Method for generating quadratic curve signal

Claim 3

A method for generating quadratic curve signals as claimed in claim 1, wherein said octant selecting step selects an octant having α and β values with different signs, when assuming that α and β are: in the first octant, α=F(x+1, y+1)-F(x, y) β=F(x+1, y)-F(x, y) in the second octant, α=F(x+1, y-1)-F(x, y) β=F(x+1, y)-F(x, y) in the third octant, α=F(x+1, y-1)-F(x, y) β=F(x, y-1)-F(x, y) in the fourth octant, α=F(x-1, y-1)-F(x, y) β=F(x, y-1)-F(x, y) in the fifth octant, α=F(x-1, y-1)-F(x, y) β=F(x-1, y)-F(x, y) in the sixth octant, α=F(x-1, y+1)-F(x, y) β=F(x-1, y)-F(x, y) in the seventh octant, α=F(x-1, y+1)-F(x, y) β=F(x, y+1)-F(x, y), and in the eighth octant, α=F(x+1, y+1)-F(x, y) β=F(x, y+1)-F(x, y).

Claim 4

A method for generating quadratic curve signals as claim in claim 2, wherein said point selecting step includes the steps of: (a) comparing the sign of F (x, y) with that of α at the point (x, y), (b) comparing the sign of F (x, y) with that of F (x, y)+β when the signs of F (x, y) and α are the same in the comparison of step (a), (c) comparing the sign of F (x, y) with that of F (x, y)+α when the signs of F (x, y) and α are different in the comparison of step (a), (d) selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y) when the signs are judged to be the same in the step (b), or when the signs are judged to be different in the step (c), and (e) selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y) when the signs are judged to be different in the step (b), or when the signs are judged to be the same in the step (c).

Claim 5

A method for generating quadratic curve signals as claimed in claim 2, wherein, when F (x, y)≧0, said point selecting step includes the steps of: (f) checking the sign of α or β, (G) checking the sign of F (x, y)+β when it is judged that the sign of α is positive, or that the sign of β is negative in the step (f), (h) checking the sign of F (x, y)+α when the sign of α is judged to be negative, or the sign of β is judged to be positive in the step (f), (i) selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y), when the sign of F (x, y)+β is judged to be positive in the step (g), or when the sign of F (x, y)+α is judged to be negative in the step (h), and (j) selecting a point that displaces by (+1) or (-1) in X direction and by (+1) or (-1) in Y direction from the point (x, y), when the sign of F (x, y)+β is judged to be negative in the step (h).

Claim 6

A method for generating quadratic curve signals as claimed in claim 2, wherein, when F (x, y)<0, said point selecting step includes the steps of: (k) checking the sign of α or β, (l) checking the sign of F (x, y)+α when it is judged that the sign of α is positive, or that the sign of β is negative in the step (k), (m) checking the sign of F (x, y)+β when the sign of α is judged to be negative, or the sign of β is judged to be positive in the step (k), (n) selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y), when the sign of F (x, y)+α is judged to be positive in the step (l), or when the sign of F (x, y)+β is judged to be negative in the step (m), and (o) selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y), when the sign of F (x, y)+α is judged to be negative in the step (l), or when the sign of F (x, y)+β is judged to be positive in the step (m).

Claim 7

A method for generating quadratic curve signals as claimed in claim 3, 4 or 5, wherein said point selecting step further comprises the steps of: (p) updating the values of F (x, y), α and β after selecting a point which displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y), according to the following equations: F(x,y)=F(x, y)+β α=α+T2 β=β+T1 wherein, T1 is: in the first and second octant, 2a (=β(x+1, y)-β(x, y)), in the third and fourth octant, 2c(=β(x, y-1)-β(x, y)), in the fifth and sixth octant, 2a(=β(x-1, y)-β(x, y)), in the seventh and eighth octant, 2c(=β(x, y+1)-β(x, y)), and T2 is: in the first octant, 2a+b(=α(x+1, y)-α(x, y)) in the second octant, 2a-b(=α(x'1, y)-α(x, y)) in the third octant, 2c-b(=α(x, y-1)-α(x, y)) in the fourth octant, 2c+b(=α(x, y-1)-α(x, y)) in the fifth octant, 2a+b(=α(x-1, y)-α(x, y)), in the sixth octant, 2a-b(=α(x-1, y)-α(x, y)), in the seventh octant, 2c-b(=α(x, y+1)-α(x, y)), and in the eighth octant, 2c+b(=α(x, y+1)-α(x, y)), and (q) updating the values of F (x, y), α and β after selecting a point that displaces by (+1) or (-1) in the X direction and by (+1) or (-1) in the Y direction from the point (x, y), according to the following equations: F(x,y)=F(x, y)+α α=α+T3 β=β+T2 wherein, T2 is: in the first octant, 2a+b(=β(x+1, y+1)-β(x, y)), in the second octant, 2a-b(=β(x+1, y-1)-β(x, y)), in the third octant, 2c+b(=β(x+1, y-1)-β(x, y)), in the fourth octant, 2c+b(=β(x-1, y-1)-β(x, y)), in the fifth octant, 2a+b(=β(x-1, y+1)-β(x, y)), in the sixth octant, 2a-b(=β(x-1, y+1)-β(x, y)), in the seventh octant, 2c-b(=β(x-1, y+1)-β(x, y)), and in the eighth octant, 2c+b(=β(x+1, y+1)-β(x, y)); and T3 is: in the first octant, 2a+2c+2b(=α(x+1, y+1)-α(x, y)) in the second octant and third octant, 2a+2c-2b(=α(x+1, y-1)-α(x, y)), in the fourth and fifth octant, 2a+2c+2b(=α(x-1, y-1)-α(x, y)) in the sixth and seventh octant, 2a+2c-2b(=α(x-1, y+1)-α(x, y)), and in the eighth octant, 2a+2c+2b(=α(x+1, y+1)-α(x, y)).

Claim 8

A method for generating quadratic curve signals as claimed in claim 6, wherein said method further comprises the steps of: (r) checking the signs of α and β updated in said step (p) or (q), (s) changing the octant to an octant in which the signs of α and β are different when the signs of α and β are judged to be the same in said step (r).