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PARAMETRIC SOFTWARES
AHTESHAN GANACHARI
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AHTESHAN GANACHARI
D r. B h a nube n Nan avat i Co llege o f Arch i tec tu re
Digital Architecture Parametric Softwares1 at BNCA 2019 Examiner: Ripple Patel, Mughdha Gandhi
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Abstract
The book contains different modeling exercises with process diagrams. Recreating already built structures by understanding the logic. Using tools like Rhinoceros and Grasshopper to model it.
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CONTENT
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1 2 3 4
MODELING 1.1 Egg Chair 1.2 Coal Drops Yard 1.3 High-rise 1.4 Serpentine Sackler Gallery
GEOMETRY 2.1 Fractal Tree 2.2 Points & Curves 2.3 Mathematical Surfaces 2.4 Recreating Felix Candela’s Shells
MECHANICS 3.1 Attractors 3.2 SDU Facade 3.3 Billboards, UK
LEAF VENATION Introduction Types Rule, Definition
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CH1 MODELING
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Egg Chair
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ARNE JACOBSEN FRONT ELEVATION
SIDE ELEVATION
PLAN
VIEW
STEP 1: Creating a grid according to Anthropometry & Ergonomics to draw two curves from Side & Front.
STEP 2: Using POINT FROM TWO CURVES to achieve desired curve.
STEP 3: Creating Chair using Loft
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High-rise
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STEP 1:
STEP 2:
STEP 3:
STEP 4:
Create a Lofted Surface and contour it.
Make the Lofted surface flat using Create UV. Draft pattern on the flat surface.
Apply the pattern on Lofted surface using Apply UV.
Split to create pattern.
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Coal Drops Yard
LONDON, UNITED KINGDOM
Steps involved in modeling Coal Drops Yard
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Serpentine Sackler Gallery Park
LONDON, UNITED KINGDOM
Steps involved in modeling Serpentine Sckler Gallery Park
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CH2 GEOMETRY
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15° 15° 15° Branching Angle Branching Angle Branching Angle Proportion Reduction 60% per Generation Proportion Reduction 65% per Generation Proportion Reduction 70% per Generation
25° 25° 25° Branching Angle Branching Angle Branching Angle Proportion Reduction 60% per Generation Proportion Reduction 65% per Generation Proportion Reduction 70% per Generation
35° 35° 35° Branching Angle Branching Angle Branching Angle Proportion Reduction 60% per Generation Proportion Reduction 65% per Generation Proportion Reduction 70% per Generation
60° 60° 60° Branching Angle Branching Angle Branching Angle Proportion Reduction 60% per Generation Proportion Reduction 65% per Generation Proportion Reduction 70% per Generation
90° 90° 90° Branching Angle Branching Angle Branching Angle Proportion Reduction 60% per Generation Proportion Reduction 65% per Generation Proportion Reduction 70% per Generation
Fractal Tree
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Angle+ Angle-
Curve From Previous Recursion
th ng
Le tor Vec
1.Production Rule
2.Production Rule Applied Twice
3.Production Rule Applied Thrice
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PARAMETRIC STAR
Create Circle
Divide Curve
Move alternate points
Weave
Surface
EXTRUDE POINT
Create Curves Loft
Divide Domain2 Isotrim
Extract centroid Extrude
ROTATING PIPES
Create Curve Perpendicular Frames
Line SDL Pipe
Series Rotate 3D
PARAMETRIC TABLE
Create Rectangle Offset and Range
Rotate 3D
Extrude
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Points & Curves PARAMETRIC STAR DEFINITION
EXTRUDE POINT DEFINITION
ROTATING PIPES DEFINITION
PARAMETRIC TABLE DEFINITION
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Twisted Eight Torus
MATHEMATICAL SURFACES
The Twisted Eight Torus is represented by the following equations. x = (R + r (cos (u / 2) sin (v) -sin (u / 2) sin (2 v))) cos (u) y = (R + r (cos (u / 2) sin (v) -sin (u / 2) sin (2v))) sin (u) z = r (sin (u / 2) sin (v) + cos (u / 2) sin (2 v)) Domain- pi to -pi
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Horn
MATHEMATICAL SURFACES The horn is represented by the following equations. x = (a + u cos (v)) sin (b pi u) y = (a + u cos (v)) cos (b pi u) + cu z = u sin (v) Domain- pi to -pi
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Klien
MATHEMATICAL SURFACES The Klein is represented by the following equations. x = sin(u) (7+cos(u/3-2 u))+2cos (u/3+v) y = cos(u) (7+cos(u/3-2 u))+2cos (u/3+v) z= sin(u/3-2 v))+2sin (u/3+v) Domain- pi to -pi
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Sine
MATHEMATICAL SURFACES The sine is represented by the following equations. x = sin(u) (-2+v sin(u/2)) y = cos(u)(-2+v sin(u/2)) z = v(cos(u/2)) Domain- pi to -pi
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RECREATING FELIX CANDELA’S SHELLS
MATHEMATICAL SURFACES Geometry 01
Base Geometry with Expression: (y2/a2)-(x2/b2)
Geometry 02
Base Geometry with Expression: a(x*y)/b
Geometry 03
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Geometry 04
Geometry 05
Geometry 06
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Geometry 07
Geometry 08
Geometry 09
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Definitions
RECREATING FELIX CANDELA’S SHELLS Geometry 03
Geometry 04
Geometry 05
Geometry 06
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Definitions
RECREATING FELIX CANDELA’S SHELLS Geometry 07
Geometry 08
Geometry 09
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CH3 MECHANICS
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ATTRACTOR POINT
Grid Triangle
Attractor Point
Range Domain
Attractors
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ATRACTOR CURVE
Grid Cylinders
Attractor Curve
Range Domain
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SDU Facade
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HENNING LARSEN
A dynamic and adaptable perforated facade for a triangular landmark The new Kolding Campus, which is part of the University of Southern Denmark (SDU), is the first low-energy university in the country. 4,500 m2 of aluminum panels manufactured with RMIG’s keyhole-perforated ImagePerf have been used to create a living and expressive facade that also gives the optimal balance of light and energy in and out of the building and thereby contributes to reduced energy consumption.
Surface Divide Domain2 Isotrim
Pattern 1 Surface Split Dispatch Cull Pattern
Pattern 2
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Billboards, UK
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GILLES MILLER
orking with the concept of ‘Wayfinding’, GMS W produced a series of large scale abstract sign-age sculptures. Square glass tiles were composed to create a centralized typology of textured shading, featuring in each sculpture, and designed to subtly evoke the movement of visitors to the next festival destination.
Surface Divide Domain2
Polygon on centroids
Giles Miller Studio created a series of installations for London’s Clerkenwell Design Week, to lead visitors around the events and showrooms of the festival.
Isotrim
Centroid
Attractor Curve Range
Axis of Rotation
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CH4 NATURAL PHENOMENON
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Leaf Venation
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NATURAL PHENOMENON
T he leaf venation pattern of plants shows remarkable diversity and species‐specificity. However, the mechanism underlying the pattern formation and pattern diversity remains unclear. A mathematical model that is based on the positive feedback regulation between plant hormone auxin and its efflux carrier. This system can generate auxin flow pathways by self‐organization from an almost homogeneous state. This result explains a well‐known experimental phenomenon referred as to “polar auxin transport.” The model can produce diverse leaf venation pat-
terns with spatial regularity under similar conditions to those of leaf development, that is, in the presence of leaf expansion and auxin sink. Final venation patterns are strikingly affected by leaf shape and leaf expansion. These results indicate that the positive feedback regulation between auxin and its efflux carrier is a central dynamic in leaf venation pattern formation. The diversity of leaf venation patterns in plant species is probably due to the differences of leaf shape and leaf expansion pattern.
TYPES OF VENATION Parallel
Openfurcute
Reticulate
e.g.Ferns Unicostate
Multicostate
Convergent
Divergent
Unicostate
Multicostate
Convergent
Divergent
Types of Venation
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NATURAL PHENOMENON
ARCUATE
CROSS-VEENULATE
DICHOTOMOUS
secondary veins bending towards apex
small veins connecting secondary veins
veins branching symmetrically in pairs
LONGITUDINAL
PALMATE
PARALLEL
veins aligned mostly along long axis of leaf
several primary veins of verging from a point
veins arranged axially, not intersecting
PINNATE
RETICULATE
ROTATE
secondary veins paired oppositely
small veins forming a network
in pellate leaves, veins radiating
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(a)–(e) The impact of the kill distance on venation patterns. From left to right, the kill distance is 40, 20, 10, 5, and 1. (f )–(h) The impact of the number of sources inserted per step (parameter ρ from Section 3.3). From left to right: 0.00006, 0.0003 and 0.006 insertions per unit leaf area per step. (i) A venation pattern generated in a leaf with slow marginal growth.
RECREATING PALMATE PATTERN
Create a circle, Populate it with points and connect them. Offset and loop them.
References
http://algorithmicbotany.org/papers/venation.sig2005.pdf https://www.brainkart.com/article/Leaf-Venation---Reticulate,-Parallel---Pinnately,-Palmately_907/ https://link.springer.com/chapter/10.1007/11919629_44
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