I have a rounded-triangle in $z$-plane that conformally mapped into unit disk in $\zeta$-plane using the Schwarz-Cristoffell method.
By definition, the conformal mapping will preserve the local angle (intersection between two lines) in the $z$-plane. In other words, the two plots should have a similar local angle between the lines.
If I have all the points to generate the two plots, how to prove that the local angle between the plots are the same?
Can someone help me on this?