ARCHITECTURE DISSERTATION - SENSE OF SPACE AND TIME IN DESIGN THROUGH TOPOLOGICAL FORMS

B.Arch DISSERTATION 2019-20

Hemant Jindal

SENSE OF SPACE AND TIME IN DESIGN THROUGH TOPOLOGICAL FORMS

Bachelor of Architecture DISSERTATION - 2019 School of Architecture and Landscape Design Shri Mata Vaishno Devi University

Entry No.: 15BAL013

Guide :

Ar Aditya Kumar Singh, Associate Professor, SoALD

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SMVDU

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CERTIFICATE This is hereby certified that this Dissertation entitled SENSE OF SPACE AND TIME IN DESIGN THROUGH TOPOLOGICAL FORMS, has been submitted by Hemant Jindal, Entry No. 15BAL013 in the partial fulfillment of the requirements for the award of the degree of Bachelor of Architecture, Session 2019-20.

Recommended By: Ar. Aditya Kumar Singh

Ar Anoop Sharma

(Dissertation Guide)

(Dissertation Coordinator)

Accepted By: (Head - SoALD) Jury Members:

(1)

(2)

(3)

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DECLARATION This Dissertation, entitled SENSE OF SPACE AND TIME IN DESIGN THROUGH TOPOLOGICAL FORMS is being submitted as partial requirements of B. Arch. Study during ninth (9th) semester by me for evaluation. The contents in this Dissertation are either my own work or compilation of data / information as gathered from case studies / survey as indicated / referenced and permitted as per rules.

No contents of this dissertation has been copied from any other dissertation / report in part or full. If at any stage it is found that this is significantly copied from any other resource, the evaluation of this reports and accordingly grade award shall automatically stands cancelled.

(Signature of Student) Hemant Jindal Entry No.: 15BAL013 B. Arch., Semester IX Session: 2019-20 School of Architecture & Landscape Design Shri Mata Vaishno Devi University

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The originality of this Dissertation has been checked using appropriate plagiarism checker / software and following parameters are compiled (tick one).

Plagiarism / Copied Contents: Not more than 10% Originality / Uniqueness: More than 90% (Certificate attached as Annexure-1).

(Signature of Student) Name: Date:

Counter-signed

(Signature of Guide/Supervisor) Name: Date:

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PREFACE Through this dissertation, I aim at focusing on implication of digital tools in architecture so that architecture rectify its regional identity in contemporary times.

There are several examples in & around the globe where computational techniques are reforming the architecture and the surrounding environment.

After the industrialization, there was a paradigm shift in architecture practices, globally. Mass construction took its pace and several identical buildings came up that dominated over the vernacular built forms. This shift is followed by another shift with the revolution of computational techniques globally.

Homogenized buildings are coming up with same kind of algorithmic approach, thus destroying their regional variations and regional identities.

This dissertation studies the role of digital design and regionalism (together) in the architecture of today and draw out the conclusion for: How the latest digital techniques can be used to rediscover the local identities?

How sensibly we (architects) should take our next steps in the new era for the overall betterment?

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ACKNOWLEDGEMENT This dissertation has been a very crucial element for me, due to the sensitive nature of its topic and study. Regardless of the risks, there were pillars supporting my work who continuously pushed me and helped my work reach this level, despite the criticisms. l'd firstly thank my Dissertation Guide Ar. Aditya Kumar Singh Sir for their undying efforts in realizing my dream project. They have spent a great amount of time in polishing and streamlining my thoughts.

This project with its unending boundaries even caught the interest of my former mentors in office namely Ar Felix Amiss .

I thank them for sparing their time and putting in valuable comments to enrich my work. Nothing is possible without the cooperation of loved ones. I thank my parents Annu JIndal for showing true confidence in me.

I also thank my friend Anindita Shrivastava for always being there.

HEMANT JINDAL

Kakryal, Dec ‌., 2019 Hemant Jindal

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CONTENTS Contents 1 INTRODUCTION....................................................................................................................................... 1 2 SYNOPSIS.................................................................................................................................................3 2.1 INTRODUCTION:...............................................................................................................................4 2.2 AIM:..................................................................................................................................................4 2.3 OBJECTIVES:..................................................................................................................................... 4 2.4 METHODOLOGY:.............................................................................................................................. 4 2.5 LIMITATIONS AND SCOPE:............................................................................................................... 5 3 LITERATURE STUDY................................................................................................................................. 6 3.1 S P A C E

P E R C E P T I O N - E M O T I O N S................................................................................7

3.2 ARCHITECTURE AS A STORY............................................................................................................. 8 3.3 SENSE OF SPACE WITH RESPECT TO THE OBJECT......................................................................... 11 3.4 S C A L E

AND

A N T H R O P O M E T R Y................................................................................12

3.5 I M P O R T A N C E 3.6

ROLE

OF

OF

S C A L E.............................................................................................. 13

S E N S E S........................................................................................................... 14

3.7 I L L U S I O N.................................................................................................................................. 18 3.8 M E M O R Y...................................................................................................................................23 3.9 M O B I U S 3.10 K L E I N 3.11 E U L E R’S

S T R I P.................................................................................................................... 26 B O T T L E....................................................................................................................29 C H A R A C T E R I S T I C S.......................................................................................31

3.12 A M B I G U O U S 4CASE 4.1

C Y L I N D E R............................................................................................... 35

S T U D Y............................................................................................................................... 36

ENDLESS

H O U S E..............................................................................................................37

4.2 C A P P A D O C I A.......................................................................................................................... 41 4.3 F J O R D E N H U S..........................................................................................................................43 4.4 H A R B I N

OPERA

H O U S E................................................................................................ 46

5 COMPARITIVE ANALYSIS OF CASE STUDIES.......................................................................................... 49 6 CONCLUSION.........................................................................................................................................52 7 REFRENCES............................................................................................................................................ 55

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1 INTRODUCTION

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ABSTRACT The concept of designing space is one of the most important feature in architecture.

The conventional way of designing is development of architectural space in three dimensional Euclidean geometry. In recent years, the concept of space that is different from three dimensional Euclidean geometry, which deals with the change of perception and movement of body, opened a new perspective of viewing architecture and space.

A certain kind of fluidity that topological surfaces provide helps to blur the identity where roofs and grounds collide. Openness, continuity and deformability can be achieved in a design with the process of topology.

This dissertation is to explore the relationship between sense of space and time in architecture by analyzing the non-metric concepts of architectural design theories.

This study will help to introduce controlled complexity and creativity which will result in forming a unique architectural design strategy. The principles of this study will continuously help to indicate the possible directions of developing architectural design.

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2 SYNOPSIS

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2.1 INTRODUCTION: The continuous deformation of building envelope without destructing the spatial sense and geometrical identity.The term ‘Abstract’ and ‘Vector’ representation of a notion of space, is directly a result of topology when it comes to design.

2.2 AIM: To study and understand the architectural spaces and volumes by exploring non-euclidean Spaces and the interaction between topological surfaces.

2.3 OBJECTIVES:

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To study how oblique axes helps to enhance the sectional perspective of a design.

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To study the concept of merging building with landscape to create a single entity.

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To understand the spaces having varying medians of anthropometry and anthropogenic forces.

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To understand how topological form creates a understanding of spatial design through continuous surfaces.

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To study the notion of calculus based forms that alter the geometrical behaviour of Cartesian spaces to flexible spaces.

2.4 METHODOLOGY:

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Selection of topic

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Exploration and understanding of the topic

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Formulation of aim, objectives, scope for the area of study

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Collection of data

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Analysis of data for developing design language

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Literature study

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Case study

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Analysis of literature study and case study

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Prepration of final report

2.5 LIMITATIONS AND SCOPE:

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The scope is limited to the study of fludic organic spaces in three dimension sectional approach.

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The study includes the understanding of dynamic relationship of form and space in Mobious strip and Klein bottle concept.

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Design using digital technologies to engage motion in architectural forms with multiplicity of vectors.

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The scope of the study deals with the volumetric properties that are under continous transformation due to the play of light, shadow and varying isometric perspectives.

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3 LITERATURE STUDY

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3.1 S P A C E

PERCEPTION-EMOTIONS

Architecture must involve a sense of wonder and spiritual satisfaction. Architectural space has the power to touch us with the intimacy, sense of beauty and memorial experience.

Architectural design must create an interest for the people it contains.

We have adopted the Cartesian grid pattern for designing as the architectural bible.

By confining our self within the cartesian, we may lose the sense of multiple nodes of experience within a space.

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B.Arch DISSERTATION 2019-20 By using only cartesian grid (Euclidean space) for architectural design, every other spatial perception of a place (awareness of your relationships with the environment around you) started resonating functional instead of emotional, which only resembles different kind of barcodes

(For ex: we remember 90% of current buildings and places only by their functional aspect like we remember co-operate buildings as its Amazon's headquarters or its a DLF mall instead of any its spatial characteristic, which is not the case with Stone Henge or Church Of Light). A space within a design must connect with thoughts, eyes, and bodies of the user.

3.2 ARCHITECTURE AS A STORY CHICHU

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ART MUSEUM

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B.Arch DISSERTATION 2019-20 Everyone loves story because they make a person think and most importantly imagine.

Architectural space must be designed to take us along for a ride inside our mind and soul.

A building must ace as a stage and spaces inside a building as artists. All these ingredients combined must create an artistic expression inside the mind and left the user to visualize and enjoy the space emotionally.

Chichu Art Museum is a perfect roller coaster to take you through the magical world in real life.

“Laughter is timeless. Imagination has no age and dreams are forever�

Entry space to the museum

High degree of enclosure and contrast

Scale shift - Explicit memory

Exposed exit to revive the contrast

ARCHITECTURE AS CRAFTED ART Art is a thing that can be created and seen in infinite ways. Every art is unique from each other and one can perceive many different things from a single piece of art and the same must be the case with architectural design. While designing a space, the architect has to come up with a new design idea which amplifies the overall design. Every architect has a different style which is unique in some sense. With time every artist develops a particular

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B.Arch DISSERTATION 2019-20 stroke style which later becomes their identity. In the same way, every architect evolves a particular design typology that differentiates their design from every other architect and designer.

Yu Qingcheng Gallery / Architectural Design and Research Institute of Tianjin University

THE VISUAL NATURE OF SPACE Perceiving and analyzing space is subjective. We experience space as a art of body and mind. With the help of our eyes, we try to consciously probe a space while making thousands of computations every second in our subconscious mind. The human eye has a very precise lens with a focal length of 22mm which helps us to consistently visualize and experience space in a self-adjusting readable way.

With the virtual and actual movement of the lens in our eye, we are allowing our mind to distort the physical space subconsciously by switching between different frames obtained from different visual points. This feature allows us to tell a lie to our minds about experiencing a space in a way that we have never seen before.

Normal

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Wide-angle

Telephoto

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3.3 SENSE OF SPACE WITH RESPECT TO THE OBJECT Space is Physical, Perceptual, Visual and is a Relative phenomenon that is solely experienced by the viewer. We visualize space around us by the help of egocentric coordinate system which comprises of mainly two axis that are primary and secondary. The primary axis is the visual axis which generates in relation to the movement of the body which is mainly straight and forward. Secondary axis, on the other hand, is based on our factual knowledge of gravity and its effects on the surroundings (Everything that goes up must comes down). In simple language, the Primary axis is the back and horizontal plane and the Secondary axis is our top-down vertical plane.

(Egocentric means taking our self as the center and perceiving every other object in relation to the body axis of self)

SELF

SPACE

OBJECTS

We perceive the world in relation to objects and objects in relation to our body. In egocentric system, every time we visually see an object our mind maps it in relation to our centric body. But what our mind never maps is space itself. It concludes that space is only perceived in relation to the object as objects help us to visualize the depth perception of space in the perceptual field.

If you have to imagine a virtual point in space inside your room, it is easy to visualize the point and make a connection of the virtual point with real observatory points. You can go out of the room and come back after a while and you can still catch the imaginary point in space with almost the same coordinates. Now imagine that you are in deep space with nothing there, just you and all the darkness. This time it will be impossible for you to visualize a virtual point in space as nothing is there to give you depth perception and to analyze the coordinates. Let's take another location that is under the water in a sea, again

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B.Arch DISSERTATION 2019-20 try to visualize the same kind of virtual point in the space full of distracting water waves.

We know that space coordinates are not changing but when we try to do this exercise, it will be very hard for us as water waves are constantly distracting our perceptional sense and we will experience an illusion of shifting coordinates, which we know are fixed and not shifting in real life. This experiment proves that everything we see and visualize is not a fixed frame. They are mostly images inside our brains that we build according to our surroundings. The environment and objects that surround us play an important role in evoking a sense of space around us.

Space perception is mainly analyzed molecular perception cues that are 

Retinal image formation: We determine an object by how large or small it appears to us. If an object is closer to us than it will cover a maximum portion of the retina and if it is far than it will cover very less portion, allowing space for surrounding to fit in. With time, we experience objects from many different locations and we get to know the average sizes of different objects which tells us that it is an object that is moving with respect to egocentric coordinates, it is not the size that is changing.

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Visual height: It is the vertical length that is observed by the user. Vista of a frame is divided into two sections namely ground and sky. Object which is closer to the ground is at less distance from the object which is more closer to the dividing horizon line.

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Motion: Closer objects travel fast than the objects that are far. For ex - buildings pass very fast because they are close but the clouds tend to pass very slow from the frame.

3.4 S C A L E

AND

ANTHROPOMETRY

Anthropometry is an identification tool that helps us to understand human bodies and also human physical and psychological cues. It involves the study of physical properties like the size and shape of the human body and helps us to alter the surroundings systematically.

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B.Arch DISSERTATION 2019-20 While designing a building or space, human body dimensions and motion capabilities are the key factors that help us to mold the structure accordingly and differently. Architectural space must be designed in a way that it constantly adapts and modify according to the user, not the vice-versa. Anthropometry helps us to set up ergonomic principles that help us to design spaces that will link to the user with a sense of belongingness.

â—?

Static anthropometry: It is the measurement of objects in space that are always static regardless of the movement of the body.

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Functional anthropometry: Functional anthropometry deals with the use of space which is visited and operated by the user. For ex - a person entering a museum and experiencing the space by moving here and there freely. For a smooth transition of the user, the spaces inside and around the museum must be precisely correct and internal spaces of the museum must provide maximum comfort to the user.

Anthropometry deals with the comfort of the space, equipment in the room and functions of the building. Anthropometry is physical as well as mental and it varies with age, race, and gender. By changing the scale of the surrounding object in a single axis or multiple axes, we are also altering the functional anthropometry that may lead us to a completely different experience for the one that was intended during the design phase.

3.5 I M P O R T A N C E

OF

SCALE

The visual perception of space is mainly related to our relationship and knowledge of space. Sense of scale is mostly perceived by visual and haptic touch feedback. Scale changes as we shift from the object along a primarily egocentric coordinate axis. This gives us three different kind of variations that are small, medium and large.

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Small /Near: This is the best suitable scale to understand the complex geometry of topological surfaces. It is easier to build a mind map of the object when we can feel and see the entire object at once by taking it in the hand and grasping it instead of feeling individual pieces one by one.

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Large /Far: When we see an object from far away, every detail started to fade out and blend with the surroundings. The complexity of architectural form smoothens up, therefore high complexity and contrast in forms with standing out colour shade is important.

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Medium /Middle: It is the distance where we experience and understand one part of an object at a time. The strong texture is important if we intend to provide clarity to the user for understanding the architecture and spaces related to it. Topological forms are the best as they are the most effective at this scale because they go beyond the perception of the human mind and scale.

3.6 R O L E

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SENSES

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B.Arch DISSERTATION 2019-20 Architecture has the power to evoke and tickle human senses and mind, disturbing the mind map and make you feel things that are not there or within you. For example, different architectural spaces can make you feel different just like magic mirrors. By crossing through a path, you may feel smaller or bigger, fat or thin, blind or deaf and all this can happen within a path with different iterations of architectural spatial sense. Architectural space can make you run faster or move slower and also can enhance your mental ability to perform.

It is possible to create different chambers that will play with different senses to provide different subtle and vibrant experiences. First is -

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Sound - Anechoic chamber: What it does is it absorbs all the sound-wave and absorb them without any reflection or deflection back to the source. Sound vibrates within the panels and compresses to negligible amplitude. In architecture, it is purely selective to design or enter a room that can harness complete silence but once a person enters the chamber and spend a couple of hours there, he will be sensitive towards the unperceived sound that was not visible apparently. This chamber absorbs all the sound from the surroundings and leaves the user hyper-conscious of sound within his body like the movement of blood, the sound of beating heart and movement of muscles.

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Sight - The black chamber: This chamber is detailed and installed by Ar. Tadao Ando in which a screen with eerie gray light is installed which initially will not be visible but with time pupil starts to adjust according to the darkness and space around us starts to make sense. This experiment shows us the power of light and darkness that can be mastered to enhance the powerful spatial experience.

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Smell - The power of scent: Smell is the sense that resonates with the memory and different parts of the brain. Different artworks of scent can evoke different feelings and sensations inside our brain.

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Taste: The space with dark wallpaper and chocolate texture and virtually trick your mind with a memory of you having chocolate and this will relate you to certain memory and feeling that is purely generated because of space.

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Touch: touch is the most underrated sense among these. It is highly sensed by the people who are deaf and blind that tells us that while roaming around a space or in a building, the sense of touch is highly crucial. A building should not be an unintended maze and one should move from one space to another with minimum efforts through the sense of touch.

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3.7 I L L U S I O N Illusion inside a space creates excitement and magical experience. Illusions are capable of producing an experience that can alter the thinking process. What we consider true depends on how you look at it. Reality is within the space and illusion starts to play when we alter these spaces. When we see the space or feel the space, it is as if it is looking at you, sensing you, and in reality we are the one who’s being experienced by the space.

Space is completely dependent on user. The interesting factor lies in the thought that what is between these walls? It’s just sir, yes, but how we create experience within this air and nothingness, without any alien object?

The spectator’s eye is very crucial point. While creating illusions, we have multiple points of reference to visualize and experience the illusion. It is a possibility that a person next to you doesn’t see your illusion because the eye is somewhere else. The space and its illusion is totally dependent on you being there, when we leave the space, these is no illusion inside the space and also no act or art. It’s in sleep mode during this time.

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B.Arch DISSERTATION 2019-20 Space should speak the language that people could relate to. The illusion in the space always put two questions in mind, how and why. It is designers work to deal with ‘why’ and after that ‘how’. and for the user there has to be only one thing in mind and that has to be the excitement full of wow. Illusion in space is just to make eye and brain tricky Glass: Sensory rich glass installation inside a space can divert our mind from reality, without letting us know about it. Monochromatic light from behind the glass, lighting up the room, creating an illusion that may not be the center show of the space while anyone sense the illusion. Lets take an example of red rose in a room with glass ceiling and semi-circular ring shaped light, illuminating the room creating an illusion with the glass ceiling, as it appears to be a circle. So when we enter the room from a dark transitional space, first thing that catches our attention and what we think is that the whole show is about the rose that is not red. Where is the colour of rose? Is it washout? How? After all this mind work, we finally realize that it was all about the play of glass which is making us feel space bigger and than it’s about the monochromatic light that is sucking up all the colors. It’s not only rose, but we ourselves are monochromatic in that room, but it took us a heavy mind work to realize that illusion.

Change of horizon, surroundings and speed of time or light can play with our mind. Let’s imagine that we are walking in a corridor and passes through a mirror in which the reflex action is slower than the actual movement and the reflection in the mirror is flipped vertically. For ex: if a person rotates his left arm in a circular motion in front of a mirror than the action reflected in the mirror are not the same as the actual action. This simply

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B.Arch DISSERTATION 2019-20 generates a curiosity inside the mind and tell us that something is different. Some illusions just look complex that consists of a very simple but effective tweak that alters the reality.

Sound is the next big factor that helps to modify the sense of space and time or simply generate sense inside a empty space. The illusions of space or within a space have to be good enough so that every user can feel and sense those illusions without over explanation, otherwise it doesn’t give the sense of smartness to the user.

Some illusions can create the question that something is just not right. For ex: if we see an iceberg inside a room, we may think that it can be an artifact but when we touch it, we get to know that it is an real iceberg . ‘its cold’ and we know that iceberg is cold because it’s ice, but we refuse to accept it for a second because of the unmatched surrounding conditions that are required to sustain the ice. But this change is behavioral that is much more emotional sensitive because it tricked the mind.

Different kinds of spaces with illusion●

Illusion of scale: Library of Celsus, settled in the Roman city generates a illusion of scale because of its architectural design style and limited site area with compact surroundings, building appears to be big than actually it is.

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Illusion of solidness and weight: Some of the architectural elements like cross vault domes from Istanbul and elements from Byzantine architecture able to fell like suspended in the air instead of there massive structure, weight and scale. Because of the hidden elements that hold these structures,, space appears to be less heavy and gives a sense of more openness and lightness.

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Illusion with mystery: Designing a space that is seen normal from one side and appears to be distorted from other angles can change the perspective of user and generates a mystery of illusion. ‘A house to die in’ project by Snohetta architects is a perfect example of illusion with mystery.

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Triangle mystery: lets say we have to create a triangle in which the some of interior angles has to be greater than 180 degrees. This is mathematically incorrect but with the help of 3d illusion, we can create a art that appears to be a normal triangle but in

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B.Arch DISSERTATION 2019-20 reality, it will be an inflated triangle from the centre. For ex: if we draw a triangle on the globe in which equator will be the bottom and lines from north and south poles will be the side edges or if we draw a triangle on a balloon and then inflate it with air than the triangle will have a sum of interior angles more than 180 degrees.

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Illusion of landscape: Spatial illusion In a space can be created with the help of ‘borrowed landscape’ technique. We can intentionally frame the view, vistas and scenes to become a part of the space itself, creating a illusion of extended axis of the space.

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Perspective illusion: This illusion of distorting the pure vision to make spatial appearance more satisfactory to the eye using design concepts is the oldest form of architectural illusion. Which is false appears to be true and spaces fell different from what actually are. Parthenon is a well know example of this illusion. This illusion can change the sense of a space, making you feel small, big, fat and many others things that are not real.

3.8 M E M O R Y Human mind is a time machine. Past, present ,and future. These are the three different time-lines that the mind deals with. What we have already experienced and have a memory inside our mind is past, and what we are going to experience is future. Past experiences and future imagination. For ex: imagine you are in a building and you have already covered half of the building, observing spaces, colour, form, shape, lighting, activities and function.

All this helped you to develop a taste for the upcoming part of the experience that lead you

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B.Arch DISSERTATION 2019-20 start imagining the space that you will going to experience. In this case, the memory of covered space is the experience in the past and the imagination inside the mind about the upcoming part is the future. To create the sense of extreme remembrance, a strong contrast in terms of spatial experience of the upcoming space can change the experience, thus creating a node of time in space with respect to memory.

Mind is the tool that helps us to feel and sense a space. Mind has the power to remember a space and its essence. A user’s past experience can be touched by architecture in a beautiful sense through human emotions and varied senses. Space and time also has the power to create a zone that can allow user to generate new meaningful experiences that can be memorable.

SENSE OF SPACE AND TIME THROUGH MEMORY: In understanding architecture, there is a very important role of memory that let us experience new things and relive the past. To create this experience, we need to understand how architectural spaces are designed in a way so that they are capable of engaging a human mind within itself, impacting the ability of decision making and psychological perception.

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MEMORY- SENSE+EMOTION: Architecture has the power to create a memory and to help us remember a memory. An architectural space helps us to experience moments by creating an environment that helps us to add sense and emotions to preserve a memory.

The function of space and time is dependent upon memory. We fell the architectural space through multiple images, just like a memory. Memory and architecture has same process of understanding. A space can be recognized by what is seen through eyes, felt through the turning head and experienced by the moving legs.

Architecture and memory are connected and interdependent on each other to make nodes between space and time.. the gap between past and present blurs and ties with each other through images.

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3.9

MOBIUS

STRIP

Mobius strip is three dimensional pattern with infinite loop which has no boundaries. It doesn’t have a start or end point. To reach the same point in time on the mobius strip, you need to travel twice the length of the actual strip. By the end of the lap, the user will cover both the faces of the strip facing up and down. This loop is generated because of the twist generated between the strip, flipping the path for the entire loop.

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B.Arch DISSERTATION 2019-20 When a cylindrical strip is made from a piece of rectangle by joining two shorter ends with same orientation, then uni-plane movement is there without any sense of space and time.

Now when the same strip is connected but with a flipped end in the opposite direction, then a multi-directional vector plane is generated which contains time node in non-euclidean geometry.

It is not possible to create this space time node in two dimensional euclidean geometry without connecting the edges. By adding time node, the geometry is now three dimensional because of the twist generated which can only exist in non-euclidean space.

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TENDRIL

GALLERY

From the architect: “Flexible mould technology & precision engineered hempcrete bricks forms the structure of this Hempcrete coiled wall. Four meter high glass windows weave between the forms 12 arches opening out onto a 360 degrees terraced area. A twisting spiral staircase becomes the sculptural centre piece which leads you up onto the roof terrace. The top of the coiled wall forms a natural barrier to the perimeter of this roof terrace without interfering with the view from this space. The gallery sits on an island accessed by a path that connects the architecture to the main land”.

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TWINE

HOUSE

From the architect: “A series of organic forms [that] twist and meanders together to form a series of arches that house the minimal glass interior spaces below�.

This Mobius inspired residential space design consists of two zones. To divide a space into two different zones without any additional dividing space, the concrete slab is extended to the ground so that two completely surrounded zones are created which are separated by the twisting slab. The first space of the Twine house cater the semi-public zones like kitchen and lounge and the other zone consists of private spaces like bedroom.

3.10 K L E I N

BOTTLE

When we extend the concept of mobius strip to three dimensional object, then a continuous tunnel is created with inside out passage without breaking the movement and this geometry is known as Klein bottle.

Keeping this idea of joining, folding and twisting, it will create a torus when the two long sides of an rectangle is joined and then folded and last two shorter ends connect, all parallel ends facing in same direction.

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TORUS

The topology of Torus gives it a special property of connected loops so that a person will never lost inside a torus inspired space. Most easy example to demonstrate the property of torus is the game of snake in old Nokia phones in which if you exit the screen from one side than you will enter the screen from exact opposite side. Its a continuous loop. But its only possible in geometry of Torus.

If we try to extend it to the planner geometry of square than it will be complex to understand and remember.

But if we twist the shorter side of rectangle in opposite direction and then roll and connect all sides as we did in a case of Torus, then the Klein bottle is generated

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B.Arch DISSERTATION 2019-20 By taking these properties of non-euclidian topological geometry and using it in spatial design, then the time nodes can be generated which will be saved inside the explicit memory. This is how we can screate a space that can tell stories and create experiences.

3.11E U L E R’S

CHARACTERISTICS

Euler characteristics is based on euler number which tells us about topological space’s shape,

structure, nature and typology without any consideration of the way how it is bent, stretched or twisted until it is braked or teared apart i.e. a sphere will remain topologically sphere regardless of stretching and twisting until it is completely flattened from three dimensions to two dimensions.

Euler characteristic gives us a value that tells us the similarity between spatial value of different shapes and objects. For example in basic geometry we know that square, triangle and circle are different from each other but according to euler characteristic value, all these three shapes are same and can be combined and connected to generate many new forms.

=

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Proof that euler theorem is topological invariant can be understood by taking the example of this polyhedral surface. If we remove an edge from any side or shift its position from one point to another, still it will remain topologically same and all its spatial quality will be preserved.

Euler characteristics proves that we can connect or combine any of these objects or any other object with similar eular value, than the resulting space will still remain same while preserving its spacial value in non-euclidean geometry.

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What we can not do is combine two surfaces or shapes with different euler value for a smooth transition. By combining two spaces with different euler characteristic, we will create a time node in space that can create contrast and add or reduce complexity according to the need of transition.

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Z

DOTS

CONECTING DOTS

PLANER GHARPH

ALTERED SPANIG TREE

DUAL GRPH

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DUAL DOTS

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3.12A M B I G U O U S

CYLINDER

It is neither a circle nor a square, it is between them and is known as ambiguous cylinder which tricks your brain by letting it think of it as a circle from one side and than from other side it will appear as a square. Its generates pure illusion which can be created by altering basic geometry than can fool the brain of any intelligence.

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4 CASE

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4.1 E N D L E S S

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Endless house is a design purely based on organic spaces and continuous surface cocept of topological forms. Its form is created by taking spheroids and than blending them and moulding them to obtain a single surface entity which houses multiple spaces with different properties of spatial characteristic, enclosure, anthropometry and voids through which different degree of light is entering into the space which makes this house holds the space-time characteristics with endless experiencing nodes of dimensions.

This typology of design can be seen in the structures of anthills in which the space is entirely developed in the non-euclidean axis, completely organic in shape.

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"All ends meet in the "Endless" as they meet in life. Life's rhythms are cyclical. All ends of living meet during twenty-four hours, during a week, a lifetime. They touch one another with the kiss of time.

They shake hands, stay, say goodbye, return through the same or other doors, come and go through multi-links, secretive or obvious, or through the whims of memory."

The spaces are very dynamic and maintain a continuous flow while maintaining the privacy and enclosure. The concordance between between mass and voids of grid surfaces links vision to the mind.

When we enter the space. Our mind start mapping these topologically articulated spaces and as we move forward, our mind and vision looses the discussion between un-grid surfaces and lost the track of what he is after because of non-euclidean geometry.

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The mellow flow of structure provide seamless transition between interiority and exteriority. Vertical and horizontal transitions are continuous with organic staircase blending into the flow of surfaces.

The form and shape is composed of bezier curve and reverse curve which makes the space more comfortable and naturally better acoustically sound proof.

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4.2 C A P P A D O C I A Cappadocia is a region in Turkey which is said to be one of the oldest places on earth. Its architectural style is very similar to ant-hill architecture style. Spaces of Cappadocia are completely based on ergonomics and anthropogenic study. The depth of spaces depend on the needs of different activities and it increases the social interaction due to more visual connection because of presence of continuous tunnel structures that consists of combination of degree two Euler characteristics.

These kind of spatial organizations helps to get most out of a space and maximum degree of usage. It seems be an very old, un-thoughtful and free form style of architectural design but actually is very precisely calculated.

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While designing topological surfaces and spaces in Cappadocia, human size has been used as a template in consideration to the shape and size. Human scale in this design varies drastically which gives the design imageability and reduces complexity. These type of structures, shape and form are self adjusting to temperature and heat at various sub-levels.

The design typology is free flowing in nature but with inclusion of topological characteristics help the design go analyze the process and provide an overall control randomness which blends the hardscape design into the nature making it organic in character.

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4.3 F J O R D E N H U S

Olafur Eliasson has designed this office building whose form looks like fortress in which voids are created and then same deleted surfaces has been added internally to make it an unique continuous surface design. The form of the design appears to be very big than actual size because of the clear backdrop with nothing to intersect with visual lines.

This structure also generates an illusion with light and marginally large internal spaces. Fjordenhus appears to be floating on the water due to which the illusion full of sense of lightness despite of its big and humongous structure.

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Its a building that looks very complex ,but, how it is buildup is very simple. The skin is penetrated by negative volumes that perfectly fits inside the inner voids.

These topologically articulated openings are used for balconies, open space or as office.

The blue spaces in here are the voids that have been carved out systematically and then divided in perfectly to make these red spaces that acts as partition. In the plan, we can see that these are four circles that have been clubbed together. Voids have been cut out to form green spaces, transition zones and viewing points alongside water which gives the user blends the user with an illusion of of that he is floating in water

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If you look at a curved wall for a long time than it appears to be flat as our mind lost the focal points just start to see the image in two dimension. But when we move suddenly than you will see that the curved wall change perspective a lot and everything around it becomes explicit.

This design perfectly merge the two world to work and function together. The main part is how building welcomes you, you start to enter through a bride into a widely large opening. Your movement through the space will be physical but it will play with your senses at different points in space.

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4.4 H A R B I N

OPERA

HOUSE

Harbin opera house in a classical example of Topological surfaces designed on non-euclidean grid with design mapped on oblique axis.

“Embedded within Harbin’s wetlands, the Harbin Opera House was designed in response to the force and spirit of the northern city’s untamed wilderness and frigid climate. Appearing as if sculpted by wind and water, the building seamlessly blends in with nature and the topography a transfusion of local identity, art, and culture. We envision Harbin Opera House as a cultural center of the future – a tremendous performance venue, as well as a dramatic public space that embodies the integration of human, art and the city identity, while synergistically blending with the surrounding nature.”

According to MAD, the building is designed "in response to the force and spirit of the northern city's untamed wilderness and frigid climate".

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Harbin opera house is a blend between nature, art, city, senses, emotion while merging with the ever changing surroundings. Its appears to be emerged from the ground and stand like water waves on the ground. the curves of the opera house resembles the soundwave that when converted into structure that holds public spaces creates a dramatic effect that that incorporate the integration of humans.

This building with topological architecture style makes the space to act as landscape. Topology provides continuity and fluidity that helps to blur the line where roofs and ground collide. Openness and deformability is there in the design.

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Design of Harbin opera house consists of metric and non-metric concepts of architecture i.e. projective space in architecture, topological space in architecture and hybridization of spaces.

Opera house’s exterior blends and folds to continue inside directly into the enterance lobby where stripped ceiling is located that makes the user to feel the taste of nature and going forward there is a large sculpted roof of glass that lets sun enter the building and fill the corners with smoothness.

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5 COMPARATIVE ANALYSIS OF CASE STUDIES

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ENDLESS

CAPPADOCIA

FJORDENHUS

HOUSE

HARBIN OPERA HOUSE

FORM - CURVE COMPLEXITY

ANTHROPOMETRY - HUMAN SCALE

SPACE SCALE

HUMAN SIZE

Varying anthropogenic forces leading to different scale of space in relation to ergonomics

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GEOMETRICAL BEHAVIOUR

Vectors parallel to different oblique axis generates different Euler’s characteristic

COMPLEXITY

Understanding the architectural spaces and volumes by exploring non-euclidean Spaces

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6 CONCLUSION

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Topology and Topological forms can provide a dramatical experience to the space which is lacked in the Cartesian geometry. The sectional perspective play can be enhanced by designing on the grid of oblique axis. Spaces merged and blended with environment and landscape can trigger the human senses to feel as a single entity.

Spaces with varying medians of anthropometry and anthropogenic forces can create different ergonomics inside a space.Continuous surfaces of topological forms can create better spatial understanding. Calculus based forms can later the behaviour of cartesian spaces to make flexible and coherent spaces.

The principles of this study will continuously help to indicate the possible directions of developing architectural design. A certain kind of fluidity that topological surfaces provide helps to blur the identity where roofs and grounds collide. Openness, continuity and deformability can be achieved in a design with the process of topology

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DESIGN RECOMENDATION

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Fludic organic spaces in three dimension sectional approach must be there to create sensory spatial nodes in time.

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Dynamic relationship of form and space must be there.

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Every space must include volumetric properties that are under continous transformation due to the play of light, shadow and varying isometric perspectives.

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Design of architectural spaces and volumes by exploring non-euclidean Spaces and the interaction between topological surfaces.

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The continuous deformation of building envelope without destructing the spatial sense and geometrical identity.The term ‘Abstract’ and ‘Vector’ representation of a notion of space, is directly a result of topology when it comes to design.

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Introduction controlled complexity and creativity which will result in forming a unique architectural design strategy.

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To build a relationship between sense of space and time in architecture by analyzing the non-metric concepts of architectural design theories.

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7 REFRENCES

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