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’N_PTS’ #consecutive# points. The condition is not met when ’NUMPOINTS’ < 3 .
( 3 <= N_PTS <= NUMPOINTS ) , (0 <= DIST )
(8) There exists at least one set of two data points separated by exactly ’K_PTS’ #consecutive#
intervening points that are a distance greater than the length, ’LENGTH1’, apart. The condition is
not met when ’NUMPOINTS’ < 3 .
1 <= K_PTS <= {NUMPOINTS - 2}
(9) There exists at least one set of three data points separated by exactly ’A_PTS’ and ’B_PTS’
#consecutive# intervening points, respectively, that cannot be contained within or on a circle of
#radius# ’RADIUS1’. The condition is not met when ’NUMPOINTS’ < 5 .
1 <= A_PTS , 1 <= B_PTS
A_PTS + B_PTS <= NUMPOINTS - 3
(10) There exists at least one set of three data points separated by exactly ’C_PTS’ and ’D_PTS’
#consecutive# intervening points, respectively, that form an #angle# such that:
angle < (’PI’ - ’EPSILON’)
or
angle > (’PI’ + ’EPSILON’)
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The second point of the set of three points is always the #vertex# of the #angle#. If either the first
point or the last point (or both) coincide with the #vertex#, the #angle# is undefined and the LIC is
not satisfied by those three points. When ’NUMPOINTS’ < 5 , the condition is not met.
1 <= C_PTS , 1 <= D_PTS
C_PTS + D_PTS <= NUMPOINTS - 3
(11) There exists at least one set of three data points separated by exactly ’E_PTS’ and ’F_PTS’
#consecutive# intervening points, respectively, that are the vertices of a triangle with area greater
than ’AREA1’. The condition is not met when ’NUMPOINTS’ < 5.
1 <= E_PTS , 1 <= F_PTS
E_PTS + F_PTS <= NUMPOINTS - 3
12) There exists at least one set of two data points, (X[i],Y[i]) and (X[j],Y[j]), separated by exactly
’G_PTS’ #consecutive# intervening points, such that X[j] - X[i] < 0. (where i < j ) The condition is
not met when ’NUMPOINTS’ < 3 .
1 <= G_PTS <= {NUMPOINTS - 2}
13) There exists at least one set of two data points, separated by exactly ’K_PTS’ #consecutive#
intervening points, which are a distance greater than the length, ’LENGTH1’, apart. In addition,
there exists at least one set of two data points (which can be the same or different from the two data
points just mentioned), separated by exactly ’K_PTS’ #consecutive# intervening points, that are a
distance less than the length, ’LENGTH2’, apart. Both parts must be true for the LIC to be true. The
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condition is not met when ’NUMPOINTS’ < 3 .
( 0 <= LENGTH2 )
14) There exists at least one set of three data points, separated by exactly ’A_PTS’ and ’B_PTS’
#consecutive# intervening points, respectively, that cannot be contained within or on a circle of
#radius# ’RADIUS1’. In addition, there exists at least one set of three data points (which can be the
same or different from the three data points just mentioned) separated by exactly ’A_PTS’ and
’B_PTS’ #consecutive# intervening points, respectively, that can be contained in or on a circle of
#radius# ’RADIUS2’. Both parts must be true for the LIC to be true. The condition is not met when
’NUMPOINTS’ < 5 .
( 0 <= RADIUS2 )
15) There exists at least one set of three data points, separated by exactly ’E_PTS’ and ’F_PTS’
#consecutive# intervening points, respectively, that are the vertices of a triangle with area greater
than ’AREA1’. In addition, there exist three data points (which can be the same or different from the
three data points just mentioned) separated by exactly ’E_PTS’ and ’F_PTS’ #consecutive#
intervening points, respectively, that are the vertices of a triangle with area less than ’AREA2’. Both
parts must be true for the LIC to be true. The condition is not met when ’NUMPOINTS’ < 5 .
( 0 <= AREA2 )
The #Conditions Met Vector# (CMV) can now be used in conjunction with the #Logical Connector
Matrix# (LCM) to form the #off-diagonal elements# of the #Preliminary Unlocking Matrix# (PUM). The
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entries in the LCM represent the logical connectors to be used between pairs of LICs to determine the
corresponding entry in the PUM, i.e. LCM[i,j] represents the boolean operator to be applied to CMV[i] and
CMV[j]. PUM[i,j] is set according to the result of this operation. If LCM[i,j] is NOTUSED, then PUM[i,j]
　
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