CMU 48-747 Shape Grammars - Forming
New
Languages
from
Old


Unformatted text preview:

48-747 Shape Grammars !Forming(New(Languages(from(Old(Spatial!Metathesis(RECAP&grammar!paradigm!Vocabulary!GRAMMAR!Spatial Relations!Rules!LANGUAGE of designs!Initial shape!x"!→ s"+"t""(additive)!s"+"t"→!!x""(subtractive)&augmented&by&the(use(of(labels(Rules!LANGUAGE!Encapsulates(“theme”( !!Explored(for(design(“styles”(Perhaps(motivated(by(revival(or(restoration(Gothic(Classical(Islamic(Eastern(styles(Languages"give"birth"to"new"languages"metathesis!transposition&of&letters,&words,&sounds,&syllables&bird&←&brid&evelate&←&elevate&&(spoonerism)&why&not&transposition&of&shapes&or&images&by&shape&replacement&?&metathesis!consider&the&letter&equivalence&&p&↔&t&pot&&tot&top&pop&by&analogy&this&leads&to&the&notion&of&shape&equivalence&&&a&↔&b&shape!equivalence!rule!Is&of&the&form&a"↔&b"&where&neither&a(nor&b"&is&empty&Apply&the&rule&to&a&spatial&relation&R,(a&set&of&shapes,(&to&produce&a&new&spatial&relation&N(provided(R(contains(a(shape(s(and(there(is(a(geometrical(transformation(f(such(that(either(s=(f(a)(or(s=f(b)(N(=&S(–(f(a)&+&f(b)&&if&&s(=(f(a)&N(=&S(–(f(b)&+&f(a)&&if&&s(=(f(b)(example!designs!if&we&can&have&shape&equivalence&rules&why&not&shape!equivalence!schemas?&shape!equivalence&schema!shape!equivalence!schema!Is&a&schema&&of&the&form&a"↔&b"&where&neither&a(nor&b"&is&empty,&a(and&b"have&open&terms&Apply&the&schema&to&a&spatial&relation&R,(a&set&of&shapes,&to&produce&a&new&spatial&relation&N(provided(R(contains(a(shape(s,(there(is(an(assignment(g(to(all(open(variables(in(a(and&b,(and(there(is(a(geometrical(transformation(f(such(that(either(s=(f(a)(or(s=f(b)(N(=&S(–(f(g[a])&+&f(b)&&if&&s(=(f(g[a])&N(=&S(–(f(b)&+&f(a)&&if&&s(=(f(g[b])(What&we&have&seen&so&far&is&a&FLIP‐FLOP&between&shapes/schemas&with&the&implicit&PROVISO&that&no&new&shapes&are&introduced&into&the&relation&what&about&introducing!new!shapes!into&the&equivalence!rule!transition(from(Romanesque(to(Gothic(arches?(any!more!variations?!We&have&a"↔&b"&We&can&construct&classes&of&spatial&relations&by&looking&at&f[h(a)]&and&g[j(b)]&&so&that&N(=&S(–(f(a)&+&g(b)&N(=&S(–(f(h(b))&+&g(j(a))(to&make&this&transition&idea&work&one&must&consider&heuristics&in&how&the&shape&equivalence&rules&are&applied.&Transformation"of(Grammars(the!basic!idea!Vocabulary&1&Vocabulary&2&Spatial&Relation&1&Spatial&Relation&2&Rules&1&Rules&2&Language&2&Language&1&metathetical&change&rules&isomorphism&derivational&structure& derivational&structure&GRAMMAR&1&GRAMMAR&2&Transformation&to!compare!languages!we&need&to&ensure&that&grammars&are&specified&in&an&normalized&fashion&–&&i.e.,&in(the(same(sort(of(way(every(time(hence,&grammars"in&normal"form"Vocabulary&Purely&Additive&rules&Purely&Subtractive&rules&Labels&are&spatial&&&–&how(&–&where(States&are&nonspatial&&–&when(nonspatial!or!state!labels!spatial!–!where"and&how"labels!state!and&spatial!labels!grammar!in!normal!form!recursive!structure!R(G)!Is&a&basic&property&of&grammars&Expresses&a&relationship&on&rules,&the&initial&shape&and&selected&typical&derivations&of&designs&in&the&grammar&R(G)&=&{(rule&x,&rule&y)&…&}where&(rule&x,&rule&y)&is&a&member&of&R(G)&whenever&• & &Rule&x&is&additive&or&is&the&initial&shape&• &


View Full Document

CMU 48-747 Shape Grammars - Forming
New
Languages
from
Old


Download Forming
New
Languages
from
Old

Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Forming
New
Languages
from
Old
 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Forming
New
Languages
from
Old
 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?