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Introduction to Architecture Francis D. Ching, James F. Clark, Michael Pause. Architects' Data, 5th Edition Ernst Neufert. Del Pico. Weygant, Harold J. Rosen, John R. Mastering SolidWorks Matt Lombard. Green Building Illustrated Francis D. Ching, Ian M. Pierce Jr. Becoming a Construction Manager John J. McKeon, Bruce D'Agostino. Fellows, Anita M. Smith, Tony Merna, Paul Jobling. Teixeira, Helder P. Leslie Simmons. Design Drawing, 3rd Edition Francis D. Ching, Steven P. Ching, Corky Binggeli.

Wakita, Nagy R. Bakhoum, Richard M. Architectural Graphics, 6th Edition Francis D. Otie Kilmer. Drawing Architecture and the Urban Sam Jacoby. Manual Drafting for Interiors Christine Cavataio. Architectural Acoustics Illustrated Michael Ermann. If the line shifts to form a plane, we obtain a two-dimensional element.

In the movement from plane to spaces, the clash of planes gives rise to body three-dimensional A summary of the kinetic energies which move the point into a line, the line into a plane, and the plane into a spatial dimension. Each element is first considered as a conceptual element, then as a visual element in the vocabulary of architectural design. As conceptual elements, the point, line, plane, and volume are not visible except to the mind's eye.

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While they do not actually exist, we nevertheless feel their presence. We can sense a point at the meeting of two lines, a line marking the contour of a plane, a plane enclosing a volume, and the volume of an object that occupies space. When made visible to the eye on paper or in three-dimensional space, these elements become form with characteristics of substance, shape, size, color, and texture. As we experience these forms in our environment, we should be able to perceive in their structure the existence of the primary elements of point, line, plane, and volume.

Conceptually, it has no length, width, or depth, and is therefore static, centralized, and directionless. At the center of its environment, a point is stable and at rest, organizing surrounding elements about itself and dominating its field. When the point is moved off-center, however, its field becomes more aggressive and begins to compete for visual supremacy.

Visual tension is created between the point and its field. To visibly mark a position in space or on the ground plane, a point must be projected vertically into a linearform, as a column, obelisk, ortower. Any such columnar element is seen in plan as a point and therefore retains the visual characteristics of a point. The equestrian statue of Marcus Aurelius marks the center of this urban space. Mont 5. Michel, France, 13th century and later. The pyramidal composition culminates in a spire that serves to establish this fortified monastery as a specific place in the landscape.

Although the points give this line finite length, the line can also be considered a segment of an infinitely longer path. Two points further suggest an axis perpendicular to the line they describe and about which they are symmetrical. Because this axis may be infinite in length, it can be at times more dominant than the described line. In both cases, however, the described line and the perpendicular axis are optically more dominant than the infinite number of lines that may pass through each of the individual points. Conceptually, a line has length, but no width or depth. Whereas a point is by nature static, a line, in describing the path of a point in motion, is capable of visually expressing direction, movement, and growth.

A line is a critical element in the formation of any visual construction. It is seen as a line simply because its , length dominates its width. The character of a line, whethertautorlimp. Even the simple repetition of like or similar elements, if continuous enough, can be regarded as a line. This type of line has significant textural qualities.

The orientation of a line affects its role in a visual construction.

While a vertical line can express a state of equilibrium with the force of gravity, symbolize the human condition, or mark a position in space, a horizontal line can represent stability, the ground plane, the horizon, or a body at rest. Place de la Concorde, Paris. The obelisk, which marked the entrance to the Amon temple at Luxor, was given by the viceroy of Egypt, Mohamed AM, to Louis Phillipe and installed in The sculptured female figures stand as columnar supports for the entablature.

Salginatobel Bridge, Switzerland, , Robert Maillart. Beams and girders have the bending strength to span the space between their supports and carry transverse loads. Katsura Imperial Villa, Kyoto, Japan, 17th century. Linear columns and beams togetherform a three-dimensional framework for architectural space.

These lines can be expressed by joints within or between building materials, by frames around windowor door openings, or by a structural grid of columns and beams. How these linear elements affect the texture of a surface will depend on their visual weight, spacing, and direction. A transparent spatial membrane can be stretched between them to acknowledge their visual relationship. The closer these lines are to each other, the stronger will be the sense of plane they convey.

A series of parallel lines, through their repetitiveness, reinforces our perception of the plane they describe. As these lines extend themselves along the plane they describe, the implied plane becomes real and the original voids between the lines revert to being mere interruptions of the planar surface. The diagrams illustrate the transformation of a row of round columns, initially supporting a portion of a wall, then evolving into square piers which are an integral part of the wall plane, and finally becoming pilasters — remnants of the original columns occurring as a relief along the surface of the wall.

A row of columns is indeed nothing buta wall, open and discontinued in several places. A colonnaded facade can be penetrated easily for entry, offers a degree of shelter from the elements, and forms a semi-transparent screen that unifies individual building forms behind it. The Basilica, Vicenza, Italy. Andrea Palladio designed this two-story loggia in to wrap around an existing medieval structure.

This addition not only buttressed the existing structure but also acted as a screen that disguised the irregularity of the original core and presented a uniform but elegant face to the Piazza del Signori. These two examples illustrate how columns can define the edges of an exterior space defined within the mass of a building as well as articulate the edges of a building mass in space. Philibert, Tournus, France, This view of the nave shows how rows of columns can provide a rhythmic measure of space.

Vertical and horizontal linear elements together can define a volume of space such as the solarium illustrated to the rig ht. Note that the form of the volume is determined solely by the configuration of the linear elements. Conceptually, a plane has length and width, but no depth. Shape is the primary identifying characteristic of a plane. It is determined by the contour of the line forming the edges of a plane.

Because our perception of shape can be distorted by perspective foreshortening, we see the true shape of a plane only when we view it frontally. The supplementary properties of a plane — its surface color, pattern, and texture — affect its visual weight and stability. In the composition of a visual construction, a plane serves to define the limits or boundaries of a volume. If architecture as a visual art deals specifically with the formation of three- dimensional volumes of mass and space, then the plane should be regarded as a key element in the vocabulary of architectural design.

The properties of each plane — size, shape, color, texture — as well as their spatial relationship to one another ultimately determine the visual attributes of the form they define and the qualities of the space they enclose. In architectural design, we manipulate three generic types of planes: Overhead Plane The overhead plane can be either the roof plane that spans and shelters the interior spaces of a building from the climatic elements, or the ceiling plane that forms the upper enclosing surface ofa room.

Wall Plane The wall plane, because of its vertical orientation, is active in our normal field of vision and vital to the shaping and enclosure of architectural space. Along with climate and other environmental conditions of a site, the topographical character of the ground plane influences the form of the building that rises from it. The building can merge with the ground plane, rest firmly on it, or be elevated above it.

The ground plane itself can be manipulated as well to establish a podium for a building form. It can be elevated to honor a sacred or significant place; bermed to define outdoor spaces or buffer against undesirable conditions; carved or terraced to provide a suitable platform on which to build; or stepped to allow changes in elevation to be easily traversed. Scala de Spagna Spanish Steps , Rome, Alessandro Specchi designed this civic project to connect the Piazza di Spagn, with Trinita de' Monti; completed by Francesco de Sanctis.

Three terraces approached by ramps rise toward the base of the cliffs where the chief sanctuary is cut deep into the rock. Machu Picchu, an ancient Incan city established c. It may be a durable covering of the ground plane or a more artificial, elevated plane spanning the space between its supports. In either case, the texture and density of the flooring material influences both the acoustical quality of a space and how we feel as we walk across its surface. While the pragmatic, supportive nature of the floor plane limits the extent to which it can be manipulated, it is nonetheless an important element of architectural design.

Its shape, color, and pattern determine to what degree it defines spatial boundaries or serves as a unifying element for the different parts of a space. Like the ground plane, the form of a floor plane can be stepped or terraced to break the scale of a space down to human dimensions and create platforms for sitting, viewing, or performing. It can be elevated to define a sacred or honorific place.

It can be rendered as a neutral ground against which other elements in a space are seen as figures. Their construction provides both privacy and protection from the This Florentine street defined by the two wings of the Uffizi climatic elements for the interior spaces of a building, while openings within or Palace links the Piazza della Signoria with the River Arno. As exterior walls mold interior space, they simultaneously shape exterior space and describe the form, massing, and image of a building in space.

As a design element, the plane of an exterior wall can be articulated as the front or primary facade of a building. In urban situations, these facades serve as walls that define courtyards, streets, and such public gathering places as squares and marketplaces. Piazza of San Marco, Venice.

The continuous facades of buildings form the "walls" of the urban space. I— t -i! A compelling way to use the vertical wall plane is as a supporting element in the bearing-wall structural system. When arranged in a parallel series to support an overhead floor or roof plane, bearing walls define linear slots of space with strong directional qualities. These spaces can be related to one another only by interrupting the bearing walls to create perpendicular zones of space.

Their visual properties, their relationship to one another, and the size and distribution of openings within their boundaries determine both the quality of the spaces they define and the degree to which adjoining spaces relate to one another. As a design element, a wall plane can merge with the floor or ceiling plane, or be articulated as an element isolated from adjacent planes. It can be treated as a passive or receding backdrop for other elements in the space, or it can assert itself as a visually active element within a room by virtue of its form, color, texture, or material.

While walls provide privacy for interior spaces and serve as barriers that limit our movement, doorways and windows reestablish continuity with neighboring spaces and allowthe passage of light, heat, and sound. As they increase in size, these openings begin to erode the natural sense of enclosure walls provide. Views seen through the openings become part of the spatial experience.

The detached vaulted ceiling plane appears to float above the bed. While we walk on a floor and have physical contact with walls, the ceiling plane is usually out of our reach and is almost always a purely visual event in a space. It may be the underside of an overhead floor or roof plane and express the form of its structure as it spans the space between its supports, or it may be suspended as the upper enclosing surface of a room or hall.

As a detached lining, the ceiling plane can symbolize the sky vault or be the primary sheltering element that unifies the different parts of a space. It can serve as a repository for frescoes and other means of artistic expression or be treated simply as a passive or receding surface. It can be raised or lowered to alter the scale of a space or to define spatial zones within a room. Its form can be manipulated to control the quality of light or sound within a space. Church at Vuoksenniska, Finland, , Alvar Aalto. The form of the ceiling plane defines a progression of spaces and enhances their acoustical quality.

The low sloping roof planes and broad overhangs are characteristic of the Prairie School of Architecture. The roof plane is the essential sheltering element that protects the interior of a building from the climatic elements. The form and geometry of its structure is established by the manner in which it spans across space to bear on its supports and slopes to shed rain and melting snow.

Asa design element, the roof plane is significant because of the impact it can have on the form and silhouette of a building within its setting. The roof plane can be hidden from view by the exterior walls of a building or merge with the walls to emphasize the volume of the building mass. It can be expressed as a single sheltering form that encompasses a variety of spaces beneath its canopy, or comprise a number of hats that articulate a series of spaces within a single A roof plane can extend outward to form overhangs that shield door and window openings from sun or rain, or continue downward further still to relate itself more closely to the ground plane.

In warm climates, it can be elevated to allow cooling breezes to flow across and through the interior spaces of a building. The overall form of a building can be endowed with a distinctly planar quality by carefully introducing openings that expose the edges of vertical and horizontal planes. These planes can be further differentiated and accentuated by changes in color, texture, or material.

Asymmetrical compositions of simple rectangular forms and primary colors characterized the de Stijl school of artand architecture. Conceptually, a volume has three dimensions: length, width, and depth. It is established by the shapes and interrelationships of the planes that describe the boundaries of the volume. Architectural forms, textures, materials, modulation of light and shade, color, all combine to inject a quality or spirit that articulates space. The quality of the architecture will be determined by the skill of the designer in using and relating these elements, both in the interior spaces and in the spaces around buildings.

It may refer to an external appearance that can be recognized, as that of a chair or the human body that sits in it. It may also allude to a particular condition in which something acts or manifests itself, as when we speak of water in the form of ice or steam. In art and design, we often use the term to denote the formal structure of a work — the manner of arranging and coordinating the elements and parts of a composition so as to produce a coherent image. In the context of this study, form suggests reference to both internal structure and external outline and the principle that gives unity to the whole.

While form often includes a sense of three-dimensional mass or volume, shape refers more specifically to the essential aspect of form that governs its appearance — the configuration or relative disposition of the lines or contours that delimit a figure or form. Shape The characteristic outline or surface configuration of a particular form. Shape is the principal aspect by which we identify and categorize forms. In addition to shape, forms have visual properties of: Size The physical dimensions of length, width, and depth of a form. While these dimensions determine the proportions of a form, its scale is determined by its size relative to other forms in its context.

Color A phenomenon of light and visual perception that may be described in terms of an individual's perception of hue, saturation, and tonal value. Color is the attribute that most clearly distinguishes a form from its environ- ment. It also affects the visual weight of a form. Texture The visual and especially tactile quality given to a surface by the size, shape, arrangement, and proportions of the parts.

Texture also determines the degree to which the surfaces of a form reflect or absorb incident light. The direction of a form relative to the ground plane, the compass points, other forms, or to the person viewing the form. The degree of concentration and stability of a form. The visual inertia of a form depends on its geometry as well as its orientation relative to the ground plane, the pull of gravity, and our line of sight. All of these properties of form are in reality affected by the conditions under which we view them. It is the primary means by which we recognize, identify, and categorize particular figures and forms.

Our perception of shape depends on the degree of visual contrast that exists along the contour separating a figure from its ground or between a form and its field. Bust of Queen Nefertiti The pattern of eye movement of a person viewing the figure, from research by Alfred L. This architectural composition illustrates the interplay between the shapes of planar solids and voids. Given any composition of forms, we tend to reduce the subject matter in our visual field to the simplest and most regular shapes. The simpler and more regular a shape is, the easier it is to perceive and understand.

From geometry we know the regular shapes to be the circle, and the infinite series of regular polygons that can be inscribed within it. Of these, the most significant are the primary shapes: the circle, the triangle, and the square. Placing a circle in the center of a field reinforces its inherent centrality. Associating it with straight or angular forms or placing an element along its circumference, however, can induce in the circle an apparent rotary motion.

The triangle signifies stability. When resting on one of its sides, the triangle is an extremely stable figure. When tipped to stand on one of its vertices, however, it can either be balanced in a precarious state of equilibrium or be unstable and tend to fall over onto one of its sides. It is a bilaterally symmetrical figure having two equal and perpendicular axes. All other rectangles can be considered variations of the square - deviations from the norm by the addition of height or width.

Like the triangle, the square is stable when resting on one of its sides and dynamic when standing on one of its corners. When its diagonals are vertical and horizontal, however, the square exists in a balanced state of equilibrium. Surface first refers to any figure having only two dimensions, such as a flat plane. The term, however, can also allude to a curved two-dimensional locus of points defining the boundary of a three-dimensional solid. There is a special class of the latter that can be generated from the geometric family of curves and straight lines.

Depending on the curve, a cylindrical surface may be circular, elliptic, or parabolic. Because of its straight line geometry, a cylindrical surface can be regarded as being either a translational or a ruled surface. Ruled surfaces are generated by the motion of a straight line. Because of its straight line geometry, a ruled surface is generally easier to form and construct than a rotational or translational surface. Rotational surfaces are generated by rotating a plane curve about an axis.

Paraboloids are surfaces all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas. Parabolas are plane curves generated by a moving point that remains equidistant from a fixed line and a fixed point not on the line. Hyperbolas are plane curves formed by the intersection of a right circular cone with a plane that cuts both halves of the cone. Hyperbolic paraboloids are surfaces generated by sliding a parabola with downward curvature along a parabola with upward curvature, or by sliding a straight line segment with its ends on two skew lines.

It can thus be considered to be both a translational and a ruled surface. Regions of downward curvature exhibit archlike action while regions of upward curvature behave as a cable structure. If the edges of a saddle surface are not supported, beam behavior may also be present.

The geometric basis for these curved surfaces can be effectively utilized in digital modeling as well as in the description, fabrication and assembly of curvilinear architectural elements and components. The fluid quality of curved surfaces contrasts with the angular nature of rectilinear forms and are appropriate for describing the form of shell structures as well as nonloadbearing elements of enclosure. Symmetrical curved surfaces, such as domes and barrel vaults, are inherently stable. Asymetrical curved surfaces, on the other hand, can be more vigorous and expressive in nature.

Their shapes change dramatically as we view them from different perspectives. It is for this reason that these are beautiful forms, the most beautiful forms. Circles generate spheres and cylinders; triangles generate cones and pyramids; squares generate cubes. In this context, the term solid does not refer to firmness of substance but rather to a three-dimensional geometric body or figure.

Sphere A solid generated by the revolution of a semicircle about its diameter, whose surface is at all points equidistant from the center. A sphere is a centralized and highly concentrated form. Like the circle from which it is generated, it is self-centering and normally stable in its environment. It can be inclined toward a rotary motion when placed on a sloping plane. From any viewpoint, it retains its circular shape.

Cylinder A solid generated by the revolution of a rectangle about one of its sides. A cylinder is centralized about the axis passing through the centers of its two circular faces. Along this axis, it can be easily extended. The cylinder is stable if it rests on one of its circular faces; it becomes unstable when its central axis is inclined from the vertical. Like the cylinder, the cone is a highly stable form when resting on its circular base, and unstable when its vertical axis is tipped or overturned. It can also rest on its apex in a precarious state of balance.

Pyramid A polyhedron having a polygonal base and triangular faces meeting at a common point or vertex. The pyramid has properties similar to those of the cone. Because all of its surfaces are flat planes, however, the pyramid can rest in a stable manner on any of its faces. While the cone is a soft form, the pyramid is relatively hard and angular.

A Cube A prismatic solid bounded by six equal square sides, the angle between any two adjacent faces being a right angle. Because of the equality of its dimensions, the cube is a static form that lacks apparent movement or direction. It is a stable form except when it stands on one of its edges or corners. Even though its angular profile is affected by our point of view, the cube remains a highly recognizable form.

They are generally stable in nature and symmetrical about one or more axes. The sphere, cylinder, cone, cube, and pyramid are prime examples of regular forms. Forms can retain their regularity even when transformed dimensionally or by the addition or subtraction of elements.

From our experiences with similar forms, we can construct a mental model of the original whole even when a fragment is missing or another part is added. Irregular forms are those whose parts are dissimilar in nature and related to one another in an inconsistent manner. They are generally asymmetrical and more dynamic than regular forms. They can be regular forms from which irregular elements have been subtracted or result from an irregular composition of regular forms. Since we deal with both solid masses and spatial voids in architecture, regular forms can be con- tained within irregularforms.

In a similar manner, irregular forms can be enclosed by regular forms. Dimensional Transformation A form can be transformed by altering one or more of its dimensions and still retain its identity as a member of a family of forms. A cube, for example, can be transformed into similar prismatic forms through discrete changes in heig ht, width, or length. It can be compressed into a planarform or be stretched out into a linear one. Subtractive Transformation A form can be transformed by subtracting a portion of its volume.

Depending on the extent of the subtractive process, the form can retain its initial identity or be transformed into a form of another family. For example, a cube can retain its identity as a cube even though a portion of it is removed, or be transformed into a series of regular polyhedrons that begin to approximate a sphere. Additive Transformation A form can be transformed by the addition of elements to its volume. The nature of the additive process and the number and relative sizes of the elements being attached determine whether the identity of the initial form is altered or retained.

A cube can be transformed into similar prismatic forms by shortening or elongating its height, width, or depth. If any of the primary solids is partially hidden from our view, we tend to complete its form and visualize it as if it were whole because the mind fills in what the eyes do not see. In a similar manner, when regular forms have fragments missing from their volumes, they retain their formal identities if we perceive them as incomplete wholes.

We refer to these mutilated forms as subtractive forms. Because they are easily recognizable, simple geometric forms, such as the primary solids, adapt readily to subtractive treatment. These forms will retain their formal identities if portions of their volumes are removed without deteriorating their edges, corners, and overall profile. Ambiguity regarding the original identity of a form will result if the portion removed from its volume erodes its edges and drastically alters its profile.

In the series of figures below, at what point does the square shape with a corner portion removed become an L- shaped configuration of two rectangular planes? The basic possibilities for grouping two or more forms are by: Spatial Tension This type of relationship relies on the close proximity of the forms or their sharing of a common visual trait, such as shape, color, or material.

Face-to-face Contact This type of relationship requires that the two forms have corresponding planar surfaces which are parallel to each other. Interlocking Volumes In this type of relationship, the forms interpenetrate each other's space. The forms need not share any visual traits. For us to perceive additive groupings as unified compositions of form — as figures in our visual field — the combining elements must be related to one another in a coherent manner. Centralized Form A number of secondary forms clustered about a dominant, central parent-form These diagrams categorize additive forms according to the nature of the relationships that exist among the component forms as well as their overall configurations.

This outline of formal organizations should be compared with a parallel discussion of spatial organizations in Chapter 4. Linear Form A series of forms arranged sequentially in a row Radial Form A composition of linear forms extending outward from a central form in a radial manner Clustered Form A collection of forms grouped together by proximity or the sharing of a common visual trait Grid Form A set of modular forms related and regulated Lingaraja Temple, Bhubaneshwar, India, c.

Pietro in Montorio, Rome, , Donato Bramante Centralized forms require the visual dominance of a geometrically regular, centrally located form, such as a sphere, cone, or cylinder. Because of their in herent centrality, these forms share the self-centering properties of the point and circle. They are ideal as freestanding structures isolated within their context, dominating a point in space, or occupying the center of a defined field.

They can embody sacred or honorific places, or commemorate significant persons or events. In the latter case, the series of forms may be either repetitive or dissimilar in nature and organized by a separate and distinct element such asa wall or path. A linear form can be segmented or curvilinear to respond to topography, vegetation, views, or other features of a site. A linear form can front on or define an edge of an exterior space, or define a plane of entry into the spaces behind it.

A linear form can be manipulated to enclose a portion of space. A linear form can be oriented vertically as a tower element to establish or denote a point in space. A linear form can serve as an organizing element to which a variety of secondary forms are attached. It combines the aspects of centrality and linearity into a single composition. I Radial forms can grow into a network of centers linked by linear arms.

The core is either the symbolic or functional center of the organization. Its central position can be articulated with a visually dominant form, or it can merge with and become subservient to the radiating arms. The radiating arms, having properties similar to those of linear forms, give a radial form its extroverted nature. They can reach out and relate to or attach themselves to specific features of a site.

They can expose their elongated surfaces to desirable conditions of sun, wind, view, or space. When viewed from ground level, its central core element may not be clearly visible and the radiating pattern of its linear arms may be obscured or distorted through perspective foreshortening. While it lacks the geometric regularity and intro- verted nature of centralized forms, a clustered organization is flexible enough to incorporate forms of various shapes, sizes, and orientations into its structure.

They can be related by proximity alone to articulate and express their volumes as individual entities. They can interlock their volumes and merge into a single form having a variety of faces. A clustered organization can also consist of forms that are generally equivalent in size, shape, and function.

These forms are visually ordered into a coherent, nonhierarchical organi- zation not only by their close proximity to one another, but also by the similarity of their visual properties. Numerous examples of clustered housing forms can be found in the vernacular architecture of various cultures.

Designing with Models

Even though each culture produced a unique style in response to differing technical, climatic, and sociocultural factors, these clustered housing organizations usually maintained the individuality of each unit and a moderate degree of diversity within the context of an ordered whole. It generates a geometric pattern of regularly spaced points at the intersections of the grid linesand regularly shaped fields defined bythegrid lines themselves. The most common grid is based on the geometry of the square. Because of the equality of its dimensions and its bilateral sym- metry, a square grid is essentially nonhierarchical and bidirec- tional.

It can be used to break the scale of a surface down into measurable units and give it an even texture. It can be used to wrap several surfaces of a form and unify them with its repeti- tive and pervasive geometry. The square grid, when projected into the third dimension, generates a spatial network of reference points and lines. Within this modular framework, any number of forms and spaces can be visually organized.

In these situations, the following forms can evolve: Circle and Square Rotated Grid o The two forms can subvert their individual identities and merge to create a new composite form. The two forms can separate and be linked by a third element that recalls the geometry of one of the original forms. The structural grid of the lower level of the museum floats over and contrasts with the geometry of the ancient Roman remains of Merida.

An articulated form clearly reveals the precise nature of its parts and their relationships to each other and to the whole. Its surfaces appear as discrete planes with distinct shapes and their overall configuration is legible and easily perceived. In a similar manner, an articulated group of forms accentuates the joints between the constituent parts in order to visually express their individuality.

In opposition to the emphasis on joints and joinery, the corners of a form can be rounded and smoothed over to emphasize the continuity of its surfaces. Or a material, color, texture, or pattern can be carried across a corner onto the adjoining surfaces to de-emphasize the individuality of the surface planes and emphasize instead the volume of a form. While a corner can be articulated by simply contrasting the surface qualities of the adjoining planes, or obscured by layering their joining with an optical pattern, our perception of its existence is also affected by the laws of perspective and the quality of light that illuminates the form.

For a corner to be formally active, there must be more than a slight deviation in the angle between the adjoining planes. Since we constantly search for regularity and continuity within our field of vision, we tend to regularize or smooth out slight irregularities in the forms we see. For example, a wall plane that is bent only slightly will appear to be a single flat plane, perhaps with a surface imperfection. A corner would not be perceived. At what point do these formal deviations become an acuteangle? If the two planes simply touch and the corner remains unadorned, the presence of the corner will depend on the visual treatment of the adjoining surfaces.

This corner condition emphasizes the volume of a form. A corner condition can be visually reinforced by introducing a separate and distinct elementthat is independent of the surfaces it joins. This element articulates the corner as a linear condition, defines the edges of the adjoining planes, and becomes a positive feature of the form. If an opening is introduced to one side of the corner, one of the planes will appear to bypass the other. The opening diminishes the corner condition, weakens the definition of the volume within the form, and emphasizes the planar qualities of the neighboring surfaces.

If neither plane is extended to define the corner, a volume of space is created to replace the corner. This corner condition deteriorates the volume of the form, allows the interior space to leak outward, and clearly reveals the surfaces as planes in space. The scale of the radius of curvature is important. If too small, it becomes visually insignificant; if too large, it affects the interior space it encloses and the exterior form it describes. The corner column emphasizes the edge of the building form. A distinct contrast between the surface color of a plane and that of the surrounding field can clarify its shape, while modifying its tonal value can either increase or decrease its visual weight.

S3 L ; v- Li A frontal view reveals the true shape of a plane; oblique views distort it. Gunnel] nnnnpg Elements of known size within the visual context of a plane can aid our perception of its size and scale. Directional or oversized optical patterns can distort the shape or exaggerate the proportions of a plane. Linear columnar elements emphasize the vertically of this high-rise structure. Linear patterns have the ability to emphasize the height or length of a form, unify its surfaces, and define its textural quality.

A grid pattern unifies the surfaces of the three-dimensional composition. The pattern of openings and cavities interrupts the continuity of the exterior wall planes. We turn clay to make a vessel; But it is on the space where there is nothing that the utility of the vessel depends. We pierce doors and windows to make a house; and it is on these spaces where there is nothing that the utility of the house depends.

Therefore, just as we take advantage of what is, we should recognize the utility of what is not. Through the volume of space, we move, see forms, hear sounds, feel breezes, smell the fragrances of a flower garden in bloom. It is a material substance like wood or stone. Yet it is an inherently formless vapor. Its visual form, its dimensions and scale, the quality of its light — all of these qualities depend on our perception of the spatial boundaries defined by elements of form. As space begins to be captured, enclosed, molded, and organized by the elements of mass, architecture comes into being.

To better comprehend the structure of a visual field, we tend to organize its elements into two opposing groups: positive elements, which are perceived as figures and negative elements, which provide a background for the figures. Two Faces or a Vase? Our perception and understanding of a composition depends on how we interpret the visual interaction between the positive and negative elements within its field. On this page, for example, letters are seen as dark figures against the white background of the paper surface.

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Consequently, we are able to perceive their organization into words, sentences, and paragraphs. In the diagrams to the left, the letter 'a' is seen as a figure not only because we recognize it as a letter in our alphabet but also because its profile is distinct, its value contrasts with that of its background, and its placement isolates it from its context.

As it grows in size relative to its field, however, other elements within and around it begin to compete for our attention as figures. At times, the relationship between figures and their background is so ambiguous that we visually switch their identities back and forth almost simultaneously. White-on-Black or Black-on-White?

In all cases, however, we should understand that figures, the positive elements that attract our attention, could not exist without a contrasting background. Figures and their background, therefore, are more than opposing elements. Together, they form an inseparable reality — a unity of opposites — just as the elements of form and space together form the reality of architecture.

Shah Jahan built this white marble mausoleum for his favorite wife, Muntaz Mahal. Line defining the boundary between solid mass and spatial void B. The form of solid mass rendered as a figure C. The form of the spatial void rendered as figure Architectural form occurs at the juncture between mass and space. In executing and reading design drawings, we should be concerned with both the form of the mass containing a volume of space as well as the form of the spatial volume itself.

Fragment of a Map of Rome, drawn byGiambattista Nolli in Depending on what we perceive to be positive elements, the figure-ground relationship of the forms of mass and space can be inverted in different parts of this map of Rome. In portions of the map, buildings appear to be positive forms that define street spaces. In other parts of the drawing, urban squares, courtyards, and major spaces within important public buildings read as positive elements seen againstthe background of the surrounding building mass. At each level, we should be concerned not only with the form of a building but also its impact on the space around it.

At an urban scale, we should carefully consider whether the role of a building is to continue the existing fabric of a place, form a backdrop for other buildings, or define a positive urban space, or whether it might be appropriate for it to stand free as a significant object in space. At the scale of a building site, there are various strategies for relating the form of a building to the space around it. A building can: A. Building as an object in space Buildings defining space Monastery of St.

Meletios on Mt. Kithairon, Greece, 9th century A. The white space in between, however, should not be seen simply as background for the walls, but also as figures in the drawing that have shape and form. Even atthe scale of a room, articles of furnishings can either stand as forms within a field of space or serve to define the form of a spatial field.

In the Theater in Seinajoki by Alvar Aalto, for example, we can distinguish several categories of spatial forms and analyze how they interact. Each category has an active or passive role in defining space.

Tonia A. Dousay

Some spaces, such as offices, have specific but similar functions and can be grouped into single, linear, or clustered forms. Some spaces, such as concert halls, have specific functional and technical requirements, and require specific forms that will affect the forms of the spaces around them. Some spaces, such as lobbies, are flexible in nature and can therefore be freely defined by the spaces or grouping of spaces around them. In a similar manner, any three-dimensional form naturally articulates the volume of space surrounding it and generates a field of influence or territory which it claims as its own.

The following section of this chapter looks at horizontal and vertical elements of form and presents examples of how various configurations of these formal elements generate and define specific types of space. This field can be visually reinforced in the following ways. Elevated Base Plane A horizontal plane elevated above the ground plane establishes vertical surfaces along its edges that reinforce the visual separation between its field and the surrounding ground.

Depressed Base Plane A horizontal plane depressed into the ground plane utilizes the vertical surfaces of the lowered area to define a volume of space. Overhead Plane A horizontal plane located overhead defines a volume of space between itself and the ground plane. The stronger the edge definition of a horizontal plane is, the more distinct will be its field. Although there is a continuous flow of space across it, the field nevertheless generates a spatial zone or realm within its boundaries.

The surface articulation of the ground or floor plane is often used in architecture to define a zone of space within a larger context. The examples on the facing page illustrate howthistype of spatial definition can be used to differentiate between a path of movement and places of rest, establish a field from which the form of a building rises out of the ground, or articulate a functional zone within a one-room living environment.

The changes in level that occur along the edges of the elevated plane define the boundaries of its field and interrupt the flow of space across its surface. If the surface characteristics of the base plane continues up and across the elevated plane, then the field of the elevated plane will appear to be very much a part of the surrounding space. If, however, the edge condition is articulated by a change in form, color, or texture, then the field will become a plateau that is separate and distinct from its surroundings. A special place is established by a platform in an artificial lake surrounded by the emperor's living and sleeping quarters.

The edge of the field is well-defined; visual and spatial continuity is maintained; physical access is easily accommodated. Visual continuity is maintained; spatial continuity is interrupted; physical access requires the use of stairs or ramps. Visual and spatial continuity is interrupted; the field of the elevated plane is isolated from the ground or floor plane; the elevated plane is transformed into a sheltering element for the space below. The elevated ground plane can be a preexisting site condition, or it can be artificially constructed to deliberately raise a building above the surrounding context or enhance its image in the landscape.

The examples on these two pages illustrate how these techniques have been used to venerate sacred and honorific buildings. Combined with a roof plane, it develops into the semiprivate realm of a porch or veranda. The Farnsworth House was constructed to rise above the flood plain of the Fox River. This elevated floor plane, together with an overhead roof plane, defines a volume of space that hovers delicately above the surface of its site.

This raised space can serve as a retreat from the activity around it or be a platform for viewing the surrounding space. Within a religious structure, it can demarcate a sacred, holy, or consecrated place.

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  7. The vertical surfaces of the depression establish the boundaries of the field. These boundaries are not implied as in the case of an elevated plane, but visible edges that begin to form the walls of the space. The field of space can be further articulated by contrasting the surface treatment of the lowered area and that of the surrounding base plane. Rock-cut churches of Lalibela, 13th century Whereas the act of stepping up to an elevated space might express the extroverted nature or significance of the space, the lowering of a space below its surroundings might allude to its introverted nature orto its sheltering and protective qualities.

    Underground village near Loyang, China The ground plane can be lowered to define sheltered outdoor spaces for underground buildings. A sunken courtyard, while protected from surface-level wind and noise by the mass surrounding it, remains a source of air, light, and views for the underground spaces opening onto it.

    He then uses the vertical bounding surfaces of the reading area for additional book storage. A sunken area can also serve as a transitional space between two floors of a building. Since the edges of the overhead plane establish the boundaries of thisfield, its shape, size, and height above the ground plane determines the formal qualities of the space. While the previous manipulations of the ground or floor plane defined fields of space whose upper limits were established by their context, an overhead plane has the ability to define a discrete volume of space virtually by itself.

    If vertical linear elements such as columns or posts are used to support the overhead plane, they will aid in visually establishing the limits of the defined space without disrupting the flow of space through the field. L i i i Similarly, if the edges of the overhead plane are turned downward, or if the base plane beneath it is articulated by a change in level, the boundaries of the defined volume of space will be visually reinforced.

    Moving the roof of a house in Guinea The major overhead element of a building is its roof plane. It not only shelters the interior spaces of a building from sun, rain, and snow, but also has a major impact on the overall form of a building and the shaping of its spaces. The form of the roof plane, in turn, is determined by the material, geometry, and proportions of its structural system and the manner in which it transfers its loads across space to its supports. The roof plane can be the major space-defining element of a building and visually organize a series of forms and spaces beneath its sheltering canopy.

    Since it need not resist any weathering forces nor carry any major loads, the ceiling plane can also be detached from the floor or roof plane and become a visually active element in a space. As in the case of the base plane, the ceiling plane can be manipulated to define and articulate zones of space within a room.

    It can be lowered or elevated to alter the scale of a space, define a path of movement through it, or allow natural light to enter it from above. The form, color, texture, and pattern of the ceiling plane can be manipulated as well to improve the quality of light or sound within a space or give it a directional quality or orientation. The following section discusses the critical role vertical elements of form play in firmly establishing the visual limits of a spatial field.

    Vertical forms have a greater presence in our visual field than horizontal planes and are therefore more instrumental in defining a discrete volume of space and providing a sense of enclosure and privacy for those within it. In addition, they serve to separate one space from another and establish a common boundary between the interior and exterior environments.

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    Vertical elements of form also play important roles in the construction of architectural forms and spaces. They serve as structural supports for floor and roof planes. They provide shelter and protection from the climatic elements and aid in controlling the flow of air, heat, and sound into and through the interior spaces of a building.

    Single Vertical Plane A single vertical plane articulates the space on which it fronts. L-shaped Plane An L-shaped configuration of vertical planes generates a field of space from its corner outward along a diagonal axis. U-shaped Plane A U-shaped configuration of vertical planes defines a volume of space that is oriented primarily toward the open end of the configuration. Four Planes: Closure Four vertical planes establish the boundaries of an introverted space and influence the field of space around the enclosure. Standing upright and alone, a slender linear element is nondirectional except for the path that would lead us to its position in space.

    Any number of horizontal axes can be made to pass through it. A column attached to a wall buttresses the plane and articulates its surface. At the corner of a space, a column punctuates the meeting of two wall planes. Standing free within a space, a column defines zones of space within the enclosure. When offset, the column will define hierarchical zones of space differentiated by size, form, and location.