148
4 Geometry standards
isSimple
The operation "isSimple" shall return TRUE if this GM_Objeet has no interior
point of self-interseetion or self-tangeney.
false
Fig. 4.26. Operation isSimple
isCycle
The operation "isCycle" shall return TRUE if this GM _ Objeet has an empty
boundary after topologieal simplifieation. A closed eurve or a sphere have empty
boundaries. This eondition is alternatively referred to as being "closed" as in a
"closed eurve". This ereates some eonfusion sinee there are two distinet and ineompatible definitions for the word "closed". The use of the word eycle is rarer but leads
to less eonfusion. Essentially, an objeet is a eycle if it is isomorphie to a geometrie
objeet that is the boundary of a region in some Euclidean spaee. Thus a eurve is a
eycle if it is isomorphie to a eircle (has the same start and end point). A surfaee is a
eycle if it is isomorphie to the surfaee of a sphere, or some torus.
true
false
u
Fig. 4.27. Operation isCycle
distance
The operation "distanee" shall return the distanee between this GM _ Objeet and
another GM_ Objeet. This distanee is defined to be the greatest lower bound of the
set of distanees between all pairs of points that include one eaeh from eaeh of the
two GM _ Objeets.
QJ C?D
d=O
d=O
Fig. 4.28. Operation distance
4 Geometry standards
isSimple
The operation "isSimple" shall return TRUE if this GM_Objeet has no interior
point of self-interseetion or self-tangeney.
false
Fig. 4.26. Operation isSimple
isCycle
The operation "isCycle" shall return TRUE if this GM _ Objeet has an empty
boundary after topologieal simplifieation. A closed eurve or a sphere have empty
boundaries. This eondition is alternatively referred to as being "closed" as in a
"closed eurve". This ereates some eonfusion sinee there are two distinet and ineompatible definitions for the word "closed". The use of the word eycle is rarer but leads
to less eonfusion. Essentially, an objeet is a eycle if it is isomorphie to a geometrie
objeet that is the boundary of a region in some Euclidean spaee. Thus a eurve is a
eycle if it is isomorphie to a eircle (has the same start and end point). A surfaee is a
eycle if it is isomorphie to the surfaee of a sphere, or some torus.
true
false
u
Fig. 4.27. Operation isCycle
distance
The operation "distanee" shall return the distanee between this GM _ Objeet and
another GM_ Objeet. This distanee is defined to be the greatest lower bound of the
set of distanees between all pairs of points that include one eaeh from eaeh of the
two GM _ Objeets.
QJ C?D
d=O
d=O
Fig. 4.28. Operation distance