Method for displaying a computer generated graphic on a raster output scanner

Claim 1

A method for displaying a computer generated image described in page description language on a raster output scanner comprising the steps of: generating a trajectory from said page description language which trajectory is described in page description language approximating a part of said trajectory by an original parabola having control points A, B and C which original parabola approximates said part of said trajectory, to within a predetermined error limit, generating for said original parabola a set of approximating parabolas which approximating parabolas together constitute two curved lines that are parallel to, and a predetermined distance away from, said original parabola, said generating step comprising: a. determining a number of segments that the original parabola must be divided into in order that an approximating parabola can be generated for each segment, b. dividing said original parabola into said segments, and c. generating an approximating parabola for each of said segments, converting said set of approximating parabolas into a bit map, and sending said bit map to a raster output scanner, wherein said determining step comprises a. testing said original parabola having control points A, B, C by dividing distance AB by distance BC if distance AB is longer or distance BC by distance AB if distance BC is longer, to generate a result K and comparing the result K to a limit which is a function of included angle ABC, b. if the result is less than the limit, the parabola does not need to be subdivided, c. if the result is greater than the limit, the parabola is subdivided, and this method returns to step a. for each resultant segment.

Claim 2

A method for displaying a computer generated image described in page description language on a raster output scanner comprising the steps of: generating a trajectory from said page description language which trajectory is described in page description language approximating a part of said trajectory by an original parabola having control points A, B and C which original parabola approximates said part of said trajectory, to within a predetermined error limit, generating for said original parabola a set of approximating parabolas which approximating parabolas together constitute two curved lines that are parallel to, and a predetermined distance away from, said original parabola, said generating step comprising: a. determining a number of segments that the original parabola must be divided into in order that an approximating parabola can be generated for each segment, b. dividing said original parabola into said segments, and c. generating an approximating parabola for each of said segments, converting said set of approximating parabolas into a bit map, and sending said bit map to a raster output scanner, wherein said determining step comprises a. testing said original parabola having control points A, B, C by dividing distance AB by distance BC if distance AB is longer or distance BC by distance AB if distance BC is longer, to generate a result K and comparing the result K to a limit which is a function of included angle ABC, b. if the result is less than the limit, the parabola does not need to be subdivided, c. if the result is greater than the limit, the parabola is subdivided, and this method returns to step a. for each resultant segment.

Claim 3

A method for displaying a computer generated image described in page description language on a raster output scanner comprising the steps of: generating a trajectory from said page description language which trajectory is described in page description language approximating a part of said trajectory by an original parabola having control points A, B and C which original parabola approximates said part of said trajectory, to within a predetermined error limit, generating for said original parabola a set of approximating parabolas which approximating parabolas together constitute two curved lines that are parallel to, and a predetermined distance away from, said original parabola, said generating step comprising: a. determining a number of segments that the original parabola must be divided into in order that an approximating parabola can be generated for each segment, b. dividing said original parabola into said segments, and c. generating an approximating parabola for each of said segments, converting said set of approximating parabolas into a bit map, and sending said bit map to a raster output scanner, wherein said generating step for each approximating parabola A, B, C comprises determining lines A 1 B 1 and B 1 C 1 which are parallel to AB and BC, respectively, and using control points A 1 B 1 C 1 to generate said approximating parabola.

Claim 4

A method for displaying a computer generated image described in page description language on a raster output scanner comprising the steps of: generating a trajectory from said page description language which trajectory is described in page description language approximating a part of said trajectory by an original parabola having control points A, B and C which original parabola approximates said part of said trajectory, to within a predetermined error limit, generating for said original parabola a set of approximating parabolas which approximating parabolas together constitute two curved lines that are parallel to, and a predetermined distance away from, said original parabola, said generating step comprising: a. determining a number of segments that the original parabola must be divided into in order that an approximating parabola can be generated for each segment, b. dividing said original parabola into said segments, and c. generating an approximating parabola for each of said segments, converting said set of approximating parabolas into a bit map, and sending said bit map to a raster output scanner, wherein said generating step for each approximating parabola A, B, C comprises determining lines A 1 B 1 and B 1 C 1 which are parallel to AB and BC, respectively, and using control points A 1 B 1 C 1 to generate said approximating parabola.