Method and apparatus for generating a set of signals representing a curve

Claim 1

A method for (i) generating a series of signals representing nodes on a locus of a curve partially defined by a set of related knots, encoded as data on storage media, with said knots defining the end points of respective segments of said curve locus and with said knots being in a successive order in relation to said locus, and for (ii) encoding and decoding said node signals as data and for use of said data in an imaging process responsive to the shape for said curve segments as represented by said encoded data, comprising the steps of: (a) defining the locations and the successive order of said knots of said curve locus and encoding as data on storage media, signals indicative of said knots, (b) for a first knot, (Z a ), representing a first end point of a first curve segment, deriving a first angle, indicative of the average of the interknot angles between said first knot (Z a ), and selected related knots and encoding as data in computer memory, signals indicative of said first angle, (c) at a second of said knots (Z b ), representing a second end point of said first curve segment, establishing a second angle for said first curve segment, and encoding as data in the computer memory, signals indicative of said second angle, (d) establishing a compiler in computer memory, which compiler generates locus points for compiling data according to a predetermined cubic parametric polynomial function between a parameter "t", said knots and angles at said end points of a curve segment and the locus of a curve segment, (e) establishing a limited range "R" of values for said parameter "t" in the compiler, (f) in the computer memory, applying said signals indicative of the said locations of said first and second knots of said first curve segment, to said compiler, (g) applying said signals indicative of the said first and second angles of said first curve segment to said compiler, (h) applying a signal indicative of a distinct selected value of said parameter "t" within said range "R", to said compiler to derive a signal indicative of a respective node location on said first curve segment, (i) repeating step (h) by applying signals indicative of additional distinct selected values of said parameter "t", within said range "R", to derive a plurality of signals indicative of respective node locations on said locus of said first curve segment for respective distinct selected values of said parameter "t", (j) encoding said signals derived in step (h) and (i), in a data base in memory for later sorting to represent said first curve segment for later generation of a visual representation of said curve by using said data signals directly to control a display process and visually display the pattern in the form of a curve, (k) accessing said data base signals encoded in step (j), and (l) controlling an imaging means responsive to said accessed signals to reproduce said curve.

Claim 2

A method for (i) generating a series of signals representing nodes on a locus of a curve partially defined by a set of related knots, encoded as data on storage media, with said knots defining the end points of respective segments of said curve locus and with said knots being in a successive order in relation to said locus, and for (ii) encoding and decoding said node signals as data and for use of said data in an imaging process responsive to the shape for said curve segments as represented by said encoded data, comprising the steps of: (a) defining the locations and the successive order of said knots of said curve locus and encoding as data on storage media, signals indicative of said knots, (b) for a first knot, (Z a ), representing a first end point of a first curve segment, deriving a first angle, indicative of the average of the interknot angles between said first knot (Z a ), and selected related knots and encoding as data in computer memory, signals indicative of said first angle, (c) at a second of said knots (Z b ), representing a second end point of said first curve segment, establishing a second angle for said first curve segment, and encoding as data in the computer memory, signals indicative of said second angle, (d) establishing a compiler in computer memory, which compiler generates locus points for compiling data according to a predetermined cubic parametric polynomial function between a parameter "t", said knots and angles at said end points of a curve segment and the locus of a curve segment, (e) establishing a limited range "R" of values for said parameter "t" in the compiler, (f) in the computer memory, applying said signals indicative of the said locations of said first and second knots of said first curve segment, to said compiler, (g) applying said signals indicative of the said first and second angles of said first curve segment to said compiler, (h) applying a signal indicative of a distinct selected value of said parameter "t" within said range "R", to said compiler to derive a signal indicative of a respective node location on said first curve segment, (i) repeating step (h) by applying signals indicative of additional distinct selected values of said parameter "t", within said range "R", to derive a plurality of signals indicative of respective node locations on said locus of said first curve segment for respective distinct selected values of said parameter "t", (j) encoding said signals derived in step (h) and (i), in a data base in memory for later sorting to represent said first curve segment for later generation of a visual representation of said curve by using said data signals directly to control a display process and visually display the pattern in the form of a curve, (k) accessing said data base signals encoded in step (j), and (l) controlling an imaging means responsive to said accessed signals to reproduce said curve.