空间任意方向圆柱面的参数方程_王兴波

286()Vol.28No.6201011JournalofFoshanUniversity(NaturalScienceEdition)Nov.2010:1008-0171(2010)06-0058-06王兴波(佛山科学技术学院机电工程系,广东佛山528000):,,:;;;:O182:A,,,,([1-2]),CNKI[3-4]Google,[5-6],,[1-2],[3],[4],,()(),[1-4],,,,,,,1,()()(),:1.1{O,X,Y,Z},V=(Vx,Vy,Vz),V3:2010-09-01:(1963-),,,,,cos=VxV=VxV2x+V2y+V2z,cos=VyV=VyV2x+V2y+V2z,cos=VzV=VzV2x+V2y+V2zV3V,[0,),V33,V3,OA,1,OA3OA3AxAyAz,cos=Ax,cos=Ay,cos=Az2,,OC1OC1OC23,OC1XOZ,OC2Z,OCZXOZOC1,YOC2,2XYZ,,21.2,,,,,?,3,OC,XYZ,sin=coscos2+cos2=CzC2y+C2z,(1)3sin=coscos2+cos2=CxC2x+C2z,(2)59第6期　　　　　　　　　　王兴波:空间任意方向圆柱面的参数方程sin=coscos2+cos2=CyC2x+C2y(3)1.3,C(x0,y0,z0),r,N=(cos,cos,cos),N,(1)(2)(3),XOY:1)X;2)Y;3)N(x0,y0,z0)3T=10000cossin00-sincos00001cos0sin00100sin0cos00001100001000010x0y0z01=cos0-sin0sinsincossincos0cossin-sincoscos0x0y0z01,(4),C(x(t)y(t)z(t)1)=(rcostrsint01)cos0-sin0sinsincossincos0cossin-sincoscos0x0y0z01,(5)x(t)=x0+rcostcos+rsintsinsin,y(t)=y0+rsintcos,z(t)=z0+rsintsincos-rcostsin,0t2(6)1.4[1],r(t)={x(t),y(t),z(t)},N={nx,ny,nz},x(t,s)=x(t)+nxs,y(t,s)=y(t)+nys,z(t,s)=z(t)+nxs,0t2,0sh,(7)(7),ts,hC,N=(cos,cos,cos),(6)(7),x(s,t)=x0+rcostcos+rsintsinsin+scos,y(s,t)=y0+rsintcos+scos,z(s,t)=z0+rsintsincos-rcostsin+scos,0t2,0sh(8),(1)(2)(3),(8)x(s,t)y(s,t)z(s,t)Matlab/Scilab::60佛山科学技术学院学报(自然科学版)　　　　　　　　　　　第28卷:(x0,y0,z0)r(nx,ny,nz)h:Step1(1)(2)(3)(nx,ny,nz)sincossincos;Step2(4)T;Step3(5)x(t)y(t)z(t);Step4(7)X=x(t,s),Y=y(t,s),Z=z(t,s);Step5:MatlabScilab,2,4Scilab5.2(2,3)2,(),XOY,(1)(cos,cos,cos),Ch()x(s,t)=x0+1-sh(costcos+sintsinsin)+scos,y(s,t)=y0+1-shsintcos+scos,z(s,t)=z0+1-sh(sintsincos-costsin)+scos,0t2,0sh(9)5Scilab5.2(1.5,3)4Scilab5Scilab,(x1,y1,z1),x(t,s)=(1-s)x1+s(x0+rcostcos+rsintsinsin),y(t,s)=(1-s)y1+s(y0+rsintcos),z(t,s)=(1-s)z1+s(z0+rsintsincos-rcostsin),0t2,0sh,(10)h=(x1-x0)2+(y1-y0)2+(z1-z0)26Scilab(2)(x0,y0,z0)abE,Eh61第6期　　　　　　　　　　王兴波:空间任意方向圆柱面的参数方程x(s,t)=x0+acostcos+bsintsinsin+scos,y(s,t)=y0+bsintcos+scos,z(s,t)=z0+bsintsincos-acostsin+scos,0t2,0sh(11)7Scilab6Scilab7Scilab3,,(1),(),,,(),(),8CAD/CAM,,,,8(2),,,,,,9,,,,910Scilab62佛山科学技术学院学报(自然科学版)　　　　　　　　　　　第28卷(3),,:[1].[M].3.:,1998:12.[2].[M].2.:,2008.[3],.[J].,2007(2):124-138.[4],.[J].,2007(3):67-70.[5].[EB/OL].[2008-09-24].[6]DARRINV.CylinderofArbitraryAxis[EB/OL].[1996-09-02].:ParametricequationofcylinderinarbitrarydirectionWANGXing-bo(DepartmentofMechatronicsEngineering,FoshanUniversity,Foshan528000,China)Abstract:Basedonthedeductionandproofoftheparametricequationofacircleonarbitraryplane,theparametricequationofcylindersinarbitrarydirectionaswellasthealgorithmforcylinderdrawingarepresented.Extensively,theparametricequationsfortheconeandtheellipse-basecylinderarealsostudied.Theresultofsuchstudiesinthispapercanbeappliedinthefieldsthatarerelatedwithcomputerdrawingssuchasmechanicalengineering,architecturalengineering,virtualplantsofagriculturalengineeringandsoon.Keywords:arbitrarydirection;cylinder;parametricequation;computerdrawings63第6期　　　　　　　　　　王兴波:空间任意方向圆柱面的参数方程