Mathematical Description of Geometrical Transform Line g:y=s·xy with s yoyo P2vP R(xR,yR O P P S·x P O(o, yo Intersection with curve: 0 (s·x-y10)2=x3+ax+b-1 Coordinates of point R: -2 R(p,-yR Mp=S -Xp-xX R yR=-(s·xR+y0) 2 2323 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 4 R' (xR , -yR ) R(xR , yR P(x ) P , yP ) Q (xQ , yQ) g Intersection with curve: (s x−y0 ) 2 = x 3 +ax+b Line g: y = s x−y0 with s y y x x Q P Q P = − − y y s x 0 = P − P  x s x x y s x y R P Q R R = − − = −  + 2 0 ( ) Coordinates of point R: Mathematical Description of Geometrical Transform