1、28 6 S/ (1 S)Vol. 28 No. 62010 M11Jo ur nal of Fo shan University ( Natural Science Edition) No v. 2010cI|: 1008-0171( 2010) 06-0058-06bW iZ_ Z王兴波(佛山科学技术学院机电工程系, 广东佛山 528000)K1: n5w bW i Z,N$ bW iZ_ Z# 9 E,B|Tw bW iZ_ a Zy i MTbT Vay# j Ey 9 mM1 5b1oM: iZ_; ; Z;9 mms |: O182DS : A3v 3FS= qT H o pi b
2、W iZ_ p5,52) Ynull; 3)“N M( x0, y0, z 0)b 3MFT =1 0 0 00cosnullsinnull00 - sinnullcosnull00 0 0 1co snull0 sinnull00 1 0 0sinnull0 cosnull00 0 0 11 0 0 00 1 0 00 0 1 0x 0 y0 z 0 1=cosnull0 - sinnull0sinnullsinnullco snullsinnullcosnull0cosnullsinnull- sinnullco snullcosnull0x0 y0 z 0 1, ( 4)yN,C Z/
3、T %( x( t)y( t)z ( t)1) = ( rcostrsint01)cosnull0 - sinnull0sinnullsinnullcosnullsinnullcosnull0cosnullsinnull- sinnullcosnullcosnull0x0 y0 z 0 1, ( 5)x( t) = x0 + rcostcosnull+ rsintsinnullsinnull,y( t) = y0 + rsintco snull,z( t) = z 0 + rsintsinnullcosnull- rcostsinnull,0t2nullb( 6)1. 4 i Z# 9 m D
4、 1 , i null Lr( t) = x ( t) , y ( t) , z ( t) , LZ_ O N= nx , ny , nz ,5B Zx( t, s) = x( t) + nxs,y( t, s) = y( t) + nys,z( t, s) = z( t) + nxs,0t2null, 0sh,( 7)T( 7), tas , h b null CL , LZ_ O nullE O N= ( cosnull, co snull, cosnull) ,yN| T( 6) T( 7) , Zx ( s, t) = x0 + rcostco snull+ rsintsinnulls
5、innull+ scosnull,y( s, t) = y0 + rsintcosnull+ sco snull,z ( s, t) = z 0 + rsintsinnullco snull- rcostsinnull+ scosnull,0t2null, 0shb( 8) 9 m H,1v T( 1)a( 2)a( 3)# f 1“9 nullanullanull?a?,vT( 8)9 x( s, t)ay( s, t)az ( s, t) Vb E /bM atlab/ ScilabI E:E : iZ_ 60 佛山科学技术学院学报(自然科学版) 第28卷 :( x0, y0, z 0)a
6、ra Z_( nx , ny , nz )#h9 V:Step 1v T( 1)a( 2)a( 3)#Z_( nx , ny, nz)9 sinnullacosnullasinnullacosnull;Step 2v T( 4)9 T;Step 3v T( 5)9 x ( t)ay( t)az ( t) ;Step 4v T( 7)9 X = x ( t, s) , Y = y( t, s) , Z= z( t, s) ;Step 5 T: V # bTM atlabScilab m, V s 2 q 9 m ?, LC y9bm4 Scilab 5. 2IZ_ (2,3)b2 iZ_ V -
7、 wvV A,5 VwLd (LL ) , -4Hq XL# XOY Zb - wvZE, 4/Tb( 1) ( cosnull, cosnull, co snull) nullE O Z_?, * CLah( )Zx( s, t) = x0 + 1 - sh ( costco snull+ sintsinnullsinnull) + scosnull,y( s, t) = y0 + 1 - sh sintcosnull+ scosnull,z( s, t) = z 0 + 1 - sh ( sintsinnullcosnull- co stsinnull) + scosnull,0t2nul
8、l, 0shb( 9)m5 Scilab 5. 2IZ_ (1. 5,3)bm4ScilabIZ_ m5ScilabIZ_ +Y, ( x1, y1, z 1) l BBe H,Zx( t, s) = ( 1 - s) x1 + s( x0 + rcostcosnull+ rsintsinnullsinnull) ,y( t, s) = ( 1 - s) y1 + s( y0 + rsintco snull) ,z ( t, s) = ( 1 - s) z 1 + s( z 0 + rsintsinnullcosnull- rcostsinnull) ,0t2null, 0sh,( 10) h
9、= ( x1- x0) 2+ ( y1- y0) 2+ ( z 1- z 0) 2bm6 Scilab Z_ b( 2) !( x 0, y0, z 0) null aa bE,5ELah Z61第6期 王兴波:空间任意方向圆柱面的参数方程x( s, t) = x0 + aco stcosnull+ bsintsinnullsinnull+ scosnull,y( s, t) = y0 + bsintcosnull+ scosnull,z( s, t) = z 0 + bsintsinnullcosnull- aco stsinnull+ scosnull,0t2null, 0shb( 11)
10、m7 Scilab Z_ bm6ScilabIZ_ m7ScilabIZ_ 3 -X #, iZ_ V U 5,/% + b( 1) dF_ V UbFB d, B ( )+ V8bF w H, L1 S$FV F)E O ,yN,| “ w V M7Tb9 BFV E1 n5y iZ_ (8)Z, LC A U( V j) ,m8 UbSCAD/ CA M q ! ?, t 5,SY q E %,1/ I 7?,91M1Tbm8 dF ( 2) 3 E V Ub ,+ , Y% b Ey H, T1 E bW 3 ,1y iZ_ 9 b4 V %B5bB,B P Z_F, m9 Ub 1 ,
11、LS q,9 CM1 Z UbyN, Ey 5,v bWbm9 m10Scilab y 62 佛山科学技术学院学报(自然科学版) 第28卷( 3) 5b y :pOb TB4,?C “Z_ qbya !9,“ fb 9 yA 1M1 ii iZ_ V Ub ID: 1 g .+ M . 3.:, 1998: 12. 2 m 3.+ M . 2.:v, 2008. 3 , . wL bWM L ZE J .m, 2007( 2) : 124-138. 4 , . ZE bW Z J .| =S S , 2007( 3) : 67-70. 5 Z?/. h Z5 EB/ OL . 2008-09-
12、24 . http: / / w ww . kaoy ansky . com/ thread-503621-1-1. ht ml. 6D AR RIN V . Cylinder o f A rbitr ar y A x is EB/ O L . 1996-09-02 . ht tp: / / mathfor um. o rg / libr ary / drm ath/ v iew /51734. html.3 I :I Parametric equation of cylinderin arbitrary directionWANG Xing-bo( Depa rtment o f M ech
13、atr onics Eng ineer ing, Fo shan U niv ersity, Fo shan 528000, China)Abstract: Based o n the deductio n and pr oof of the parametric equation of a circle on arbitrary plane,the parametric equation of cy linders in arbitrary dir ectio n as w ell as the algor ithm for cylinder draw ingare presented. E
14、x tensiv ely , the param etric equatio ns for the cone and the ellipse-base cylinder are alsostudied. The r esult of such studies in this paper can be applied in the fields that are related w ithco mputer drawings such as mechanical eng ineer ing , architectur al eng ineer ing , virtual plants ofagricultural engineering and so on.Key words: ar bitrary direction; cylinder; parametric equation; computer draw ing s63第6期 王兴波:空间任意方向圆柱面的参数方程
