Curvature Topology

CURVATURE TOPOLOGY Workshop ONE | Mostafa ElSayed + Apostolis Despotidis Ariadna A. Lopez | Leo Claudis Beiling | Ruilin Yang

[2]

WORKSHOP BRIEF + TIMELINE

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EXPLORATION ONE: CURVATURE THROUGH PATTERN

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EXPLORATION TWO: CURVATURE CONTOL

EXPLORATION THREE: CURVATURE PARAMETRIZATION

[14]

[22]

EXPLORATION FOUR: CURVATURE TORSION

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EXPLORATION FIVE: CURVATURE TORSION 2.0

[38]

CASTING INDEX: STITCHING RATIO VS. FOCE APPLIED

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CONTENTS

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THE DESIGN METHODOLOGY OF THIS WORKSHOP IS DEPENDENT UPON A CONTINUOUS STUDY OF MATERIAL BEHAVIOUR THROUGH DEVELOPING STITCHING PATTERNS IN LYCRA AND CASTING THEM IN PLASTER. CURVATURE TYPOLOGY FOCUSES ON THE INVESTIGATION OF MORPHING A LINE /2D PLANE TO A CURVE / 3D SURFACE THROUGH THE PATTERN APPLIED TO THE FABRIC IN CONJUNCTION WITH GRAVITATIONAL FORCES DURING THE CASTING PROCES. THE INVESTIGATION FOCUSED ON DEVELOPING A SUITABLE PATTERN WHICH WOULD FUNCTION STRUCTURALLY ONCE CASTED WITH PLASTER. THE PARAMETERS SET BY THE PATTERN ALLOWED US TO CONTROL THE FLOW OF PLASTER AND UNDERSTAND THE RESISTANCE AND DEFORMATION OF THE MATERIALS. THE TEAM CONDUCTED FIVE EXPLORATIONS OF CURVATURE, STARTING WITH UNDERSTANDING THE POINTS OF INFLECTION THAT FORM A SIMPLE TWO-DIMENSIONAL CURVE AND FINALIZING WITH POINTS OF TORSION THAT BEGIN TO TRANSORM A CURVE INTO THREE-DIMENSIONAL SPACE.

EXPLORATION ONE

EXPLORATION TWO

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WORKSHOP BRIEF + TIMELINE

EXPLORATION THREE

EXPLORATION FOUR

EXPLORATION FIVE

WORKSHOP BRIEF + TIMELINE

[5]

[6]

EXPLORATION ONE:

CURVATURE THROUGH PATTERN

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CORN FOCUSED ON GETTING ACQUAINTED WITH THE TECHINIQUE OF CREATING FOLD STITCHES IN THE FABRIC IN ORDER TO CREATE AN INTERDEPENDENT RELATIONSHIP BETWEEN THE INFLECTION POINTS IN A CURVE AND THE PLASTER BEHAVIOUAR . IN THIS CASE, THE UNIFORM FOLDS PRODUCED A UNIFROM CURVE WITH VERY LITTLE WEAK POINTS ALONG THE CAST.

corn

top

top

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

middle middle

bottom

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

bottom

[8]

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

EXPLORATION ONE: OVERVIEW

HES

PATTERN PRESSURE POINT B

BEFORE CASTING: X-Y AXES

FOLD STITCHES

PRESSURE POINT B

AFTER CASTING: X-Y-Z AXES

FOLD STITCHES PRESSURE POINT A

PRESSURE POINT

AFTER CASTING: X-Y-Z AXES

BACK FAC EXPANSIO

BACK FACE CURVATURE CAUSED BY EXPANSION OF FOLDS

EQUAL EXPANSION

EXPLORATION ONE: DIAGRAMS

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FOLD STITCHES

7th Cast (Corn)

PRESSURE POINT A

PRESSURE POINT B

7 CM

1 CM

60 CM

6 CM

A B

90 CM

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EXPLORATION ONE: PATTERN

60 CM

10 CM

10 CM

5 CM

5 CM

5 CM

5 CM

12 CM

A' A'

B' B'

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TOP VIEW

SIDE VIEW [12]

EXPLORATION ONE: OVERVIEW

BACK FACE DETAIL

FOLD DETAIL

PATTERN DETAIL

EXPLORATION ONE: DETAILS

[13]

[14]

EXPLORATION TWO:

CURVATURE CONTROL

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GARLIC FOCUSED ON UNDERSTADING THE SCALEABILITY OF THE PATTERN IN ORDER TO CREATE A SELF-STANDING CAST. THE PATTERN DEVELOPED IN THIS INSTANCE IS A GRADIENT OF SIZE FOLDS IN X-Y AXES, ALLOWING FOR MORE ARTICULATED CURVATURE AFTER CASTING.

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b

garlic

corn

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

Fold stitch: 13 Pressure point A: 12 Pressure point B: 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

EXPLORATION TWO: OVERVIEW

GRADIENT OF FOLDS IN X-Y AXES

PATTERN

GRADIENT OF FOLDS IN X-Y AXES

GRADIENT OF FOLDS IN X-Y AXES

PLASTER FLOW

EXPANSION

EXPANSION

EXPANSION

EXPLORATION TWO: PATTERN

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FOLD STITCHES PRESSURE POINT A

8th Cast (Garlic)

PRESSURE POINT B

91 CM

8.5 CM 1 CM 8 CM 1 CM 7.5 CM 1 CM 7 CM 1 CM 6.5 CM1 CM 6 CM 1 CM6.5 CM1 CM 7 CM 1 CM

102 CM

[18]

EXPLORATION TWO: PATTERN

10 CM

10 CM

9.5 CM

9.5 CM

9 CM

9 CM

8.5 CM

8.5 CM

8.5 CM

8.5 CM

8 CM

8 CM

7 CM

7 CM

6.5 CM

6.5 CM

6 CM

6 CM

5.5 CM 5 CM 4.5 CM 4 CM

5.5 CM 5 CM 4.5 CM 4 CM

9 CM

EXPLORATION TWO: PATTERN 91 CM

91 CM

7.5 CM

7.5 CM

8 CM CM 1 CM 8.5 CM 1 CM M 7 CM1 CM 1 CM8.5 7.5CM CM 11 CM CM 89CM 11 CM 11 CM

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BACK VIEW [20]

EXPLORATION TWO: OVERVIEW

TOP SECTION DETAIL

MIDDLE SECTION DETAIL

BOTTOM SECTION DETAIL

EXPLORATION TWO: DETAILS

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[22]

EXPLORATION THREE:

CURVATURE PARAMETRIZATION

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BANANA TREE FOCUSES ON THE PARAMETRIZATION OF THE CURVATURE IN THE CAST. EACH SECTION OF THE PATERN IS DEVELOPED TO CONTROL THE AMOUNT OF INFLECTION POINTS IN THE CURVATURE, THUS THE CAST IS ABLE TO SHIFT BETWEEN DIFFERENT CURVE PROFILES.

banana tree

garlic

13 12 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

Fold stitch: 6 Pressure point A: 6 Pressure point B: 5

13 12 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

Fold stitch: 24 Pressure point A: 24 Pressure point B: 23

13 12 13

Fold stitch: 11 Pressure point A: 10 Pressure point B: 6

Fold stitch: 3 Pressure point A: 3 Pressure point B: 2

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EXPLORATION THREE: OVERVIEW

ERN

PATTERN

PRESSURE POINT B

FOLD STITCHES

PRESSURE POINT B

PLASTER FLOW

PRESSURE FOLD STITCHES POINT B

PLASTER FLOW

EXPANSION 1X

EXPANSION 2X

EXPANSION 1X

EXPLORATION THREE: DIAGRAMS

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FOLD STITCHES PRESSURE POINT A

10th Cast (Banana Tre

PRESSURE POINT B

13 CM

83 CM

1 CM 14 CM

6 CM 1 CM 7 CM

2.5 CM 1 CM

87 CM

3.5 CM

6 CM 1 CM 7 CM

14 CM 13 CM

1 CM

28 CM 27 CM

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1 CM

EXPLORATION THREE: PATTERN

5 CM

11 CM

11 CM

23 CM

23 CM

9 CM 9 CM 6 CM 3 CM 6 CM

9 CM

6 CM

3 CM 6 CM

9 CM

87 CM

5 CM

87 CM

6 CM 9 CM 9 CM 12 CM 9 CM

9 CM

6 CM

9 CM

12 CM

9 CM

9 CM

9 CM

Tree)

11 CM

11 CM

5 CM

5 CM

2 CM

2 CM

EXPLORATION THREE: PATTERN

Fold Stich

Fold St

Pressure Point B

Pressu

Pressure Point A

Pressu

[27]

BACK VIEW [28]

EXPLORATION THREE: OVERVIEW

TOP SECTION DETAIL

MIDDLE SECTION DETAIL

BOTTOM SECTION DETAIL

EXPLORATION THREE: DETAILS

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[30]

EXPLORATION FOUR:

CURVATURE TORSION

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CACTUS FOCUSES UNDERSTANDING THE TORSION OF A CURVE; MANIPULATING OUR FINDINGS IN A TWODIMENSIONAL CURVE INTO A THREE-DIMENSIONAL ONE. IN THIS INSTANCE, THE CHALLENGE BECAME THE INFLECTION POINT IN WHICH THE CURVATURE CHANGED DIRECTIONS THREE-DIMENSIONALLY.

banana tree

cactus

Fold stitch: Pressure line:

9 9

Fold stitch: 24 Pressure point A: 24 Pressure point B: 23

Fold stitch: Pressure line:

9 9

Fold stitch: 3 Pressure point A: 3 Pressure point B: 2

Fold stitch: Pressure line:

9 9

11 10 6

Fold stitch: 6 Pressure point A: 6 Pressure point B: 5

11 10 6

11 10 6

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EXPLORATION FOUR: OVERVIEW

TTERN

ONT FACE

W

PATTERN

AFTER STITCHING

BACK FACE

AFTER STITCHING

BACK FACE

FRONT FACE

PLASTER FLOW

TORSION: OPPOSING EXPANSION FORCESTORSION: OPPOSING CURVATURE EXPANSION ANALYSIS FORCES : WEAK CURVATURE POINT ANALYSIS : WEAK POINT TORSION: OPPOSING EXPANSION FORCES

EXPLORATION FOUR: DIAGRAMS

[33]

CUR

FOLD STITCHES PRESSURE POINT A

12th Cast (Cactus)

PRESSURE POINT B

1 CM

6 CM

8 CM

1 CM

9 CM

10

CM

CM

37 CM

5

92 CM

CM

5

CM

CM

5

55

CM

5

CM

5

CM

5

CM

5

CM

11

10 CM

FRONT FACE AFTER FOLDING

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10 CM

FRONT FACE BEFORE FOLDING

EXPLORATION FOUR: PATTERN

10 CM

CM

92 CM

CM

5

CM

5

CM

41 CM

11

5 CM

55

CM

CM

5 5 CM 5 CM 5 CM 5 CM 5 CM 11 10

1 CM 1 CM

6 CM

8 CM

CM

CM

9 CM

BACK FACE BEFORE FOLDING

Fold S

Pressu 10 CM

BACK FACE AFTER FOLDING

EXPLORATION FOUR: PATTERN

[35]

SIDE VIEW [36]

EXPLORATION FOUR: OVERVIEW

TOP SECTION BACK VIEW DETAIL

MIDDLE SECTION BACK VIEW DETAIL

PATTERN DETAIL

EXPLORATION FOUR: DETAILS

[37]

[38]

EXPLORATION FIVE:

CURVATURE TORSION 2.0

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PINAPPLE FOCUSED ON MASTERING THE TORSION OF THE CURVATURE. IN THIS INSTANCE, THE PATTERN SIZE WAS SCALED DOWN AND MIRRORED TO ALLOW THE TROSION OF THE CURVE TO HAPPEN MORE NATURALLY AS IT WAS BEING CASTED.

banana tree

Fold stitch: Pressure line:

9 9

Fold stitch: 24 Pressure point A: 24 Pressure point B: 23

Fold stitch: Pressure line:

9 9

Fold stitch: 3 Pressure point A: 3 Pressure point B: 2

Fold stitch: Pressure line:

9 9

1 0 6

Fold stitch: 6 Pressure point A: 6 Pressure point B: 5

1 0 6

1 0 6

[40]

p

cactus

EXPLORATION FIVE: OVERVIEW

PATTERN PATTERN

PRESSURE POINT A

FOLD STITCHES FOLD STITCHES

PLASTER FLOW

CONTRACTION OF BACK FACE FOLDS

EQUAL EXPANSION

EXPLORATION FIVE: DIAGRAM

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14th Cast FOLD STITCHES 14 CM 2 CM 1 CM

M 5C

PRESSURE POINT A

10 CM 10 CM 10 CM 10 CM CM

100

10 10 CM 10 CM M

C 10 M

C 10 M

10 C 9 CM

50 CM

7 CM

FRONT FACE

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EXPLORATION FOUR: PATTERN

8 CM

8 CM

50 CM

7 CM

8 CM

8 CM 9 CM

10 C

10

CM

10

CM

10

CM

10

CM

5C M

M

10

CM

10

CM

100 10 C

M

M

10 C

5C

M

M

C 10

10 C

M

M

C 10 M

5C

M

10 C

14 CM

BACK FACE

EXPLORATION FOUR: PATTERN

[43]

SIDE VIEW [44]

EXPLORATION FIVE: OVERVIEW

PATTERN DETAIL

BACK PATTERN DETAIL

BOTTOM SECTION DETAIL

EXPLORATION FIVE: DETAILS

[45]

CORN GARLIC Distance Distance Expansion ratio

1.2

Width before folding

90cm

Distance between rows Expansion ratio Size of stitches Width beforeoffolding Number stitches at the same height

5cm 0.5mm 12

Distance between rows Size of stitches

8.0 Risk index 8.0 Risk index

6.0 6.0

4.0 4.0

2.0 2.0

Number of stitches at the same height

0 0

Width before folding Width before folding

BANANA TREE CACTUS

Distance Distance

(MIDDLE PART) Expansion ratio

8.0 Risk index 8.0 Risk index

6.0 6.0

4.0 4.0

2.0 2.0

0 0

40cm

Distance between rows

8cm

Size of stitches Expansion ratio

1.53 2.0mm

Number of stitches Width before foldingat the same height

5 83cm

Distance between rows

9cm

Size of stitches (BOTTOM PART) Number of stitches at the same height Expantion ratio

0.5mm

Width before folding

90cm

6 2.0

Distance between rows

5cm

Size of stitches

1.5mm

Number of stitches at the same height

9

Width before folding Width before folding Failure:

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2.0

Width before folding

CASTING INDEX

- Middle par tFailure: Uncont - Stitch type

CACTUS (MIDDLE PART)

Distance

Expansion ratio

2.0

Width before folding

40cm

Distance between rows

8cm

Size of stitches

2.0mm

Number of stitches at the same height

5

(BOTTOM PART) Expantion ratio

0 2.0 4.0 6.0 Risk index

8.0

2.0

Width before folding

90cm

Distance between rows

5cm

Size of stitches

1.5mm

Number of stitches at the same height

9

Width before folding Failure:

- Middle par tFailure: Uncont - Stitch type

Expansion ratio

1.54

PINEAPPLE Distance

2

0

Width before folding

115cm

Distance between rows

5.25cm

Size of stitches

0.5mm

Number of stitches at the same height

5

distance

2.0 4.0 6.0 Risk index

8.0

Width before folding

CASTING INDEX

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CURVATURE TYPOLOGY

CURVATURE TYPOLOGY

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ARCHITECTURAL ASSOCIATION SCHOOL OF ARCHITECTURE DESIGN RESEARCH LABARATORY [DRL] LONDON, UK 2016