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HIVE

Mohammad Farzadnia

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Jan 2020


PROJECT INSPIRATION

VIDEO

BEE HIVE FLASHING

One of the main questions of the project was: How is it possible to simulate patterns and algorithms found in nature both in computer simulation and physical prototypes? Hive is a kinetic sculpture which its concept is “bee hive flashing” swarm intelligence. There are certain types of honeybees that create mesmerising waves when they feel threatened . When a wasp or some other large insect gets too close to the hive, the honeybees work together to disorient the enemy. This wave effect makes it difficult for an insect to single out and attack an individual honeybee.

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BEHAVIOUR SIMULATION

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A superficial visual script is written in Rhino and Grasshopper for a flat surface. This script breaks a surface into hexagons and then calculates the distance between them and one or more points and then decides what panels move based on their distances.

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BEHAVIOUR SIMULATION

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MECHANICAL TESTS FIRST TEST PHYSICAL MODEL

The computer simulation is satisfactory for now and it is the time to test if it can be brought into reality. So focus is on making one tile to test different mechanisms. The first idea is to use a servo motor behind a surface (paper) and use Arduino to control this motor. This micro servo then rotates between 0-180 and causes the panel to open as shown.

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MECHANICAL TESTS FIRST TEST DRAWING

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MECHANICAL TESTS SECOND AND THIRD TESTS DRAWING

Several tests were done including piston mechanism to see if there is a better method to use for panels.

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MECHANICAL TESTS SECOND AND THIRD TESTS PHYSICAL MODEL

Left photo is when servo is on its OFF mode and the right one is the ON mode. However, all of these mechanisms are making the process complicated. The best option is to use microservo itself to move the petal without connecting a third part.

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FIRST PROTOTYPE MECHANISM SERVO HOLDER DRAWING

Nut M3

Nut M3

Micro Servo 9g

Micro Servo 9g Screw

Screw Screw: M3/ 12 mm

Screw: M3/ 12 mm Plywood 3 mm

Plywood 3 mm

After several tests, The final mechanism for the first prototype is to make a servo holder that connects them to panels.

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FIRST PROTOTYPE MECHANISM SERVO HOLDER PHYSICAL MODEL

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FIRST PROTOTYPE MECHANISM SERVO HOLDER PHYSICAL MODEL

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FIRST PROTOTYPE COMPUTER MODEL

The goal of making first prototype was to see if there is an integration between computer codes and physical model. This is a 190 * 190 * 75 mm box containing 4 panels. No glue was used in order to make model detachable. The main material is 3 mm plywood connecting with M3*12mm screws and nuts.

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FIRST PROTOTYPE PHYSICAL MODEL

Movements of tiles were not satisfactory and needed to be softer like petaling movement. Also, The gap between petals and base needed to be removed.

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MATERIAL STUDIES HINGE TECHNIQUE

So hinge technique was used in order to bend stiff material (Plywood). Different patterns and density were tested in order to receive the appropriate result.

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PATTERN DENSITY STUDIES: GRAVITY AFFECT ISSUES HINGE TECHNIQUE PHYSICAL MODEL

Part of the interesting things about these panels is that you can change their flexability and behaviour based on the pattern that you laser cut them. There are differe nt parameteres for controlling the pattern including: number of seperator columns, distance between them, offset between cut lines and the original hexagon, thickness of lines. number of lines, ... .

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PATTERN DENSITY STUDIES: GRAVITY AFFECT ISSUES HINGE TECHNIQUE

All of the possible numbers were gathered for creating different patterns. These are 128 tests. However, due to time and budget limitation, only some of them were tested.

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PATTERN DENSITY STUDIES: GRAVITY AFFECT ISSUES HINGE TECHNIQUE PHYSICAL TESTS

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GRAVITY TEST HINGE TECHNIQUE PHYSICAL MODEL

On of the important factors was gravity effects on pattern density. These are behaviour of different patterns under the gravity force. Tests were done in different directions as patterns show different behaviour by changing the rotation of petals.

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GRAVITY TEST HINGE TECHNIQUE PHYSICAL MODEL

Altough, a non-bended pattern is not necesserilly a good pattern since petaling movement needs to also be considered. After several experiments, one finally was chosen. Another set of experiments also were done with bigger hexagons size for understanding the logic between pattern density and petals size. The final code can create a pattern for each size of hexagons.

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SERVO LOCATION STUDIES

In order for the support structure to be designed, a servo holder mechanism must be developed and then positioned behind the petals so that the support structure can be built based on their locations. Several tests were done to obtain the best position and rotation of the motor behind the petal some of which are shown here.

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SERVO LOCATION STUDIES

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PETAL MOVEMENT BY SERVO MOTOR

Here is the servo motor hitting the petal.

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GEOMETRY STUDIES

Top View

Side View

A little actuator was generated and the first thing to do was to work with a simple spherical geometry. In the meantime, project was leading us to expand hexagons around none-flat complex surfaces. Sphere was chosen because it has the most curve surface amongst basic geometries. Shapes were generated around a hemisphere in order to prevent second prototype from becoming both complex in modelling and expensive in cost.

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HEXAGON SCATTERING ON BASIC GEOMETRIES

However, using hexagone generating tools in software did not produce the resault that was expected because of different petals sizes. So penthagonal geometries was chosen to be used for second prototype. The one with least panel was chosen because of both complexity in making and budget limitation.

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SECOND PROTOTYPE COMPUTER MODEL

Top View

Right View

Front View

Perspective

This is the second model which was not built unfortunaetly due to school closure because of Covid-19.

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DESIGN FOR DOME: UNEXPECTED ISSUES WITH SUPPORT STRUCTURE

It bacame clear that as when you go for larger numbers of tiles, it becomes much more complicated to be able to design the support structure and if you have a non-standard geometry where each tile is slightly different to each other, it is extremely difficult to arrange the whole tiles and the whole support structure and wiring and so on and so forth.

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SECOND PROTOTYPE BEHAVIOUR SIMULATION

Here is a simulation of petals movement by Cinema 4D.

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SECOND PROTOTYPE BEHAVIOUR SIMULATION

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FIRST SKETCH OF AN INSTALLATION PROTOTYPE CYLINDRICAL HIVE

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RESEARCH PROBLEM: GENERATING TILES FOR NON STANDARD GEOMETRY

On of the first challenge was that how I take a piece of geometry and breake it down into hexagons. I was trying to develop a generative system that can be applied to any surface so the first step is to generate a variety of mesh surfaces, and I was trying to apply any hexagons to that surface. But there was another problem which is a physical one and that is fitting a structure behind hexagons. How do I build a support structure which is able to catch all of these petals without creating an enormous expensive 3D printed parts and cheap machinable parts to maintain low cost modular approach.

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TESSELLATION & PLANARIZATION STUDIES KANGAROO PHYSICS ENGINE

Kangaroo 2 is a physic engine which is able to find solutions by balancing between input constraints through a series of iterations. A variety of solver types exist within Kangaroo 2. For this projects the ‹bouncy solver› was chosen because it is able to show each iteration.

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TESSELLATION & PLANARIZATION STUDIES KANGAROO PHYSICAL ENGINE ENGINE ACCURACY

It was important to test the ‘length’ component since designed petal has equal edges. Figure 10 shows a written code to calculate the minimum and the maximum length. The numbers before and after relaxation are confirmed to be equal and it means kangaroo can fully find the solution.

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TESSELLATION & PLANARIZATION STUDIES KANGAROO PHYSICAL ENGINE

These are kangaroo tests on a single surface with various parameteres.

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TESSELLATION & PLANARIZATION STUDIES SELF PLANARIZER

Another method is planarizing panels on their locations without using kangaroo. There are several components for this purpose. In a written definition, a surface is tessellated by the ‘lunchbox’ add-on and then the ‘planarize’ component in the ‘Heteroptera’ add-on makes them co-planar. It has both advantages and disadvantages. It does not deform hexagons like kangaroo, and it allows deviation between edges of the hexagons (discontinuity). However, it can be considered as an advantage due to the fact that space is needed between petals. In other words, space creates a solution for planarization more easily.

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TESSELLATION & PLANARIZATION STUDIES

REFERENCE

BFF: BOUNDARY FIRST FLATTENING

Flattened mesh

Filling border by hexagons

Mapping hexagons from 2D mesh to 3D mesh

Boundary First Flattening (BFF) is a free and open source application for surface parameterization. Unlike other tools for UV mapping, BFF allows free form editing of the flattened mesh, providing users direct control over the shape of the flattened domain rather than being limited by whatever the algorithm provides. The initial flattening is fully automatic, with mathematically guaranteed distortion to be as low as any other conformal mapping tool. The method also offers several state-of the-art flattening strategies not present in the normal UV mapping applications which can significantly minimize field distortion, and smooth maps that help eradicate irregularities while maintaining equal texture detail across all cuts. BFF is highly programmable, allowing for immersive mesh editing of millions of triangles. By this method, a definition for flattening a mesh sphere on the XY plane which contains the ‘NGon’ add-on was written in grasshoppe. PROJECT HIVE

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TESSELLATION & PLANARIZATION STUDIES BFF: BOUNDARY FIRST FLATTENING SEAMLESS TEST

Although hexagons do not appear to be distorted, there are some sections of the sphere which are not covered with hexagons because the borders are not seamless. In this test, flattened mesh is uniform which produces a seamless 3D mapping structure. However, the pattern is stretched. The test results explored in this section indicate that the appropriate method of planarization is largely dependent on the particular surface. Consequently, designing the Hive surface is necessary, before a suitable planarization method can be chosen.

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COMPLEX SURFACE GENERATIONS FOR TESSELLATION STUDIES

The simplest method of form generation is a deformed sphere. It was chosen because it is a simple shape which is both doubly curved and closed. A set of spheres were generated by changing the height and the scale of them by random numbers. In this script, when a new random number is generated, it changes mentioned factors and produces a new geometry. At the end, geometries will be baked into rhino viewport. Results were similar to each other and hive needed more variance in the geometry. 4D noise was added to the sphere. The model is coloured to show what part of the surface is convex (Positive) or concave (Negative). If the concavity or convexity of the surface affects the tessellation and planarization of the hexagons, the colour applied on a surface can warn the designer that this part will be deformed. PROJECT HIVE

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TESSELLATION & PLANARIZATION TESTS ON FREEFORM SURFACES

A selection of surfaces needs to be tessellated to determine which methods of planarization discussed in the planarization section is appropriate. Amongst the tessellation tests which have been done on the generation, the BFF method works better on generations. The methods developed in kangaroo were not effective for this type of surfaces since they neither keep the relationship between hexagons edges such as: length and angle nor planarize them. The selfplanarization method can stretch petals, and it depends on the base surface type and hexagons locations on the base surface (Concave or Convex).

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PETAL SCATTERING ISSUES

The petal model is then defined as a ‘block’ object, so that all blocks can be updated simultaneously by changing one of them. It also decreases the size of the 3D model file. This block is then oriented to align with the edge of a hexagon. Although, Hexagon is not included in the block object as each hexagon has unique size.

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SERVO SUPPORT ISSUUES

Because each hexagon has unique size, the base of servo holder (orange piece) does not match with petals.

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BASE GENERATOR BASED ON HEXAGON SIZE

A code was written for producing unique base for each hexagon. In this code, a curve is oriented behind petals. The relevant hexagon top edge is then defined, and lines are created between them. They are all then joined and extruded.

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SUPPORT STRUCTURE CONNECTION STUDIES

34.64

34.64

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34.64 45 34.64

98.97 62.35 65.81 45 65.81

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98.97 98.97

96.99 62.35 34.64 98.97 62.35

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Once the servo blocks are oriented, a support structure can be designed to connect the blocks together. There are many ways to connect hexagons. This image shows different patterns of connections and the length each pattern consumes. This is important because it affects the material consumption, stiffness and weight of the support structure. Fourth pattern was chosen, as it has balance between rigidity and material consumption. Other options were not chosen because they consume too much material. For making the chosen structure stronger, material can be considered thicker.

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62.35 96.99

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3D PRINT SUPPORT STRUCTURE

In the code used to produce support structure, the centre point of the red piece in each block is used to create the chosen pattern. Connected lines are then used to create a 3D surface. This geometry is then used to link petals together. This image shows a sample of connected petals. Thickness of the geometry can be altered within the code to change the rigidity and material consumption.

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3D PRINT SUPPORT STRUCTURE DETAIL, COST & TIME ISSUES

This code is then applied to all petals. This image shows a generated support structure by the code. This support structure; however, cannot be built because 3D printers have a limitation on the size of the object, they are printing. So, the structure needs to be exploded into many small parts, which creates another problem that is designing a mechanism for connecting them together. Moreover, 3D printing all of the support structure can be costly and time consumable. Therefore, a different type of support structure needs to be designed to take these parameters into account.

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SUPPORT STRUCTURE CONNECTION ISSUES CONNECTION PRODUCER

Because plywood is both cheaper and less time-consuming than 3D printing, it was chosen as the main material for the support structure. A code was written to create male-female connection between geometries. In this code, the intersections between a list of ‘Brep’ are calculated, split in half, and then cut out of the geometries.

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SUPPORT STRUCTURE CONNECTION ISSUES HEXAGON ROTATION

This can be used to connect red piece to the support structure; However, they cannot be connected directly together since petals can rotate in space due to the concave and convex parts on the main surface which was used for hexagon tessellating. The petals can be rotated around three main axes: X, Y and Z. It can also be a mixture of these axes. Laser cutters can only cut materials in Z direction. Accordingly, a third piece is needed to solve this problem. The blue piece can solve this problem:

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SUPPORT STRUCTURE CONNECTION ISSUES PLYWOOD CONNECTORS

A definition was then written to create a support structure behind the petals. Curves are produced behind each column of hexagons, and then extruded to be used to create male-female connections. Thickness, length and width of the support structure can be altered.

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SUPPORT STRUCTURE CONNECTION ISSUES HEXAGON ROTATION

This image show the third type of rotation. In this case, even the blue part cannot resolve this connection, because it would require off axis slotting which is not possible on a laser cutter. So, a new piece needs to be designed and replaced.

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SUPPORT STRUCTURE CONNECTION ISSUES 3D PRINTABLE CONNECTORS

Here are 3D printed models that match both the servo and the support structure. Their starts and ends are parallel to both directions (Perpendicular vector on the petal and perpendicular vector on the support structure) which means rotation (Twist) happens in the middle of the model.

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SERVO DRIVER PLACEMENT ON SUPPORT STRUCTURE

As a result, drivers need to be positioned in the support structure. A code was written to create rectangles on the support structure for every 16 petals. To control motors, however a limited number of servos can be connected to a standard Arduino board, and so servo driver boards are needed to extend the capacity. Each driver supports up to 16 servos. Here is a PCA 9685 servo driver with dimensions of 62.5 mm *25.4 mm * 3 mm:

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SERVO DRIVER PLACEMENT ON SUPPORT STRUCTURE LOCATION CONTROLLER & CABLE ROUTING

Driver location on supportstructure can also be altered. Lines are then created between servos and their relevant drivers for cable cost estimation.

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HORIZONTAL STRUCTURE

Horizontal supports are then added to connect all parts together.

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FABRICATION: DIFFICULTIES IN SEPARATING HEXAGONS

Clustering is the process of categorizing data into different lists. There are different methods of clustering such as: Machin learning (K-Mean and Gaussian mixture) and Row-Column. Here is a chosen generation which is clustered. Each row is categorized in one different list and each list has a different colour. Each row has a number starting from 0 at the bottom to 12 (in this example) at the top. They are numbered based on their Z location, and they need to be installed in this order since assembler can’t access inside the model otherwise. So, the first petal in first row is numbered ‘0;0’, and the first petal in row number two is numbered ‘1;0’. At the time of assembly, each petal will be positioned based on their numbers.

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FILE PREPARATION FOR FABRICATION PANEL ORIENTATION

Since Petals are in 3D mode, they needed to be planar so laser cutter can cut the pattern. Component ‘orient’ was used for mapping petals from their 3D location onto XY plane. This image shows petals which are oriented while keeping their cluster details.

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FILE PREPARATION FOR FABRICATION PATTERN PREPARATION

Since each hexagon is different in its size, there was a need for a code to produce pattern for each petal. In this code, curves are produced based on petals numbers which are lasered at the time of assembly, so each petal is positioned in its right location. Additionally, Curves are divided into two different groups (colours) for preventing material from melting in the time of laser cutting.

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FILE PREPARATION FOR FABRICATION HOLDER PREPARATION

Like hexagons, 3D bases needed to be planar on 2d mode. Planes which were used for hexagons orientation were used for making sure that they match together on 2D like 3D. This image shows a set of oriented hexagons with their holders. Like petals, they are clustered and their characteristic match their petals.

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FILE PREPARATION FOR FABRICATION SUPPORT STRUCTURE

Each column and row of the support structure is numbered, and curves for engraving are generated on female connections which are used for assembling. These include the relevant petal and the servo driver pin.

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FILE PREPARATION FOR FABRICATION LASER CUTTER SHEET PREPARATION

For reducing material usage, it is needed to arrange shapes in sheets and compress them as much as possible. Two tests were done with different plugins for nesting, rhino nest and open nest. Both plugins can optimise and nest objects in a same rate. Although, Rhino nest is a bit faster in process. Shapes need to be in a group with their tag curves or otherwise nested individually. It was resolved during the coding process. Cutting curves and engraving curves have different layers and colours as the laser cutters understand which one to cut or engrave on the basis of colour. All the geometries needed to be lasered are collected and nested.

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FILE PREPARATION FOR FABRICATION 3D PRINT FILE PREPARATION

Each piece is numbered based on the clustering section and printed with models. Each piece is exported individually in the code for using in 3D printers.

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COST ESTIMATION

Number of petals

This project focused on low cost freeform kinetic sculpture. The SG90 was chosen as it is the cheapest motor amongst servos, and it works with low voltage power which decreases the power supply cost and the energy usage .Plywood was chosen as the main material for the support structure and the petal since it is cheaper than any other material such as: metal and plastic. For power supply, each servo needs between 400mA (4.8V) and 500mA (6V) which means each servo driver needs to provide between 5-6V and between 6.4A and 8.0A for 16 servos if they work simultaneously. Therefore, power supply needs to be provided. Common adaptors provide 5V 1A and cannot be used for drivers. There are laptop chargers that provide 5V 10A. As a result, one adaptor is needed for each driver. There are DC bench power supplies which convert AC to DC and adjust it to 5V, 50A and even higher currents which can be used instead of adaptors. Prices of these equipment highly depend on the output range. Eventually, number of items, their prices and Total price are calculated automatically inside the code and then exported as an excel file.

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SYSTEM INFORMATION

This is an an example of one-click 3D output of the created system. In other words, the code was provided with a surface and all of these information were produced by pressing one click.

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EARLY IDEA: MAKING A MODULAR PAVILION

The early idea is to model one single surface and then array computationally whereby, a massive installation with complex space can be created automatically.

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MANUAL MINIMAL SURFACE MODELLING

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MANUAL MINIMAL SURFACE MODELLING

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MINIMAL SURFACE STUDIES ON BASIC GEOMETRIES

These are first tries to create minimal surfaces with basic geometries as a base.

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MINIMAL SURFACES WITH DOUBLE CURVATURE TESSELLATION TESTS

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MATHEMATICAL GEOMETRIES CLEBSCH

However, There are certain types of surfaces which can be produced by a formula. In the written code, a mathematical formula is feeded to the system and it produces the surface.

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MATHEMATICAL GEOMETRIES DIAMOND

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MATHEMATICAL GEOMETRIES NEOVIUS

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MATHEMATICAL GEOMETRIES GYROID

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MATHEMATICAL GEOMETRIES INTERIOR SPACE

And imagine the architectural space these types of surfaces can create. So by only making one module, the rest of the space will be created.

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SPACE PRODUCER BY LOCATION VELOCITY

Top view

Side view

Space creator is another method which takes some points as input and then tries to form space around them. In the meantime, It uses velocity (Fields) of each point in order to calculate the surface form. The more points are provided, the more complex surface is produced.

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60 GENERATIONS

60 generations of this type of surface were produced some of which can be considered for the pavilion. But for seperating suitable forms, depends on certain factors.

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TESSELATION OF SELECTED GENERATIONS

This is tessellation of my algorithm on selected geometries from which I was able to select a few interesting element. It becomes much more complex when you are dealing with these types of geometries and I was testing my algorithm to find its weaknesses.

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TESSELATION OF CHOSEN GENERATIONS FABRICABLE HEXAGON STUDIES

Since the hexagons which were developed have specific sizes, on of the factors for choosing the pavilion is if its petals are fabricable or not. Hexagons which were in the possible fabrication domain were seperated and are shown in green colour.

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TESSELATION OF CHOSEN GENERATIONS STRUCTURAL STUDIES ON GENERATIONS

Another factor is if the code can create a support structure for peddals. the images shown are clustered hesxagons which means Hive system can accurately differentiate hexagons. The only weakness that it currently has is that it doesnt understand holes on the model which creates continuous support structure even in empty areas. This needs to be addressed in later versions of the code.

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HIVE PAVILION

Considering all of the parameteres, a pavilion is chosen which contains 4500 hexagons.

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192 CHOSEN HEXAGONS FROM PAVILION FOR FABRICATION POSSIBLE OPTIONS

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TESSELLATION OF SELECTED HEXAGONS

Front view

Front view_Behind petals

Side view

As a code test, 192 petals are chosen from the pavilion for fabrication to see if physical model is a match with computer simulation.

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TESSELLATION OF SELECTED HEXAGONS SUPPORT STRUCTURE COLLISION_TOP VIEW

Hive system has some impairments. It is unable to prevent collisions on the support structure and needs to be resolved in later versions.

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TESSELLATION OF SELECTED HEXAGONS

Front view

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Front view_Behind petals

Side view

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TESSELLATION OF SELECTED HEXAGONS SUPPORT STRUCTURE COLLISION_TOP VIEW

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TESSELLATION OF SELECTED HEXAGONS

Front view

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Front view_Behind petals

Side view

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TESSELLATION OF SELECTED HEXAGONS CHOSEN MODEL

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TESSELLATION OF SELECTED HEXAGONS

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ONE ASSEMBLED PETAL WITH 3D PRINTED CONNECTOR

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PETAL ASSEMBLY

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PETAL ASSEMBLY

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SUPPORT STRUCTURE

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FABRICATED MODEL

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FABRICATED MODEL

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FABRICATED MODEL

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HIVE


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