| OCR Text |
Show 31 the When and have we is Hessian the zero inflection an radius point. of is infinite the simpler curvature In actuality Fu Fv Fuv H is function H Fu2 = Fvv 2 - Fv2 + n For the if used be can only parameter space by the will intersect inflection points. Fu=Fv=O Hn lie If immediate their level any This zero. point order of curve F stationary points at that means To curve. what of happens expand the derivatives Taylor series and get: of Fu(uo,vo) + du Fuu(uo,vo) + dv Fuv(uo,vo) Fv(u,v} Fv(uo,vo) + du Fuv(uo,vo) + dv Fvv(uo,vo) is Hn = first stationary point Fu(uO,vO)=Fv(uO,vO)=O c this Fu du Fuu + dv Fuv Fv du Fuv + dv Fvv into Hn (FuuFvv-Fuv2) term of this we (du2 F, points stationary see its at Fu(u,v) uO,vO in formed we neighborhood first own Substituting The is inflection the on their in and curve a 0 (F) addition, In is equation n curve required. there F(u,v) H This of sign function given a the Fuu in F and get Fuu expression + 2 is du dv Fuv + independant dv2 Fvv) of (du,dv). |
