▁tang ents ▁for ▁intervals ▁sharing ▁end points ▁are ▁equal . ▁The ▁interpol ated ▁curve ▁then ▁consists ▁of ▁piece wise ▁cub ic ▁Herm ite ▁spl ines , ▁and ▁is ▁glob ally ▁continu ously ▁differenti able ▁in ▁. ▁ ▁The ▁choice ▁of ▁tang ents ▁is ▁non - unique , ▁and ▁there ▁are ▁several ▁options ▁available . ▁ ▁Fin ite ▁difference ▁ ▁The ▁simplest ▁choice ▁is ▁the ▁three - point ▁difference , ▁not ▁requiring ▁constant ▁interval ▁lengths , ▁ ▁for ▁internal ▁points ▁, ▁and ▁one - s ided ▁difference ▁at ▁the ▁end points ▁of ▁the ▁data ▁set . ▁ ▁Card inal ▁spl ine ▁▁▁ ▁A ▁cardinal ▁spl ine , ▁sometimes ▁called ▁a ▁canonical ▁spl ine , ▁is ▁obtained ▁if ▁ ▁is ▁used ▁to ▁calculate ▁the ▁tang ents . ▁The ▁parameter ▁ ▁is ▁a ▁t ension ▁parameter ▁that ▁must ▁be ▁in ▁the ▁interval ▁. ▁In ▁some ▁sense , ▁this ▁can ▁be ▁interpreted ▁as ▁the ▁" length " ▁of ▁the ▁tang ent . ▁Cho osing ▁ ▁yields ▁all ▁zero ▁tang ents , ▁and ▁choosing ▁ ▁yields ▁a ▁Cat m ull – R om ▁spl ine . ▁ ▁Cat m ull – R om ▁spl ine ▁▁▁ ▁For ▁tang ents ▁chosen ▁to ▁be ▁ ▁a ▁Cat m ull – R om ▁spl ine ▁is ▁obtained , ▁being ▁a ▁special ▁case ▁of ▁a ▁cardinal ▁spl ine . ▁This ▁assumes ▁uniform ▁parameter ▁spacing . ▁ ▁The ▁curve ▁is ▁named ▁after ▁Ed win ▁Cat m ull ▁and ▁Rap ha el ▁Rom . ▁ ▁The ▁principal ▁advantage ▁of ▁this ▁technique ▁is ▁that ▁the