Line smoothing techniques

Details Line smoothing techniques Line smoothing techniques

G - Physics

06

F

G06F 3/033 (2006.01) G06T 11/20 (2006.01)

Patent

CA 2167237

Improved curve plotting techniques are disclosed for drawing a substantially smooth curve in real time, from a plurality of sampled points, as the points are sampled, on a point-by-point basis. The curve is substantially smooth in that it has a continuously changing slope of G1 continuity, as opposed to a slope which changes in a discontinuous or stepwise manner. The curve plotting is performed by representing the x coordinates of the curve using a parametric equation x = [ax * (t2)] + [bx * t] + [cx], and by representing the y coordinates of the curve using a second parametric equation y = [ay * (t2)] + [by * t] + [cy], wherein ax, ay, bx, by, cx, and cy comprise six unknown quantities, and t is a "dummy" valuable. The derivatives of the parametric equations are employed to calculate and to plot the smooth curve.

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