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projection

Definitions

  • Isometric projection
    Isometric projection
  • WordNet 3.6
    • n projection the act of expelling or projecting or ejecting
    • n projection the act of projecting out from something
    • n projection any structure that branches out from a central support
    • n projection the representation of a figure or solid on a plane as it would look from a particular direction
    • n projection a prediction made by extrapolating from past observations
    • n projection a planned undertaking
    • n projection the projection of an image from a film onto a screen
    • n projection the acoustic phenomenon that gives sound a penetrating quality "our ukuleles have been designed to have superior sound and projection","a prime ingredient of public speaking is projection of the voice"
    • n projection (psychiatry) a defense mechanism by which your own traits and emotions are attributed to someone else
    • n projection any solid convex shape that juts out from something
    • ***

Additional illustrations & photos:

Orthographic projection Orthographic projection

Webster's Revised Unabridged Dictionary
  • Interesting fact: The projection light used for IMAX theaters can be seen from space.
    • Projection A jutting out; also, a part jutting out, as of a building; an extension beyond something else.
    • Projection (Geog) Any method of representing the surface of the earth upon a plane.
    • projection See under Globular Gnomonic, etc.
    • Projection The act of scheming or planning; also, that which is planned; contrivance; design; plan.
    • Projection The act of throwing or shooting forward.
    • Projection (Persp) The representation of something; delineation; plan; especially, the representation of any object on a perspective plane, or such a delineation as would result were the chief points of the object thrown forward upon the plane, each in the direction of a line drawn through it from a given point of sight, or central point; as, the projection of a sphere. The several kinds of projection differ according to the assumed point of sight and plane of projection in each.
    • ***
Century Dictionary and Cyclopedia
  • Interesting fact: Gutzon Borglum, the sculptor of the four Presidents on Mount Rushmore, died a few months before the project was completed. It took him 14 years.
    • n projection The act of projecting, throwing, or shooting forward: as, the projection of a shadow upon a bright surface; hence, the act or process of throwing, as it were, something that is subjective into the objective world; the act of giving objective or seeming reality to what is subjective: as, the projection of a sensation of color into space as the quality of an object (a colored thing).
    • n projection That image or figure which results from the act of projecting an idea or a sensation.
    • n projection That which projects; a part projecting or jutting out, as of a building extending beyond the surface of the wall; a prominence.
    • n projection The act of projecting, or scheming or planning: as, he undertook the projection of a new enterprise.
    • n projection In geometry, the act or result of constructing rays or right lines through every point of a figure, according to certain rules. These rays are called projecting rays. In central projection, often called projection simply, the projecting rays all pass through one point called the center of projection. In this way a point is projected into a ray, a straight line into a plane. In axial projection, a plane, called a projecting plane, is passed through every point of the figure, all these planes containing one line called the axis of projection.
    • n projection The act or result of constructing rays through every point of a figure, all passing through one point, and cutting these rays by a plane or other surface, so as to form a section on that surface which corresponds point for point with the original figure.
    • n projection In chartography, the act or result of constructing a figure upon a plane or other surface, which corresponds point by point with a sphere, spheroid, or other figure; a map-projection (which see, below).
    • n projection The mental operation in consequence of which objects of the imagination or retinal impressions appear to be seen external to us.
    • n projection In alchemy, the act of throwing anything into a crucible or other vessel, especially the throwing of a portion of philosopher's stone upon a metal in fusion with the result of transmuting it; hence, the act or result of transmutation of metals; humorously, the crisis of any process, especially of a culinary process.
    • n projection Same as gromonic map-projection.
    • n projection Same as zenithal map-projection. — Clarke's map-projection, a perspective map-projection in which the distance of the eye from the center of the sphere is 1.368 times the radius. This projection was invented by the English geodesist Colonel A. R. Clarke. — Collignon's map-projection.
    • n projection The quadrilateral map-projection.
    • n projection The central equivalent projection. — Conform map-projection. Same as orthomorphic map-projection. — Conical map-projection.
    • n projection Properly, a map-projection the development of a tangent or secant cone upon which the sphere is conceived to have been projected by lines of projection perpendicular to its axis.
    • n projection Any projection which may naturally be regarded as the development of a projection upon a cone. — Cylindrical map-projection.
    • n projection A parallelogrammatic or square map-projection.
    • n projection A map-projection showing the earth in repeated stripes, as Mercator's.
    • n projection A perspective or central projection in which the center is at infinity. — Delisle's map-projection, the secant conical projection proposed by Mercator, and applied by J. N. Delisle to the great map of Russia. — Discontinuous map-projection, a map-projection which follows one law in one part, and another in another part. Also called broken map-projection, irregular map-projection. — English map-projection. Same as globular map-projection . — Equidistant map-projection, a zenithal map-projection in which the radius of each almucantar is equal to its angular distance from the zenith. This map-projection, invented by the French mathematician Postel in the sixteenth century, is frequently employed for star-maps, etc. — Equivalent map-projection, a map-projection which represents all equal surfaces on the spheroid by equal areas on the map. Also called equal-surface map-projection. — Equivalent stereographic map-projection, an equivalent map-projection in which the parallels are represented by parallel straight lines at distances from the equator proportional to the tangents of half the latitudes. This projection was proposed in 1862 by M. de Prépetit Foucaut. — Flamsteed's map-projection. Same as sinusoidal map-projection. — Foucaut's map-projection, the equivalent stereographic map-projection. — Fournier's map-projection.
    • n projection A meridional map-projection in which the meridians are equidistant ellipses, while the parallels are circular arcs equally dividing the central and extreme meridians.
    • n projection A map-projection in which the meridians are as in, but the parallels are straight lines as in the meridional orthogonal projection. These map-projections were proposed in 1646 by the French geographer Fournier. — Gauss's map-projection. Same as Lagrange's map-projection. — Glareanus's map-projection, a discontinuous map-projection differing from that of Apianus only in setting the parallels at the same distances as in the meridional orthographic map-projection. It was invented by the Swiss mathematician Loriti or Glareanus, and published in 1527.
    • n projection Globular map-projection. Any projection of a hemisphere with curvilinear meridians and parallels.
    • n projection A meridional hemispherical map-projection in which the equator is a straight line, the semimeridians are circular arcs dividing the equator into equal parts, and the parallels are circular arcs dividing the extreme and central meridians into equal parts. This projection, invented in 1660 by the Italian Nicolosi, has been extensively employed ever since.
    • n projection La Hire's map-projection. — Gnomonic map-projection.
    • n projection A perspective map-projection from the center of the sphere. All great circles are represented by straight lines.
    • n projection Hence, by extension — Any map-projection representing all great circles by straight lines. Such a projection can contain but one half of the sphere on an infinite plane. This system is probably ancient. — Harding's map-projection. Same as Lagrange's map-projection. — Herschel's map-projection. Same as Lagrange's map-projection. — Homalographic (or homolographic) map-projection, an equivalent map-projection in which the meridians are ellipses meeting at the poles, and the parallels and equator are parallel straight lines: invented by the German mathematician Mollweide in 1805. It has been considerably used. — Intermediary map-projection, a zenithal map-projection in which, z being the zenith distance of an almucantar, r its radius on the map, and n a constant
    • n projection r = n tan z/n.
    • n projection This projection was invented by A. Germain. — Irregular map-projection. Same as discontinuous map-projection. — Isocylindric map-projection. an equivalent map-projection the development of a cylinder upon which the sphere has been orthogonally projected. It was invented by the German mathematical philosopher J. H. Lambert. — Isomeric map-projection, the zenithal equivalent map-projection, invented by J. H. Lambert, and the best of the equivalent projections. — Isospherical map-projection. Same as isomeric map-projection. — Jaeger's map-projection, a discontinuous projection in the shape of an eight-pointed star. It was proposed by Jaeger in 1865, and was modified by Petermann. — James's map-projection, a perspective map-projection in which the center of projection is distant from that of the sphere by 1.5 times the radius. It was invented by the English geodesist Sir Henry James. — Lagrange's map-projection, an orthomorphic map-projection in which the sphere is shown a finite number of times on a finite number of sheets, but in which all the north poles (or zeniths) coincide, as well as all the south poles (or nadirs). The projection was invented by J. H. Lambert, and has been called by many names. It has been used in a government map of Russia. — La Hire's map-projection, a perspective projection having the center of projection at a distance from the center of the sphere equal to 1.707 times the radius. This projection, proposed by the French geodesist La Hire in 1701, has been frequently used. — Littrow's map-projection, an orthomorphic projection in which the meridians are hyperbolas and the parallels ellipses, all these conies being confocal. This projection has two north and two south poles, all four coincident at infinity, and shows the sphere twice on two sheets, which are merely perversions of each other. It has many remarkable properties. It was invented by the Bohemian astronomer Littrow in 1833. — Lorgna's map-projection. Same as isomeric map-projection. — Map-projection by balance of errors, that zenithal projection which makes the “misrepresentation” a minimum, as determined by least squares. If r is the radius of an almucantar on the chart, z its zenith distance, and Z that of the limit of the chart, which cannot exceed 126° 24′ 53″, then
    • n projection r = cot ½z log sec ½z + tan ½z cot½Z log sec ½Z.
    • n projection Map-projection by development, a projection upon a developable surface which is then developed into a plane. — Mercator's map-projection, an orthomorphic map-projection in which the whole sphere is shown in equal repeating stripes. The point at infinity represents the whole sphere, and the zenith and nadir do not elsewhere appear. As ordinarily used, the poles are taken as these points, when the meridians appear as equidistant parallel lines, and the parallels as parallel lines cutting them at distances from the equator proportional to log tan ½ latitude. This has the advantage that the points of the compass preserve the same directions all over the map. This projection, invented by the Flemish cosmographer Mercator in 1550, is the most useful of all. — Meridional map-projection, a map-projection which seems to be projected upon the plane of a meridian, showing the poles at the extremities of a central meridian. — Modified Flamsteed's map-projection. Same as Bonne's map-projection. — Mollweide's map-projection. Same as homolographic map-projection. — Murdoch's map-projection, one of three conical map-projections in which the part of the cone of which the map is a reduced development is equal to the spherical zone represented. These were invented by Patrick Murdoch in 1758. — Orthographic map-projection, a perspective map-projection from an infinitely distant center. — Orthomorphic map-projection, a map-projection which preserves all angles — that is, the shapes of all infinitesimal portions of the sphere. When one such map-projection has been obtained, say the polar stereographic, which is the simplest, all others may be derived from this by a transformation of the plane. Let r and θ be the polar coördinates of any point on the polar stereographic projection, let i denote the imaginary whose square is — 1, and let F denote any function having a differential coefficient. If, then, F (r cos θ; + r sin θ.i) be put into the form x + yi, x and y will be the rectangular coördinates of the corresponding point on another orthomorphic projection. Also called conform map-projection. — Parallelogrammatic map-projection, a map-projection in which the parallels are represented by equidistant straight lines, and the meridians by equidistant straight lines perpendicular to the parallels. This is an ancient projection. Also called rectangular map-projection. — Parent's map-projection, one of two perspective map-projections. In Parent's first map-projection the center of projection is distant from the center of the sphere 1.595 times the radius. In his second this distance is 1.732. — Perspective map-projection, a true projection of the sphere by straight lines from a center of projection intersecting the plane of the map. — Petermann's map-projection, a discontinuous map-projection showing the sphere in the form of an eight-pointed star. It is used to decorate the title-page of Stieler's atlas. — Polar map-projection, a map-projection showing one of the poles in the center. — Polyconic map-projection, a map-projection in which the surface of the earth is cut into an infinite number of zones parallel to the equator; a central meridian is then developed into a straight line, and then each zone is developed separately. This projection, invented by Hassler, superintendent of the United States Coast Survey, is used in all government maps of the United States. — Quadrilateral map-projection, a broken equivalent projection in which one meridian has the form of a square, of which another meridian and the equator are the diagonals. It was invented by Collignon. — Quincuncial map-projection, an orthomorphic projection of the earth into repeating squares, invented by C. S. Peirce in 1876. — Rectangular map-projection. Same as parallelogrammatic map-projection. — Ruysch's map-projection, a conical projection in which the cone cuts the equator and has its vertex at one pole, and the sphere is projected upon the cone by lines perpendicular to the axis. It was invented by Ruysch in 1508. — Sanson's map-projection. Same as sinusoidal map-projection. — Schmidt's map-projection, a meridional map-projection in which the meridians are represented by ellipses cut at equal distances by the parallels. It was proposed by the physicist G. G. Schmidt in 1801. — Sinusoidal map-projection, an equivalent map projection in which the parallels are equidistant straight lines to which the central meridian is perpendicular. This projection (so called from the form of the meridians) was first used by the French chartographer Sanson in 1650. — Square map-projection, the projection of a map which the successive meridians and parallels cut up into squares. — Stenoterous map-projection, an equivalent projection which represents the whole earth on the sector of a circle, the pole being at the center and the parallels concentric circles. It was invented by J. H. Lambert. — Stereographic map-projection, the simplest of all projections, representing the whole sphere once on one infinite plane, the parts at infinity being considered as a point. All circles on the sphere are represented circles, and the angles are preserved. The stereographic projection of the sphere is a perspective projection, a point on the surface being the center of projection; but the stereographic map-projection of the spheroid is not a perspective projection. The stereographic projection was known to the ancients, and has always been employed for special purposes. — Textor's map-projection, a modification of the isocylindrical map, by J. C. von Textor, 1808. — Transverse map-projection, a meridional map-projection. — Trapeziform map-projection, a map-projection in which the space between two meridians and two parallels is represented by a trapezoid, the sides of which are divided proportionally to determine other straight lines representing meridians and parallels. — Werner's map-projection, that equivalent map-projection which has the parallels concentric and equidistant arcs of circles, with the north pole at the center. The whole sphere has a heart shape. This was invented by Johann Werner, 1514. — Zenithal map-projection, a map-projection which is symmetrical about a central point, the almucantars being represented by concentric circles.
    • n projection The foot of the perpendicular from a point to a straight line is the projection of the point upon the line.
    • n projection The localization of pressure sensation at the extremity of a pencil, cane, etc., held in the hand, rather than in the hand itself.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: The fleshy projection above the bill of a turkey is called a snood.
    • n Projection the act of projecting: that which juts out: a plan or design: a delineation: a representation of any object on a plane, esp. (geom.) the earth's surface:
    • n Projection (alch.) the act of throwing anything into a crucible, hence the act or result of transmutation of metals: the crisis of any process, esp. a culinary process
    • ***

Quotations

  • Norman Vincent Peale
    Norman%20Vincent%20Peale
    “It is a fact that you project what you are.”
  • Jeremy Collier
    Jeremy Collier
    “How many feasible projects have miscarried through despondency, and been strangled in their birth by a cowardly imagination.”
  • Napoleon Hill
    Napoleon%20Hill
    “It takes half your life before you discover life is a do-it-yourself project.”
  • Thomas Hardy
    Thomas%20Hardy
    “I am the family face; flesh perishes, I live on, projecting trait and trace through time to times anon, and leaping from place to place over oblivion.”
  • Gertrude Stein
    Gertrude%20Stein
    “It is extraordinary that whole populations have no projects for the future, none at all. It certainly is extraordinary, but it is certainly true.”
  • Lillian Troll
    Lillian Troll
    “Always have some project underway an ongoing project that goes over from day to day and thus makes each day a small unit of time.”

Etymology

Webster's Revised Unabridged Dictionary
L. projectio,: cf. F. projection,

Usage

In literature:

The buttresses at the corner of the choir project but slightly.
"Bell's Cathedrals: Wimborne Minster and Christchurch Priory" by Thomas Perkins
Italy is the central one of the three great peninsulas which project from the south of Europe into the Mediterranean Sea.
"A Smaller History of Rome" by William Smith and Eugene Lawrence
Determined to make no mistake, he halted under the projecting ledge and spent several minutes in peering around in the gloom.
"Two Boys in Wyoming" by Edward S. Ellis
It was a dreamer's plaything and I bought it with scant savings that should have been spent on another project.
"David Lannarck, Midget" by George S. Harney
This case evidently differs very appreciably from the projected German usufruct of neighboring countries in Europe.
"An Inquiry Into The Nature Of Peace And The Terms Of Its Perpetuation" by Thorstein Veblen
It is a common mistake among beginners to let the cutter project too far.
"Handwork in Wood" by William Noyes
It was up to him to see that the project was brought to a successful conclusion.
"Ten From Infinity" by Paul W. Fairman
Approach, please, one of you, and grasp with a hand the projecting metal knob.
"The Galaxy Primes" by Edward Elmer Smith
Let's see you project your thoughts!
"Islands of Space" by John W Campbell
Before they could reach the projecting point, the savages had got up, and were clustering around it.
"The Lone Ranche" by Captain Mayne Reid
After dragging ourselves wearily through the soft, yielding sand, we reached the summit, and halted on a projecting ridge.
"The Rifle Rangers" by Captain Mayne Reid
This made Tony more anxious to carry out our long-projected undertaking.
"On the Banks of the Amazon" by W.H.G. Kingston
He, however, had to wait some time before he could carry out his project.
"In the Eastern Seas" by W.H.G. Kingston
Rak and his group were stuck with the Plasmoid Project a lot more solidly than she was.
"Legacy" by James H Schmitz
These in effect "turned" the project "down.
"Experiences of a Dug-out, 1914-1918" by Charles Edward Callwell
Might not votes for one project be traded for the other?
"Union and Democracy" by Allen Johnson
The frog is projected with great accuracy, but not without a smack and splash on the water.
"Bass, Pike, Perch, and Others" by James Alexander Henshall
But the work projected at the Pyramid of Meydum was never completed, and I can tell you why.
"Tales of Secret Egypt" by Sax Rohmer
This, however, I believe may be the remains of some early irrigation project.
"The Archaeology of the Yakima Valley" by Harlan Ingersoll Smith
This was only one of the many projects germinating in the fertile mind of Hamilton.
"Alexander Hamilton" by Charles A. Conant
***

In poetry:

Out he flew as if projected
From a sling, and, snorting wrath,
Screamed: "Now you're our own elected!
Brr! But what a vapour bath!"
"Twardowski's Wife" by Adam Mickiewicz
Thus shall the men that hate the saints
Be blasted from the sky;
Their glory fades, their courage faints
And all their projects die.
"Psalm 129" by Isaac Watts
LELIUS. And a cloud,
From whose burning womb extended
The wild lightnings, the loud thunders,
Awful embryos were projected,
Fell upon us.
"The Wonder-Working Magician - Act III" by Denis Florence MacCarthy
My Conscience would my Will withstand,
Did Will project a world like this:
Better Eternal vacuum still,
Than murder, lust, and heartlessness!
"The Door Of Humility" by Alfred Austin
I am fond of this Thy stubborn project,
And to play my part I am content.
But another drama is in progress,
And, this once, O let me be exempt.
"Hamlet" by Boris Pasternak
Here still an aged elm aspires,
Beneath whose far — projecting shade
(And which the shepherd still admires
The children of the forest play'd!
"The Indian Burying Ground" by Philip Morin Freneau

In news:

This story is part of a larger project on book challenges in Missouri and the US Find the full project here.
A Sanpete County water project — long talked about but oft delayed — inched closer to reality this week, but opponents of the Narrows Project dam vow to still fight it.
Volunteers who assisted in the Red Dirt Road waterline project gathered at Big Fox Community Church Thursday to celebrate the project's completion.
JAY SULLIVAN, BRAVO Seven Hills native Suede (aka Stephen Whitney Baum) was a contestant on "Project Runway" in 2008 and returns this fall for the second season of "Project Runway All Stars".
Owners of a proposed Rusk County refinery project are working with the Angelina and Neches River Authority on other financing options for the project after one avenue dried up, ANRA announced Monday.
The Paisano Green Community Project construction continues, on the project being built by the El Paso Housing Authority.
NBC News declares Barack Obama as the projected winner of the Presidency of United States, with a projected win in Ohio carrying him over the 270 electoral votes needed for victory.
In response to Ms Williams's letter to the editor (NK Herald Sept 18) please allow me to state the facts about the new City Hall project and clear up any misconceptions or misinformation surrounding the project budget and timeline.
Scarab Seshambeh Project 5 Seshambeh Project, the.
The Southwire Flora facility routinely produces quantities for projects using volumes similar to, or greater than, the volumes projected for use by the Rock Island Clean Line project.
An existing road project will be modified starting Sunday evening and a new project will get underway Monday.
Philip Branson, project manager of the recent expansion of the Dallas/Fort Worth International Airport, has been selected lead the Convention Center expansion project.
New modules extend reach of Newforma Project Center Eighth Edition, the company's core project information management solution.
"A group of us from Google started Project Glass to build this kind of technology, one that helps you explore and share your world, putting you back in the moment," Google wrote on its Google+ page for Project Glass Wednesday.
Budgeted home costs on this project are projected to be $104,000.
***

In science:

Let X be projective manifold or more generally, a normal projective variety.
Generically nef vector bundles and geometric applications
If φ ∈ Irr(I ) lying above θ, then φ = θ0 τ, where θ0 is a character of an irreducible projective representation of I of degree θ(1) and τ is a character of an irreducible projective representation of I /M .
Simple linear groups $PSL_4(q)$ are determined by the set of their character degrees
If χ ∈ Irr(G) lying above θ, then χ = θ0 τ, where θ0 is a character of an irreducible projective representation of G of degree θ(1) and τ is a character of an irreducible projective representation of G/M .
Quasisimple classical groups and their complex group algebras
The projection of formula F onto scope S, which can be defined for scopes S and formulas F as projectS (F ) ≡ forgetALL−S (F ), where ALL denotes the set of all literals, serves this purpose.
Computing with Logic as Operator Elimination: The ToyElim System
Thus, if f factors through a projective A-module, then we see that b f also factors through a projective B-module. X .
Generalized Auslander-Reiten conjecture and derived equivalences
Then, we get HomA (Wr (X ), A) is a projective Ao p -module and consequently, Wr (X ) is a projective A-module.
Generalized Auslander-Reiten conjecture and derived equivalences
Then Ωi (M )/J Ωi (M ) ∼= Ωi (M )i is a projective A0 -module for each i > 0, or equivalently, Ωi (M ) ⊆ J P i−1 where P i−1 is a graded projective cover of Ωi−1 (M ), where Ω is the Hel ler operator.
A generalized Koszul theory and its application
In particular, M is projective viewed as an A0 -module (or equivalently, Mi is a projective A0 -module for every i > 0).
A generalized Koszul theory and its application
Then a graded A-module M is Koszul if and only if it is quasi-Koszul as an A-module and projective as an A0 -module (or equivalently al l Mi are projective A0 -modules).
A generalized Koszul theory and its application
The Canadian Advanced Network for Astronomical Research (CANFAR) is a project at the Canadian Astronomy Data Centre (CADC) to provide an infrastructure for data-intensive astronomy projects.
Discussion on "Techniques for Massive-Data Machine Learning in Astronomy" by A. Gray
In an effort to detect and characterize halo substructures, we have been working on a project to obtain full phasespace information (positions and full 3-D space motions) for individual stars in Kapteyn’s Selected Areas (SAs; see Casetti-Dinescu et al. 2006 for an overview of this project).
Kinematics and Chemistry of Stars Along the Sagittarius Trailing Tidal Tail and Constraints on the Milky Way Mass Distribution
Our algorithm is based on a random-projection algorithm of Halko, Martinsson and Tropp [HMT11], which involves two steps: range finding and projection.
Beating Randomized Response on Incoherent Matrices
Hence, all that remains to be done is to compute the orthonormal projection operator PY into the span of Y, and to compute the projection PY A.
Beating Randomized Response on Incoherent Matrices
Projection: Compute the projection B = PY A.
Beating Randomized Response on Incoherent Matrices
Lemma 1 [cf., th. 6.2.22] The set of generalized connections (cid:9) is the projective limit of the projective family H Xl, pl ' l Ll€l 'œ(cid:10) .
A Topos Model for Loop Quantum Gravity
***