Rectilinear Projection - Revision history

Erik Krause: Prepared for new glossary template

2007-11-18T19:21:01Z

Prepared for new glossary template

Imroy: copyedit

2007-09-24T13:27:14Z

copyedit

WikiSysop: 7 revision(s)

2006-07-13T20:31:17Z

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2006-07-13T20:30:06Z

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2006-07-13T19:56:42Z

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Erik Krause: Image comment

2005-12-15T22:24:42Z

Image comment

Erik Krause: Image comment

2005-12-15T22:24:42Z

Image comment

Erik Krause: Image comment

2005-12-15T22:24:42Z

Image comment

New page

[[image:big_ben_rectilinear.jpg|right|Rectilinear projection, with permission from Ben Kreunen]]

This is a type of [[Projections|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.

The is a fundamental projection in panoramic imaging, because most ordinary (non-fisheye) camera lenses produce an image very close to being rectilinear over their entire field of view. Pin-hole cameras, in fact, provide exactly a tangent-plane mapping of the sphere onto their detector planes, and most simple imaging systems (consumer cameras with non-fisheye lenses among them) approximate this quite well. Thus it is the most common source image projection for partial panoramas.

The rectilinear projection also has the fundamental property that straight lines in real 3D space are mapped to straight lines in the projected image. This property makes the rectilinear image very useful for printed panoramas which do not cover an excessively large range of longitude or latitude (e.g. <120 degrees). Many [[Panorama Viewers]] which show only a portion of a scene at a time do so using the rectilinear projection (regardless of what projection the full sphere source image was in).

The [[Cubic Projection]] is a special sub-case of the rectilinear projection, in which 90 by 90 degree rectilinear sub-projections are made onto 6 faces of a cube.
[[Category:Glossary]]

Jdsmith: Added big ben image.

2005-12-15T00:49:49Z

Added big ben image.

Jdsmith: Added big ben image.

2005-12-15T00:49:49Z

Added big ben image.

← Older revision		Revision as of 19:21, 18 November 2007
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		+	{{Glossary\|A projection in which every straight line in the world stays straight in the image.}}
	[[image:big ben rectilinear.jpg\|right\|Rectilinear projection, with permission from Ben Kreunen]]		[[image:big ben rectilinear.jpg\|right\|Rectilinear projection, with permission from Ben Kreunen]]

← Older revision		Revision as of 22:24, 15 December 2005
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−	[[image:big_ben_rectilinear.jpg\|right]]	+	[[image:big_ben_rectilinear.jpg\|right\|Rectilinear projection, with permission from Ben Kreunen]]

	This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.		This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.

← Older revision		Revision as of 22:24, 15 December 2005
Line 1:		Line 1:
−	[[image:big_ben_rectilinear.jpg\|right]]	+	[[image:big_ben_rectilinear.jpg\|right\|Rectilinear projection, with permission from Ben Kreunen]]

	This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.		This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.

← Older revision		Revision as of 00:49, 15 December 2005
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		+	[[image:big_ben_rectilinear.jpg\|right]]
		+
	This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.		This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.

← Older revision		Revision as of 00:49, 15 December 2005
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		+	[[image:big_ben_rectilinear.jpg\|right]]
		+
	This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.		This is a type of [[Projections\|projection]] for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.

@@ Line 1: / Line 1: @@
-[[image:big_ben_rectilinear.jpg|right|Rectilinear projection, with permission from Ben Kreunen]]
+[[image:big ben rectilinear.jpg|right|Rectilinear projection, with permission from Ben Kreunen]]
-This is a type of [[Projections|projection]] for mapping a portion of the surface of a sphere to a flat image.  It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center.  [http://mathworld.wolfram.com/GnomonicProjection.html Mathworld's page] has an example and describes the mathematics underlying this projection.
+'''Rectilinear''' is a type of [[Projections|projection]] for mapping a portion of the surface of a sphere to a flat image.  It is also called the "gnomic", "gnomonic", or "tangent-plane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the spheres' center. Mathworld's page has an example and describes the mathematics underlying this projection.[http://mathworld.wolfram.com/GnomonicProjection.html]
 The is a fundamental projection in panoramic imaging, because most ordinary (non-fisheye) camera lenses produce an image very close to being rectilinear over their entire field of view.  Pin-hole cameras, in fact, provide exactly a tangent-plane mapping of the sphere onto their detector planes, and most simple imaging systems (consumer cameras with non-fisheye lenses among them) approximate this quite well.  Thus it is the most common source image projection for partial panoramas.
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 The [[Cubic Projection]] is a special sub-case of the rectilinear projection, in which 90 by 90 degree rectilinear sub-projections are made onto 6 faces of a cube.
 [[Category:Glossary]]

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