Regular patches:distance bound (cont.) Boundb,,b.with the second order norm M,it follows'that 小su,W-Fu,s1-w+1-M Distance bound function of s(4,v)with respect to F(u,v) 9 B(4,W=2u1-0+W1-v.(,)e2 ■Diagonal D(t)=B(t,t)=t(l-t),0≤t≤1 By symmetry, max B(u,v)=max D(t)= (u,v)EQ 0≤1≤1 4 Regular patches: distance bound (cont.)  Bound with the second order norm , it follows that  Distance bound function of with respect to is ◼ Diagonal  By symmetry, , , i j b b i j − M 1 ( , ) ( , ) ( (1 ) (1 )) 2 S F u v u v u u v v M −  − + − S( , ) u v F( , ) u v 1 B( , ) ( (1 ) (1 )), ( , ) 2 u v u u v v u v = − + −  ( , ) 0 1 1 max B( , ) max D( ) u v t 4 u v t    = = D( ) B( , ) (1 ),0 1 t t t t t t = = −  