Expression 6: "T" left parenthesis, "p" , "t" , right parenthesis equals left brace, 0 less than or equal to "t" less than or equal to 1 : left parenthesis, "p" . "x" plus "n" "t" , "p" . "y" , right parenthesis , 1 less than or equal to "t" less than or equal to 2 : "R" left parenthesis, left parenthesis, "p" . "x" plus "n" , "p" . "y" , right parenthesis , StartFraction, pi Over 2 , EndFraction left parenthesis, "t" minus 1 , right parenthesis , right parenthesis , "R" left parenthesis, left parenthesis, "p" . "x" plus "n" , "p" . "y" , right parenthesis , StartFraction, pi Over 2 , EndFraction , right parenthesis , right braceTp,t=0≤t≤1:p.x+nt,p.y,1≤t≤2:Rp.x+n,p.y,π2t−1,Rp.x+n,p.y,π2
6
Expression 7: "R" left parenthesis, "p" , theta , right parenthesis equals left parenthesis, left parenthesis, "p" . "x" minus "n" minus 1 , right parenthesis cos theta plus left parenthesis, "p" . "y" minus "n" , right parenthesis sin theta , negative left parenthesis, "p" . "x" minus "n" minus 1 , right parenthesis sin theta plus left parenthesis, "p" . "y" minus "n" , right parenthesis cos theta , right parenthesis plus left parenthesis, "n" plus 1 , "n" , right parenthesisRp,θ=p.x−n−1cosθ+p.y−nsinθ,−p.x−n−1sinθ+p.y−ncosθ+n+1,n