Orientation (redirected from orientational)

orientation, in architecture, the disposition of the parts of a building with reference to the points of the compass. From remote antiquity the traditional belief in the efficacy of religious ceremonials performed at dawn toward the rising sun has influenced the orientation of temples and other sacred structures. In Mesopotamia and Egypt, in Mayan Central America, even at Stonehenge in England, entrances and other important architectural features were designed to point toward the east; the temples of Greece and Rome often, though not invariably, faced the rising sun. In medieval Europe and, consequently, in modern Europe and the Americas, it became customary to have the congregation and the priest at the altar facing east. So strong was this custom that "west front" came to be a generic term for the facade of a church. Some churches were so built that a central line of the axis of the church pointed exactly to the rising sun on the day of the saint for whom the church was named. Such orientation was, however, by no means universal. St. Peter's at Rome, continuing an earlier tradition, faces in the opposite direction. Important secular buildings in the West often face toward the cardinal points of the compass, and the gridiron pattern of a city's streets is frequently so laid out. Practical problems also govern orientations. The disposition of a building in relation to the prevailing wind or to the sun has long been an important consideration in construction. Early commentators on the problem were Xenophon and Vitruvius. Examples of the concern for climatological orientation can be found in ancient Rome, where there were laws regarding the placement and heights of buildings, or in Puebla, Mexico, where in 1554 the streets were planned so that winds would not sweep through the city. Although orientation in accordance with climatic conditions was in many instances ignored in the 19th cent., modern architects have considered it and have tended to design their buildings accordingly.

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orientation

In architecture, the position of a building on its site. In Mesopotamia and Egypt, as well as in pre-Columbian Central America, a building's important features, such as entrances and passages, faced the rising sun. Mosques are oriented so that the mihrab faces Mecca. Christian churches have usually been oriented with the apse or altar at the eastern end. Orientation is frequently planned to take maximum advantage of daily and seasonal variations of sunlight. A structure's optimal orientation is usually a compromise between its function, location, and the prevailing environmental factors of solar radiation, light, humidity, and wind that make up the site's microclimate.

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orientation

In typography, the direction of print across a page. See portrait.

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orientation

1. position or positioning with relation to the points of the compass or other specific directions

2. Chiefly US and Canadian

a. a course, programme, lecture, etc., introducing a new situation or environment

b. (as modifier): an orientation talk

3. Psychol the knowledge of one's own temporal, social, and practical circumstances in life

4. Biology the change in position of the whole or part of an organism in response to a stimulus, such as light

5. Chem the relative dispositions of atoms, ions, or groups in molecules or crystals

6. Archit the siting of a church on an east-west axis, usually with the altar at the E end

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orientation [‚ȯr·ē·ən′tā·shən]

(crystallography)

The directions of the axes of a crystal lattice relative to the surfaces of the crystal, to applied fields, or to some other planes or directions of interest.

(electromagnetism)

The physical positioning of a directional antenna or other device having directional characteristics.

(engineering)

Establishment of the correct relationship in direction with reference to the points of the compass.

(mathematics)

A choice of sense or direction in a topological space.

An orderingp₀,p₁, …,p_nof the vertices of a simplex, two such orderings being regarded as equivalent if they differ by an even permutation.

For a simple graph, a directed graph that results from assigning a direction to each of the edges.

(physics)

The direction of some vector or set of vectors, such as the direction of the electric vector and the propagation direction of plane polarized light, or the direction of a preponderance of nuclear spins in a crystal near absolute zero, relative to some other directions of interest.

Any process in which vectors associated with atoms or molecules in the substance are organized relative to some direction, rather than pointed at random; examples include dipole moments of polar molecules in an electric field, and nuclear spins in a crystal in a magnetic field at temperatures near absolute zero.

(physical chemistry)

The arrangement of radicals in an organic compound in relation to each other and to the parent compound.

(psychology)

Determination of one's relation to the environment.

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orientation

1. The placement of a structure on a site with regard to local conditions of sunlight, wind, and drainage.

2. The siting of a Christian church so that the main altar is housed toward the east end of the building, a common ritual disposition.

3. The relationship of a building site plan to the points of a compass.

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Orientation 

a generalization of the concept of direction on a line to more complex geometrical figures.

Orientation on a line. A point can move along a line in two opposite directions. For example, on the horizontal line AB (Figure 1,a) it is possible to move either from right to left or from left to right. A line that has a specific direction indicated on it is termed an oriented line.

Orientation on a curve. Analogously to orientation on a line, every closed curve can be oriented either counterclockwise (Figure 1,b) or clockwise (Figure 1,c).

Orientation in a plane. If a region of a plane is bounded by a simple closed curve, that is, a closed curve free of multiple points, the curve can be oriented in two different directions. Orienting the curve orients the plane region the curve bounds. Two simple closed curves in a plane are considered to be identically oriented if when the curves are traversed in the indicated direction, the plane regions the curves bound remain on the same side, in both cases either on the right or on the left. For example, the curves in Figure 1,b and 1,d are oriented in the same direction, but the curve in Figure 1,c has an opposite orientation. It is sufficient to choose the orientation of a single closed curve on the plane in order to define the corresponding orientation of all other such curves lying in the same plane.

A plane for which a specific orientation has been chosen for the simple closed curves it contains is called an oriented plane. Each plane can be oriented in two directions. The orientation of a plane can also be given by choosing a system of Cartesian coordinates. If the x-axis and the y-axis are chosen with specific positive directions, this choice corresponds to an orientation of the plane such that a circle centered on the origin is oriented in the direction from the positive x-axis to the positive y-axis. For example, the coordinate systems in Figure 1,e and 1,f define the

Figure 1

same orientation of the plane. The coordinate system in Figure 1,g is oriented in the opposite direction.

The coordinates (x, y) and (x′, y′) in two rectangular coordinate systems on the plane are linked by the relations

x′ = a₁₁x + a₁₂ + b₁

y′ = a₂₁x + a₂₂ + b₂

where the determinant

is nonzero. The coordinate systems (x, y) and (x′, y′) are oriented in the same direction if Δ > 0 and in opposite directions if Δ < 0. This fact can be used to construct a rigorous analytic theory of orientation on the plane. It is easy to see that the set S of all rectangular coordinate systems can be divided into two subsets S′ and S″ such that all the coordinate systems in S′ are related by transformations with Δ > 0, as are all the systems in S″, and any coordinate system in S′ is related to a coordinate system in S′ by a transformation with Δ < 0. Choosing an orientation of the plane means choosing one of the sets S″ or S″. The choice of orientation on a plane determines the signs of angles located in the plane and of the areas bounded by oriented closed curves. For example, the formula

for the area s bounded by the closed curve c, which is oriented in the direction indicated by the arrow, leads in a right-handed coordinate system (Figure 1,e and 1,0 to a positive area for Figure 1,b and 1,d and to a negative area for Figure 1,c. Conversely, in a left-handed coordinate system (Figure 1,g) the area s, as computed by the above formula, will be positive for Figure 1,c and negative for Figure 1,b and 1,d.

Orientation of a surface. The orientation of any surface dividing space into two parts, for example, a sphere, can be defined in a manner similar to the above definition of the orientation of a plane. Let us consider regions of the surface that are bounded by simple closed curves. To orient such a surface region means to choose a specific orientation for the curve bounding the region. Two regions of a surface are said to be oriented the same way if when the curves bounding the regions are traversed in the indicated direction the regions remain on the same side. For example, the surfaces of the two cubes in Figure 1,h and 1,i are oriented in the same direction, but the surface of the cube in Figure 1,j is oriented in the opposite direction. A surface on which regions bounded by simple closed curves have a specific orientation is called an oriented surface. Not all surfaces can be oriented. Surfaces that bound a region of space, however, are always orientable.

Orientation of a space. When a closed surface bounds a certain region of three-dimensional space, the surface is said to have a right-handed orientation if its regions are oriented counterclockwise when viewed from the outside, like the cubes in Figure 1,h and 1,i. Conversely, the orientation of a closed surface bounding a region of space is considered to be left-handed if regions of the surface are oriented in a clockwise direction when viewed from outside, like the cube in Figure 1,j. The choice of a specific orientation for closed surfaces that lack self-intersections yields the orientation of the space. Thus, there are two possible orientations for three-dimensional space: right-handed and left-handed.

The orientation of three-dimensional space may also be established by choosing a system of Cartesian coordinates. Suppose we choose an x-axis, a y-axis, and a z-axis on each of which a positive direction is defined. The corresponding orientation of the space is then defined in the following way. Consider any tetrahedron OABC with vertex O at the origin and vertices A, B, and C lying, respectively, on the positive x-, y-, and z-axes (Figure 1,k and 1,1), and assume that the triangle ABC on the surface of the tetrahedron is oriented in the order ABC, that is, from the x-axis to the y-axis and then to the z-axis. The orientation of the tetrahedron’s surface is thereby defined, as is, consequently, the orientation of the entire space. The choice of axes in Figure 1,k corresponds to a right-handed orientation of space, and the choice in Figure 1,1 corresponds to a left-handed orientation of space. This principle divides the coordinate systems in space into right-handed and left-handed systems. The choice of spatial orientation determines the sign of volumes bounded by oriented surfaces, the sense of the vector product of two vectors, and so forth.

Both left-handed and right-handed coordinate systems are used in scientific literature. For example, a left-handed system is widely used in Soviet works on mathematics, while a right-handed system is used in engineering and physics.

The concept of orientation can be extended to multidimensional spaces.

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Orientation 

the determination of one’s position relative to the points of the compass by means of a compass, map, or aerial photograph. Approximate orientation is possible using local natural and artificial points of reference or the position of the sun, moon, and stars, as well as with the aid of radio, light, and sound signals.