PARAMETRIC SOFTWARES Rhinoceros 3D | Grasshopper Bhoomika U| DA1903
2019- 20| Sem 01 Digital Architecture | BNCA Tutors : Ripple Patel | Mugdha Gandhi
D r. B h a n u b e n N a n av a t i Co l l e g e o f A rc h i t e c t u re
Abstract The book is about exploring the parametric software - Rhinoceros and Grasshopper. The book contains three chapters. 1. Modeling in Rhino - Exploring the basics of Rhinoceros tools and modeling. 2 .Parametric modeling in Grasshopper - Exploring the basics using the parameters with logic building. 3. Rule based modeling in grasshopper-agent based modeling Studying a Natural Phenomena - Flocking and it’s rule sets. Explored agent based modeling plug-in based on the Flocking logic. In all the chapters, the process and the logic behind each modeling are documented sequentially.
1
M ODELING 1.1 Curve 1.2
Loft
1.3 UV curves & Boolean 1.4 Recreating - Coal drop 1.5 Recreating - Serpentine Sackler gallery
Co nt ent
2
3 4
P ARAMETRIC MODELING 2.1
Point & Curve
a) Parametric star b) Sequential cylinder rotation
2.2
Planes & surfaces
2.3
Transformations
a) Mathematical surfaces b) Recreating Felix candela
a) Single attractor point b) Multiple attractor points c) Attractor curve d) Recreating - SUD building facade e) Recreating - Hybrid facade_ Ideea lab
R ULE BASED MODELING 3.0 Natural Phenomena- Flocking a) Introduction b) Study
B IBLIOGRAPHY
01 Modeling
Rhinoceros
Rhinoceros, also known as Rhino or Rhino3D, is a 3D CAD modeling software package that enables you to accurately model your designs ready for rendering, animation, drafting, engineering, analysis, and manufacturing. Rhino is a free-form NURBS surface modeler.
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1.1
Curves Chair design
This gracefully curving chair is created using the basic tools in Rhino. Using curve through interpolate point command the side profile (Fig. 01) and the front profile of the chair is drawn (Fig. 02). Curves from 2 views is used to derive the profile of the chair (Fig. 03). Using the profile, framework is created and it is lofted for the geometry (Fig. 04). Thus the profile of chair is achieved (Fig. 05)
Process
Curves (2 profile)
Fig. 01 : Side profile
Fig. 02 : Front profile
Curves from 2 views
Fig. 03 : Combining the profiles
Loft
Fig. 04 : Framework
Fig. 05
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1.2
Curves- loft
Iterations of lofted geometries
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1.3
Curves
H i g h
Curves
Loft
r i s e
Taper
Contour
Boolean High rise
Profile
Split with xz-plane
Taper
Boolean
Contour
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1.4
UV curves H i g h
Curves
r i s e
Loft
UV curve and split surface for pattern
Contour
Curves
Taper
Loft
UV curve and split surface for pattern
Twist
Contour
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1.5
Coal drop Kings cross
Process
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1.6
Serpentine Sackler Gallery
Process
Three circles of varied size
A curved surface is intersected to the column
Profile of the column
Split the column with a curved surface as shown
The final profile is offset for the thickness
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02
P A R A M E T R I C MODELING
Grasshopper Algorithmic modeling for Rhino Parametric design is an algorithmic process where parameters and rules are assembled to define the relationship between design intent and design response.
2.1Points & Curves
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2.1a
Parametric star Point | List
Create a star with parametric method. Create circle and divide the circle into even divisions (Fig. 02). The alternative points to be selected using dispatch list (Fig. 03). dispatch list provides two list of true an false. Alternative points are moved inwards to with a vector (Fig. 04). The points on the circumference of the circle and the points moved inward are weaved with a certain pattern (Fig. 05). The parametric star is formed. Altering the radius of circle the iteration of stars are achieved (Fig. 01)
Fig. 01 : Parametric star- varying the radius of circle
Fig. 02 : Create circle and divide it to even divisions
Fig. 03 : Select alternative points
Fig. 04 : Move the alternate points inwards with a vector
Fig. 05 : Weave the points with a pattern and create polyline
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2.1b
Sequential rotation C U RV E | R O TAT E | R E M A P
Create a series of cylinders and rotate it sequentially. Create a curve - guides the rotation axis and divide the curve into equal divisions (Fig. 02). Cylinders are created on the curve considering the divided points as the center points (Fig. 03). The cylinders are rotated sequentially with the remapped angles along the curve(Fig. 04). Remapping creates a new mapped values / domain within the set bound. Altering the rotation angle the cylinders are rotated sequentially.(Fig. 01)
Fig. 01 : Sequential rotation of cylinder through parameters
Fig. 02 : Create curve and divide it
Fig. 03 : Create cylinders considering the divided points as center
Fig. 04 : Remap the co-ordinates and rotate the cylinders accordingly
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2.2Planes & Surfaces
2.2a
Side view
Henneberg’s Surface
MATHEMATICAL SURFACE Mathematical equation: x = 2 cos (v) sinh (u) - 0.667 cos (3 v) sinh (3 u) y = 2 sin (v) sinh (u) + 0.667 sin (3 v) sinh (3 u) z = 2 cos (2 v) cosh (2 u)
U and V values are the parameters to represent the surface U- domain of set of numbers [-1 , +1] V - domain of set of numbers [-pi/2, +pi/2 ]
Grasshopper definition:
Front view
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Front view
Trianguloid Trefoil Surface MATHEMATICAL SURFACE Mathematical equation: x = 2 sin(3 u)/(2 + cos(v)) y = 2 (sin(u) + 2 sin(2 u))/(2 + cos(v + 2 pi/3)) z = (cos(u) - 2 cos(2 u)) (2 + cos(v)) (2 + cos(v + 2 pi/3))/4 U and V values are the parameters to represent the surface U- domain of set of numbers [+pi , -pi] V - domain of set of numbers [-pi, pi]
Side view Grasshopper definition:
Top view
Trefoil Surface MATHEMATICAL SURFACE Mathematical equation: x = 3.25 * sin(-3 * u)/(1.25+ cos(v)) y = 3.15 * (sin(u) + 2 .15 * sin(2 * u))/(2.05 + cos(v 1.70 * pi / 2.65)) z = (2.25 * cos(u) - 2.5 * cos(2*u)) (3.5 + cos(v)) * (2 .85 + cos(v + 2.25 * pi / 3.25))/6 U and V values are the parameters to represent the surface U- domain of set of numbers [+pi , -pi] V - domain of set of numbers [-pi, pi]
Side view Grasshopper definition:
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2.2b
Recreating Felix Candela MATHEMATICAL SURFACE |PLANES
Basic geometry - 01 Expression: z = (y²/a²)-(x²/b²)
Basic geometry - 02 Expression: z = a*(x*y)/b
Geometry 01
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Geometry 02
Geometry 03
Geometry 04
Geometry 05
Geometry 06
Geometry 07
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Geometry 01
Recreating Felix Candela Grasshopper definitions Geometry 02
Geometry 03
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Geometry 04
Geometry 05
Geometry 06
Geometry 07
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2.3Transformation
2.3a
Attractor point Single attractor point
Attractor point
Fig. 01 : Hexagonal grid
Fig. 02 : Attractor point on the hexa-grid scales the closest polygons
Grasshopper definition:
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2.3b
Attractor point
Multiple attractor points
Attractor points
Fig. 01 : Hexagon on square grid
Grasshopper definition:
Fig. 02 : Attractor points on the square-grid scales the closest polygons
2.3c
Attractor point Curve attractor
Attractor curve
Fig. 01 : Circles on a grid of points
Fig. 02 : Attractor curve on the grid scales the closest circles
Grasshopper definition:
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2.3d
SDU Building
Responsive facade by Henning Larsen Architects
Fig. 01 : Divide the Surface
Fig. 02 : Extract the points for the triangular panels
Fig. 03 : Assign the rotation angles for the panels using attractor point
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2.3e
Hybrid facade
Responsive facade by IDeEa lab
Fig. 01 : Divide the Surface
Fig. 03 :Extracting the points
Fig. 02 : Select the alternative division
Fig. 04 : Polygon from the centroid
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Fig. 05 : Extract points and move the points
Fig. 06 : Extract and extrude the module
Fig. 07 : Create axis of rotation for each module
Fig. 08 : Rotate modules using remap
Create Hexagonal Grid
Hybrid facade
Recreating with Hexa-grid
Deconstruct and Scale Each Cell
Create Face Each Cell using Scale NU (Scale Non-Uniform)
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Loft the Faces to get the Cell (Create Surface, Simplify Tree, Merge Data and Loft)
Module of hybrid facade
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03
R U L E B A S E D MODELING
3.1
FLOCKING
Natural Phenomena
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Figure. 1 Flocking of birds
3.1
FLOCKING INTRODUCTION
Figure. 2 School of fishes
Flocking/ Swarm is a collective behavior exhibited by entities, particularly animals, of similar size which aggregate together, perhaps milling about the same spot or perhaps moving in masses or migrating in some direction. Swarm behavior was simulated on a computer in 1987 by Craig Reynolds with his simulation program, Boids. This program simulates simple agents (boids) that are allowed to move according to a set of basic rules. Swarm intelligence systems are typically made up of a population of simple agents such as boids interacting locally with one another and with their environment. The agents follow very simple rules, and although there is no centralized control structure dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of intelligent global behavior, unknown to the individual agents. This system is used widely in various fields. In Architecture field, it is used in Urban analysis crowd movement pattern, optimized design strategies, form finding, generating facade skin and many more. Swarm could be generated into an architectural design process.
Figure. 3 Colony of ants
Figure 5: School of fishes when a
prediator approaches
Figure. 4 Herd of sheeps
3.2
Agent
Neighbors
Analysis
X
Components Main components observed in flocking: • Agent - A single entity or character. • Neighborhood - A certain area around the agent, used to look for other agents.
Neighborhood
D
A
Neighborhood
X - Agent’s direction of flight D - distance (measured from the center of the agent) A - angle, measured from the agent’s direction of flight
Behaviors in pattern Three behaviors can be observed: 1. Separation 2. Cohesion 3. Alignment
Separation:
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Alignment: Remain close to neighbors
Cohesion: Avoid collisions with neighbors
Driven factors The flocking pattern is driven by the following factors : Agent : A single entity or character. Neighborhood : A certain area around the agent, used to look for other agents. Velocity vector : An agent’s current velocity. Resultant : The vector obtained from the calculations of the rule.
The affect of three behaviors /rules in the behavioral pattern :
1. Avoid : Prevents agents from colliding with their flock mates • This rule with the shortest range implies a highest impact on the agent’s behavior. • An agent that feels an avoidance force will ignore align or approach forces - Repulsion
Avoidance - shortest range/distance
2. Align: Agents that are part of the same flock to have the same general direction. • If there are multiple flock mates in the alignment range, the boid tries to move towards the average direction of those flock mates.
Aligns Towards the closest agent
3. Approach: Agents move towards the center of the group of flock mates that they can see. • Each agents feels a gravitational force towards the center of all flock mates in its approach range. Approach Towards the center range (holds the group in neighborhood)
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4.0
Bibliography
G ras s h o p p e r
Algorithmic modeling for Rhino
[1] Mathematical equations -- www.mathworld.wolfram.com/ [2] Yuxing Chen ; Swarm Intelligence in Architectural Design [3] Keisam Thoiba Meetei ; A Survey: Swarm Intelligence vs. Genetic Algorithm; International Journal of Science and Research (IJSR); Volume 3 Issue 5, May 2014 [4] Daniel Sinkovits; Flocking Behavior; May 5, 2006 [5] Zebra - Agent based modeling plug-in tutorial [6] Parametric house
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Bhoomika U| DA1903 PA R A M E T R I C S O F T WA R E
2019-21| Sem 01 Digital Architecture
Dr. Bhanuben Nanavati College of Architecture