import and export.

Danh sch file format ca cc phn mm

CAD thng dng1. 3dxml Dassault Systemes graphic representation2. ART ArtCAM model3. ASC BRLCAD Geometry File (old ASCII format)4. ASM Solidedge Assembly, Pro/ENGINEER Assembly5. BIN, BIM Data Design System DDSCAD6. CATDrawing CATIA V5 Drawing document7. CATPart CATIA V5 Part document8. CATProduct CATIA V5 Assembly document9. CATProcess CATIA V5 Manufacturing document10. DWG AutoCAD and Open Design Alliance

applications


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Danh sch file format ca cc phnmm CAD thng dng

11. DFT Solidedge Draft12. DGK Delcam Geometry13. DMT Delcam Machining Triangles14. DXF ASCII Drawing Interchange file format

AutoCAD15. DWF AutoDesk's Web Design Format; AutoCAD &

Revit can publish to this format; similar in concept toPDF files; AutoDesk Design Review is the reader

16. FM FeatureCAM Part File17. GLM KernelCAD model


18. IAM Autodesk Inventor Assembly file19. IDW Autodesk Inventor Drawing file20.IGES Initial Graphics Exchange Specification21. IPN Autodesk Inventor Presentation file22. IPT Autodesk Inventor Part file23. model CATIA V4 part document24. PAR Solidedge Part25. PRT NX (recently known as Unigraphics),

Pro/ENGINEER Part, CADKEY Part26. PSM Solidedge Sheet27. PSMODEL PowerSHAPE Model


28. RLF ArtCAM Relief29. SLDASM SolidWorks Assembly drawing30. SLDDRW SolidWorks 2D drawing31. SLDPRT SolidWorks 3D part model32. STEP Standard for the Exchange of Product model data33. STL Stereo Lithographic data format used by various CAD

systems and stereo lithographic printing machines.34. TCW TurboCAD for Windows 2D and 3D drawing

35. UNV IDEAS IDEAS (Integrated Design and Engineering AnalysisSoftware)36. WRL Similar to STL, but includes color. Used by various CAD

systems and 3D printing rapid prototyping machines. Also used forVRML models on the web.


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C ( )

M hnh khung dy (wire frame)

M hnh mt (surface model)

M hnh khi rn (solid model)

M hnh ch c biudin bng cc cnh vin

M hnh ny thngxut hin trong cc phnmm CAD th h u

Kh quan st v dnhm ln i vi cc chitit phc tp

M hnh mt c s dng ph bin trong thit k cc

sn phm thuc ngnh hng khng v t.

M hnh c biu din bng cc b mt, v mt cbiu din bng cc cnh (edges) v cc nh (vertex)

Surface Representation

C

1. M hnh mt s cp (primitive)

2. M hnh mt c bn (basic surface)

3. M hnh mt phc tp (advanced surface)

4. M hnh mt ghp t cc li tam gichoc t gic (facets)

M hnh mt s cp Cc loi mt s cp trong m hnh mt l: (box,

pyramid, wedge, dome, sphere, cone, torus, dish andmesh)

Cc mt s cp c th d dng m t bng cc cngthc ton hc s cp c bn

Phng trnh ton ca mt s mt s cp

Mt cu

Vi mt cu c tm ti gc, phng trnh tham s l:

(0 2, 0 2 v a l khong cch t gc ta n tm mt ct)

Mt xuyn:

Mt cn: , dng tham s

2222)()()( Rzzyyxx ccc =++

=

=

=

cos

sinsin

cossin

az

ay

ax

=

+=

+=

sin

sin)cos(

cos)cos(

bz

bay

bax

02

2

2

2

2

2

=+

c

z

b

y

a

x

=

=

=

uz

auy

aux

sin

cos


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A planeis an infinite surface that is perfectly flat. Can be infinite or a

bounded region

A plane is defined by a point and a normal vector. The parameterizationof a plane is defined by two additional parameters: a vectorperpendicular to the normal that specifies the uparameter directionand scaling, and a flag that specifies whether the parameterization ofthe plane is righthanded or lefthanded.

( )

is a surface of revolutiongenerated by

revolving a circle in three dimensional spaceabout an axis coplanar with the circle.

Trong trng hp tng qut, mtc s ca mt cn l mt ellipse,trng hp c bit l ngtrn.

The geometry of a cone is definedby a base ellipseand the sine andcosine of the ofthe cone.

The normal of the base ellipserepresents the axis of the cone.

Mt tr l mt trng hp cbit ca mt cn.

M hnh mt c bn

1. L cc m hnh mt c to ra bng ccphp qut hnh c bn nh php xoay(revolve), php n (extrude, rule) v qut(sweep) theo ng dn. i tng 2D cqut theo mt qu o no khng trng

mi mt phng cha i tng 2D

M hnh mt c bn2. M hnh mt c th c to ra bng cc

ghp cc mt a gic

3. Hoc dng cc k thut m hnh s dng ccng cong phc tp nh Bsplines hocNURBS ( )

C

1. Php xoay (revolve)

2. Php n (extrude)

3. Qut theo ng dn(sweep)


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V m hnh mt c bn trong Pro/E

Mt n (Extrude)

Mt trn xoay(Revolve)

Trcquay

i tng2D

i tng2D

Hng n

V m hnh mt trong Pro/Engineer

Mt qut theo ng dn

ng dn

ng dn

Mt ct 2D

Kt qu

ng dn

Mt ct 2D

V m hnh mt trong ProE

Mt trm (Blend)

Mt trm t cc tit din nmtrong cc mt phng song song

Truc Z

R1=100

R2=120

R3=140R4=160 600

600

50x5

0

60x60

70x70

80x80

Gocxoay

Sau khi

Smooth

Mt trm t cc tit din xoay

Khnglm trn

Lm trn Khnglm trn

Lm trn

( )

M hnh mt nng cao da

trn cc php qut hnh phc

tp hoc to cc mt cong

Bezier, mt cong BSpline, mt

cong NURBS t cc ma trn

im.

B

Datum point

Datum curve 1

Datum curve 2

120

60

Datum curve 3

Datum curve 1

Datum curve 3

Datum curve 2

Dung e tao ra mat cong i qua hai ng bien oi dienvamot ng ieukhien gia.


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07/11/12

4

Datum curve 1

Datum curve 3

Datum curve 2

Approx curve 3

R1.5

R5

ng dng mt nng cao m hnh ha mtsn phm PET ng nc gii kht

()

Mt cong t do c xy dng trn c s ca cc ngcong t do nh Spline, Bezier, NURBS (s hc sau)

Mt li a din (facets) F B

Faceted models consist of groups of

polygons (often triangles). In contrast,

most ComputerAided Engineering

(CAE) models originate from Computer

Aided Design (CAD) systems which

typically use continuous surface and

edge definitions based on NURBS.

CAE simulations then break down this NURBS representation intofacets by a process known as meshing. The mesh (or grid) is thenused as the basis to perform simulations such as ComputationalFluid Dynamics (CFD) and finite element analysis (FEA).

F

Li th (coarse mesh) Li mn (fine mesh)Li trung bnh(medium mesh)

Trong cng ngh to mu nhanh, dng chun ca file CAD c nh dng dng STL (stereo lithography), kt ni gia phn mm CAD v my to mu 3D.

Cc file STL xp x cc b mt ca vt th (thng c v bng m hnh mtcong NURBS) thnh cc li tam gic hoc t gic. n mn ca li cng cao th chnh xc so vi m hnh gc cng cao.

u nhc im ca m hnh mt

1. Trc quan hn m hnh khung dy.2. C th t bng.3. C th phn bit c cc phn t c bit trn mt nh cc

l trng.4. Xc nh c giao ca cc b mt.5. C th thc hin cc php tnh ton v din tch.6. C th dng lm d liu lp trnh CAM thc hin gia cng

phay mt cong bng my CNC.

1. Ch m t lp bin ca i tng, khng c thuc tnh bn

trong.2. Nu dng m hnh mt v tt c cc mt bao ca vt th

ri to thnh khi rn th tn nhiu thi gian hn so vi sdng m hnh khi rn.

3. Phc tp hn m hnh khung dy, lng d liu ln hn.


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07/11/12

5

M hnh khi rn

Phn ln cc phn mm CAD s dng 2phng php m hnh ha khi rn:

1. M hnh khi rn theo php i s Boole(CSG Contructive solid geometry)

2. M hnh khi rn theo mt bin kn(Boundary representation)

3. M hnh Hybrid (dng c CSG v Brep)

M hnh khi rn theo php i sBoole (CSG)

Vt th c xy dngtrn c s phi hp cckhi rn c bn nhhp, cu, xuyn, t din,chm, cn

Cc php ton i sBoole nh php hi (),giao () v php tr ()c dng thao tcloi m hnh ny

M hnh khi rn theo CSGPhp hi (), tc

php cng

Php tr ()

Php tr ()

Php giao() ly phnchung ca 2 vt th

CG

1. CSG c dng khi m t cc m hnh khi m chnh xc ca m hnh l yu cu quan trng.

2. CSG rt ph bin v kh n gin khi xy dng mhnh, mt m hnh phc tp c th c xydng t cc vt th n gin.

3. Nu cc vt th c tham s ha (c th thayi kch thc v v tr), ngi thit k d dngthay i v tr, kch thc v cc php ton i sBoole c c m hnh mi.

c tnh v ng dng ca CSG

4. u im ca CSG l lun lun m bo m hnhthc s l c (solid), hay cn c hiu l knnc. iu ny quan trng i vi mt s yucu trong ch to v phn tch tnh ton mhnh

5. u im na ca CSG l d dng xc nh mtim bt k cho trc c nm trong hay nmngoi khi rn. iu ny rt cn thit i vi ccbi ton v kim tra s va chm ca cc vt th.

Cu trc ca m hnh khi rn theo CSG

Cc vt thCSG thngc cu trctheo m hnhcy nh phn

Cc ll cckhi rn c sv cc ntlcc php toni s Boole


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7

()

E l mt phn t topology 1D c th dng to thnh ng bao ca face. Edge do curvetothnh v b gii hn bi 2 vertex

Nhiu edge c th tn ti trn cng mt curve,tuy nhin hai edge trn cng mt body khngth c chng ln nhau.

Topologyelement

Vertex l thc th topology(entity) khng c chiu (0dimensional) dng gii hncc edge. Ni chung, mt edgec gii hn bi 2 vertex nhhnh v bn.

Nu edge kn, c hai u caedge b gii hn bi cng m

vertex. Cng c trng hp mt edge

c chiu di bng khng, gi lnull edge, ch b chn bi mtvertex

Topologyelement

Khi nim v manifold v nonmanifold

Mi im trn bin ca mt khirn manifold solid s chia khnggian m hnh ra hai phn: mintrong khi rn v min ngoi khirn. Nu tn ti mt im trnbin khng tha mn iu kin nyth khi rn c coi l non

manifold ti im . Ni cch d hiu hn: Manifold c

ngha l vt rn c th gia cngch to c. Ngc li, NonManifold th khng

A nonmanifold object

Mt s v d v nonmanifold B

The basic method for BREP was developedindependently in the early 1970sby both Ian C.Braidin Cambridge(for CAD) and Bruce G.Baumgart at Stanford(for computer vision).

Braid continued his work with the research solidmodeller BUILD which was the forerunner ofmany research and commercial solid modellingsystems. Braid worked on the commercialsystems ROMULUS, the forerunner of Parasolid,and on ACIS. Parasolid and ACIS are the basis formany of today's commercial CAD systems.


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8

So snh CSG v BREP

So vi CSG, phng php ch s dng cc vt th cbn v php ton i s Boole phi hp, m hnh Brep linh hot hn v c nhiu php thao tc hn.

CSG ch c dng cc phn mm CAD th h u vn d thc hin hn. Ngy nay, Brep c xem l lachn tt nht cho cc h thng CAD hin i.

Brep cng s dng cc php ton i s Boole, ngoira cn s dng cc php n (extrusion) hoc qut(sweeping), vt cnh (chamfer), bo gc (fillet), to mtnghing (drafting), xon (tweaking ), to v mng(shelling) xy dng cc m hnh phc tp

u im ca Brep

D dng biu din c cc m hnh khi rnphc tp thn xe hoc v my bay m chngkhng th to ra bng cc phi hp cc khirn c bn nh cch ca CSG

D dng chuyn i m hnh khi rn Brepsang m hnh khung dy v bin ca Brep cnh ngha tng t nh khung dy

Cc thut ton ca Brep tin cy v mnh hncc thut ton da trn CSG

Nhc im ca Brep

i hi nhiu khng gian nh th n phi chacc phng trnh tng minh biu din lpbin

Dong di v phc tp hn CSG

Brep xp x (gn ng) (Faceted Brep) to t

cc mt phng khng thch hp cho vic chto

Exact Vs Faceted Brep Schemes

Exact Brep: If the curved objects are represented byway of equationsof the underlying curves and sufacesthen the scheme is Exact Brep.

Approximate or faceted Brep :In this scheme ofboundary representation any curved face divided intoplanar faces.

u im ca m hnh khi rn1. Xc nh y cc thuc tnh khi lng2. M hnh thit k r rng, trc quan, c bit cho

nhng ngi khng quen vi bn v 2D3. D dng phn bit vng bn trong, trn mt v bn

ngoi vt th4. m bo t ng xa cc ng khut5. D t ng xy dng cc hnh chiu khi mun trnh

by bn v6. Thay i thit k d dng hn7. D dng chuyn d liu hnh hc sang cc phn mm

phn tch bng FEM8. D dng trong lp rp v m phng chuyn ng, tnh

ton ng lc hc

Nhc im ca m hnh khi rn

1. Tiu tn nhiu b nh v i hi cu hnhmy tnh mnh,

2. Thao tc v tnh ton chm,

3. Kh trao i d liu gia cc file CAD 3Dtham s t cc phn mm CAD khc nhau.


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02/04/13

2

Php quay 2 chiu

P(x,y)

P*(x*,y*)

x

y

R

x= R.cos y= R.sin x*= R.cos (+) = R(cos cos sin sin )y*= R.sin (+) = R(sin cos + cos sin )Vit di dng ma trn ta c:

* *

os sin 0

1 1 sin os 0

0 0 1

c

x y x y c

=

[ ] [ ]*P P T =

Php quay trong khng gian 3 chiu

* * *

os sin 0 0

sin os 0 01 1

0 0 1 0

0 0 0 1

c

cx y z x y z

=

1. Quay quanh trc Z

2. Quay quanh trc y

3. Quay quanh trc x

[ ]

os 0 sin 0

0 1 0 0

sin 0 os 0

0 0 0 1

Y

c

Rc

=

[ ]

1 0 0 0

0 os sin 0

0 sin os 0

0 0 0 1

X

cR

c

=

Php quay quanh mt trc bt k

1. Tnh tin trc sao cho im u ca n trng vi gc ta ,

2. Thc hin php quay quanh trc x mt gc a n vmtphng XZ,

3. Thc hin php quay quanh trc y mt gc a trc btkvtrng vi trc z,

4. Quay quanh trc z mt gc mong mun,

5. p dng php quay ngc li quanh trc y,6. p dng php quay ngc li quanh trc x,

7. p dng php tnh tin ngc li di trc bt kvvtr banu ca n trong khng gian.

Gi s cn quay quanh mt trc c xc nh bng mt vct iqua hai im (x1, y1, z1) v (x2, y2, z2). Trnh t thc hin nh sau:

[ ] [ ][ ] [ ] [ ] [ ] [ ] [ ] 1

x y z y xH T R R R R R T

=

Php quay quanh mt trc bt k

x

y

z

(0,0,0)

(a,b,c)l

l

d(0,b,c)

im chiu

im sau khiquay

x

y

z

(0,0,0)

(a,b,c)

d

(0,0,) (a, 0 ,d)

im chiu

Tnh gc quay quanh trc x Tnh gc quay quanh trc y

2 2sin

b b

db c = =

+

2 2os

c cc

db c= =

+

si n

o s

a

l

dc

l

=

=

2 2 2 2

2 2 2

l a b c

d b c

= + +

= +

Bi tp Quay mt hnh hp ch nht c cnh l a, c tm nm trng gc ta

ton cc, cc cnh song song vi h trc ta Oxyz, mt gc 45

quanh mt trc c xc nh bng mt vct i qua hai im (x1, y1, z1)v (x2, y2, z2), trong x1 = 10, x2 = 10

Y1=15+0.5*s th t trong danh sch mn hc Y2=25+0.5*s th t trong danh sch mn hc z1=5+0.5*s th t trong danh sch mn hc z2=20+0.5*s th t trong danh sch mn hc a = 50+0.5*s th t trong danh sch mn hc

V v ghi kch thc hnh hp ch nht ti v tr ban u bngphn mm Solidworks, v trc quay v v hnh hp ch nht saukhi quay n v tr mi. Dng Measure xc nh ta ta 8 nhca hnh ch nht ti v tr mi (khi measure mi nh (vertex), hycopy mn hnh sang file MS Word)

S dng cng thc ca php quay tnh ta ca 8 nh cahnh hp ti v tr mi (Vit phng trnh, sau dng MS Excelhoc Matlab thao tc nhn cc ma trn)

Php i xng

Dng tng qut ca php i xng qua trc x, y hoc

gc ta nh sau:

:

Nu i xng qua trc x th a = 1, b = 1 (v ch c ta theo trc y l i du)

Nu i xng qua trc y th a = 1, b = 1 Nu i xng qua gc ta th a = 1, b = 1

[ ]

0 0

0 0

0 0 1

a

M b

=


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3

Php i xng qua ng thng 2D bt k

1. Tnh tin ng thng mt on C a i qua gc ta

2. Quay ng thng mt gc n trng vi trc x

3. Ly i xng i tng qua trc x

4. Quay ngc ng thng mt gc v v tr ban u

5. Tnh tin ng thng v v tr ban u

1 0 0 cos sin 0 1 0 0 cos sin 0 1 0 0

[ ] 0 1 sin cos 0 0 1 0 sin cos 0 0 1

0 0 1 0 0 1 0 0 1 0 0 1 0 0 1

T C C

=

[ ] [ ]*P T P = Ch : Ma trn bin hnh [T] ang vit theo dng cng thc

:

os2 sin 2 sin 2

[T]= sin 2 os2 (cos 2 1)

0 0 1

c C

c C

+

Php bin dng

Php bin dng thay i gi tr cc ta bngcch thm vo mt hm tuyn tnh. Ma trn binhnh tng qut c dng sau:

[ ]

1 0

1 0

0 0 1

sh

b

T c

=

Xt trng hp c bit: bin dng theo trc x(ch nh hng n ta x), mt im P(x, y,1) s tr thnh P*(x+shx*y, y, 1). Biu din didng ma trn nh sau:

Tng t, nu bin dng theotrc y, im P(x, y, 1) s tr thnhP*(x, y+shy*x, 1)

[ ]

1 0 0

1 0

0 0 1

sh xxT sh

=

[ ]

1 0

0 1 0

0 0 1

y

sh y

sh

T

=

Php quay gc ta dng ma trn

Xt hai h ta XYZ v UVW chuyn ng quaytng i quanh gc O trng nhau.

Gi ix, jy, kzv iu, jv, kwln lt l cc vc t n vtrn cc trc ca hai h ta XYZ v UVW. Nu mtim M trong h ta XYZ c biu din bngvct

th trong h ta UVW c biu din bng vct

( , , )T

xyz x y zr r r r r =

w( , , )

T

uvw u vr r r r r =

Php quay gc ta dng ma trn

Nu vit di dng ma trn

w

w

w w

.

x x u x v x u

y y u y v y v

z z u z v z

r i i i j i k r

r j i j j j k r

r k i k j k k r

=

[ ]w

w

w

x u x v x

y u y v y

z u z v z

i i i j i k R j i j j j k

k i k j k k

=

[ ]

os( , ) os( , ) os( ,w )

os( , ) os( , ) os( , w)

os( , ) os( , ) os( , w)

c x u c x v c x

R c y u c y v c y

c z u c z v c z

=

[ ] 1

w

.

u x

v y

z

r r

r R r

r r

=


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1

M t ng congM t ng cong

1. Biu din bng ma trn cc im (chui im)

2. S dng cc phng trnh gii tch dng athc bc n

1

1 1 0

0

( ) ...n

n n n

n n i

i

p x a x a x a x a a x

=

= + + + + =

H ,

1. Phng trnh tng minh; y =f(x,y,z)

2. Phng trnh n: f(x,y) =0 ( 2D)

3. Phng trnh tham s: x=x(t), y=y(t), z=z(t)

V mt l thuyt c th s dng bt k dng ton hcno ca ng cong m t ng cong trong cngngh CAD. Dng phng trnh tham s c dng

nhiu nht. Mi dng c mt s thun li v kh khntrong mt s trng hp: D

? D

?

Gi s phng trnh tham s ca mt phnon ng cong c dng:

x=x(t);(a) y=y(t) (b)

c bin i sang dng n f(x,y) = 0

C 1: S dng phng php th i vitrng hp n gin (bc nht hoc bc 2)

C 2: S dng phng php trong c sdng tch chp hai a thc (p dng cho bc 3hoc bc 4)

Phn loi ng cong

Phn loi theo phngphp xy dng:

1. ng cong chnhxc (cc ng congconic)

2. ng cong ni suy(interpolation)

3. ng cong xp x(approximation)

Phn loi theo tn gi:

1. ng cong tham sbc 3 (ng congFerguson )

2. ng cong Spline3. ng cong Bezier4. ng cong Bspline5. ng cong hu t

(NURBS)

Dng ngconic

Dng tham s Dng n

ng trn

Elip

Parapol

Hypepol

cosx r =

siny r =

2 2 2x y r+ =

cosx a =siny b =

2 2

2 2 1

x y

a b+ =

2x a=

2y a=2

4y ax=

coshx a =sinhy b =

2 2

2 2 1

x y

a b =


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02/04/13

2

3 ng cong tham s bc 3 c dng:

Trong () l mt im trn ng cong.Khai trin v tch ra thnh 3 thnh phn

trong khng gian ta c:

x(t) = a3xt3 + a2xt

2+ a1xt + a0xy(t) = a3yt

3 + a2yt2+ a1yt + a0y

z(t) = a3zt3 + a2zt

2+ a1zt + a0z

3

0

( ) i

i

i

P t a t =

=

P(t)

x

y

y

O

3

Phng trnh trn c 4 h s a cn xc nh,c th tm bng cch dng cc iu kin bin:

i qua hai im cho trc (2 phng trnh)

Cc vect tip tuyn ti im u v imcui xc nh (2 phng trnh)

3

0

( ) i

i

i

P t a t =

=

P1

P0

Tip tuyn ti P1

Tip tuyn ti P0

3

Dng ma trn

Sau khi s dng iu kin bin, tm c:

3

23 2

1

0

( ) [ 1]

a

aP t t t t

a

a

=

0

1

2

3

(0)

'(0)

3 ( 0) 3 (1) 2 '( 0) '(1)

2 (0) 2 (1) '( 0) '(1)

a P

a P

a P P P P

a P P P P

=

=

= + = + +

Suy ra: 3 2

2 2 1 1 (0)

3 3 2 1 (1)( ) [ 1]

0 0 1 0 '(0)

1 0 0 0 '(0)

P

PP t t t t

P

P

=

V ng cong tham s bc 3 bngcch no?

Cho tham s t chy t 0 n 1

3 2

2 2 1 1 (0)

3 3 2 1 (1)( ) [ 1]

0 0 1 0 '(0)

1 0 0 0 '(0)

P

PP t t t t

P

P

=

Ma trn Hermite(khng i)

Ma trnh s

hnh hc(G)

3

ng cong Spline bc c biu din bngmt a thc bc 3 c o hm bc 2 lin tc ticc im ni chung gia cc phn on

Phng trnh tham s ca ng Spline bc 3cho mi phn on c dng nh phng trnhtham s bc 3 chnh tc

3 2

2 2 1 1 (0)

3 3 2 1 (1)( ) [ 1]

0 0 1 0 '(0)

1 0 0 0 '(0)

P

PP t t t t

P

P

=

3

ng cong spline phi tha mn tnh lin tcca o hm bc hai

o hm bc hai ca im cui phn on trcphi bng o hm bc hai ca phn on sau.

Nh rng buc ny, ngi ta xc nh c cctip tuyn ti cc im nt ca ng Spline

Phn on i1

Phn on iPiPiPi

Pi+1Pi+1Pi+1

Pi1Pi1Pi1


28/32

02/04/13

3

,

Sau khi xc nh c cc tip tuyn Piti

cc im nt, thay cc gi tr ny vo phngtrnh tham s trn tng phn on

3 2

2 2 1 1 (0)

3 3 2 1 (1)( ) [ 1]

0 0 1 0 '(0)

1 0 0 0 '(0)

P

PP t t t t

P

P

=

1

0 0

1 2 0

2 3 1

2 1 3

1 1

' '1 0 . . . .

' 3( )1 4 1 0 . .

' 3( )0 1 4 1 0 .

. .. . . . . .

' 3( ). . 0 1 4 1

' '. . . . 0 1

m m m

m m

P P

P P P

P P P

P P P

P P

=

Sau khi xc nh c cc tip tuynPiti cc im nt, thay

cc gi tr ny vo phng trnh tham s trn tng phn on

(hai tip tuyn ti hai im u v cui P0v Pm1bng 0)1

0 1 0

1 2 0

2 3 1

2 1 3

1 1 2

' 3( )2 1 . . . .

' 3( )1 4 1 0 . .

' 3( )0 1 4 1 0 .

. .. . . . . .

' 3( ). . 0 1 4 1

' 3( ). . . . 1 2

m m m

m m m

P P P

P P P

P P P

P P P

P P P

=

3 2

2 2 1 1 (0)

3 3 2 1 (1)( ) [ 1]

0 0 1 0 '(0)

1 0 0 0 '(0)

P

PP t t t t

P

P

=

S dng Excel tnh tonv xy dng ng cong Spline

1. Nhp ma trn ta cc im nt

2. Nhp ma trn h s ca phng trnh xcnh tip tuyn

3. Tnh ma trn ct v phi ca phng trnh

tnh tip tuyn4. Tnh ma trn ct cc tip tuyn bng lnh

nhn ma trn Mmult(Array1, Array2)



5. Tnh ta ca ca cc phn on spline


6. V th (v ng Spline)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 2 4 6 8

V d ng cong Spline t do i qua 4 im nt cho trc


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02/04/13

4

ng cong Bezier ng cong Bezier l l ng cong xp x cc

im cho trc ch khng i qua chnh xc ccim ny nh cch ca cc ng con ni suy

Cho php ngi thit k mm do hn.

Thng c ng dng trong thit k v t,my bay v tu thy.

ng cong ny do P. Bezier lm vic cho cng tyxe hi Citroen nghin cu t nhng nm 1960

V0

V1V2

V3

ng cong Bezier Phng trnh tng qut ca ng cong

Bezier c n+1 im iu khin (V0, V1,, Vn)nh sau:

H B, B, B

,

0

( ) ( )n

i i n

i

P t V B t =

=

1

, ( ) (1 )i i n

i n nB t C t t

=

!

!( )!

n

i

nC

i n i=

ng cong Bezier bc 2 v bc 3

Bc 2 i qua 3 im iu khin

() = (1)2 0+2(1)1+ 22

Bc 3 i qua 4 im iu khin

() = (1)3 0+3(1)21+32(1)2+ 33

0

2

1

2

1 2 1

( ) [ 1] 2 2 0

1 0 0

V

P t t t V

V

=

0

13 2

2

3

1 3 3 1

3 6 3 0( ) [ 1]

3 3 0 0

1 0 0 0

V

VP t t t t

V

V

=

Dng ma trn

Dng ma trn

Tnh cht ca ng cong Bezier

1. i qua im iu khin u v cui

2. Tip tuyn vi hai on thng ni hai imu tin v cui cng


3. Nm hon ton trong a gic to bi cc nhca cc im iu khin


4. ng cong Bezier thay i theo v tr mtim iu khin cc b


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5

Tnh cht ca ng cong Bezier5. ng cong Bezier thiu s iu khin cc b

(tc l c s iu khin ton cc)

Tnh cht ca ng cong Bezier6. Bc ca ng cong Bezier ph thuc vo s

im iu khin

gia bc ca ng cong thp, c th linkt nhiu phn on li vi nhau

ng cong Bspline

Khc phc c 2 nhc im ca ng congBezier (bc cao v tnh iu khin ton cc)

1. Hm c s to ra ng cong a thc thams tng on ring l thng qua mt s imiu khin

2. Bc ca a thc c chn c lp vi s lng

cc im iu khin (bng chnh bc ca hm cs), n quyt nh bc ca ng cong Bspline

3. Cc ng cong Bspline c th iu khin ccb (ch mt vi phn on b nh hng)

ng cong Bspline

Phng trnh tng qut ca ng cong Bspline c n+1 im iu khin (V0, V1,, Vn)nh sau:

H , 1

K 1 B

,

0

( ) ( )n

i k i

i

P t N t V =

=

1

,1

, , 1 1, 1

1 1

1 if t t( )

0

( ) ( ) ( )

i i

i

i i ki k i k i k

i k i i k i

tN t

nguoc lai

t t t t N t N t N t

t t t t

+

+

+

+ + +

=

= +

Dng ma trn ca ng cong Bspline

ng Bspline bc 2 u (s dng 3 im

iu khin)

ng Bspline bc 3 u (4 , 3 )

1

2

1

1 2 11

( ) [ 1] 2 2 02

1 1 0

i

i i

i

V

P t t t V

V

+

=

1

3 2

1

2

1 3 3 1

3 6 3 01( ) [ 1]

3 0 3 06

1 4 1 0

i

i

i

i

i

V

VP t t t t

V

V

+

+

=

Tnh cht ca ng cong Bspline

ng cong Bspline c th thay i hnhdng cc b khi thay i im iu khin

Hnh dng ca ng cong Bspline cn phthuc v cc vect nt t trong hm c s(u/tun hon v khng u/khng tunhon)

ng cong Beizer l mt trng hp con cang cong Bspline khng u khi cc vctnt = [0 0 0 1 1 1]


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ng cong Bspline

ng cong thay i thi thay i vct nt

ng cong Bezier l trnghp c bit ca ng cong

Bspline khng u

ng cong BSpline khng u vi sthay i cc b

Phng php ni suy, xp x v phi hp c

ng cong t do v cc ng conic l s dngcc hm a thc hu t (rational)

Nh vo cc trng s, c th chnh dng ngcong theo mong mun

Khng hu t

Hu t

,

0

( ) ( )n

i n i

i

P t B t V =

= ,0

( ) ( )n

i k i

i

P t N t V =

=

,

0

,

0

( )

( )

( )

n

i n i i

i

n

i n i

i

B t wV

P t

B t w

=

=

=

,

0

,

0

( )

( )

( )

n

i k i i

i

n

i k i

i

N t wV

P t

N t w

=

=

=

Trong biu thc hu t ni trn, nu cc trngs u bng mt th ng cong tr thnhkhng hu t.

,

0

,

0

( )( )

( )( )

( )

n

i n i iw

i

n

i n i

i

B t wVP t

P tw t

B t w

=

=

= =

Cc trng s cung cp thmmt bc t do cho vic thitk ng cong (Khi trng sln th ng cong b kov im )

ng cong Bspline hu t khng u(NURBS Non uniform Rational Bspline)

NURBS l ng cong c s dng ph binv n bao gm c ng cong Bezier v ngcong Bspline

NURBS biu din nhiu dng ng cong khcnhau trong c c cc ng conic

,

0

,

0

( )

( )

( )

n

i k i i

i

n

i k i

i

N t wV

P t

N t w

=

=

=

u im ca ng cong NURBS

iu chnh hnh dng ca ng cong,ngoi vic iu chnh ta cc im iukhin, c th th thay i trng s wi

Cc ng conic c th c biu din chnhxc bng phng trnh ng cong NURBS

cc ng cong conic, Bezier v Bspline uc th chuyn v ng cong NURBS tngng.

V d v ng trn bng cch sdng ng cong NURBS

Cp ng cong: k=3 S im iu khin: 9 (tc n =8) Cc im iu khin tng ng (v d) l: V0(1,0),

V1(1,1), V2(0,1), nh hnh v Cc trng s tng ng vi cc im iu khin: w

={1,2/2,1, 2/2,1, 2/2,1} Cc vct nt: m= n+k = 8+3 =11

t = [0 0 0 1 1 2 2 3 3 4 4 4]


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Phn cp ng cong trong phn mmMaxsurf Ty chn ng cong trong phn mmMaxsurf

Ni suy Lagrange

Cho mt dy cc im trn mt phng (x0,y0),(x1,y1), (x2,y2), (xn,yn), ng cong ni suybc n1 i qua n im nh sau:

Trong

,

0

n

n i i n

i

f y L=

=

0 1 1 1,

0 1 1 1

( )( )...( )( )...( )( )

( )( )...( )( )...( )

i i ni n

i i i i i i i n

x x x x x x x x x xL x

x x x x x x x x x x

+

+

=

Bi tp nhm Chia lp thnh 5 nhm:1. Nhm 1 xy dng v v ng cong tham s bc 3 i qua 2 im c

2 rng buc tip tuyn hai u (s dng excel hoc matlab). Sliu c th t cho.

2. Nhm 2 xy dng ng cong Spline t nhin i qua 4 im (sdng excel hoc matlab). S liu c th t cho.

3. Nhm 3 xy dng v v ng cong Bezier bc 3 theo 4 imcontrol (s dng excel hoc matlab). S liu c th t cho. iuchnh v tr ca 1 trong 2 im gia, tnh ton li ng cong v sosnh 2 ng cong trn cng mt th

4. Nhm 4 xy dng ng cong BSpline bc 3 theo 4 im control(s dng excel hoc matlab). S liu c th t cho.

5. Nhm 5 xy dng v v ng ni suy Lagrange i qua 5 im tcho (s dng excel hoc matlab).

6. Nhm 6:V th ni suy spline bc 3 ca ng cong y=sin(x) iqua 5 im x=0, x=/2, x=, x= 3/2 v x=2 x=, sau so snhvi kt qu ni suy ca excel trn cng mt th. Lp bng tnh sais gia ni suy v kt qu chnh xc ca hm ti 50 im chia utrong khong [0,2]

Cong nghe CAD-CAM (merged file).pdf

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