a  c  a  d  e  m  i  c

r e s e a r c h

C o n s t r u c t i n g   D e s i g n   C o n c e p t s :   A Computational Approach to the Synthesis of Architectural Form Kotsopoulos S, Ph.D. Dissertation, Massachusetts Institute of Technology, 2005

II.     Shape Computation Theory                                                                                                      4.2 1.  What is a shape rule ?      4.2 2.  What is a derivation ?      A shape rule of the form  a  --> b, relates two shapes  a, b in a particular way.  In the example two shapes a, b made     out of lines are manipulated on the plane, in  the algebra U12, according to the following rule:

The rule  applies on some initial shape C under some transformation t to produce a desired spatial relationship.     Each time the rule applies on shape C a new shape C' is produced. A concise way to express the  productive         process is the next sequence of shapes, which is called derivation.

The rule can apply recursively to produce a series of shapes C, C1, C2, … Cn