Generating Islamic Geometric Motif‐Based Structures Using Shape Grammars
Zahra Sayed
Supervisors: Dr.I.J.Palmer & Prof. H.Ugail
27th March 2014
Islamic Art
Islamic Geometric Patterns (IGP)
• Symmetry
• Emergence
• Self‐Similarity
Types of IGP
Star Patterns Field Patterns
Construction Methods
•
•
•
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Strapwork Method
Modular Design System
Polygons‐in‐Contact (PIC)
Shape Grammar
Strapwork Method
• Uses a straightedge (ruler) & compass
• Creates simple shapes
• Can be tedious & can create errors
Modular Design System
• Small sets or modules/shapes
• Create a square/rectangular motif
• Produces a large number of motifs
Polygons‐in‐Contact (PIC)
• Uses a polygonal grid
• Calculates mid‐points of each polygon
• Base is removed
Shape Grammar
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•
•
•
Formal Computational Grammar
Based on an ‘Initial shape’ and ‘Shape rules’
Automatically creates algorithms
Creates both original and new designs/patterns
Parametric Shape Grammar
• Extension of Shape Grammar
• Sub‐rules are generated
• Advantage of flexibility in pattern generation
• Example:
• Translation in the y‐axis of ‘x’ amount (simple Shape Grammar rule)
• Translate 2/5 units in the y‐axis (Parameterized by 2 & 5)
Aim of Research
• 3D modelling tool to automatically generate IGP using Shape Grammars
• Generate new forms of IGP
• Construct architectural structures using the motifs
Methodology
• Use of Shape Grammar method
• Initial Shape – Hexagon
• Implementing in Maya Python Grammars Generated • Parameterized Shape Grammar (PSG)
• Generates original/new motif
• Rules of translation, rotation, scale, Boolean, add & duplicate (Parameterized)
• Auto‐Parameterized Shape Grammar (APSG)
• Constructs the motif‐based structures
• Rules of translation, rotation & scale (Defined by algorithms)
Motif‐Based Structures
Create the Motif
Translate in the y‐axis
Intersect including ‘IS’
Duplicate & rotate 60° (x5) from centre
Add Initial Shape (IS)
Generating the Motif
Constructing the Wall
START
CREATE MOTIF
for i = 1 to N
DUPLICATE
END
TRANSLATE
i
(x*(‐1), y*i, 0)
j
TRANSLATE
(w*j, 0, 0)
DUPLICATE
for j = 1 to M
i
Constructing the Column
CREATE MOTIF
START
TRANSLATE
(0, 0, )
for i = 1 to N
DUPLICATE
ROTATE
(0, *i, 0)
END
TRANSLATE
(0, y*i, 0)
j
ROTATE
(0, *j, 0)
DUPLICATE
for j = 1 to M
i
Constructing the Star
CREATE MOTIF
START
TRANSLATE
(0, , 0)
for i = 1 to N
DUPLICATE
SCALE
(s*i, s*i, 1)
END
ROTATE
(0, 0, *i)
j
ROTATE
(0, 0, *j)
DUPLICATE
for j = 1 to M
i
Constructing the Dome
CREATE MOTIF
ROTATE
(90, 0, 0)
TRANSLATE
(0, , 0)
ROTATE
( , 0, 0)
START
for i = 1 to N
DUPLICATE
SCALE
(s*i, 1, s*i)
END
ROTATE
( *s, *i, 0)
j
ROTATE
(0, *j , 0)
DUPLICATE
for j = 1 to M
i
Limitations
• Generates only 6‐fold geometry
• Only constructs 4 simple structures
• Creates the motif automatically
Future Work
• Combine the 2 Shape Grammars
• Structures constructed of more than one type of motif
• Tessellate in more than one direction
• Generate a 3D Shape Grammar
Thank You