From topologies to shapes

Parametric shape grammars implemented by graphs

A method for imple­ment­ing para­met­ric shape gram­mars is pre­sent­ed. Sub­graph detec­tion is used to find sub­shapes. Para­met­ric shapes are described by restrict­ing topologies.


Difficulties in communicating shape grammar rules to a digital interpreter

The rule edi­tor of a para­met­ric shape gram­mar inter­preter is pre­sent­ed. The prob­lems that arise are dis­cussed along with their solutions.

On Shapes and Topologies

Graph theoretic representations of shapes and shape computations

Shape gram­mars are an estab­lished method in the field of design com­pu­ta­tion. Since their ini­tial for­mu­la­tion in the 70s the under­ly­ing the­o­ry has been devel­oped inten­sive­ly. Appli­ca­tions have most­ly been restrict­ed to show­case gram­mars remod­el­ling exist­ing bod­ies of work. Dif­fi­cul­ties in automat­ing shape gram­mars have restrict­ed their extra­mur­al impact. This the­sis attempts to rem­e­dy the […]

Sort Machines

A graph gram­mar for the gen­er­a­tion of topolo­gies for the U.S. fed­er­al cour­t­house typol­o­gy is intro­duced. Pos­si­ble con­fig­u­ra­tions are enu­mer­at­ed and a nomen­cla­ture is proposed.

Transformational Palladians

GRAPPA, an imple­men­ta­tion of the Pal­la­di­an gram­mar, is intro­duced. Graphs are used for the under­ly­ing rep­re­sen­ta­tion, graph gram­mars take over the com­pu­ta­tion. Once a set of graph gram­mar rules equiv­a­lent to the orig­i­nal set of shape rules is defined, deriva­tions, in the form of attrib­uted graphs, are gen­er­at­ed. These graphs con­tain all nec­es­sary infor­ma­tion to […]


A parametric shape grammar implementation

An imple­men­ta­tion of a shape gram­mar inter­preter is described. The under­ly­ing graph-the­o­ret­ic frame­work is briefly dis­cussed to show how alter­na­tive rep­re­sen­ta­tions from graph the­o­ry includ­ing graphs, over­com­plete graphs and hyper­edge graphs can sup­port some of the intu­itions han­dled in shape gram­mars by direct visu­al com­pu­ta­tions with shapes. The result­ing plu­g­in imple­ment­ed in Rhi­no, code-named GRAPE, […]

Palladian Graphs

An automated implementation of the Palladian grammar

An imple­men­ta­tion of the Pal­la­di­an gram­mar using a graph gram­mar and a graph to shape map­ping is pre­sent­ed. The appli­ca­tion is embed­ded in a para­met­ric CAD envi­ron­ment and allows the explo­ration of Pal­la­di­an vil­las by hand or by using a ran­dom generator.

Spatial Sieves

Xenakis’ sieves are a pow­er­ful for­mal tool to cre­ate inte­ger-sequence gen­er­a­tors that can be used for the gen­er­a­tion of var­i­ous numer­i­cal pat­terns to rep­re­sent pitch scales, rhythm sequences, as well as pat­terns of loud­ness, den­si­ty, tim­ber and so forth. The key idea in the design of the sieves is the notion of a vocab­u­lary of […]

Combining Triples

Using a Graph Grammar to Generate Courthouse Topologies

A graph gram­mar for the gen­er­a­tion of topolo­gies for the u.s. fed­er­al cour­t­house typol­o­gy is intro­duced. Pos­si­ble con­fig­u­ra­tions are enu­mer­at­ed and a nomen­cla­ture is pro­posed. Embed­ded with­in a larg­er project on the analy­sis and gen­er­a­tive descrip­tion of u.s. fed­er­al cour­t­hous­es, the aim of this task was to enu­mer­ate, gen­er­ate and name pos­si­ble topolo­gies for the courthouses […]

Point Worlds

A com­pu­ta­tion­al approach for the auto­mat­ed graph rep­re­sen­ta­tion and dia­gram­mat­ic nota­tion of all under­ly­ing sym­me­try struc­tures of three-dimen­­sion­al shapes with a cen­ter of sym­me­try is briefly pre­sent­ed and some appli­ca­tions with shape gram­mars to illus­trate these ideas are dis­cussed in the end. CUMINCAD