▁usually ▁only ▁used ▁for ▁convex ▁pol yg ons . ▁ ▁Properties ▁ ▁As ide ▁from ▁the ▁properties ▁of ▁all ▁tri ang ulations , ▁fan ▁tri ang ulations ▁have ▁the ▁following ▁properties : ▁ ▁All ▁convex ▁pol yg ons , ▁but ▁not ▁all ▁pol yg ons , ▁can ▁be ▁fan ▁tri ang ulated . ▁ ▁Pol yg ons ▁with ▁only ▁one ▁con ca ve ▁vertex ▁can ▁always ▁be ▁fan ▁tri ang ulated , ▁as ▁long ▁as ▁the ▁diag on als ▁are ▁drawn ▁from ▁the ▁con ca ve ▁vertex . ▁ ▁It ▁can ▁be ▁known ▁if ▁a ▁polygon ▁can ▁be ▁fan ▁tri ang ulated ▁by ▁solving ▁the ▁Art ▁gallery ▁problem , ▁in ▁order ▁to ▁determine ▁whether ▁there ▁is ▁at ▁least ▁one ▁vertex ▁that ▁is ▁visible ▁from ▁every ▁point ▁in ▁the ▁polygon . ▁ ▁The ▁tri ang ulation ▁of ▁a ▁polygon ▁with ▁ ▁vertices ▁uses ▁ ▁diag on als , ▁and ▁generates ▁ ▁tri angles . ▁ ▁Gener ating ▁the ▁list ▁of ▁tri angles ▁is ▁trivial ▁if ▁an ▁ordered ▁list ▁of ▁vertices ▁is ▁available , ▁and ▁can ▁be ▁computed ▁in ▁linear ▁time . ▁As ▁such , ▁it ▁is ▁unnecessary ▁to ▁explicitly ▁store ▁the ▁list ▁of ▁tri angles , ▁and ▁therefore , ▁many ▁graph ical ▁libraries ▁implement ▁primit ives ▁to ▁represent ▁pol yg ons ▁based ▁on ▁this ▁tri ang ulation . ▁ ▁Although ▁this ▁tri ang ulation ▁is ▁fit ▁for ▁solving ▁certain ▁problems , ▁such ▁as ▁R aster isation , ▁or ▁collision ▁detection , ▁it ▁may ▁be ▁un fit ▁for ▁other ▁tasks ▁because ▁the ▁origin ▁vertex ▁accum