Quad tree layout generator

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Parametric variants

This work examines the potential of generative CAD software for programming parametric generators, in this case, the creation of a layout grid generator based on a randomized quadtree subdivision. Quadtrees are tree data structures in which each internal node has either exactly four or no child elements. They are mainly used in graphics programming for the recursive subdivision of two-dimensional surfaces.44 The generator presented here operates by scattering a point cloud within a pre-defined two-dimensional area – the chosen document size. These points are used to subdivide the surface iteratively until each quadrant contains only a defined number of elements. The generated quadrants are proportional to the chosen document format (ie rectangular for non-square paper sizes) thus always fitting without overlap.

Quadtree of a random point cloud

The generator can be controlled with the following parameters:

  • Height and width of the document format
  • The number of rows and columns
  • The quantity of points
  • The degree of randomisation of the point coordinates
  • The number of permitted points per quadrant
  • Allocation of
    • Text areas
    • Image areas
    • White space
  • Quantitive ratio of
    • text area
    • image area
    • white space

parametric generated variants of grids

44 Finkel, R., Bentley, J.L.: Quad Trees: A Data Structure for Retrieval on Composite Keys. In: Acta Informatica Volume 1. Nr. 4. 1974. Page 1–9.