Fast, symmetric, integer bezier curve to polygon conversion

A printer comprising:

• a transceiver adapted for bidirectional communication with a communications channel;
• a memory;
• a print engine adapted for placing color dots on a printed page according to received image data and control signals;
• and
• a programmable data processor connected to said transceiver, said memory and said print engine, said programmable data processor programmed to
• receive print data corresponding to pages to be printed from the communications channel via said transceiver;
• convert said print data into image data and control signals for supply to said print engine for printing a corresponding page, said conversion including converting a curve expressed as a Bezier curve into a corresponding set of line segments by:
• expressing the Bezier curve in a pair of parametric equations in horizontal and vertical coordinates in a parametric variable,
• selecting a plurality of points at equally spaced intervals of said parametric variable having a number in proportion to an estimated length of the Bezier curve, the selected plurality being an integral power of 2, said selecting performed by
• dividing the estimated length of the Bezier curve expressed in terms of an adjacent pixel distance by a predetermined factor, and
• selecting the number of computed points as a next larger integral power of 2 than the estimated length of the Bezier curve,
• computing respective horizontal and vertical coordinates of said selected plurality of points,
• forming line segments between respective adjacent computed points;
• and
• controlling said print engine according to said image data and control signals to print a corresponding page.

The computer implemented method of converting a curve expressed as a Bezier curve into a corresponding set of line segments comprising the steps of:

• expressing the Bezier curve in a pair of parametric equations in horizontal and vertical coordinates in a parametric variable;
• computing respective horizontal and vertical coordinates of a plurality of points at intervals of the parametric variable selected to provide integral steps in the vertical coordinate, including for each computed horizontal and vertical coordinate
• adding a selected interval of the parametric variable to a prior value of the parametric variable to obtain a new value of the parametric variable,
• computing the vertical coordinate employing the new value of the parametric variable,
• comparing the change in the vertical coordinate from the prior value of the parametric variable to the new value of the parametric variable with a desired integral interval in vertical coordinates,
• adjusting the interval of the parametric variable dependent upon said comparison and repeating said steps of adding, computing and comparing until the computed vertical coordinate is within a predetermined range of the desired integral interval, and
• computing the horizontal coordinate employing the value of the parametric variable placing the computed vertical coordinate within the predetermined range of the desired integral interval;
• and
• forming line segments between respective adjacent computed points.

The computer implemented method of converting a curve expressed as a Bezier curve into a corresponding set of line segments comprising the steps of:

• expressing the Bezier curve in a pair of parametric equations in horizontal and vertical coordinates in a parametric variable;
• computing respective horizontal and vertical coordinates of a plurality of points at intervals of the parametric variable selected to provide integral steps in the vertical coordinate;
• testing adjacent computed vertical coordinates to detect an inflection point in the Bezier curve;
• said step of computing respective horizontal and vertical coordinates of the plurality of points initially advances said parametric variable from 0.0 toward 1.0 unless and until an inflection point is detected, and thereafter computing respective horizontal and vertical coordinates of the plurality of points advancing said parametric variable from 1.0 toward 0.0;
• and
• forming line segments between respective adjacent computed points.

A printer comprising:

• a transceiver adapted for bidirectional communication with a communications channel;
• a memory;
• a print engine adapted for placing color dots on a printed page according to received image data and control signals;
• and
• a programmable data processor connected to said transceiver, said memory and said print engine, said programmable data processor programmed to
• receive print data corresponding to pages to be printed from the communications channel via said transceiver;
• convert said print data into image data and control signals for supply to said print engine for printing a corresponding page, said conversion including converting a curve expressed as a Bezier curve into a corresponding set of line segments by:
• expressing the Bezier curve in a pair of parametric equations in horizontal and vertical coordinates in a parametric variable,
• computing respective horizontal and vertical coordinates of a plurality of points at intervals of the parametric variable selected to provide integral steps in the vertical coordinate including for each computed horizontal and vertical coordinate by
• adding a selected interval of the parametric variable to a prior value of the parametric variable to obtain a new value of the parametric variable,
• computing the vertical coordinate employing the new value of the parametric variable,
• comparing the change in the vertical coordinate from the prior value of the parametric variable to the new value of the parametric variable with a desired integral interval in vertical coordinates,
• adjusting the interval of the parametric variable dependent upon said comparison and repeating said steps of adding, computing and comparing until the computed vertical coordinate is within a predetermined range of the desired integral interval,
• computing the horizontal coordinate employing the value of the parametric variable placing the computed vertical coordinate within the predetermined range of the desired integral interval;
• forming line segments between respective adjacent computed points;
• and
• controlling said print engine according to said image data and control signals to print a corresponding page.

A printer comprising:

• a transceiver adapted for bidirectional communication with a communications channel;
• a memory;
• a print engine adapted for placing color dots on a printed page according to received image data and control signals;
• and
• a programmable data processor connected to said transceiver, said memory and said print engine, said programmable data processor programmed to
• receive print data corresponding to pages to be printed from the communications channel via said transceiver;
• convert said print data into image data and control signals for supply to said print engine for printing a corresponding page, said conversion including converting a curve expressed as a Bezier curve into a corresponding set of line segments by:
• expressing the Bezier curve in a pair of parametric equations in horizontal and vertical coordinates in a parametric variable,
• computing respective horizontal and vertical coordinates of a plurality of points at intervals of the parametric variable selected to provide integral steps in the vertical coordinate;
• forming line segments between respective adjacent computed points;
• test adjacent computed vertical coordinates to detect an inflection point in the Bezier curve;
• compute respective horizontal and vertical coordinates of the plurality of points initially advances said parametric variable from 0.0 toward 1.0 unless and until an inflection point is detected;
• thereafter compute respective horizontal and vertical coordinates of the plurality of points advancing said parametric variable from 1.0 toward 0.0;
• and
• controlling said print engine according to said image data and control signals to print a corresponding page.