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US 4,789,954 AGranted
Method for generating quadratic curve signal
AssigneeInternational Business Machines Corporation
InventorsHideaki Iida, Johji Mamiya, Yutaka Morimoto
Life of this patent
Estimating the term…
Abstract
Assuming that a given equation representing a quadratic curve is: F(x, y)=ax.sup.2 +bxy+cy.sup.2 +dx+ey+f=0, the method for generating quadratic curve signals repeatedly selects a point close to F (x, y)=0 in only one of either the region of F (x,y).gtoreq.0 or the region of F (x,y)<0. This method allows to generate quadratic curve signals by using only a few parameters and without using complicated calculations. A hardware implementation is also disclosed.
Claims7
A method for generating signals representing a line approximate to a quadratic curve
- F(x, y)=ax.sup.2 +bxy+cy.sup.2 +dx+ey+f=0
- by repeating a step selecting a new point close to F(x, y)=0 from among eight points (x+1, y+1), (x+1, y), (x+1, y-1), (x, y-1), (x-1, y-1), (x-1, y), (x-1, y+1) and (x, y+1) adjacent to a current point (x, y) in a Cartesian coordinates system, characterized in that said step selecting one of said eight points consists of a step selecting a new point close to F (x, y)=0 in only one of either the region of F (x, y).gtoreq.0 or the region F (x, y)<0, said step selecting a new point close to F (x, y)=0 comprising:
- an octant selecting step selecting one octant from among the first octant in which point (x+1, y+1) or (x+1, y) can be selected, the second octant in which point (x+1, y) or (x+1, y-1) can be selected, the third octant in which point (x+1, y-1) or (x, y-1) can be selected, the fourth octant in which point (x, y-1) or (x-1, y-1) can be selected, the fifth octant in which point (x-1, y-1) or (x-1, y) can be selected, the sixth octant in which point (x-1, y) or (x-1, y+1) can be selected, the seventh octant in which point (x-1, y+1) or (x, y+1) can be selected, the eighth octant in which point (x, y+1) or (x+1, y+1) can be selected, and
- selecting a point close to F(x, y)=0 in either one region of F (x, y).gtoreq.0 or F (x, y)<0 from two selectable points in the octant selected by said octant selecting step.
1 more element
Dependencies are inferred from the claim text.