Let CβPn be a rational normal curve and let
βOβ:Pn+1β’Pn be any tangential
projection form a point OβTAβC where AβC. Hence X:=βOβ(C)βPn is a linearly normal cuspidal curve with degree n+1. For any P=βOβ(B), BβPn+1, the X-rank rXβ(P) of P is the
minimal cardinality of a set SβX whose linear span contains P. Here
we describe rXβ(P) in terms of the schemes computing the C-rank or the
border C-rank of B.Comment: 7 page