A representation of digital hyperbolas y = 1/x alpha + beta

Abstract It is proved that digital hyperbola segments and their least squares hyperbola fits are in one-to-one correspondence. This enables a constant space representation of a digital hyperbola segment inscribed into the integer grid. Such a representation is ( x 1 , n , a , b ), where x 1 , is the x -coordinate of the left endpoint of the digital hyperbola segment, n is the number of its integer points,, while a and b are the coefficients of the least squares hyperbola fit Y = 1 x a + b of the given digital hyperbola segment. An O( n max { loh n , log x 1 }) algorithm for obtaining a digital hyperbola segment from its least squares hyperbola fit is described.