空间曲线切向量和法向量向平面曲线的转移

:2001204216:100428626(2001)0220054202,(,102600):,:;;;;:O172.1:B,,,,,,,,,,,:,11.1L:x=U(t)y=W(t)t=t0tx=U(t)y=W(t)z=V(t)tT={U(t),W(t),V(t)},L:x=U(t)y=W(t)z=0,T={U(t),W(t),0}Lt={U(t),W(t)}1.2L:y=y(x)xty=y(x)z=z(x)xT={1,y(x),z(x)},L:y=y(x)z=0,T={1,y(x),0}Lt={1,y(x)}1.3L:F(x,y)=0xtF(x,y,z)=0G(x,y,z)=0xT={1,y(x),z(x)},L:F(x,y)=0Z=0,T={1,y(x),z(x)}={1,y(x),0};F(x,y)=0y(x)=-FxFy,92Vol19No12JournalofBeijingInstituteofGraphicCommunication20016Jun12001T=1,-FxFy,0T={Fy,-Fx,0}LT={1,y(x)}T={Fy,-Fx}22.1L:F(x,y)=0xnF(x,y,z)=0(x,y,z)N={Fx(x,y,z),Fy(x,y,z),Fz(x,y,z)}F(x,y)=0,z;(x,y,0)N={Fx(x,y),Fy(x,y),0}L(x,y)n,Ln={Fx(x,y),Fy(x,y)}2.2L:y=y(x)xny=y(x)F(x,y)=y(x)-y=0,1,Ln={y(x),-1}2.3L:x=U(t)y=W(t)tn:y(x)=W(t)U(t),2,Ln{y(x),-1}=W(t)U(t),-1{W(t),-U(t)}1F(x,y)=x3+y3-2xy=0,M0(1,1):Fx(1,1)=(3x2-2y)û(1,1)=1,Fy(1,1)=(3y2-2x)û(1,1)=1,t={Fy(1,1),-Fx(1,1)}={1,1};n={Fx(1,1),Fy(1,1)}={1,1}2x=a(t-sint)y=a(1-cost),t=P4:xP4=a(1-cost)ût=P4=a1-22,yP4=asintût=P4=22at=(1-22)a,22a;n=22a,22-1a:[1].[M].:,1996.[2].[M].:,1992.552,: