Andre Agi Portfolio

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AA

AN DRÉ

AG I

BACHELOR PORTFOLIO 2010 -20 13


Table of contents 01

VISITOR CENTRE OPTIMIZED STRUCTURES | FALL 2012 | PUBLIC

A project where we got to design a visitor centre in the city of Trollhättan for people visiting the beautiful area around the water sluices.

13

OPERA HOUSE BACHELOR THESIS | SPRING 2013 | PUBLIC

As my bachelor thesis we entered a competition held by the Acoustical Society of America with the

21

PASSIVE HOUSES BUILDING & CLIMATE | SPRING 2012 | RESIDENTIAL

The purpose of this project was to train the ability to design beautiful and practical residential houses, and explore the relationship between design, indoor climate and energy conservation.

29

KING’S PARK BUILDING & STRUCTURE | FALL 2011 | PUBLIC

In this project we got to design a facility, located in King’s Park in Gothenburg, that would attract people to visit the park which is in todays situation a forgotten place.

33

PARAMETRIC WORK VIRTUAL TOOLS | SPRING 2013 | GRASSHOPPER

Various assignments including form finding optimization, sun studies, load distortion and more.


VISITOR CENTRE The idea of the project is to illustrate and lighten the historical importance of the water locks area at the city of Trollh채ttan by providing the place with a visitor centre. In this centre the visitors can understand and learn about the historical background of the various existing water locks (three locks from 1800, 1844 and 1917) and enjoy the beauty of the landscape. The centre will provide the visitor with a clear idea of how the locks were built and improved upon in different eras. They will learn about the history of the many famous industrial factories which could flourish by taking advantage of natural sources, such as regaining energy through water power. The course program stated that the centre was supposed to placed above or inside of the 1800-year lock without taking support from its walls or the ground.

COURSE YEAR EXTENT EXAMINER SITE TYPE RELATED ENGINEERING COURSE TOOLS

Optimized Structures Fall 2012 7.5 hp Morten Lundh Trollh채ttan, Sweden Public Structure Mechanics AutoCAD, Rhino, Grasshopper, VRay, Adobe Creative Suite 1 | VISITOR CENTRE


Introduction The three locks are surrounded by a magnificent landscape with a rhich topography consiting of mountains, rivers and parkland. A landscape that you as a visitor want to explore and embrace its vast variety of heights. This was my main inspiration I worked under while designing my proposal. By creating a structure that shoots out from the cliff on its highest part I was aiming to give the visitor a mesmerizing view over the whole area. And to enhance the experience and awareness of the height a quite unique connection between the building and the lock is constructed, which lets the visitors travel down inside the mountain presenting them with a thrilling scene with falling water, rocky cave and a special light glow.

2 | VISITOR CENTRE


Concept & Analysis

3 | VISITOR CENTRE


The building

Materials

The building is located on the high part of the 1800-sluice to provide a dramatic view of the landscape, this by letting a considerable part of the building flow over the deep and hollow sluice in a challenging construction.

By using mainly natural materials such as stone, glass, wood and grass the building gets an organic architectural expression which plays in harmony with its surroundings.

The building is integrated with its surroundings by letting some of its main parts be dug in under the ground in the rocky hill and thereby creating a balance between preservation of the landscape and new architectural expressions. The building’s wider part is well attached to the ground which gives a feeling of both holding and pulling back the whole structure and preventing it from “falling off the cliff”. Meanwhile the roof gives you a feeling of freedom by trying to fly up over the sluice due to its lightened angle and tapered shape. This creates a dramatic contrast in shape, construction and expression.

SEDUM (ROOF) The sedum plants need low maintenance and provide instant greening to the roof

IPE WOOD (DECK)

STONE (WALLS)

A type of wood known for its durability, strength, and its natural resistance to decay and wet conditions.

Stonewalls and rocks play a central role in the design to give the building a rustic feel

“Integrated with its surroundings, the building clings to the cliff and provides a dramatic view of the landscape” 2 | VISITOR CENTRE

WATER (INTERIOR & EXTERIOR) Water has been brought into play both on the inside and outside to enhance the dynamic scenes


A-A

Plans

GROUND FLOOR

1:200

.................................

GROUND PLAN Through a well dimensioned vestibule, the visitors arrive at the main hall, a generously open area with unlimited view over the landscape through the curved curtain glass wall and terrace. At the main hall the visitors have direct access to wardrobe, toilets, information desk and elevator and get to rest by sitting down and admire the view. In the middle of the room there is a circular hole, with approximately 2 meters diameter, going through the bottom floor and all the way down to a cave. Looking down the hole you can see the streaming water, arriving from outdoor, falling down along the rocky walls. This tunnel creates a big impact and curiosity for the visitor to travel down the tunnel and it also

2 3 4

5

1

Entrance

2

Staff/Kitchen/Toilet/Storage

3

Cloakroom/Toilets

4

Reception

5

Hole

6

Elevator

7

View deck

1

7

allows a direct contact between the different levels of the complex.

6

The entrance floor is well provided with daylight through the embracing curtain glass walls and from the big hole in the ceiling, placed directly above the circular hole in the floor, which also lets the light travel all the way down the hole to the cave. The elevator and staircase is by purpose placed to hide one part of the view, when entering the building, to get the visitors curious to walk deeper inside the room before letting them discover the outside deck with a panorama view.

BOTTOM PLAN The bottom floor is designed in a way which preserves the feeling that the building is dug into the mountain by letting the cliff form a main part of the surrounding walls and in some parts the cliff penetrates through both floors, giving the interior a rustic felling.

N

BOTTOM FLOOR

1:200

.................................

1

Staircase down to sluice

2

Work room for scientists

3

Hole

4

Entrance/tunnel to cave from the sluice below

5

Elevator

1

2 3

5

4

5 | VISITOR CENTRE


THE CAVE CAVE

You reach the cave either by taking the elevator down from the building, or by entering it from the trail down by the lock. When taking the elevator down to the cave you get to travel alongside the rocky walls with its falling water and experience a tremendous blend of light, water, sound and space.

1:200

.................................

1

Water pit

2

Elevator

3

Trail alongside the sluice

4

Sluice

1

2

3

4

taking the elevator down to the cave you get to travel alongside the rocky walls with its falling water and experience a tremendous blend of light, water, sound and space.

6 | VISITOR CENTRE

HOLE connecting the cave with the building

ELEVATOR for connection between lock and building


The experience The areas character with rich amount of water and beautiful rocky hills with its variation in height was for me the main inspirational sources. That’s why you can see that water, wood and stone have a great impact on my design.

BRINGING WATER INTO PLAY Already when leaving the parking area, the visitor is led by an arranged water path starting from the existing water dam and leading all the way to the main entrance. Just in front of the entrance the water enters a pipe which leads it in under the main floor where it’s then separated into two different directions. One pipe leading it out to the terrace where it falls down into the sluice in a magnificent waterfall and the other one leading it to the big hole, placed in the centre of the ground floor, where it falls along the rocks down to the bottom cave and then out into the sluice.

7 | VISITOR CENTRE


8 | VISITOR CENTRE


Open spaces MAIN FLOOR The entrance floor with its open plan is welcoming and once you step inside you feel in complete contact with the magnificent view of the surroundings through its transparent curtain glass walls. Looking down in to the central hole you will enjoy a spectacular scene which emerges due to the falling water which pours along the rocky walls down to the cave.


10 | VISITOR CENTRE


Rustic interior BOTTOM FLOOR The staircase down to the bottom floor is on one side sweeping along the rocky walls while on the opposite side you have a completely free view of the whole sluice. The bottom floor is designed to create the feeling that you are in a cave. With lots of vegetation and rocky walls together with the connection between both floors through the circular hole and the magnificent view, the bottom floor offers a great experience for the visitor.


Reflections I’m very content with the outcome of this project in both visual appearance and experience. I believe that I reached my primary goals in this project by designing a building that plays in harmony with the landscape and gives the visitors an enhanced and thrilling nature experience. The design process went quite smoothly as I stuck with my initial ideas and sketches. For the first time in a project I never felt any doubt or hesitation over the outcome whereas I was very confident with my concept. Since I had some quite unusual ideas for the landscape experience and wanted to emphasize them, I felt that it was important to visualize them in images. Therefor I spent a lot of time in Vray and Photoshop trying to improve my skills in rendering and photo manipulation. If I had more time, I would have developed the meeting between volumes, material and the landscape. My ambition is to always try to create a peaceful harmony between density/material, color, expression, shape and construction. I would also have made a structure study over the loadbearing parts of the building, especially the roof.

Some of my first sketches for the design

12 | VISITOR CENTRE


SHARDS OPERA HOUSE As my bachelor thesis we entered a competition held by The Acoustical Society of America’s Technical Committee. A competition intended to encourage students to express their knowledge of architectural acoustics and noise control in the design of an opera in which acoustical considerations were of significant importance. During the design we made continously acoustical calculations in collaboration with an acoustical master student. The results affected the design and vice-versa.

COURSE YEAR EXTENT EXAMINER COLLABORATORS SITE TYPE RELATED ENGINEERING COURSE TOOLS

Bachelor’s degree project Spring 2013 15 hp Morten Lundh, Mendel Kleiner Arvid Söderholm, Tor Möller Westmount, Montreal, Canada Public Climate Systems AutoCAD, Rhino, Grasshopper, VRay, Adobe CS, SketchUp, CATT Acoustics 13 | OPERA HOUSE


Introduction Acting as an urban sculpture and a new landmark for the city of MontrÊal, the opera offers to both citizens and tourists a place for exploration, music, events and activities. The distinctive design along with it’s magnificent height separates the building from its surroundings and engages the spectator to explore its various heights and revealing geometric meetings.

14 | OPERA HOUSE


CONCEPT

SITE

The conceptual idea is inspired by the shape and natural beauty of broken ice shards. This idea was taken into reality by picking out the shards created from an impact to a block of ice and then bent and rotated in different ways to form the walls, windows and roof of the building.

The opera has a welcoming approach with the main entrance and all attractions facing the open areas to the northern and estern sides of the site. The site poses a great challenge regarding noise transmission with multiple external sources such as aircrafts, railroad and traffic. The tesson is accordingly planned with great care to meet the strict noise level requirements.

A block of ice is smahed into small shards with a hammer. Suitable pieces are selected to form the shape of the exterior and giving the building it’s organic shape

15 | OPERA HOUSE


ACCESS & ACTIVITIES As a visitor of the opera you are offered a number of activities and rooms to explore. Access, openings and views are orientated towards the eastern site where the water lies as a mirror in front of the opera and the green park on the opposite side.

Café A relaxing area with view over the water and Montreals skyline. Offers both indoor and outdoor seating. On the second floor of the café you have the VIP lounge. A

A

Water and Ice Skating Water surrounds the building on both sides and is connected through a passage underneath the foyer which is visible from both the foyer and the exhibition area. During winter the water pools freezes and functions as a ice sakting rink. People can then ice skate between both sides.

Ice passage underneath foyer and beside exhibition area

Roof Visitors of the opera can reach the roof terrace from several places and enjoy a magnificent view over the city and at the same time getting some fresh air during breaks between acts.

Exhibition The exhibition area on the bottom floor is reached from both sides of the foyer. It’s in direct contact with the ice passage and is lit up by skylight penetrating all the way from the roof of the foyer.

Section A-A


Exterior view of foyer and exhibition area

Exterior view of entrance

Section B-B

17 | OPERA HOUSE


18 | OPERA HOUSE


AUDITORIUM Entering the performance hall the whole volume shimmers in the light shining through perforated Butong, forming the balcony fronts and wall sections. Wooden panels on the side walls bring warmth to the room and offer a tasteful contrast to the ridged stone partitions and the bright ceiling reflectors. The entire auditorium is designed as an isolated inner shell to terminate noise from the lobby as well as structure borne vibrations from the roof and outer balconies. A double door sound lock system with highly absorptive walls and ceiling allows visitors and personnel to move in and out during performances.

1200

T30

seatings

1.5

MULTIPURPOSE

seconds

The balcony fronts consist of Butong, a perforated concrete with a warm, shimmering glow when lit from behind. By controlling the size and depth of the perforations the Butong panels can form both broadband diffusers and low end absorbers.

use

ACUSTICS Fully crowded the performance hall offers a reverberation time of 1.5 s and clarity in the -2 dB range, suitable for music and opera performances. . The sidewalls and balconies are shaped to provide the early reflection pattern necessary to induce a strong sense of envelopment. Variable acoustics allow the reverberation time to be lowered and the clarity to be increased, without compromising the warmth of the sound.

5

0

-3

Sound pressure levels are evenly distributed

The reverberation time shows only minor deviations

A consistent clarity (C80) throughout the

throughout the auditorium, the strength ranges in

vouching for a good balance in material properties

auditorium means suitable weighting in surface

the 3-5 dB region.

and balcony dimensions. Reverberation time (T30)

properties as far as balance between early

around 1,5 s

reflections, scattering and absorption.

19 | OPERA HOUSE


IDEA & PROCESS The process consisted of several iterations where we started to build multiple small concept models of cardboard and had discussions in small groups during a seminar criticism. We then selected the concept we liked best and made more, and more detailed models in bigger scales. In the project’s initial phase, we also had some experimental acoustic exercises and lectures with our acoustics professor Mendel to get an overview of the subject.

The conceptual idea is inspired by the shape and natural beauty of broken ice shards. This idea was taken into reality by picking out the shards created from an impact to a block of ice and then bent and rotated in di.erent ways to form the walls, windows and roof of the building. The shapes does not only inspire the exterior of the opera but also the balcony fronts in the auditorium and in the foayer.

20 | OPERA HOUSE

CONCEPT MODELS


PasSive houses

The purpose of this project was to train the ability to design beautiful and practical residential houses, with empathy in the residents’ daily lives and site conditions and also explore the relationship between design, indoor climate and energy conservation. The site we got was an area south of the Gothenburg district Ruddalen. The area was situated next to the newly constructed project Äppelträdgården.

COURSE YEAR EXTENT EXAMINER COLLABORATORS SITE TYPE RELATED ENGINEERING COURSE TOOLS

Building & Climate Spring 2012 7.5 hp Kajsa Crona, Ola Nyström Alexander Gösta, Niklas Nordström Västra Frölunda, Gothenburg, Sweden Residential Building Physics AutoCAD, Rhino, VRay, Adobe Creative Suite

21 | PASSIVE HOUSES


in collaboration with Alexander Gรถsta and Niklas Nordstrรถm


Idea & Concept Rowhouses are classical types of buildings in the Swedish building construction. They are space-efficient, energy-saving and rational to build. However, they often tend to have a dark center as a result of them only having windows on two sides. The houses in the neighborhood Pine Hill utilizes the rowhouses’ space-efficiency and energy benefits, but challenging its traditional expressions in a design where light flows into the building through a central path. This passage is also the buildings’ heart to which all internal and external rooms connect.

MATERIALS Fasaden domineras av en smal mörkbetsad furupanel. Husen i en länga har olika betsning för att kunna särskiljas ifrån varandra, så att de boende kan känna identitet med sitt hus. Träet livar upp fasaderna och ger husen en varm hemkänlsa. Husets profiler och ljuspassagens innertak är täckta med finkornig vit puts. Materialet ger ett tyngre uttryck vilket brtyer mot den mer påtagliga trädfasaden.

EXTERIOR WOOD

EXTERIOR CONCRETE

INTERIOR WOOD

23 | PASSIVE HOUSES


PASSIVE HOUSE The houses in the area are the passive house standard, which means that they consume a very small amount of energy. Energy requirements are met largely thanks to each house sharing two of the four outer walls. With the family-friendly site and surroundings in mind, the houses are dimensioned to suit families with children. Today, approximately half of all families have two children and a fifth have three or more. To meet the requirements and to fit today’s large families, the houses have been provided with four bedrooms, three of which are large enough to use as playing- or workingarea.

24 | PASSIVE HOUSES


Plans The main entrance is located between the house’s two volumes in the glazed path that goes right through the building. The passage in the middle provides the house with light through two glazed short sides and a glass slot close to the roof which extends along the entire length of the passageway and. The middle passage functions as a hub that takes care of horizontal and vertical communication between all outdoor and indoor rooms. From the entrance, the visitor has an overview of the entire home. Directly to the right is the entrance hall with storage for outerwear and the possibility to sit down. From the hall you can reach a generously sized toilet with shower and opportunity to place a washing machine and dryers. To the left of the entrance is the kitchen with a dining area that is linked to the living room. On the ground floor there’s also a bedroom of 13 m2 which can also act as workroom. Upstairs are the more private rooms. There is a roof terrace which can be glazed into a winter room, a large bathroom with space for a double sink, and three bedrooms of various sizes. The bedroom facing the street has its own balcony. The houses have private gardens on both sides. The front is a little more public and usually also protected from the afternoon sun. Here, a coffee group could be set up which lets you enjoy having breakfast in lovely morning sun. In each front the house has its own carport where there is also space for bicycles, tools and other items. The back is protected from both wind and transparency by placing the houses inclined to the street. There is space for dining table, grill, sunbeds or even a small vegetable garden?

SEKTION A-A

GROUND FLOOR

FIRST FLOOR

.................................

.................................

Living room

17 m2

Bedroom 1

14 m2

Kitchen

14 m2

Bedroom 2

13 m2

Bedroom

13 m2

Bedroom 3

10 m2

Coatroom

5 m2

Light passage

9 m2

Light passage

13 m2

WC

6 m2

WC

6 m2

Terrace

16 m2

Storage

4 m2

Balcony

7 m2

Total

72 m2

Total

SEKTION B-B

51 m2

25 | PASSIVE HOUSES


the inside

From the front side garden an axis can be drawn through the large window with entrance past the stairs and out the glass to the back side. Most of the movement in the house is along this axis. This strong axis between the two garden areas is reinforced by letting the material from the facade continue inside the building. There are lines of sight in the house between the ground floor and first floor via the passage in the middle and the one on the first floor. This part is marked by having a hard stone floor while the surrounding rooms have wooden parquet. The kitchen and the living room are separated by a wall section containing fridge and freezer. You are able to pass this section on both sides which makes you able to have visual contact from the kitchen with the street through the kitchen windows, the hall via the opening to the passage and the rear garden via the living room.

26 | PASSIVE HOUSES


Energy consumption

ENERGY LOSS DISTRIBUTION OVER A YEAR

The passive houses in this area challenge passive houses traditional look but still manages to meet the demanding requirements for energy consumption required for passive classification. It is largely made possible by technological solutions that are installed where energy losses are high. Warm air and water recycles 78% and 55% of from the flow energy. In addition, there are 14 m2 of solar panels on the roof for heating the water.

Heating of water Energy consumption for fans and pumps Heating of air Transmission loss Air leakage

27.2

0,17

8.89

ENERGY CONSUMPTION

POWER DEMAND

U-VALUES

Specific energy is defined as: “The energy which, in normal use, is consumed for heating, cooling, domestic hot water, and operation of the building installations and other building electricity during a normal year“ (bbr). These houses specific energy consumption is 27.2 kWh/m2 and year, compared with a maximum value for passive houses of 50 kWh/m2. The average of the calculated specific energy for homes in southern Sweden is 77 kWh/m2 according to Boverket’s report Monitoring of new buildings specific energy consumption (2009).

House power demand is at its most 8.89 W/m2. To be classified as passive house according to FEBY a power requirement for 10 W/m2 is required. The maximal power demand is calculated from the lowest expected ambient temperature during the year.

U-value, or heat permeability is a measure of how much energy that leaks out through a particular konstruction. For passive houses it is recommended to have very low U-values​​. The total amount should preferably be below 0.1 W/m2K.

27 | PASSIVE HOUSES


REFLECTIONS Designing homes was a new and challenging project that forced one to take many aspects into account. I found it to be very pleasing working in a group as we discussed every idea and problem that we dealt with. This made you reflect on what we humans expect from our living qualities and how different our views on optimal design and feelings are. Something I had wanted to sketch further on if I had more time was the expression of the facades and the layout of the area/neighborhood. The best thing I brought with me from this project was the experience of working and communicating in a group while working towards our design. I also learned to construct houses that meet the requirements of Swedish standards and developed my understanding of cold bridges and construction parts.

28 | PASSIVE HOUSES


King’s park COURSE YEAR EXTENT EXAMINER SITE TYPE RELATED ENGINEERING COURSE TOOLS

The purpose of this project was to design a facility, located in King’s Park in Gothenburg, that would attract people to visit the park which is in todays situation a forgotten place. The facility should provide places to sit down and have a picnic.

Building & Structure Fall 2011 7.5 hp Kia Andersson Kungsparken, Gothenburg, Sweden Public Solid Mechanics AutoCAD, Rhino, VRay, Adobe Creative Suite

29 | KING’S PARK


Introduction King’s Park is an elongated park with a lot of vegetation in central Gothenburg. The park is located along the south side of the moat that crosses the city and is considered in the current situation to be forgotten and is used primarily as a transport route between Vasastaden and Kungsportsplatsen. Despite its very central location, it offers good opportunities to find secluded places where you can escape from all movement and noise of the city, but due to the lack of places to sit down at it becomes almost a forgotten park. The facility is located in the eastern part of King’s Park adjacent to the moat and the Basar bridge where a lot of people are flowing past. The place is relatively open and flat with some pompous trees and a beautiful view of the canal against Kungsportsplatsen and the Market Hall.

30 | KING’S PARK


Plan The buildings’ distinctive entrance welcomes passing people with open large areas containing seats facing north so you can enjoy the tranquil view and the noise of traffic on the avenue is foreclosed by the building in the back. The area extends over 60m and is “encircled” by steel arches that protect against wind and noise. They also provide the facility’s north side with seating when they cut the ground, creating a terraced lawn. The main building has two entrances, a main entrance where you enter directly into the dining area. The toilet- and dining area separated by a corten wall that cuts the building and divide the surface into two rooms. Behind the dining area are all the staff rooms such as a kitchen, storage, cleaning and staff toilet. During warm periods, the facility offers opportunities for outdoor dining in the courtyard.

SEKTION A-A

N 31 | KING’S PARK


REFLECTIONS It was during this project that I for the first time came in contact with 3D modeling and parametric design within Rhino. To visualize and express your ideas in this program was a true relief compared working in other programs. By parameterizing your objects it made changes in you design not so painful since everything was linked together. I was very satisfied with the outcome considering this was my second architecture project. Especially I was pleased with the relationship between the different geometries and materials, how walls and volumes interact and intersect in creating balance and space. This was also pointed out to me during the critique as I received very good response from the teachers. However, I’m not convinced in my attempt on creating a place that would attract more people into having a picnic in the park or just come to relax. This because most of the facility is enclosed by the curved wall which gives it a “private” feel. But I believe that this could easily be fixed by dividing the curved wall and making its elements more consistent and spread out over the park.

32 | KING’S PARK


PARAMETRIC WORK Following are some selected assignments from a course named Virtual Tools in which we studied how computer programs and programming can aid in designing advanced forms and parameterizing objects in architecture. By combining a 3D modeling software with mathematics we acquire some very powerful tools which can help creating a design/object defined by initial algorithms fulfilling partial demands. This is yet another example on something unique for our education. The course focused mainly on Grasshopper (a plugin for Rhino 3D) and C# (C-sharp) which we for example used to study the amount of solar radiation on a faรงade as well as coding our own components to recreate solutions to various buildings across the globe.

33 | PARAMETRIC WORK


Facade Optimization In this assignment we studied how the geometry of a face can be changed based on its proximity to a given test point. Attractors can be used to create field effects of gradual change. The idea is that geometry will change its size or form based on its distance from a point. The further the object is from the point, the larger or smaller it will get. We also made a sun radiation study of the facade by letting a given point circualte around the facade and “shooting“ vectors against it which was then recalculated as radiation/ energy.

Chris William’s roof at the British Museum Inspired by Chris William’s engineering work with the British museum’s courtyard roof (the roof was designed mathematically) we were given this task in the course linear algebra, a course focusing on optimization and mathematical visualization. Just as two-dimensional curves can be shaped differently depending on how you define equations, you can likewise control the shape of a surface mathematically. With the boundary condition that the surface had to rest on the unit square, it was necessary to construct the surface so that the function value z(x,y) is equal to 0 where x = 1 or y = 1 (independently). Another requirement was that the z-value of the function had to be above zero. After having sketched the roof mathematically the form was structurally optimized with a dynamic relaxation-script. This script also placed diagonals in the grid in an optimized way. 34 | PARAMETRIC WORK


Recreating King Abdulaziz center The objective with this assignment was to recreate a simplified version of the script used to generate the facade geometry for “King Abdulaziz center of knowledge and culture” by coding our own components in grasshopper using C#. The picture to the left shows the concept for the facade which is based on wrapping a steel wire around a pebble stone. This wrapping pattern is mimicked by repeatedly offsetting a closed curve initially lying on the “stone”. In order to simplify the task slightly we performed the offset on an open surface.

EXCERPT FROM CODE //Adding desired number of evaluation points along the curve for (double i = tMin; i <= tMax; i += stepSize) { //Calculate each point at value i Point3d point = startCurve.PointAt(i); //Calculate curve tangents at eval points Vector3d tangent = startCurve.TangentAt(i); double u = 0; double v = 0; surface.ClosestPoint(startCurve.PointAt(i), out u, out v); Vector3d normal = surface.NormalAt(u, v); //Cross product Vector3d crossVector = Vector3d.CrossProduct(tangent, normal); crossProducts.Add(crossVector); //Moves the point Vector3d crossVectorDist = Vector3d.Multiply(crossVector, offsetDist); Point3d offsetPoints = Point3d.Add(point, crossVectorDist); //Projects the offset points onto the surface surface.ClosestPoint(offsetPoints, out u, out v); Point3d projSrfPoints = surface.PointAt(u, v); curvePoints.Add(projSrfPoints); }

35 | PARAMETRIC WORK


Dynamic Relaxation In this assignment we looked at how to use dynamic relaxation in order to form find a pure compression structure (catenary). The component we created performs a form finding for a sequential row of line elements by solving the differential equation of motion through a iterative process stepping through time with small increments.

anchor points

EXCERPT FROM CODE Vector3d zeroVec = new Vector3d(0, 0, 0); nodeForce.Add(zeroVec); nodeAcceleration.Add(zeroVec); nodeVelocity.Add(zeroVec); for (int j = 0; j < (nodes.Count - 1); j++) { nodeForce.Add(zeroVec); nodeAcceleration.Add(zeroVec); nodeVelocity.Add(zeroVec); barForce.Add(zeroVec); } CalcSlackLength(nodes, slackLength); FindLockedNodes(anchorpoints, nodes, isLocked); for (int i = 0; i < iterations; i++) { CalcBarForce(slackLength, nodes, barForce, stiffness); CalcNodeForce(isLocked, barForce, gravity, nodeForce); CalcAcceleration(isLocked, nodeForce, nodeAcceleration); CalcVelocity(dt, nodeAcceleration, nodeVelocity); CalcPosition(dt, nodeVelocity, nodes); } formFoundCurves = UpdateGeometry(nodes);

36 | PARAMETRIC WORK

FORM FOUND STRUCTURE Initial grid Relaxed structure


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