Variations in 2D and 3D Models by a New Family of Subdivision Schemes and Algorithms for its Analysis

Algorithm 1

Continuity of the schemes by Laurent polynomial.

(1)	input: The symbol of the proposed schemes, i.e. , , , (optional) (⊳) are the coefficients (depends on ) of respectively in
(2)	ifthen
(3)
(4)	for to do
(5)	calculate:
(6)	for to do
(7)	calculate: ,
(8)	end for
(9)	calculate: max
(10)	ifthen
(11)	return scheme corresponding to is -continuous for
(12)	else
(13)	go to 26
(14)	end if
(15)	end for
(16)	else
(17)	(⊳) are the coefficients (depends on ) of respectively in
(18)	for to do
(19)	calculate:
(20)	for to do
(21)	calculate: an interval, say , for by solving ,
(22)	end for
(23)	calculate: intersection, say , of the intervals
(24)	return scheme is -continuous for
(25)	end for
(26)	end if
(27)	output: Level of continuity of the proposed schemes for an interval of or for