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Topic: Perspective projection

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Perspective (graphical)

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	Perspective projection distortion - Wikipedia, the free encyclopedia
		Both types of projection involve a distortion; parallel lines never intersect in nature, but they always intersect in perspective projections, with the rare exception wherein both the surface of projection is planar and an object plane is spatially parallel to the plane of projection.
		Mathematically, the difference between artifical perspective projection (perspective projection onto a flat surface) and natural perspective projection (perspective projection onto a spherical surface) is a distortion resulting from the small-angle approximation which results from projecting onto a flat surface.
		In an artificial perspective projection, every car on the road would be drawn at the same size, even though it is clear in reality, that the farther away from the center of the picture that a car is, the farther away from the viewer that car would be.
	en.wikipedia.org /wiki/Perspective_projection_distortion (2050 words)

	Perspective (graphical) - Wikipedia, the free encyclopedia
		Perspective in the graphic arts, such as drawing, is an approximate representation on a flat surface (such as paper) of an image as it is perceived by the eye.
		Natural perspective projection is the name given by Leonardo to the projection that produces the image beheld by the human eye.
		Both types of projection involve a distortion; parallel lines never intersect in nature, but they always intersect in perspective projections (with the exception in classical perspective projection where the parallel lines are parallel to the picture plane).
	en.wikipedia.org /wiki/Perspective_(graphical) (2009 words)

	Perspective
		By the foregoing statement regarding parallel perspective, it is obvious that the parallels of latitude project as concentric circles.
		As required to be a projection onto the equator, the k component is zero.
		Theorem: The center of the projection of the azimuth circle is at r (- i tan(phi) + j sec(phi)) tan(alpha) and its radius is radius = r sec(phi) sec(alpha).
	www.rism.com /Trig/perspective.htm (2717 words)

	Perspective projection - Wikipedia, the free encyclopedia
		Perspective projection is a type of drawing, or rendering, that graphically approximates on a planar (two-dimensional) surface (e.g.
		A perspective projection drawing must be made according to an established geometric protocol.
		All perspectives on a planar surface have some degree of distortion, similar to the distortion created when portraying the earth's surface on a planar map.
	en.wikipedia.org /wiki/Perspective_projection (137 words)

	PlaneView 3D Planar Geometric Projections Tutorial
		Divisons within perspective projections are consistent in that the center of projection (PRP) is placed at a finite distance from the viewplane.
		The reduction in length of the projected line is attributed to the decreasing distance between the two projectors as the viewing surface becomes nearer to the center of projection.
		In this projection, the viewplane is positioned in front of the cube and parallel to the x- and y-plane.
	www.mtsu.edu /~csjudy/planeview3D/tutorial-perspect.html (673 words)

	Four-Space Visualization of 4D Objects - Chapter 4 (Site not responding. Last check: 2007-10-21)
		To calculate the perspective projection of point P', we need to project the point to the viewplane and then to normalize the values so that points on the Z axis are projected to X (or Y) = 0, and so that the values of X (or Y) range from -1 to +1.
		In equation 4.2b, the X and Y eye coordinates are divided by the Z eye coordinate to yield the perspective projection.
		In the 4D to 3D perspective projection, this ``depth'' is similarly achieved by dividing by the W eye coordinate (which corresponds to the four-dimensional line-of-sight).
	stevehollasch.com /thesis/chapter4.html (3746 words)

	Encyclopedia: Perspective projection
		Also see: Perspective projection distortion, Perspective (visual), Perspective distortion A picture plane is the imaginary flat surface which is usually located between the station point and the object being viewed and is ordinarily a vertical plane perpendicular to the horizontal projection of the line of sight to the objects order of interest.
		Reverse perspective also called inverse perspective or Byzantine perspective, is a technique of perspective drawing where the further the objects are, the larger they are drawn.
		Perspective when used in the context of vision and visual perception refers to the way in which objects appear to the eye based on their spatial attributes or dimension and the position of the eye relative to the objects.
	www.nationmaster.com /encyclopedia/Perspective-projection (439 words)

	GeneralVerticalPerspective Map Projection -- 3DSoftware.com (Site not responding. Last check: 2007-10-21)
		It is a perspective projection that shows the Earth as it would be viewed from near space, such as from the position of a satellite or a manned rocket.
		Geometric projection of the parallels of the polar Perspective projections, Vertical and Tilted.
		The Tilted Perspective is not covered here, but it is worth noting, as it is the projection that accurately models photographs taken by astronauts from space, in the Gemini and Apollo missions, with the hand-held camera not pointed directly at the Earth's center.
	www.3dsoftware.com /Cartography/USGS/MapProjections/Azimuthal/GeneralVerticalPerspective (946 words)

	Untitled Document (Site not responding. Last check: 2007-10-21)
		Perspective Projection: A perspective projection in space is determined by the projection center c, and a projection plane pi.
		The perspective projection of a point q is the intersection q* of the line qc with the plane pi.
		When the perspective projection is a monotonic projection, then it is also a regular and minimum crossing projection.
	www.cs.mcgill.ca /~spark55/property.htm (225 words)

	Perspective Viewing Projection
		A problem with a perspective transformation is that it does not preserve straight lines or planes, i.e., straight lines are not transformed into straight lines and planes are no longer planar after the transformation.
		Any set of parallel lines that are not parallel to the projection plane will converge to a vanishing point.If the set of lines is parallel to one of the three principal axis then it is called a principal vanishing point.
		Since the projection plane is normal to the Z axis there is only one principal vanishing point.
	www.siggraph.org /education/materials/HyperGraph/viewing/view3d/perspect.htm (845 words)

	Types of Projection (Site not responding. Last check: 2007-10-21)
		This projection is somewhat similar to the fisheye but it projects the image onto a rectangle instead of a circle.
		There are four different types of cylindrical projections depending on the orientation of the cylinder and the position of the viewpoint.
		The spherical projection is similar to the fisheye projection, in that the scene is projected on a sphere.
	www.blastwave.org /docs/povray-3.50c/povdoc_182.html (706 words)

	Projection Principles (Site not responding. Last check: 2007-10-21)
		Projection, as we refer to it here, is when you reduce the three dimensions of a real or virtual (computer) object to two dimensions.
		With a multiview projection, the projection lines are oriented parallel to one of the principle axes of the object.
		Axonometric projections are classified according to the orientation of the principle axes relative to the projected surface.
	www2.ncsu.edu:8010 /unity/lockers/project/scivishome/lessons/projprinc/projprinc.html (2215 words)

	Types of perspective projection (Site not responding. Last check: 2007-10-21)
		Different types of perspective projection are named after the finite number of vanishing points.
		Conversely, when the projection plane is perpendicular to one of the principal axis, one point perspective occurs.
		If the projection plane is parallel to one of the principal axes or if the projection plane intersects exactly two principal axes, a two-point perspective projection occurs.
	www.cs.fit.edu /wds/classes/cse5255/thesis/perspTypes/perspTypes.html (174 words)

	Mathematics of Perspective Drawing
		The isometric projections are that class or parallel projections for which a round sphere projects to a round circle.
		Perspective transformations have the property that parallel lines on the object are mapped to pencils of lines passing through a fixed point in the drawing plane.
		The usual construction is to draw a square around the circle, and then project the perspective view of the square by finding its edges using the vanishing points and measuring points, the center by drawing the diagonals, and then sketching the projected circle by drawing it tangent to the projected square.
	www.math.utah.edu /~treiberg/Perspect/Perspect.htm (5252 words)

	Perspective projection matrix
		Due to the perspective division it is no longer possible to determine z'' as a linear function of z, as was the case in the third step of §5.1.
		For asymmetrical perspective projection the frustum is first transformed such that its axis coincides with the negative Z-axis.
		Figure 6: An asymmetrical perspective projection reduces to a symmetrical perspective projection by a shearing transformation: a translation perpendicular to the Z-axis over a distance proportional to -z.
	www.cs.kuleuven.ac.be /cwis/research/graphics/INFOTEC/viewing-in-3d/node8.html (655 words)

	Perspective projection
		The perspective projection corresponds more closely to the way a human observer (with one eye) perceives a 3D scene.
		In the case of the perspective projection, the part of the 3D space that should be visualized (the viewing frustum), is a truncated pyramid in the eye coordinate system with its top in the origin (see figure 4).
		The symmetrical perspective projection is extremely important: in this case, the reference point is projected in the center of the image.
	www.cs.kuleuven.ac.be /cwis/research/graphics/INFOTEC/viewing-in-3d/node6.html (451 words)

	Perspective projection
		Perspective projection is the principle used by artists for drawing 3D objects and scenes [1].
		The image produced by perspective projections are similar to that produced by a camera (or cyclops).
		The perspective projection of objects behind the center of projection appear upside down and backward onto the viewplane.
	www.cs.fit.edu /~wds/classes/cse5255/thesis/persProj/persProj.html (276 words)

	Linear perspective -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Linear perspective is the (The creation of beautiful or significant things) art of representing three-dimensional constructions on a two-dimensional surface.
		In other words, two-point perspective is derived from one-point perspective by yawing the line of vision so that the line of vision will be at an acute angle away from the focus.
		Interpreted according to (The geometry of properties that remain invariant under projection) projective geometry, the horizontal parallel lines of one-point perspective are actually concurrent, intersecting at the (Click link for more info and facts about point at infinity) point at infinity [1:0:1].
	www.absoluteastronomy.com /encyclopedia/l/li/linear_perspective.htm (637 words)

	Perspective Projection Expert (Site not responding. Last check: 2007-10-21)
		Among all the features in the 2D perspective projection image of a 3D scene, perhaps the most significant information--carrying feature is the 2D geometry of the projected object.
		This is so because perspective projection preserves, in a definite mathematical way, much of the geometry of the objects in the 3D scene.
		In this project, we are developing an optimal algorithm which, with a suitable perspective projection knowledge base, will have an expected computational complexity which is linear in the number of features.
	www.ee.washington.edu /research/isl/projects/persproj.html (110 words)

	Perspective Projection vs. Perspective Transformation (Site not responding. Last check: 2007-10-21)
		Perspective Projection calculates the perspective view (i.e., foreshortening) of a 3D object onto a 2D projection plane.
		The effect of viewing in perspective is achieved, and, of course, the z-values (depth information) are discarded in the process.
		The Perspective Transformation allows us to see how the perspectively foreshortened and projected polygons will overlap, without discarding the z-values (which we need to use later for depth comparison).
	www.cs.brown.edu /stc/summer/2ViewRender/2ViewRender_11.html (66 words)

	The Perspective Transformation (Site not responding. Last check: 2007-10-21)
		The perspective transformation transforms the perspective canonical view volume to a cuboidal view volume which is easily transformed to the canonical view volume for parallel projection.
		However if the perspective divide by W is carried out at this stage to produce three dimensional co-ordinates for clipping to the (now) rectangular box that the perspective view volume has become then something goes wrong.
		In fact any point behind the centre of projection will be transformed to a corresponding point with a z co-ordinate greater than 1/(1-zmin) and the resultant clipped line will not be the same as obtained by (correctly) clipping first to the perspective view volume and then carrying out the perspective transformation.
	www.ece.eps.hw.ac.uk /~dml/cgonline/hyper00/polypipe/projection/persptrans.html (661 words)

	Perspective Projection and 3-D Viewing Pipeline (Site not responding. Last check: 2007-10-21)
		For this part of the lab, we implemented the 3D perspective projection and setup the view structure as defined in the lab procedure.
		Perspective projection consists of transforming the world into a canonical view volume and projecting this volume onto a 2D image.
		To do a perspective projection, we translate the view plane to the origin, scale everything to fit into the conical view volume, and then project that volume onto a 2D image using the focal length to determine the 3D->2D projection.
	graphics.battletothedeath.net /lab6 (1056 words)

	Wide-angle geometry (Site not responding. Last check: 2007-10-21)
		Images created by perspective lenses (as opposed to composites made from several images) are effectively cropped at 120-140 degrees by a cos^4 drop-off in intensity.
		Stereographic projection is also a closer approximation to the behavior of our video camera lenses than perspective projection.
		Interestingly, the lens with the widest field of view is closest to perspective, and we found the worst deviation from perspective in a lens with only a 50 degree field of view.
	www.cs.hmc.edu /~fleck/iowa-lab/wide.html (623 words)

	Plugin.com - Perspective Plugin, by Hot Door, Inc. - Plug In to Plugin.com (Site not responding. Last check: 2007-10-21)
		Perspective adds realistic drawing and projection tools to Illustrator 8, 9 or 10 Hot Door Perspective is a complete dimensional drawing environment for Adobe Illustrator.
		Project flat art as faces - Perspective allows you to instantly project flat artwork - even outlined text - as faces based on your grid settings.
		Projection is very useful for turning 3-view drawings into 'objects' or projecting curved paths in perspective.
	www.plugin.com /product/10611 (538 words)

	CS184 Lecture 7 summary
		Perspective projection is a much better approximation to what physical cameras (including the human eye) see when viewing a 3D scene.
		To compute perspective projection, draw light rays from object points to the viewer's origin, and intersect those with the viewing screen.
		Note that perspective projection exhibits foreshortening, that is, close objects appear larger (because their z-coordinate magnitude is smaller).
	www.cs.berkeley.edu /~jfc/cs184f98/lec7/lec7.html (563 words)

	Perspective Camera Models (Site not responding. Last check: 2007-10-21)
		Most Structure from Motion (linear and non-linear) techniques begin by assuming a perspective projection model as shown in Figure 3 which can be traced back to Durer and Renaissance painters.
		The projection of the COP onto the image plane along the optical axis is called the principal point.
		This perspective projection is often referred to as a pinhole camera.
	www1.cs.columbia.edu /~jebara/htmlpapers/SFM/node6.html (282 words)

	CS 4611: Projections
		The next stage takes the camera coordinates (VCS) and applies an orthographic or perspective transformation to create "clipping coordinates" (so that the object as view by the camera is clipped against the planes of the view volume.) The viewable, projected, and clipped object's coordinates are then converted in to normalized device coordinates.
		A parallel projection is one in which coordinates of the points of an object are transfered to the viewplane along parallel projectors (e.g., lines.) The edges of an object that is projected in parallel have the projected edges preserved and geometrically similar.
		A perspective projection is one in which coordinates of the points of an object are transfered to the viewplane to projection coordinates along projectors (e.g., lines) that vanish to a center of projection (COP)(sometimes called a vanishing point).
	www.csl.mtu.edu /cs4611/www/nine04.html (1242 words)

	Augmented Reality Home Page - Minimal Calibration
		A weak perspective projection model for the camera is used to approximate the perspective projection process.
		The tracker attached to the selected camera is queried for the new projection matrix which is calculated from the projections of the affine basis points as described in Section 2.5.
		This new affine projection matrix is transmitted to the graphics server which then renders the scene with the new projections.
	www.se.rit.edu /~jrv/research/ar/thesis.html (3794 words)

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