Building Construction Illustrated by Francis DK subiecte.info Cargado por raesquivel Download as PDF, TXT or read online from Scribd. Flag for inappropriate. Space and Order 3rd subiecte.info - Ebook download as PDF File .pdf) or read book online. Architecture - Form, Space and Order 3rd edition -Francis D.K. Ching-. PDF | When we asked Professor Francis D.K. Ching to-write an article for our magazine he replied by sending us several of the drawings he did.
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In all other cases, it is usually easier to justify—align vertically—a drawing title with either the drawing itself or its field. Each category has an active or passive role in requirements, and require specific forms that will affect the forms of the defining space. Foreground elements typically possess dark, saturated colors and sharply defined contrasts in value. The primary emphasis should remain on articulating the section cut and the relative depth of elements beyond the plane of the cut. In a similar manner, irregular forms can be enclosed by regular forms.
All volumes can be analyzed and understood to consist of: It is established by the shapes and interrelationships of the planes that describe the boundaries of the volume. As the three-dimensional element in the vocabulary of architectural design, a volume can be either a solid—space displaced by mass—or a void—space contained or enclosed by planes. It is important to perceive this duality, especially when reading orthographic plans, elevations, and sections.
A series of buildings enclose an urban square. The interior rooms surround a cortile— the principal courtyard of an Italian palazzo. The sanctuary is a volume of space carved out of the mass of solid rock. 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 In the context of this study, form suggests reference to both internal external appearance that can be recognized, as that of a chair or the structure and external outline and the principle that gives unity to the whole.
It may also allude to a particular condition in While form often includes a sense of three-dimensional mass or volume, shape which something acts or manifests itself, as when we speak of water in the refers more specifically to the essential aspect of form that governs its form of ice or steam. In art and design, we often use the term to denote the appearance—the configuration or relative disposition of the lines or contours formal structure of a work—the manner of arranging and coordinating the 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 is the attribute that most clearly distinguishes a form from its environment.
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. Position The location of a form relative to its environment or the visual field within which it is seen. Orientation The direction of a form relative to the ground plane, the compass points, other forms, or to the person viewing the form. Visual Inertia 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.
Bust of Queen Nefertiti The pattern of eye movement of a person viewing the figure, from research by Alfred L. In architecture, we are concerned with the shapes of: 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. 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.
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.
This class of curved surfaces include the following: 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.
Because of its straight line geometry, a ruled surface is generally easier to form and construct than a rotational or translational surface. 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. It can thus be considered to be both a translational and a ruled surface. If the edges of a saddle surface are not supported, beam behavior may also be present.
The type of structural system that can best take advantage of this doubly curved geometry is the shell structure—a thin, plate structure, usually of reinforced concrete, which is shaped to transmit applied forces by compressive, tensile, and shear stresses acting in the plane of the curved surface.
The structure consists of a radial arrangement of eight hyperbolic paraboloid segments. Like shell structures, gridshells rely on their double curvature geometry for their strength but are constructed of a grid or lattice, usually of wood or steel. Gridshells are capable of being formed into irregular curved surfaces, relying on computer modeling programs for their structural analysis and optimization and sometimes their fabrication and assembly as well.
See also pages — for a related discussion of diagrids. Symmetrical curved surfaces, such as domes and barrel vaults, are inherently stable. Asymmetrical 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.
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. 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 contained within irregular forms. In a similar manner, irregular forms can be enclosed by regular forms.
Note how the diagrid pattern becomes more dense in areas where moment stresses are higher. 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 height, width, or length. It can be compressed into a planar form 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 pyramid can be transformed by altering the dimensions of the base, modifying the height of the apex, or tilting the normally vertical axis.
A cube can be transformed into similar prismatic forms by shortening or elongating its height, width, or depth. Carlo, Project, 17th century, Francesco Borromini St. 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 this series of figures, at what point does the square shape with a corner portion removed become an L- shaped configuration of two rectangular planes?
Khasneh al Faroun, Petra, 1st century A. 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. Edge-to-Edge Contact In this type of relationship, the forms share a common edge and can pivot about that edge.
Face-to-Face Contact This type of relationship requires that the two forms have corresponding planar surfaces which are parallel to each other. The forms need not share any visual traits. For us to perceive additive groupings as unified compositions of A number of secondary forms clustered about a form—as figures in our visual field—the combining elements must dominant, central parent-form be related to one another in a coherent manner.
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 Lingaraja Temple, Bhubaneshwar, India, c. Because of their inherent 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 as a wall or path.
It combines the aspects of centrality and linearity into a single composition. 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 introverted nature of centralized forms, a clustered organization is flexible enough to incorporate forms of various shapes, sizes, and orientations into its structure.
Considering their flexibility, clustered organizations of forms may be organized in the following ways: 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 organization 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. 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.
Habitat Israel, Project, Jerusalem, , Moshe Safdie Vernacular examples of clustered forms can be readily transformed into modular, geometrically ordered compositions which are related to grid organizations of form. It generates a geometric pattern of regularly spaced points at the intersections of the grid lines and regularly shaped fields defined by the grid 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 down the scale of a surface 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: The centrality of a circular form enables it to act as a hub and unify forms of contrasting geometry or orientation about itself.
The interior space of this mosque is oriented exactly with the cardinal points so that the quibla wall faces in the direction of the holy city of Mecca, while its exterior conforms to the existing layout of the fort.
Its surfaces appear as discrete planes with adjoining surfaces to de-emphasize the individuality of the surface planes and distinct shapes and their overall configuration is legible and easily emphasize instead the volume of a form. In a similar manner, an articulated group of forms accentuates the joints between the constituent parts in order to visually express their individuality. A form can be articulated by: 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 acute angle? 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 element that 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 unadorned corners of the forms emphasize the volume of their mass. The timber joinery articulates the individuality of the members meeting at the corner. The corner column emphasizes the edge of the building form. 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. 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: 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. Consequently, we are able to perceive their organization into words, sentences, and paragraphs. 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 Two Faces or a Vase? 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 B. The form of solid mass C. The form of the spatial void between solid mass and rendered as a figure rendered as a figure spatial void 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 by Giambattista 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 against the 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 A 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: D Building as an object in space Buildings defining space Monastery of St. Meletios on Mt. Kithairon, Greece, 9th century A. H Buildings Defining Space: Building as an Object in Space: 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 at the 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. Some spaces, such as offices, have specific but similar functions and can determined by, the form of the spaces around it.
Alvar Aalto, for example, we can distinguish several categories of spatial forms B. Some spaces, such as concert halls, have specific functional and technical and analyze how they interact.
Each category has an active or passive role in requirements, and require specific forms that will affect the forms of the defining space. 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 how this type 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. The edge of the field is well-defined; 1 visual and spatial continuity is maintained; physical access is easily accommodated. Visual continuity is maintained; 2 spatial continuity is interrupted; physical access requires the use of stairs or ramps.
Visual and spatial continuity is 3 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 this and the preceding page 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. 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. A contrast in form, geometry, or orientation can also visually reinforce the identity and independence of the sunken field from its larger spatial context. Creating a stepped, terraced, or ramped transition from one level to the next helps promote continuity between a sunken space and the area that rises around it. 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 or to its sheltering and protective qualities.
The natural change in level benefits both the sightlines and the acoustical quality of these spaces. 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 this field, 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. 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.
It not only Steel Joist 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.
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. Bandung Institute of Technology, Bandung, Indonesia, , Henri Maclaine Pont 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.
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. Parallel Planes Two parallel vertical planes define a volume of space between them that is oriented axially toward both open ends of the configuration.
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. When located within a defined volume of space, a column will generate a spatial field about itself and interact with the spatial enclosure. 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 centered in a space, a column will assert itself as the center of the field and define equivalent zones of space between itself and the surrounding wall planes.
When offset, the column will define hierarchical zones of space differentiated by size, form, and location. Linear elements serve this purpose in marking the limits of spaces that require visual and spatial continuity with their surroundings. Two columns establish a transparent spatial membrane by the visual tension between their shafts. Three or more columns can be arranged to define the corners of a volume of space. This space does not require a larger spatial context for its definition, but relates freely to it.
The edges of the volume of space can be visually reinforced by articulating its base plane and establishing its upper limits with beams spanning between the columns or with an overhead plane. A repetitive series of column elements along its perimeter would further strengthen the definition of the volume. In the example above, the tokobashira, often a tree trunk in natural form, is a symbolic element that marks one edge of the tokonoma in a Japanese tearoom.
Piazza of St. Four columns can establish the corners of a discrete volume of space During the Renaissance, Andrea Palladio incorporated the tetrastyle theme in within a larger room or setting. Supporting a canopy, the columns form the vestibules and halls of a number of villas and palazzi. The four columns not an aedicule, a diminutive pavilion that serves as a shrine or the symbolic only supported the vaulted ceiling and the floor above but also adjusted the center of a space.
Traditional Roman houses typically were organized about an atrium open In the Sea Ranch condominium units, four posts along with a sunken floor and to the sky and surrounded by a roof structure supported at the corners by an overhead plane define an intimate aedicular space within a larger room.
Vitruvius termed this a tetrastyle atrium. Condominium Unit No. Michel, France, — A regularly spaced series of columns or similar vertical elements form a colonnade. This archetypal element in the vocabulary of architectural design effectively defines an edge of a spatial volume while permitting visual and spatial continuity to exist between the space and its surroundings.
A row of columns can also engage a wall and become a pilastrade that supports the wall, articulates its surface, and tempers the scale, rhythm, and proportioning of its bays.
A grid of columns within a large room or hall not only serves to support the floor or roof plane above. The orderly rows of columns also punctuate the spatial volume, mark off modular zones within the spatial field, and establish a measurable rhythm and scale that make the spatial dimensions comprehensible.
This type of construction, in particular the use of concrete columns to support floor and roof slabs, afforded new possibilities for the definition and enclosure of spaces within a building.
Interior spaces could be defined with non-load-bearing partitions, and their layout could respond freely to programmatic requirements. Sketches for The Five Points of the New Architecture, , Le Corbusier On the facing page, two contrasting examples of the use of a column grid are illustrated: A column grid establishes a fixed, neutral field of space in which interior spaces are freely formed and distributed.
A grid of columns or posts corresponds closely to the layout of the interior spaces; there is a close fit between structure and space. A round column has no preferred direction except for its vertical axis. A square column has two equivalent sets of faces and therefore two identical axes. A rectangular column also has two axes, but they differ in their effect. As the rectangular column becomes more like a wall, it can appear to be merely a fragment of an infinitely larger or longer plane, slicing through and dividing a volume of space.
A vertical plane has frontal qualities. Its two surfaces or faces front on and establish the edges of two separate and distinct spatial fields. These two faces of a plane can be equivalent and front similar spaces.
Or they can be differentiated in form, color, or texture, in order to respond to or articulate different spatial conditions. A vertical plane can therefore have either two fronts or a front and a back. The field of space on which a single vertical plane fronts is not well-defined. The plane by itself can establish only a single edge of the field. To define a three- dimensional volume of space, the plane must interact with other elements of form.
When 2-feet high, a plane defines the edge of a spatial field but provides little or no sense of enclosure. When waist-high, it begins to provide a sense of enclosure while allowing for visual continuity with the adjoining space.
When it approaches our eye level in height, it begins to separate one space from another. Above our height, a plane interrupts the visual and spatial continuity between two fields and provides a strong sense of enclosure. The surface color, texture, and pattern of a plane affect our perception of its visual weight, scale, and proportion. When related to a defined volume of space, a vertical plane can be the primary face of the space and give it a specific orientation.
It can front the space and define a plane of entry into it. It can be a freestanding element within a space and divide the volume into two separate but related areas.
Agostino, Rome, —, Giacomo da Pietrasanta larger volume. The partitions never form closed, geometrically static areas. While this field is strongly defined and enclosed at the corner of the configuration, it dissipates rapidly as it moves away from the corner. The introverted field at the interior corner becomes extroverted along its outer edges.
While two edges of the field are clearly defined by the two planes of the configuration, its other edges remain ambiguous unless further articulated by additional vertical elements, manipulations of the base plane, or an overhead plane. If a void is introduced to one side of the corner of the configuration, the definition of the field will be weakened. The two planes will be isolated from each other and one will appear to slide by and visually dominate the other. If neither plane extends to the corner, the field will become more dynamic and organize itself along the diagonal of the configuration.
One of the arms of the configuration can be a linear form that incorporates the corner within its boundaries while the other arm is seen as an appendage to it. Or the corner can be articulated as an independent element that joins two linear forms together.
A building can have an L-shaped configuration to establish a corner of its site, enclose a field of outdoor space to which its interior spaces relate, or shelter a portion of outdoor space from undesirable conditions around it. L-shaped configurations of planes are stable and self- supporting and can stand alone in space. Because they are open-ended, they are flexible space-defining elements.
They can be used in combination with one another or with other elements of form to define a rich variety of spaces. Typically, sheltered by the building form and to which interior spaces can be directly one wing contains the communal living spaces while the other contains related.
In the Kingo Housing estate, a fairly high density is achieved with this private, individual spaces. The service and utility spaces usually occupy a type of unit, each with its own private outdoor space. The outdoor space enclosed by the architect's studio in Helsinki is used as an amphitheater for lectures and social occasions. It is not a passive space whose form is determined by the building that encloses it. Rather, it asserts its positive form on the shape of its enclosure.
The History Faculty Building at Cambridge uses a seven-story, L-shaped block to functionally and symbolically enclose a large, roof-lit library, which is the most important space in the building. The open ends of the field, established by the vertical edges of the planes, give the space a strong directional quality.
Its primary orientation is along the axis about which the planes are symmetrical. Since the parallel planes do not meet to form corners and fully enclose the field, the space is extroverted in nature. The definition of the spatial field along the open ends of the configuration can be visually reinforced by manipulating the base plane or adding overhead elements to the composition.
The spatial field can be expanded by extending the base plane beyond the open ends of the configuration. This expanded field can, in turn, be terminated by a vertical plane whose width and height is equal to that of the field. If one of the parallel planes is differentiated from the other by a change in form, color, or texture, a secondary axis, perpendicular to the flow of the space, will be established within the field.
Openings in one or both of the planes can also introduce secondary axes to the field and modulate the directional quality of the space. Sets of parallel vertical planes can be transformed into a wide variety of configurations. Their spatial fields can be related to one another either through the open ends of their configurations or through openings in the planes themselves.
Apollinare in Classe, Ravenna, Italy, — Champ de Mars, Paris The directional quality and flow of the space defined by parallel planes are naturally manifested in spaces used for circulation and movement, such as the streets and boulevards of towns and cities.
These linear spaces can be defined by the facades of the buildings fronting them, as well as by the more permeable planes established by colonnades, arcades, or rows of trees. The parallel planes that define a circulation space can be solid and opaque to provide privacy for the spaces along the circulation path.
The planes can also be established by a row of columns so that the circulation path, open on one or both of its sides, becomes part of the spaces through which it passes. Their repetitive pattern can be modified by varying their length or by introducing voids within the planes to accommodate the dimensional requirements of larger spaces. These voids can also define circulation paths and establish visual relationships perpendicular to the wall planes. The slots of space defined by parallel wall planes can also be modulated by altering the spacing and configuration of the planes.
They not only provide structural support for the floors and roofs of each housing unit, but also serve to isolate the units from one another, curb the passage of sound, and check Entry level the spread of fire. The pattern of parallel bearing walls is particularly appropriate for rowhousing and townhouse schemes where each unit is provided with two orientations.
At the closed end of the configuration, the field is well defined. Toward the open end of the configuration, the field becomes extroverted in nature. The open end is the primary aspect of the configuration by virtue of its uniqueness relative to the other three planes. It allows the field to have visual and spatial continuity with the adjoining space.
The extension of the spatial field into the adjoining space can be visually reinforced by continuing the base plane beyond the open end of the configuration. If the plane of the opening is further defined with columns or overhead elements, the definition of the original field will be reinforced and continuity with the adjoining space will be interrupted.
If the configuration of planes is rectangular and oblong in form, the open end can be along its narrow or wide side. In either case, the open end will remain the primary face of the spatial field, and the plane opposite the open end will be the principal element among the three planes of the configuration.
If the field is entered through the open end of the configuration, the rear plane, or a form placed in front of it, will terminate our view of the space. If the field is entered through an opening in one of the planes, the view of what lies beyond the open end will draw our attention and terminate the sequence. If the end of a long, narrow field is open, the space will encourage movement and induce a progression or sequence of events.
If the field is square, or nearly square, the space will be static and have the character of a place to be in, rather than a space to move through.
If the side of a long, narrow field is open, the space will be susceptible to a subdivision into a number of zones. U-shaped configurations of building forms and organizations have the inherent ability to capture and define outdoor space. Their composition can be seen to consist essentially of linear forms. The corners of the configuration can be articulated as independent elements or can be incorporated into the body of the linear forms.
They can also focus on an important or significant element within their fields. When an element is placed along the open end of its field, it gives the field a point of focus as well as a Sacred Precinct of Athena,Pergamon, Asia Minor, 4th century B.
A U-shaped building form can also serve as a container and can organize within its field a cluster of forms and spaces. The cells form an enclave for a village of community rooms. Athens early Anatolian or Aegean house U-shaped enclosures of interior space have a specific orientation toward The Hotel for Students at Otaniemi, Finland, by Alvar Aalto, demonstrates the their open ends.
These U-shaped enclosures can group themselves around use of U-shaped enclosures to define the basic unit of space in double-loaded a central space to form an introverted organization. These units are extroverted. They turn their back on the corridor and orient themselves to the exterior environment.
CL O SURE Four vertical planes encompassing a field of space is probably the most typical, and certainly the strongest, type of spatial definition in architecture. Since the field is completely enclosed, its space is naturally introverted. To achieve visual dominance within a space or become its primary face, one of the enclosing planes can be differentiated from the others by its size, form, surface articulation, or by the nature of the openings within it.
Well-defined, enclosed fields of space can be found in architecture at various scales, from a large urban square, to a courtyard or atrium space, to a single hall or room within a building complex. The examples on this and the following pages illustrate enclosed spatial fields in both urban and building-scale situations.
Historically, four planes have often been used to define a visual and spatial field for a sacred or significant building that stands as an object within the enclosure. The enclosing planes may be ramparts, walls, or fences that isolate the field and exclude surrounding elements from the precinct. The enclosure may consist of arcades or gallery spaces that promote the inclusion of surrounding buildings into their domain and activate the space they define. Plan of the Agora at Priene and its surroundings, 4th century B.
Forum at Pompeii, 2nd century B. The examples on these two pages illustrate the use of enclosed volumes of space as ordering elements about which the spaces of a building can be clustered and organized. These organizing spaces can generally be characterized by their centrality, their clarity of definition, their regularity of form, and their dominating size. They are manifested here in the atrium spaces of houses, the arcaded cortile of an Italian palazzo, the enclosure of a Greek House No.
In contrast, other buildings can be seen to be dominated by the form of their exterior, enclosing wall planes. Exterior walls determine to a great extent the visual character of a building, whether they have the weight and opacity of load-bearing walls, the lightness and transparency of nonbearing curtain walls supported by a structural framework of columns and beams, or a combination of both.
This ambiguity results from the alignment of lines in the foreground with those in the background. In such cases, a plan oblique might be a better choice. Digital graphics programs, however, allow the use of any desired angle. This should be the longest, the most significant, or the most complex face of the subject. In sketching or when using digital drawing tools, we need not be as precise, but once we establish an angle for the receding lines, we should apply it consistently.
By varying the angle, the horizontal and vertical sets of receding planes can receive different degrees of emphasis. When constructing and presenting a paraline drawing, keep in mind that paraline views are easiest to understand if vertical lines in space are also oriented vertically on the drawing surface. It involves constructing a paraline view of a transparent rectangular box that encompasses the entire volume of the subject, and then working in a subtractive manner to remove material and reveal the form.
It requires drawing a paraline view of the parent form first, and then adding the subordinate forms. It begins with a paraline view of a horizontal plane of the subject or the profile of a vertical section cut. We can then extrude the shape vertically or extend it back into the depth of the drawing. To draw such a circle in a paraline drawing, we must first draw a paraline view of the square that circumscribes the circle.
Then we can use either of two approaches to drawing the circle within the square. By dividing the square into quadrants and drawing diagonals from each corner to quarter points along the sides of the square, we can establish eight points along the circumference of the circle.
We can use a grid to transfer curvilinear or free-form shapes from an orthographic view to the paraline view. This grid may either be uniform or correspond to critical points in the shape. The more complex the shape, the finer the grid divisions should be. It may therefore be difficult to define this hierarchy of line weights without first transferring the graphic image to a two-dimensional environment. These techniques allow us to gain visual access to the interior of a spatial composition or the hidden portions of a complex construction.
We categorize these techniques into expanded views, cutaway views, phantom views, and sequential views. Expanded Views To develop what we call an expanded or exploded view, we merely shift portions of a paraline drawing to new positions in space.
The finished drawing appears to be an explosion frozen at a point in time when the relationships between the parts of the whole are most clear. Remember that, as with other drawing types, the larger the scale of a paraline drawing, the more detail you have to show.
This strategy can also effectively manifest the relation of an interior to the exterior environment. Removing a floor permits a view up into a space. When a composition exhibits bilateral symmetry, we can make this cut along the central axis and indicate the footprint or plan view of the part removed. In this case, the trajectory of the cut should clarify the nature of the overall form building as well as the organization and arrangement of interior spaces.
Indicating the external form of what is removed helps the viewer retain a sense of the whole. This strategy effectively allows us to unveil an interior space or construction without removing any of its bounding planes or encompassing elements.
Thus, we are able to simultaneously see the whole composition and its internal structure and arrangement. By organizing elements and assemblies of a three-dimensional construction into separate groups or layers, we can selectively control their location, visibility, and appearance, as illustrated on this and the facing page.
In this case, each floor level successively builds upon the preceding one. Linear perspective is a technique for describing three-dimensional volumes and spatial relationships on a two-dimensional surface by means of lines that converge as they recede into the depth of a drawing. While multiview and paraline drawings present views of an objective reality, linear perspective offers scenes of an optical reality. It depicts how a construction or environment might appear to the eye of an observer looking in a specific direction from a particular vantage point in space.
L i n e ar Pe r s pe ctive Linear perspective is valid only for monocular vision. A perspective drawing assumes that the observer sees through a single eye.
We almost never view anything in this way. Even with the head in a fixed position, we see through both eyes, which are constantly in motion, roving over and around objects and through ever-changing environments. Thus, linear perspective can only approximate the complex way our eyes actually function.
Still, linear perspective provides us with a method for correctly placing three-dimensional objects in pictorial space and illustrating the degree to which their forms appear to diminish in size as they recede into the depth of a drawing.
The uniqueness of a linear perspective lies in its ability to provide us with an experiential view of space.
This distinct advantage, however, also gives rise to the difficulty often connected with perspective drawing. The challenge in mastering linear perspective is resolving the conflict between our knowledge of the thing itself—how we conceive its objective reality—and the appearance of something—how we perceive its optical reality—as seen through a single eye of the observer.
This convergence of sight lines differentiates perspective projection from the other two major projection systems—orthographic projection and oblique projection—in which the projectors remain parallel to each other.
The picture plane is always perpendicular to the central axis of vision CAV. The cone of vision serves as a guide in determining what is to be included within the boundaries of a perspective drawing. Only a small portion Elevation of the immediate foreground falls within the cone of vision.
As the cone of vision reaches out to gather in what the observer sees, it widens its field, and the middleground and background become more expansive. Being familiar with these pictorial effects helps us understand how lines, planes, and volumes should appear in linear perspective and how to place objects Pa c ral correctly in the space of a perspective drawing.
If the lines are extended to infinity, they will appear to meet at a point on the picture plane PP. This point is the vanishing point VP for that particular pair VP for ab, cd of lines and all other lines parallel to them. VP for ad, bc The first rule of convergence is that each set of parallel lines has its own vanishing point. A set of parallel lines consists only of those lines that Perspective View are parallel to one another.
If we look at a cube, for example, we can see that its edges comprise three 3 principal sets of parallel lines, one set of vertical lines parallel to the X-axis, and two sets of horizontal lines, 3 perpendicular to each other and parallel to the Y- and 3 Z-axes. Each line in the PP set, however, will diminish in size according to icular to Perpend its distance from the observer.
If it Fall slopes downward as it recedes, its vanishing ing awa point lies below HL. Therefore, the projected size of an element remains the same regardless of its distance from the picture plane. In linear perspective, however, the converging projectors or sight lines alter Orthographic Projection the apparent size of a line or plane according to its PP distance from the picture plane.
As the same-size tiles recede, they appear smaller and flatter as they rise and approach the horizon. Other Pictorial Effects Perspective drawings also possess other pictorial characteristics found in multiview and paraline drawing systems. As this viewpoint changes—as the observer moves up or down, to the left or right, forward or back—the extent and emphasis of what the observer sees also change. SP of the perspective.
A distinct advantage in using 3D CAD and modeling programs is that once the necessary data is entered for a three-dimensional construction, the software allows us to manipulate the perspective variables and fairly quickly produce a number of perspective views for evaluation.
Judgment of what a perspective image conveys, whether produced by hand or with the aid of the computer, remains the responsibility of its author. Illustrated on this and the facing page are examples of computer-generated perspectives, showing how the various perspective variables affect the resulting images.
The differences in the perspective views may be subtle but they do affect our perception of the scale of the spaces and our judgment of the spatial relationships the images convey.
However, one should perspective view. Widening the angle of view to include more always attempt to maintain a reasonable position for of a space within a perspective can easily lead to distortion of the observer within the space being represented.
The closer PP is to the station point SP , the smaller the perspective image. The farther away PP is, the larger the image. Assuming all other variables remain constant, the perspective images are identical in all respects except size. Based on these three major sets of lines, there are three types of linear perspective: The subject does not change, only our view of it, but the change of view affects how the sets of parallel lines appear to converge in linear perspective.
The lines that are parallel with CAV, however, will appear to converge at the center of vision C. This is the one point referred to in one-point perspective. The two sets HL of horizontal lines, however, are now oblique to the picture plane PP and will appear to converge, one set to the left and the other to the right.
These are the two points referred to in two- point perspective. These are the three points referred to in three-point perspective. Note that each type of perspective does not imply that there are only one, two, or three vanishing points in a perspective. For example, if we look at a simple 4 gable-roofed form, we can see that there are potentially five 1 5 vanishing points, since we have one set of vertical lines, two 2 sets of horizontal lines, and two sets of inclined lines.
All lines parallel to these axes are also parallel to the picture plane PP , and therefore retain their true orientation and do not appear to converge. For Parallel to PP this reason, one-point perspective is also known as parallel perspective.
This is the particular n dic rpe vanishing point referred to in one-point perspective. Pe The one-point perspective system is particularly Parallel to PP effective in depicting the interior of a spatial volume because the display of five bounding faces provides a clear sense of enclosure.
For this reason, designers often use one-point perspectives to present experiential views of street scenes, formal gardens, courtyards, colonnades, and interior rooms.
The three-dimensional network of uniformly spaced points and lines enables us to correctly establish the form and dimensions of an interior or Plan Views Perspective Views exterior space, as well to regulate the position and size of objects within the space. What do we wish to illustrate in the perspective view and why? PP need not be drawn at the same scale as the plan setup.
The position of C can be determined from the plan setup. The unit of measurement is typically one foot; we can, however, use smaller or larger increments GL depending on the scale of the drawing and the amount of detail desired in the perspective view. We call this vanishing point a diagonal point DP. A half-distance point will cut off two- foot increments in depth for every one-foot increment in width: With the same grid, we can also locate the positions and relative sizes of other elements within the space, such as furniture and lighting fixtures.
Note that, particularly in interior views, properly cropped foreground elements can enhance the feeling that one is in a space rather than on the outside looking in.
The center of vision C is closer to the left-hand wall so that the bending of the space to the right can be visualized. The change in scale between the right-hand shelving and patio doors beyond, and a similar change between the foreground table and the window seat beyond, serve to emphasize the depth of the perspective.
It therefore is able to illustrate both the constructional aspects of a design as well as the quality of the spaces formed by the structure. Because the section cut is assumed to be coincident with the picture plane PP of the perspective, it serves as a ready reference for making vertical and horizontal measurements for the HL C DPR perspective drawing.
The height of HL and position of C determine what is seen within the perspective view. As a rule of thumb, the distance from C to DPL or DPR should be at least as great as the width or height of the building section, whichever is larger. The principal vertical axis is parallel to PP, and all lines parallel to it remain vertical and parallel in the perspective drawing.
The two principal horizontal axes, however, are oblique to PP. All lines parallel to these axes therefore appear to converge to two vanishing points on the horizon line HL , one set 3 to the left and the other to the right. These are the two points referred to in two-point perspective. Unlike one-point Horizonta nta l l Horizo perspectives, two-point perspectives tend to be neither 1 2 symmetrical nor static. A two-point perspective is par- ticularly effective in illustrating the three-dimensional form of objects in space ranging in scale from a chair to the massing of a building.
The orientation of the two horizontal axes to PP determines how much we will see of the two major sets of vertical planes and the degree to which they are foreshortened in perspective. Determine what you wish to illustrate.
Look toward the most significant areas and try to visualize from your plan drawing what will be seen in the foreground, middleground, and background.
Review the perspective variables on pages — Remember that the vanishing point for any set of parallel lines is that point at which a line drawn from SP, parallel to the set, intersects PP. The diagonal point in one-point perspective is one example of such a measuring point.
In two-point perspective, you can establish two measuring points MPL and MPR for transferring dimensions along the ground line GL to the two major horizontal baselines that are receding in perspective.
This intersection is MPR. For example, if you have a series of parallel diagonals in your design, establish their vanishing point as well. This scale need not be the same as the scale of the plan setup. The unit of measurement typically is one left baseline in perspective by drawing lines to foot; we can use smaller or larger increments, however, MPR. Transfer scale measurements on GL to the depending on the scale of the drawing and the amount right baseline by drawing lines to MPL.
These are of detail desired in the perspective view. It is important measurements along the major horizontal baselines to see the perspective grid as a network of points in perspective. When one-foot squares The grid of squares facilitates the plotting of become too small to draw accurately, use two-foot points in three-dimensional space, regulates or four-foot squares instead. Each unit of measurement can represent a foot, four feet, a hundred yards, or even a mile. Rotating and reversing the grid can also vary the point of view.
Therefore, you can use the same 8 grid to draw an interior perspective of a room, an exterior perspective of a courtyard, as well as an aerial view of a city block or neighborhood.
Note that the left vanishing point VPL lies within the drawing, enabling three sides of the space to be shown and a greater sense of enclosure to be felt.
Because VPL lies within the drawing, greater emphasis is placed on the right- hand portion of the space. If the left-hand side of the space is to be emphasized, use a reverse image of the grid. But there are techniques we can use to determine the relative heights, widths, and depths of objects in the pictorial space of a perspective drawing.
Measuring Height and Width In linear perspective, any line in the picture plane PP displays its true direction and true length at the scale of the picture plane. We can therefore use any such line as a measuring line ML to scale dimensions in a perspective drawing. While a measuring Vertical ML line may have any orientation in the picture plane, it typically is vertical or horizontal and used to measure true heights or widths.
The ground line GL is one example of a horizontal measuring line. Digital Measurements Perspective measurements are not a major issue in 3D-modeling programs because the software uses mathematical formulas to process the three-dimensional data we have already entered.
Various methods of perspective construction establish depth in different ways. Once we establish an initial depth judgment, however, we can make succeeding depth judgments in proportion to the first. Subdividing Depth Measurements There are two methods for subdividing depth measurements in linear perspective: Method of Diagonals In any projection system, we can subdivide a rectangle into four equal parts by drawing two diagonals.
Lines drawn through this midpoint, parallel to the edges of the plane, will subdivide the rectangle and its receding sides into equal parts. We can repeat this procedure to subdivide 5e par qual sp a rectangle into any even number of parts. These mark off the desired spaces, which diminish as they recede in perspective.
If the receding line is horizontal in space, then ML will be a horizontal line in the drawing. These lines subdivide the receding line into the same proportional segments. B A Extending a Depth Measurement If the forward edge of a rectangular plane is parallel to the picture plane PP , we can extend and duplicate its depth in perspective.
The distance from the first to the second edge is identical eq. The reason for this is that, in the latter perspective drawing. If perpendicular or oblique to PP, however, an inclined set of lines will appear to converge at a vanishing point above or below the horizon line HL. The easiest way to do this is to visualize the inclined line as being the hypotenuse of a right triangle. If we can draw the sides of the triangle in proper perspective, we can connect the end points to establish the g isin inclined line.
An inclined l set of parallel lines is not horizontal and therefore z onta Hori will not converge on HL. If the set rises upward as it recedes, its vanishing point will be above HL; if it falls as it recedes, it will appear to converge L in ef below HL. This intersection is the vanishing point VPi for the inclined line and all other lines parallel to it.
Mark this point A. The horizon line, Plan for example, is the vanishing trace along which SP all horizontal sets of parallel lines converge. This is the vanishing trace for the vertical plane containing the inclined set of parallel lines. We are not concerned yet with the individual treads of the stairway. This occurs most frequently when the plane of the circle is horizontal and at the height of the horizon line HL , or when the plane of the circle is vertical and aligned with the central axis of vision CAV.
The larger the circle, the more subdivisions are necessary to ensure smoothness of the elliptical shape. Checking the relationship Tangent between the major and minor axes of elliptical shapes helps to ensure accuracy of the foreshortening of circles in perspective. A reflecting surface Object presents an inverted or mirror image of the object being reflected.
For example, if an object is resting SP directly on a reflecting surface, the reflected image is a direct, inverted copy of the original. Thus, in a perspective view of the reflection, the reflected image follows the same perspective system of lines already established for the original image. Each reflection therefore doubles the apparent dimension of the space in a direction perpendicular to the mirrored surface.
Therefore, the major sets of parallel lines in the reflection appear to converge to the same vanishing points as do the corresponding sets of lines in the subject. For example, the waterline establishes the horizontal reflecting plane. Point o lies in this plane. While lines are essential to the task of delineating contour and shape, there are also visual qualities of light, texture, mass, and space that cannot be fully described by line alone.
In order to model the surfaces of forms and convey a sense of light, we rely on the rendering of tonal values. Ton a l Val u e s Vision results from the stimulation of nerve cells in the retina of the eye, signaling patterns of light intensity and color.
Our visual system processes these patterns of light and dark, and is able to extract specific features of our environment—edges, contours, size, movement, and color. If seeing patterns of light and dark is essential to our perception of objects, then establishing contrasts in value discernible to the eye is the key to the graphic definition of light, form, and space.
Through the interplay of tonal values we are able to: The visual effect of each technique varies according to the nature of the stroke, the medium, and the texture of the drawing surface.
Regardless of the shading technique we use, we must always be fully aware of the tonal value being depicted. For example, a tonal value superimposed upon a darker tone will appear lighter than the same value set against a lighter tone. Covering the paper surface entirely can cause a drawing to lose depth and vitality.
The strokes may be long or short, mechanically ruled or drawn freehand, and executed with either a pen or a pencil on smooth or rough paper. When spaced close enough together, the lines lose their individuality and merge to form a tonal value.
We therefore rely primarily on the spacing and density of lines to control the lightness or darkness of a value. While thickening the linear strokes can serve to deepen the darkest values, using too thick of a line can result in an unintentional coarseness and heaviness of texture. Maintaining the diagonal direction of the strokes in this manner avoids confusion with the underlying drawing and unifies the various tonal areas of a drawing composition.
Remember that direction alone, however, has no impact on tonal value. With texture and contour, the series of lines can also convey material characteristics, such as the grain of wood, the marbling of stone, or the weave of fabric.
Be careful not to use too dense a grade of lead or press so hard that the pencil point embosses the drawing surface. You can only control the spacing and density of the hatching. As with hatching, the strokes may be long or short, mechanically ruled or drawn freehand, and executed with either a pen or a pencil on smooth or rough paper. The multidirectional nature of the hatching also makes it easier describe the orientation and curvature of surfaces.
While simple hatching creates the lighter range of values in a drawing, crosshatching renders the darker range. The freehand nature of scribbling gives us great flexibility in describing tonal values and textures. We can vary the shape, density, and direction of the strokes to achieve a wide range of tonal values, textures, and visual expression.
Applying stippling is a slow and time-consuming procedure that requires the utmost patience and care in controlling the size and spacing of the dots. The best results occur when using a fine- tipped ink pen on a smooth drawing surface. The procedure involves applying stippling over faintly drawn shapes of the areas to be toned. We use tightly spaced dots to define sharp, distinct edges, and a looser spacing of dots to imply softer, more rounded contours. If the scale of the dots is too large for the toned area, too coarse a texture will result.
Image-processing software further allows the creation and application of visual textures, some of which mimic the traditional techniques outlined on the previous pages. Shown on this and the facing page are two digital examples using simple gray tones and gradients. The first illustrates a line-and-tone technique to model the forms.
Instead, the range of tonal values serves primarily to define the orientation of the surfaces relative to an assumed light source. In between exists an intermediate range of grays. A familiar form of this range is represented by a gray or value scale having ten equal gradations from white to black. It is worthwhile to practice producing both a stepped series and a graduated scale of tonal values using a variety of media and techniques.
It can also describe the characteristic surface qualities of familiar materials, as the hewn appearance of stone, the grain of wood, and the weave of a fabric. This is tactile texture that can be felt by touch.
Our senses of sight and touch are closely intertwined. As our eyes read the visual texture of a surface, we often respond to its apparent tactile quality without actually touching it. We base these physical reactions on the textural qualities of similar materials we have experienced in the past. In most cases, tonal value is more critical than texture to the representation of light, shade, and the way they model forms in space.
Shading with tonal values extends a simple drawing of contours into the three-dimensional realm of forms arranged in space. Since the definition of edges gives rise to shape recognition, we look to edges to discover the configuration of the surfaces of a three-dimensional form.
We must therefore be careful how we define the nature of the edge or boundary wherever two shapes of contrasting values meet. The skillful manipulation of tonal edges is critical to defining the nature and solidity of a surface or object. We define hard edges with an abrupt and incisive shift in tonal value. We create soft edges with a gradual change in tonal value or diffuse tonal contrast.
Light is the radiant energy that illuminates our world and enables us to see three-dimensional forms in space. We do not actually see light but rather the effects of light.
Within these patterns of light and dark shapes, we can recognize the following elements: The simplest approach is ray casting. Ray Casting Ray casting is a technique that analyzes the three-dimensional geometry of forms and determines the illumination and shading of surfaces based on their orientation to an assumed light source. The primary advantage of ray casting is the speed with which an illuminated three-dimensional image or scene can be generated, often in real-time.
This makes ray casting a useful tool in preliminary design to study the solar consequences of the massing and composition of building forms and the shadows they cast. See pages — for examples. Ray casting, however, does not take into account the way light travels after intersecting a surface and therefore cannot accurately render reflections, refractions, or the natural fall off of shadows.
For this, ray tracing is necessary. Ray tracing is a digital technique for tracing these paths to simulate the optical effects of illumination. Local illumination is a basic level of ray tracing that is limited to direct illumination and the specular reflections of light rays.
While local illumination does not take into account the diffuse inter-reflection of light among the surfaces in a three-dimensional space or scene, some ray tracing programs can approximate this ambient light in their lighting algorithms.
Local illumination: Global illumination techniques use sophisticated algorithms to more accurately simulate the illumination of a space or scene.
These algorithms take into account not only the light rays that are emitted directly from one or more sources. They also track the light rays as they are reflected or refracted from one surface to another, especially the diffuse inter- reflections that occur among the surfaces in a space or scene.
This enhanced level of simulation comes at a cost, however. The process requires time and is computationally intensive, and should therefore be used only when appropriate to the design task at hand. Global illumination: These two drawings of the Piazza San Marco in Venice illustrate how the tonal contrast can be achieved either by rendering the building as a dark figure against a light background or by reversing the figure-ground relationship and rendering the tonal values of the site.
These values can effectively isolate and provide a base for elements that are situated above the floor plane. The lower the floor plane, the darker its value. Be sure, however, that there is sufficient contrast to emphasize the dominance of the cut elements. If necessary, outline the cut elements with a heavy line weight.
The most important distinctions to establish are between the cut through the ground plane in front of the building elevation and the building itself, and between the building elevation and its background. Tonal values are therefore used primarily to articulate the orthogonal relationship between horizontal and vertical planes.
Toning the horizontal planes not only establishes a visual base for the drawing but also aids in defining the shape and orientation of the vertical planes. Perspective drawings should use the principles of atmospheric perspective to enhance the sense of spatial depth. Digital Rendering Although improvements continue to be made, the rendering of atmospheric and texture perspective remains problematic in many graphics programs.
Image-processing software, however, allows us to modify digital drawings and simulate the pictorial effects of atmospheric and texture perspective. The depiction of light, shade, and shadow can model the surfaces of a design, describe the disposition of its masses, and articulate the depth and character of its details. The sun is so large and distant a Su source that its light rays are considered to be parallel.
The ne corollary to this is that any point that is not in light cannot do w li Sha cast a shadow because light does not strike it. A shadow can never be cast on a surface in shade, nor can it exist within another shadow. It generally requires two related views—either a plan and elevation or two related L ig elevations—and the transferring of information back ht ray Pro Pro and forth from one view to the other.
This convention produces shadows of width or depth equal to the width or depth of the projections that cast the shadows. This feature can be especially useful in the schematic design phase to study the form of a building or the massing of a building complex on a site and to evaluate the impact of the shadows they cast on adjacent buildings and outdoor areas.
While efficient and useful for preliminary design studies, ray casting does not take into account the way the light rays from an illuminating source are absorbed, reflected, or refracted by the surfaces of forms and spaces.
For a visual comparison of digital lighting methods, see pages — The hypotenuse of the triangular shadow end points. If the line intersects the surface, plane establishes the direction of the light rays, its shadow must begin at that juncture. This is also true when the line is parallel to the straight lines in a curved surface receiving the shadow. The shape of the shadow is elliptical since the section of a cylinder cut by any plane oblique to its axis is an ellipse.
The most convenient method of determining the shadow of a circle is to determine the shadow of the square or octagon circumscribing the given circle, and then to inscribe within it the elliptical shadow of the circle. It is usually best to begin by determining the Plan View shadows of significant points in the form, such as the end points of straight lines and the tangent points of curves.
The shadow of the line will appear to be straight regardless of the shape of the surface receiving the shadow. In clarifying the relative depth of projections, Elevation View overhangs, and recesses within the massing of a building, shade and shadows can also model the relief and texture of surfaces. Rather, they merely indicate the relative heights of the parts of a building above the ground plane.
However, they may be used to emphasize the cut elements and the relative heights of objects within the space. However, they can be used effectively to distinguish Alti tud e between horizontal and vertical elements, and the three- dimensional nature of their forms. To construct shade and shadows in a paraline drawing, it is necessary to assume a source and direction of light.
Deciding on a direction of light is a problem in composition as well as communication. It is important to remember that cast shadows should clarify rather than confuse the nature of forms and their spatial relationships.
There are occasions when it may be desirable to determine the actual conditions of light, shade, and shadow. For example, when studying the effects of solar radiation and shadow patterns on thermal comfort and energy conservation, it is necessary to construct shades and shadows using the actual sun angles for specific times and dates of the year. Within the shadow or area in shade, there is usually some variation in value due to the reflected light from adjacent lit surfaces. This intersection s represents the source of the light rays, and is above HL when the light source is in front of the observer and below HL when behind the observer.
The shadow and the bearing direction therefore share the same vanishing point. Determine where the bearing of the shadow meets the vertical surface. Both the casting edge and its shadow therefore VP for light rays share the same vanishing point. In each of the major drawing systems, we do this by extending the ground line and plane to include adjacent structures and site features.
In addition to the physical context, we should indicate the scale and intended use of spaces by including human figures and furnishings. We can also attempt to describe the ambience of a place by depicting the quality of light, the colors and textures of materials, the scale and proportion of the space, or the cumulative effect of details.
Pe op l e The viewer of a drawing relates to the human figures within it and is thus drawn into the scene. Therefore, in the drawing of architectural and urban spaces, we include people to: Scale Important aspects to consider in the drawing of human figures are: We can Use and Activity therefore simply scale the normal height of people in elevations and section drawings.
Since the view is three- dimensional, however, the figures should have some degree of roundness to indicate their volume. Then we can extend this spot vertically and place the eyes of the head of each figure on the horizon line. The principles of linear perspective can be used to shift the figure right or left, up or down, or into the depth of the perspective. We therefore need to draw human figures in proper size and proportion. Instead, figures should be given a sense of volume, especially in paraline and perspective views.
Then the established proportions are used to draw the same person sitting down. What activity should occur in important spatial features or distract from the focus of this room or space? The same principles that govern the scale, clothing, placement, and gesturing in hand drawing should apply to the use of digital images of people in architectural settings.
The ability to produce photorealistic images of people is seductive. Keep in mind that the graphic style with which we populate architectural drawings should not distract or detract from the architectural subject matter. The figures should have a similar level of abstraction and be compatible with the graphic style of the drawn setting. Their placement should remind us that there should be places on which to sit, lean, rest our elbow or foot, or simply touch.
Digital Libraries Many CAD and modeling programs include ready-made libraries or templates of furniture elements. These can be easily copied, resized, and placed directly into drawings. These include: With these landscaping elements, we can: Different types of branch structures are illustrated below. The amount of detail rendered should be consistent with the scale and style of the drawing.
Draw these outlines freehand to give the foliage a textural quality. It is therefore necessary to differentiate between deciduous trees, conifers, and palms. As always, the type of trees selected should be appropriate to the geographic location of the architecture.
The outline of foliage can be suggested with dotted or lightly drawn freehand lines. Foreground elements typically possess dark, saturated colors and sharply defined contrasts in value. As elements move farther away, their colors become lighter and more subdued, and their tonal contrasts more diffuse. This can sometimes be accomplished simply with an articulated profile line.
This area therefore requires more detail and sharp contrasts in tonal value. Trees and landscaping are shown merely as shapes of tonal value and texture. As with digital images of people, the ability to produce photorealistic images of trees and other landscape elements can be seductive. Keep in mind that the graphic style of site and contextual elements should not distract or detract from the architectural subject matter.
Their graphic description should have the same level of abstraction and be compatible with the graphic style of the drawn setting.
These drawings describe a design proposal in a graphic manner intended to persuade an audience of its value. The audience may be a client, a committee, or merely someone browsing for an idea. Although the drawings that comprise a presentation may be excellent two-dimensional graphics worthy of an exhibition, they are merely tools for communicating a design idea, never ends in themselves. A rc hi te c tural Presentatio ns Unless presentation drawings are comprehensible and persuasive—their conventions understood and their substance meaningful—a presentation will be weak and ineffective.
An effective presentation, however, also possesses important collective characteristics. Point of View Be clear about design intent. A presentation should communicate the central idea or concept of a design scheme. Graphic diagrams and text are effective means of articulating and clarifying the essential aspects of a design scheme, especially when they are visually related to the more common types of design drawing.
Efficiency Be economical. An effective presentation employs economy of means, utilizing only what is necessary to communicate an idea. Any graphic elements of a presentation that are distracting and ends in themselves can obscure the intent and purpose of the presentation. Clarity Be articulate.
At a minimum, presentation drawings should explain a design clearly and in enough detail so that viewers unfamiliar with it will be able to understand the design proposal. Eliminate unintended distractions, such as those caused by ambiguous figure-ground relationships or inappropriate groupings of drawings. Too often, we can be blind to these glitches, because we know what we want to communicate and therefore cannot read our own work in an objective manner.
Accuracy Avoid presenting distorted or incorrect information. Presentation drawings should accurately simulate a possible reality and the consequences of future actions so that any decisions made based on the information presented are sound and reasonable.
In an effective presentation, no one segment is inconsistent with or detracts from the whole. Unity, not to be confused with uniformity, depends on: Continuity Each segment of a presentation should relate to what precedes it and what follows, reinforcing all the other segments of the presentation. The principles of unity and continuity are mutually self-supporting; one cannot be achieved without the other.
The factors that produce one invariably reinforce the other. At the same time, however, we can bring into focus the central idea of a design through the placement and pacing of the major and supporting elements of the presentation. Only through a coordinated presentation of related drawings can the three-dimensional form and character of a design be communicated. To explain and clarify aspects that are beyond the capability of the drawings, we resort to diagrams, graphic symbols, titles, and text.
In any design presentation, therefore, we should carefully plan the sequence and arrangement of all of the following elements: Slide and computerized presentations involve a sequence in time.
In either case, the subject matter presented should progress in sequence from small-scale to large-scale graphic information, and from the general or contextual view to the specific. Whenever possible, orient plan drawings with north up or upward on the sheet. When each drawing successively builds on the preceding one, work from the bottom up or proceed from left to right. Typical examples include a series of floor plans for a multistory building or a sequence of building elevations.
The spacing and alignment of these individual drawings, as well as similarity of shape and treatment, are the key factors in determining whether we read these drawings as a set of related information or as individual figures.
Do not fill up white space unless absolutely necessary. Avoid using lines, however, when spacing or alignment can achieve the same purpose.
Be aware, however, that using too many frames can establish ambiguous figure-ground relationships. A darker background for an elevation drawing, for example, can merge with a section drawing. The foreground for a perspective can become the field for a plan view of the building. These scales are especially useful because they remain proportional when a drawing is enlarged or reduced. Graphic symbols rely on conventions to convey information. To be easily recognizable and readable, keep them simple and clean—free of extraneous detail and stylistic flourishes.
In enhancing the clarity and readability of a presentation, these devices also become important elements in the overall composition of a drawing or presentation.
The impact of graphic symbols and lettering depends on their size, visual weight, and placement. Size The size of a graphic symbol should be in proportion to the scale of the drawing and readable from the anticipated viewing distance.
Visual Weight The size and tonal value of a graphic symbol determines its visual weight. If a large symbol or typeface is required for readability but a low value is mandatory for a balanced composition, then use an outline symbol or letter style.
Placement Place graphic symbols as close as possible to the drawing to which they refer. Whenever possible, use spacing and alignment instead of boxes or frames to form visual sets of information.
You should therefore spend time on the appropriate selection and use of fonts rather than attempt to design new ones. Keep in mind that we may read different portions of a presentation—project overviews, diagrams, details, text, and so on—at different distances. It has been the mechanically measuring the distance between the extremities of each letter. Leading also the leap into electronic typesetting, remaining essentially unchanged.
Beyond this size, the letters require a width beyond what a single pen or pencil stroke is capable of producing. The visual movement of slanted lettering can be distracting in a rectilinear drawing scheme. The most important characteristics of a lettering style are readability and consistency in both style and spacing. Drawing Titles Arrange titles and graphic symbols into visual sets that identify and explain the contents of a drawing. By convention, we always place titles directly below a drawing.
In this position, titles can help stabilize drawing fields, especially irregularly shaped ones. Use symmetrical layouts with symmetrical drawings and designs. In all other cases, it is usually easier to justify—align vertically—a drawing title with either the drawing itself or its field.
Text Organize text into visual sets of information and relate these sets directly to the portion of the drawing to which they refer. The line spacing of text should be more than one-half of the letter height used, but no more than the letter height itself. The space between blocks of text should be equal to or greater than the height of two lines of text.
Project Title The project title and associated information should relate to the overall sheet or board, not to any single drawing within the field of the panel. In planning the layout for a presentation, first identify the essential relationships you want to achieve. Then use a storyboard or small-scale mockup of the presentation to explore alternative drawing arrangements, alignments, and spacing prior to beginning the final presentation drawings.
This information should be in the same relative position on each panel. Doing so can create the impression of a figure on a background that itself has a background. Attention would be diverted from the figure, where it belongs, to the frame around it.
The underlying sense of order created by the grid allows a great variety of information to be presented in a uniform manner. However, because what we see on a monitor may not necessarily match the output from a printer or plotter, a trial layout should always be printed or plotted to ensure that the results are satisfactory. Presentation software enables us to plan and present slide shows of static graphic images as well as animations.
Whereas we can roam and ponder a series of drawings displayed on a wall of a room, our viewing of a computer- based presentation is sequential and controlled by the presenter. The tactile, kinesthetic nature of freehand drawing in direct response to sensory phenomena sharpens our awareness in the present and enables us to collect visual memories of the past.
During the design process itself, the freehand drawing of diagrams allows us to further explore these ideas and develop them into workable concepts. D r aw in g f r o m Observatio n Drawing from observation sharpens our awareness of environmental settings, fosters our ability to see and understand architectural elements and relationships, and enhances our ability to build and retain visual memories.
It is through drawing that we are able to perceive our environment in a fresh way and appreciate the uniqueness of a place. We draw from observation to notice, to understand, and to remember. To Notice We often walk, bike, or drive by places daily without noticing them.
Drawing from direct observation, on location, helps us become more aware of where we live, work, and play—the architectural landscape, the urban spaces the architecture creates, and the life these spaces nourish and sustain.
Moreover, beyond interpreting the optical image taken in by our visual system, the drawing process involves visual thinking that can stimulate the imagination and help us consider the two-dimensional patterns and three-dimensional relationships that comprise the built environment. Revisiting the resulting drawings at a later time can help us recall past memories and bring them forward to the present to be relished once again. The line, however, remains the single most essential drawing element, You may want to experiment with the feel and capabilities of other media, such one that is capable of a wide range of expression.
It as charcoal pencils and markers. Try to determine the limits of expression can define shape and form and even imply a sense of of which each is capable and how its characteristics affect the nature of depth and space. A line can portray hard as well as a drawing.
For example, you should find that a fine-tipped pen or pencil soft materials; it can be light or heavy, limp or taut, encourages you to focus on minute details. Because it takes innumerable fine bold or tentative. On the other hand, sketching with a broad- tipped pencil or marker fosters a broader view and the omission of details. Even when assigned a subject to draw, consider what aspect or quality of the subject attracts your attention.
Possible subjects for drawing from observation may vary in scale from fragments of buildings to landscapes. Since our perception is discriminating, we should also be selective in what we draw. How we frame and compose a view, and what we emphasize with our drawing technique, will tell others what attracted our attention and what visual qualities we focused on.
In this way, our drawings will naturally communicate our perceptions with an economy of means. Composing a perspective view of a scene involves positioning ourselves at an advantageous point in space and deciding how to frame what we see. Composing a View Pay attention to the proportions of a chosen scene. Some scenes may suggest a vertical orientation for the composition while others are more horizontal in nature.
The proportions of others may depend on what one chooses to emphasize in the scene. All three should not have equal emphasis; one should dominate to heighten the pictorial space of the drawing. Visualizing Extents Before touching pen or pencil to paper, we should first visualize the horizontal and vertical extents of the view. Often, especially when working top down, we may run out of room for the foreground that places our position within a scene.
Most scenes, however, are asymmetrical, having a focus or point of interest that is off- center.