Mathematical Description of Geometrical Transform Tangent g:y=S·x-yo dy 3xd+a dx 2yp P(xp, yp) R(R, yR P S·x P Intersection with curve 0 (s·x-y10)2=x3+ax+b-1 Coordinates of point R: -2 R'(xR,-VR) S·X+y 2 2424 Intersection with curve: (s x−y0 ) 2 = x 3 +ax+b x s x y s x y R P R R = − = −  + 2 0 2 ( ) Coordinates of point R: -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 4 R' (xR , -yR ) R (xR , yR ) P(xP , yP ) g Tangent g: y = s x−y0 s dy dx x a y P P = = 3 + 2 2 y y s x 0 = P − P  Mathematical Description of Geometrical Transform