Line Designs for the Computer

Line designs are created by connecting points on lines or curves with straight line segments.  When carried out on cardboard with sewing needle and thread, the process is referred to as Curve Stitching or String Art.
If the family of straight line segments that comprise a line design are generated by a particular mathematical rule, a classic mathematical curve will be outlined.  Each of the line segments will be tangent to the curve in question.  Mathematicians refer to the family of line segments as an envelope.  By simulating the connection process on a computer, you can explore the different curves (or collection of curves) that can be generated and see what happens when the values of the variables associated with a mathematical rule are changed.

Select a line design program from the drop down list  below and press Load.  [You will find links to information about each of the line design programs beneath the applet screen.]  Click on the applet screen when the corresponding typed program appears, type "r" for run and then hit Enter.  Many of the programs will allow you to change different aspects of the design you are creating.  When asked questions, type in the desired values and hit Enter.  When done, use the drop down list to select another program.

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Line Design Programs

Below are links to each of the different line designs that can be created.  On the page for any particular design, there is a  a screen dump of the design (generated by a PC/DOS Spectrum Emulator), an explanation of how the design was created, and suggested values for your own creations.  Do not feel that you have to stick to the suggested values.  Have fun and see what happens if you enter something completely different.

01: Parabolas in a Polygon

x02: Parabolas in Six Polygonsx

03: Parabolic Star

04: Six Parabolic Stars

05: Curves in a Circle

xxx06: Curves in Six Circlesxxx

07: Eight Parabolas in a Square

08: Parabola Design

09: Ellipse from Inverses

10: Ellipse from Chords

17: Decreasing Chords

18: Mystic Rose

19: Six MysticRoses

20: Concentric Circles

21: Two Linked Circles

22: Three Linked Circles

23: Envelope of a Roulette

26: Epicycloid

27: Six Epicycloids

28: Cardioid from Circles

29: Nephroid from Circles

30: Cycloid

31: Hypocycloid

32: Six Hypocycloids

33: Astroid

34: Four Curves

35: Spiral

The applet in this web page is the ZZ Spectrum 16/48/128K Spectrum Emulator  (c) 2001 Troels Noergaard.  The web pages for each of the designs were created by Shaunna Dent and Brian Webb.  The 33 line design programs were all taken from the first edition of the book Curve Stitching by Jon Millington and numbered accordingly.  Recent/current editions feature QBASIC versions of the programs.  The book is available from

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