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Theory of Architecture 1 Input Lecture – Plane & Its Attributes

PLANE AND ITS ATTRIBUTES∗ 1. FORM AS PLANE On a two-dimensional surface, all flat forms that are not commonly recognized as points or lines are forms as planes. A planar form is bound by conceptual lines which characteristics of these conceptual lines and their interrelationships determine the shape of the planar form. Planar forms have a variety of shapes, which may be classified as follows: 1. Geometric- constructed mathematically.

2. Organic- bounded by free curves, suggesting fluidity and growth.

3. Rectilinear- bound by straight lines which are not related to one another mathematically.

4. Irregular- bound by straight and curved lines which are not related to another mathematically.

5. Hand-drawn- calligraphic or created with the unaided hand.

6. Accidental- determined by the effect of special processes or materials, or obtained accidentally.

Planar forms may be suggested by means of outlining. In this case, the thickness of the lines used should be considered. Points arranged in a row can also outline a planar form.

Points or lines densely and regularly grouped together can also suggest planar forms. They become the texture of the plane.

∗

Extracted from Chapter 2- Form (Two-Dimensional Design), Chapter 2- Designing A Form (Two-Dimensional Form) and Chapter 2- Serial Planes (Three-Dimensional Design) of Wucious Wong’s Principles of Form and Design, 1993, John Wiley & Sons, Inc. This handout is meant for guideline only. Further reading on the topic is highly recommended.

1

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

2. DESIGNING A FORM (PLANE) a) THE ADDITION OF PLANES Two planes can be combined, or added, whether or not they are of the same shape or size. Planes might overlap or intersect with other planes, while the shape of an individual plane maintains its separate identity. Shapes thus created are less seen as singular forms, but more as plural or compound forms. Two planes that have been combined might have some common edges, which result in a shape without easily discernible components. b) THE SUBTRACTION OF PLANES When a negative plane overlaps a positive plane, space appears to have been subtracted from the positive plane. The resulting shape shows a missing portion where the negative plane merges with the background. Sometimes subtraction leads to loose parts. A smaller negative plane can be completely contained within a larger positive plane. c) THE INTERPENETRATION OF PLANES Two planes can create a transparent effect by forming a negative shape within an overlapped area.

Negative shapes might become positive when overlapped within a design that includes the interpenetration of more than two planes.

d) VARYING THE SIZE OF PLANES A plane can be enlarged gradually, or dilated. Smaller planes can then be placed within larger planes concentrically, or with slight variations in the direction or position of elements. Alternate positive and negative shapes might be overlapped.

e) THE TRANSFORMATION OF PLANES Planar shapes (or flat form) can be rotated gradually to achieve transformation. The transformed shapes can then be superimposed. In addition, the size of shapes can be altered to suggest receding and advancing elements in space. As with size variations, alternate positive and negative shapes might be overlapped. 2

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

3. SERIAL PLANES Points determine a line. Lines determine a plane. Planes determine a volume. A line can be represented by a series of points.

A plane can be represented by a series of lines.

A volume can be represented by a series of planes.

When a volume is represented by a series of planes, each plane is cross section of the volume. Thus, to construct a volumetric form, we can think in terms of its cross sections, or how the form can be sliced up at regular intervals, which will result in serial planes. Each serial plane can be considered as a unit form which may be used either in repetition or in gradation. As mentioned, repetition refers to repeating both shape and size of the unit forms. Gradation∗ refers to gradual variation of the unit form, and it can be used in three different ways: Gradation of size but repetition of shape

Gradation of shape but repetition of size

Gradation of both shape and size

POSITIONAL VARIATIONS Position has to do with, first of all, spacing of the planes. If no directional variations are introduced, all the serial planes will be parallel to one another, each following the next successively, with equal spacing between them. If one plane follows another in a straight manner, then the two vertical edges of the planes trace two parallel straight lines, with a width the same as the breadth of the planes.

Spacing between planes can be made narrow or wide, with different effects. Narrow spacing gives the form greater feeling of solidity, whereas wide spacing weakens the suggestion of volume.

∗

Further information on Gradation can be found in Wucius Wong’s Principles of Form and Design, Chapter 6-Gradation (Two-Dimensional Design).

3

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

Without changing the spacing between the planes, the position of each plane can be shifted gradually towards one side or back and forth. This causes the volumetric shape to undergo various distortions. Again without changing the spacing between the planes, the position of each plane can be shifted gradually upwards or downwards. This can be easily done if the planes are hung or supported in midair.

If the planes are placed on a baseboard, we can reduce the height of the planes to suggest the effect of their gradual sinking- in just by positional variation in a vertical manner. DIRECTIONAL VARIATIONS Direction of the planes can be varied in three different ways: •

Rotation on a vertical axis Rotation on vertical axis requires a diversion of the planes from parallel arrangement. Position is definitely affected, because every directional change simultaneously demands positional change.

The plane in this case can be arranged in radiation, forming a circular shape. Or they can form a shape with curves left and right. •

Rotation on a horizontal axis Rotation on horizontal axis cannot be done if the planes are fixed on a horizontal baseboard. If they are fixed on a vertical baseboard, their rotation on a horizontal axis would be essentially the same as the rotation on a vertical axis described above.

•

Rotation on its own plane Rotation on its own plane means that the corners or edges of each plane are moved from one position to another without affecting the basic direction of the plane itself. This results in a spirally twisted shape.

The planes can be physically curled or bent if desired.

4

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PLANE AND ITS ATTRIBUTES∗ 1. FORM AS PLANE On a two-dimensional surface, all flat forms that are not commonly recognized as points or lines are forms as planes. A planar form is bound by conceptual lines which characteristics of these conceptual lines and their interrelationships determine the shape of the planar form. Planar forms have a variety of shapes, which may be classified as follows: 1. Geometric- constructed mathematically.

2. Organic- bounded by free curves, suggesting fluidity and growth.

3. Rectilinear- bound by straight lines which are not related to one another mathematically.

4. Irregular- bound by straight and curved lines which are not related to another mathematically.

5. Hand-drawn- calligraphic or created with the unaided hand.

6. Accidental- determined by the effect of special processes or materials, or obtained accidentally.

Planar forms may be suggested by means of outlining. In this case, the thickness of the lines used should be considered. Points arranged in a row can also outline a planar form.

Points or lines densely and regularly grouped together can also suggest planar forms. They become the texture of the plane.

∗

Extracted from Chapter 2- Form (Two-Dimensional Design), Chapter 2- Designing A Form (Two-Dimensional Form) and Chapter 2- Serial Planes (Three-Dimensional Design) of Wucious Wong’s Principles of Form and Design, 1993, John Wiley & Sons, Inc. This handout is meant for guideline only. Further reading on the topic is highly recommended.

1

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

2. DESIGNING A FORM (PLANE) a) THE ADDITION OF PLANES Two planes can be combined, or added, whether or not they are of the same shape or size. Planes might overlap or intersect with other planes, while the shape of an individual plane maintains its separate identity. Shapes thus created are less seen as singular forms, but more as plural or compound forms. Two planes that have been combined might have some common edges, which result in a shape without easily discernible components. b) THE SUBTRACTION OF PLANES When a negative plane overlaps a positive plane, space appears to have been subtracted from the positive plane. The resulting shape shows a missing portion where the negative plane merges with the background. Sometimes subtraction leads to loose parts. A smaller negative plane can be completely contained within a larger positive plane. c) THE INTERPENETRATION OF PLANES Two planes can create a transparent effect by forming a negative shape within an overlapped area.

Negative shapes might become positive when overlapped within a design that includes the interpenetration of more than two planes.

d) VARYING THE SIZE OF PLANES A plane can be enlarged gradually, or dilated. Smaller planes can then be placed within larger planes concentrically, or with slight variations in the direction or position of elements. Alternate positive and negative shapes might be overlapped.

e) THE TRANSFORMATION OF PLANES Planar shapes (or flat form) can be rotated gradually to achieve transformation. The transformed shapes can then be superimposed. In addition, the size of shapes can be altered to suggest receding and advancing elements in space. As with size variations, alternate positive and negative shapes might be overlapped. 2

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

3. SERIAL PLANES Points determine a line. Lines determine a plane. Planes determine a volume. A line can be represented by a series of points.

A plane can be represented by a series of lines.

A volume can be represented by a series of planes.

When a volume is represented by a series of planes, each plane is cross section of the volume. Thus, to construct a volumetric form, we can think in terms of its cross sections, or how the form can be sliced up at regular intervals, which will result in serial planes. Each serial plane can be considered as a unit form which may be used either in repetition or in gradation. As mentioned, repetition refers to repeating both shape and size of the unit forms. Gradation∗ refers to gradual variation of the unit form, and it can be used in three different ways: Gradation of size but repetition of shape

Gradation of shape but repetition of size

Gradation of both shape and size

POSITIONAL VARIATIONS Position has to do with, first of all, spacing of the planes. If no directional variations are introduced, all the serial planes will be parallel to one another, each following the next successively, with equal spacing between them. If one plane follows another in a straight manner, then the two vertical edges of the planes trace two parallel straight lines, with a width the same as the breadth of the planes.

Spacing between planes can be made narrow or wide, with different effects. Narrow spacing gives the form greater feeling of solidity, whereas wide spacing weakens the suggestion of volume.

∗

Further information on Gradation can be found in Wucius Wong’s Principles of Form and Design, Chapter 6-Gradation (Two-Dimensional Design).

3

Theory of Architecture 1 Input Lecture – Plane & Its Attributes

Without changing the spacing between the planes, the position of each plane can be shifted gradually towards one side or back and forth. This causes the volumetric shape to undergo various distortions. Again without changing the spacing between the planes, the position of each plane can be shifted gradually upwards or downwards. This can be easily done if the planes are hung or supported in midair.

If the planes are placed on a baseboard, we can reduce the height of the planes to suggest the effect of their gradual sinking- in just by positional variation in a vertical manner. DIRECTIONAL VARIATIONS Direction of the planes can be varied in three different ways: •

Rotation on a vertical axis Rotation on vertical axis requires a diversion of the planes from parallel arrangement. Position is definitely affected, because every directional change simultaneously demands positional change.

The plane in this case can be arranged in radiation, forming a circular shape. Or they can form a shape with curves left and right. •

Rotation on a horizontal axis Rotation on horizontal axis cannot be done if the planes are fixed on a horizontal baseboard. If they are fixed on a vertical baseboard, their rotation on a horizontal axis would be essentially the same as the rotation on a vertical axis described above.

•

Rotation on its own plane Rotation on its own plane means that the corners or edges of each plane are moved from one position to another without affecting the basic direction of the plane itself. This results in a spirally twisted shape.

The planes can be physically curled or bent if desired.

4

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