Form Generation and Evolution

  • Daniela Bertol


This chapter investigates the creation of CAD models of three-dimensional forms according to the foundations established in Chapter I. The syntax used in generating models of architectural forms is the same as that used in creating geometrical forms, especially in computer-aided design, where any architectural configuration is defined initially by its geometric interpretation. Forms in architecture and in geometry clearly have two different semantic contents. As already emphasized, while geometric forms exist in “intellectual space” and are subject only to logical relations, architectural forms deal with the constraints of the physical world as well as functional requirements. Nevertheless, at the syntactic level, architectural and geometric forms can both be investigated in terms of their descriptions as sets of points, lines, and surfaces in three-dimensional space, and how they determine a series of perceptual dualistic relations, particularly those of solid-void and inside-outside.


Boolean Operation Transformation Rule Geometric Form Primitive Element Geometric Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. AutoCAD® Release 12 - Advanced Modeling Extension® Release 2.1 ReferenceGoogle Scholar
  2. AutoCAD® Release 12 - Command ReferenceGoogle Scholar
  3. Autodesk 3D Studio™ Release 2 - Reference ManualGoogle Scholar
  4. Coxeter, H. S. M., and S. L. Greitzer, Geometry Revisited, Random House, New York, 1967zbMATHGoogle Scholar
  5. Coxeter, H. S. M., Regular Polytopes, Dover, New York, 1973Google Scholar
  6. do Carmo, Manfredo R, Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, 1976Google Scholar
  7. Foley, J. D., and A. Van Dam, Fundamentals of Interactive Computer Graphics, Addison-Wesley, 1984Google Scholar
  8. Greenberg, Marvin Jay, Euclidean and Non-Euclidean Geometries, W. H. Freeman, New York, 1980Google Scholar
  9. Mandelbrot, Benoit B., The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1977Google Scholar
  10. Modenov, P. S., and A. S. Parkhomenko, Geometric Transfonnantims, Academic Press, New York, 1965Google Scholar
  11. Yaglom, Y. M., Geometric Transformations, Random House, New York, 1962zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Daniela Bertol
    • 1
  1. 1.New York CityUSA

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