Second order norm Each interior edge P,P,in the control mesh can be associated with a mixed second difference (MSD): P,+P-P.-Pm The second order norm M of the control mesh of Loop patch s is defined as the maximum norm of n+9 MSDs: M max{P1 P2-Pn+1-Pall,{P1+P:-Pi-1-Pi+1l 3sis n}, IP1+Pn+1-Pn-P2ll,P2+Pn+1-P1-Pn+2ll, IP2+Pn+2-Pn+1-Pn+3ll,IP2+Pn+3-Pn+2-Pn+4ll, P2+Pn+4-Pn+3-P3,P2+P3-Pn+4-P1ll, IPn+1+Pn -P1 -Pn+6ll,IPn+1+Pn+6-Pn -Pn+5ll, IPn+1+Pn+5-Pn+6-Pn+2ll,Pn+1+Pn+2-Pn+5-P2ll} =max{a:i=1,,n+9}.Second order norm Each interior edge in the control mesh can be associated with a mixed second difference (MSD): The second order norm of the control mesh of Loop patch is defined as the maximum norm of n+9 MSDs: M PPP P i jkm + −− S P Pi j