Geometric transformations between general concurrent charts and tangential contact charts

Abstract

The general geometric transformations between the general concurrent charts of three variables and the general tangential contact charts of three variables are researched in this paper. General geometric transformations treated here are of the form: $u(x,y)\bar{x}+v(x,y)\bar{y}+w(x,y)=0$, by which the general concurrent charts in $(x,y)$-plane and the general tangential contact charts in $(\bar{x},\bar{y})$-plane are transformed to cach other, by the envelope method or the contact transformation method.