Introduction to shape gramamars
Shape grammars perform computations with shapes in
two steps: a recognition of a particular shape and its possible
replacement.
Rules specify the particular shapes to be replaced and
the manner in which they are replaced. Underlying the rules
are transformations that permit one shape to be part of
another. There is one rule associated with this page.
The rule
contains two shapes, separated by an arrow:- the
pattern on the left hand side and the replacement on the
right. The gray marker shows how to align the two
shapes.The rule replaces any triangle similar to the pattern
by the replacement shape suitably transformed. The result is
to move a single triangle of any size, a specific
distancealong its altitude, in a direction perpendicular to
andaway from the base. This can be seen when the two
shapes are drawn as one with a different colors for the
pattern and replacement shapes:
Placing the cursor over the chevron at the left hand side
of the page, changes it to a five-pointed star.
Moving the cursor anywhere else causes the star to
disappear and be replaced by a chevron, and the bottom of
the page shows the orientation of the resulting triangle
associated with this page.
Placing the cursor over the Introduction link on the left
has no effect.
Placing the cursor over one of the other five circles on
the left triggers the recognition of one of the five triangles in
the shape.
Placing the cursor over the text to the left of the circle
triggers its replacement. This has the effect of removing the
triangle from the figure in the upper left-hand corner
yielding a chevron and of moving the triangle, shown in the
figure in the bottom right hand corner.
While this page only shows the orientation of the resulting
triangle, the Home Page
uses a grey mark to show the relative positions of
both shapes. The resulting shape is actually the result of
aligning the chevron in the upper left hand corner with the
triangle in the lower right hand corner. The rule
replaces the star by the two shapes drawn as one.
The shape grammar formalism has a long history.
The first papers was formally presented in 1971 and
published in the following year. Since this paper may be
difficult to find, here is an online copy of that paper:
Stiny G, Gips J, 1972, "Shape Grammars and the
Generative Specification of Painting and Sculpture", in C V
Freiman (ed), 1972,Proceedings of IFIP Congress71,
Amsterdam: North-Holland 1460-1465. Republished in O R
Petrocelli (ed), The Best Computer Papers of
1971: Auerbach, Philadelphia 125-135.
It is included in the bibliography of the field of
shape grammars.