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Implementation of Curved Shape Grammars

Author

Listed:
  • Iestyn Jowers

    (School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, England)

  • Christopher Earl

    (Faculty of Mathematics, Computing and Technology, The Open University, Milton Keynes MK7 6AA, England)

Abstract

Research into shape grammar implementation has been largely concerned with rectilinear shapes and there has been limited research into implementation on shapes composed of curves. This reflects developments of the shape grammar formalism which has been defined largely according to straight lines, planes, and associated volumes. In this paper, implementation of shape grammars on curved shapes is examined using algorithms for shape operations on shapes composed of parametric curves. These algorithms have been implemented in a shape grammar interpreter for shapes composed of quadratic Bézier curves, which is illustrated via application of a shape grammar that generates Celtic knotwork patterns. Implementing shape grammars on shapes composed of Bézier curves highlights difficulties that arise when the shape grammar formalism is applied to curved shapes, and the paper concludes with a discussion that explores these difficulties and indicates potential implications for the shape grammar formalism.

Suggested Citation

  • Iestyn Jowers & Christopher Earl, 2011. "Implementation of Curved Shape Grammars," Environment and Planning B, , vol. 38(4), pages 616-635, August.
    • Handle: RePEc:sae:envirb:v:38:y:2011:i:4:p:616-635
    DOI: 10.1068/b36162
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