Method and apparatus for approximating polygonal line to curve

Claim 1

A method of approximating a polygonal line to a curve on a graphic display comprising the steps of: receiving curve diagram data; converting said curve diagram into a plurality of coordinate points; generating a plurality of line segments approximating a curve based on said coordinates wherein a number of line segments generated is based upon an amount of curvature along portions of said curve; converting said plurality of line segments into a graphic curve; and displaying said graphic curve on a display device.

Claim 2

A method of approximating a polygonal line to a curve on a graphic display comprising the steps of: receiving curve diagram data; converting said curve diagram into a plurality of coordinate points; generating a plurality of line segments approximating a curve based on said coordinates wherein a number of line segments generated is based upon an amount of curvature along portions of said curve; converting said plurality of line segments into a graphic curve; and displaying said graphic curve on a display device.

Claim 10

A method of approximating a polygonal line to a curve on a graphic display comprising the steps of: receiving curve diagram data; converting said curve diagram into a plurality of coordinate points; generating a plurality of line segments approximating a curve based on said coordinates wherein a number of line segments generated is based upon an amount of curvature along portions of said curve, said plurality of line segments generated by the steps of dividing said curve into two curve portions at a division point on said curve, determining an amount of curvature of each curve portion lining said start point and said end point of said curve with said division point, determining whether or not said amount of curvature of each curve portion is smaller than a predetermined value, generating said line segment as one part of said polygonal line, when said amount of curvature is smaller than said predetermined value, and repeating the process of said curvature amount determining step, said predetermined value determining step, and said line segment generating step by further dividing each of said curve portions when said amount of curvature is not smaller than said predetermined value; converting said plurality of line segments into a graphic curve; and displaying said graphic curve on a display device.

Claim 11

A method of approximating a polygonal line to a curve on a graphic display comprising the steps of: receiving curve diagram data; converting said curve diagram into a plurality of coordinate points; generating a plurality of line segments approximating a curve based on said coordinates wherein a number of line segments generated is based upon an amount of curvature along portions of said curve, said plurality of line segments generated by the steps of dividing said curve into two curve portions at a division point on said curve, determining an amount of curvature of each curve portion lining said start point and said end point of said curve with said division point, determining whether or not said amount of curvature of each curve portion is smaller than a predetermined value, generating said line segment as one part of said polygonal line, when said amount of curvature is smaller than said predetermined value, and repeating the process of said curvature amount determining step, said predetermined value determining step, and said line segment generating step by further dividing each of said curve portions when said amount of curvature is not smaller than said predetermined value; converting said plurality of line segments into a graphic curve; and displaying said graphic curve on a display device.

Claim 12

An apparatus for approximating a polygonal line to a curve comprising: a data input circuit for generating curve portions of a start point, a first control point, a second control point, and an end point for a cubic Bezier curve; a first middle point calculating circuit, connected to said data input circuit, for calculating a first middle point between said first and second control points of said cubic Bezier curve; a second middle point calculating circuit, connected to said data input circuit, for calculating a second middle point of a line segment linking said start and end points of said cubic Bezier curve; an error calculating circuit, connected to said first and second middle point calculating circuits, for calculating an error between said first and second points; and an error determining circuit, connected to said error calculating circuit, for determining whether or not said error is smaller than a predetermined value; and a line segment generating circuit, connected to said error determining circuit, for generating a line segment linking said start and end points of said cubic Bezier curve as one part of aid polygonal line, when said error is smaller than said predetermined value, said error determining circuit repeating operation of said first middle point calculating circuit, said second middle point calculating circuit, and said line segment generating circuit, by dividing said cubic Bezier curve into two further cubic Bezier curves when said error is not smaller than said predetermined value wherein a number of said line segments generated is based upon an amount of curvature along each curve portion.

Claim 13

An apparatus for approximating a polygonal line to a curve comprising: a data input circuit for generating curve portions of a start point, a first control point, a second control point, and an end point for a cubic Bezier curve; a first middle point calculating circuit, connected to said data input circuit, for calculating a first middle point between said first and second control points of said cubic Bezier curve; a second middle point calculating circuit, connected to said data input circuit, for calculating a second middle point of a line segment linking said start and end points of said cubic Bezier curve; an error calculating circuit, connected to said first and second middle point calculating circuits, for calculating an error between said first and second points; and an error determining circuit, connected to said error calculating circuit, for determining whether or not said error is smaller than a predetermined value; and a line segment generating circuit, connected to said error determining circuit, for generating a line segment linking said start and end points of said cubic Bezier curve as one part of aid polygonal line, when said error is smaller than said predetermined value, said error determining circuit repeating operation of said first middle point calculating circuit, said second middle point calculating circuit, and said line segment generating circuit, by dividing said cubic Bezier curve into two further cubic Bezier curves when said error is not smaller than said predetermined value wherein a number of said line segments generated is based upon an amount of curvature along each curve portion.

Claim 16

An apparatus for approximating a polygonal line to a curve having a start point and an end point, said apparatus comprising: a curve dividing circuit for dividing said curve into two curve portions, at a division point; an error calculating circuit, connected to said curve dividing circuit, for calculating an error between a line segment linking said start and end points and said division point; and an error determining circuit, connected to said error calculating circuit and said curve dividing circuit, for determining whether or not said error is smaller than a predetermined value; and a line segment generating circuit, connected to said error determining circuit, for generating said line segment as one part of said polygonal line, when said error is smaller than said predetermined value, said error determining circuit repeating operation of said error calculating circuit by replacing said curve with each of said curve portions, when said error is not smaller than said predetermined value wherein a number of said line segments generated is based upon an amount of curvature along each curve portion.

Claim 17

An apparatus for approximating a polygonal line to a curve having a start point and an end point, said apparatus comprising: a curve dividing circuit for dividing said curve into two curve portions, at a division point; an error calculating circuit, connected to said curve dividing circuit, for calculating an error between a line segment linking said start and end points and said division point; and an error determining circuit, connected to said error calculating circuit and said curve dividing circuit, for determining whether or not said error is smaller than a predetermined value; and a line segment generating circuit, connected to said error determining circuit, for generating said line segment as one part of said polygonal line, when said error is smaller than said predetermined value, said error determining circuit repeating operation of said error calculating circuit by replacing said curve with each of said curve portions, when said error is not smaller than said predetermined value wherein a number of said line segments generated is based upon an amount of curvature along each curve portion.