Polynomial transformations

Bilinear transformation

x' = a_x x y + b_x x + c_x y + d_x
y' = a_y x y + b_y x + c_y y + d_y

Biquadratic transformation

x' = a_x x² y² + b_x x² y + c_x x² + d_x x y² + e_x y² + f_x x y + g_x x + h_x y + i_x
y' = a_y x² y² + b_y x² y + c_y x² + d_y x y² + e_y y² + f_y x y + g_y x + h_y y + i_y

Linear-cubic transformation

x' = a_x x³ y + b_x x² y + c_x x y + d_x x³ + e_x x² + f_x x + g_x y + h_x
y' = a_y x³ y + b_y x² y + c_y x y + d_y x³ + e_y x² + f_y x + g_y y + h_y