Sphere projections. Medical search. Frequent questions

Delisle's map-projection , the secant conical projection proposed by Mercator, and applied by J. N. Delisle to the great map of Russia. (wordnik.com)
This process can be accomplished in innumerable ways by combining different map projections and grids, for example, the widely recognized Mercator projection and a square grid. (uber.com)
Mercator projection displays shapes well at the expense of size. (explainxkcd.com)

Riemann, for example, used stereographic projection in his model of the complex plane. (maa.org)
Figure 4: Stereographic projection of circles onto the plane. (maa.org)
The article also discusses stereographic projection and the world of visible spheres. (wisc.edu)
The facinating picture above shows the famous Penrose singular foliation of the 3-sphere by tori and two circles after a stereographic projection into Euclidean 3-space. (lu.se)

This is similar to spherical projection mapping but doesn't use a whole sphere. (business.com)
This gives a regular partition of the sphere into 12 congruent spherical pentagons. (maa.org)
The sum of the spherical excesses is multiplied by the square of the sphere radius to obtain the surface area of the spherical polygon. (scipy.org)

Projections are of fundamental importance in geometry, and ray tracers make them easily visible. (maa.org)
The POV-Ray generated video Mobius Transformations Revealed provides a beautiful exposition of Riemann's brilliant insight into the geometry of the Mobius functions where translations, dilations, rotations and inversions are all revealed to correspond to simple motions of the sphere [ 1 ]. (maa.org)
Level 2 processing is done to correct image geometry to match appropriate map projections. (usgs.gov)
As mentioned previously, since Sky shares a rendering engine with Earth, the geometry of the sky is, in fact, a slightly oblate spheroid (technically, the WGS84 projection). (ogleearth.com)
The GIS community has developed a number of tools for handling re-projections of images using this geometry, most notably the Geospatial Data Abstraction Library (GDAL). (ogleearth.com)
begin{comment} :Title: Steradian cone in sphere :Tags: 3D;Angles;Intersections;Shadings;MMathematics;Geometry :Author: Bartman :Slug: steradian-cone-sphere A graphical representation of a steradian. (stackexchange.com)
My question is - From observing the area of the tumbling polytope's shadow, or two-dimensional projection over time, what can we learn about it's geometry? (mathoverflow.net)

It can be as simple as a tiny glass sphere or a type of prism formed from glass or plastic. (makezine.com)
The evaluation was carried out in a large aerosol test chamber where relatively uniform concentrations of polydisperse sodium chloride and glass-sphere particles were generated to test the system with nano- and micro-size particles. (cdc.gov)

Figure 4 depicts a sphere tangent to a plane at its south pole. (maa.org)
noun 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. (wordnik.com)
This software can warp images from one projection (including a tangent plane) to another and encodes the geometric information necessary for registering the image on the sphere in either an image header (analogous to a FITS header) or an associated "world file", depending on the image format. (ogleearth.com)

Cylindrical map-projection. (wordnik.com)
A Simple Cylindrical projection was used at a resolution of 500 m. (usgs.gov)

This allows everyday objects of varying shapes and textures (including people) to act as projection screens, creating immersive visuals and effects. (business.com)

It is a modified Lambert azimuthal equal-area projection, most often applied to a polyhedral globe consisting of an icosahedron. (wikipedia.org)
It consists of 20 hexagons on the surface of the sphere and 12 pentagons centered on the 12 vertices of the icosahedron. (wikipedia.org)
Buckminster Fuller 's Dymaxion maps are based on a projection of the Earth's sphere onto an icosahedron. (newworldencyclopedia.org)

Snyder equal-area projection is a polyhedral map projection used in the ISEA (Icosahedral Snyder Equal Area) discrete global grids. (wikipedia.org)
Then project the hexagon back onto the sphere using the Inverse Snyder Icosahedral equal area projection. (wikipedia.org)
PROJ guide's "Icosahedral Snyder Equal Area", proj.org/operations/projections/isea.html D. Carr et al. (wikipedia.org)

The video shows an equirectangular projection. (imaginary.org)
You can include rectilinear clips and titles in a 360° project-for example, you might want to place a logo or a title within the 360° equirectangular projection . (apple.com)
You can turn on the 360° Transform controls to project the title correctly into the equirectangular projection. (apple.com)

allows you to install orthographic projections, i.e. dial the view angles. (stackexchange.com)

I haven't seen such map projections used for cartography, except for patriotic joke maps, where one's beloved home town or country is shown in a much larger scale than the rest of the world. (maptools.org)

Each photograph is a two-dimensional projection of the celestial sphere. (universetoday.com)
All-sky space-based astrometry leads to a global solution and provides a rigid sphere for a celestial reference frame that cannot be accurately obtained with any other method. (lu.se)

This 3D projection of the data comes from an pseudo time algorithm called DDRTree. (lu.se)
This 3D projection of the data comes from an algorithm called tSNE. (lu.se)

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. (wordnik.com)
Equidistant map-projection , a zenithal map-projection in which the radius of each almucantar is equal to its angular distance from the zenith. (wordnik.com)
The map projections are based on a sphere having a radius of 1,562.09 kilometers. (usgs.gov)

Inverse perspective projection distort sphere. (speakerdeck.com)

The circumcenters of all tetrahedra in the system are calculated and projected to the surface of the sphere, producing the Voronoi vertices. (scipy.org)
I have multiple planes whose vertices are transformed to a position on a sphere in the vertex shader. (stackexchange.com)

noun Any projection which may naturally be regarded as the development of a projection upon a cone. (wordnik.com)

rolling shutters, lens abberations, and theater dome projections are just some of the possibilities this enables. (pixar.com)

Sphere, cylinder, and torus projections can be used to render environment maps and panoramic images. (pixar.com)

Threshold for detecting duplicate points and mismatches between points and sphere parameters. (scipy.org)

Fiscal 2024 EPS estimates have largely declined from projections of $2.54 per share a month ago to forecast of an adjusted loss of -$1.77 a share. (yahoo.com)

In addition, the proposed tool simultaneously achieved static projection mapping that projected the image content onto a fixed object, and dynamic projection mapping that projected the image content onto a user's body, by tracing the moving user. (techscience.com)
In addition to these films, there is a large library of films and static image projections from the American Science on a Sphere (external link). (lu.se)

Let $V$ be a body in $\mathbb{R}^3$ bounded by a smooth sphere with principal curvatures at most 1 (by absolute value). (mathoverflow.net)
There exist two different polytopes $P_1$ and $P_2$ such that for every unit vector $v\in\mathbb R^3$, the areas of the two projections along $v$ are equal. (mathoverflow.net)

A recent study showed that several N95 FFR models performed as well as surgical N95 FFRs in synthetic blood penetration tests that evaluate resistance to penetration by horizontal projection. (cdc.gov)

This is usually used to create a horizontal, wide-screen projection. (business.com)
All of these projection modes work equally well for both horizontal and vertical panoramas / HDR panoramas. (adobe.com)

It is named for John P. Snyder, who developed the projection in the 1990s. (wikipedia.org)
He came out of retirement specifically to address projection problems with the original EMAP grid (see Snyder, 1992). (wikipedia.org)
The underlying imagery used in Sky resides in a lat/long projection (Snyder 1926). (ogleearth.com)

The subsequent effort was to be devoted to the recording of the effects of the impact of steel spheres on the entire lens/frame combination when positioned on a simulation of a human head. (cdc.gov)

Various types of strikers and methods of projection were to be employed' against a series of simply-supported plano and prescription lenses and also against such lenses when emplaced in a frame mounted on an anthropometric headform. (cdc.gov)

There is no limit to which structures or materials can be used as canvases, as long as the software used to develop projections can account for lighting and texture. (business.com)
The specifics of the projection space, like its color, lighting and texture, affect the adjustments and calculations the software will use to form optimal media. (business.com)

This is a projection within a sphere in all directions, 360 degrees, involving multiple projectors and sophisticated video output to make all parts of the projection look seamless. (business.com)

Projection mapping is a technological feature that projects video that represents your brand onto surfaces. (business.com)
Equivalent map-projection , a map-projection which represents all equal surfaces on the spheroid by equal areas on the map. (wordnik.com)
Each little sphere in the graph represents a cell in the data. (lu.se)

The collective work of Iulia Anghel, Elena Banciu, Flavius Pană, and Ana Maria Birtalan from the Ecological University of Bucharest closes the section and discusses how the concept of the 'public sphere' reconfigured in Romania along with digitalization. (lu.se)

It is the solid angle subtended at the center of a unit sphere by a unit area on its surface. (stackexchange.com)
You cannot recover a convex polytope from its projection areas, even if you know the whole function (unit vector) $\mapsto$ (area of projection along this vector). (mathoverflow.net)

This is the most basic kind of projection mapping: projecting media onto a flat surface. (business.com)
Making a Sphere Look Flat. (mapresources.com)
When you add a standard title (a title not optimized for 360° video) to a 360° project, the title looks "flat" in the viewer but appears as if it is pasted on the inside of the 360° sphere in the 360° viewer. (apple.com)
When 360° Transform is on, the title appears on a flat plane within the 360° sphere. (apple.com)
Any flat map projection of a sphere must have inaccuracies. (explainxkcd.com)

Light shining from a bulb situated inside the sphere casts the fivefold pattern as shadows onto the surrounding walls. (olafureliasson.net)
Using a ray tracer, projections like this come for free: just place a light at the center of the sphere and let the shadows of the edges of polyhedron fall on the surface of the sphere. (maa.org)

I can calculate UV of the sphere myself. (stackexchange.com)
that let's me calculate and characterize two-dimensional surface projections of convex polytopes! (mathoverflow.net)

Projection mapping can be an impressive, high-impact advertising technique. (business.com)
This proposition isn't cheap, so before hiring an agency that specializes in projection mapping, or before your next event, it's important to understand what goes into planning this type of ad as well as some of the legal issues. (business.com)
What is projection mapping? (business.com)
Some popular projection mapping effects are optical illusions, creating the appearance of movement on a static object and enhancing the target mood of an environment. (business.com)
How does projection mapping work? (business.com)
Projection mapping uses software to spatially map media onto a three-dimensional object. (business.com)
Once the space and content have been determined, projection mapping software's preproduction process fits media onto a 3D model of the area where it will be projected, recreating the way the projection will function with a real object. (business.com)
The projection mapping production process can take eight to 14 weeks. (business.com)
Projection mapping has amazing capabilities. (business.com)
Using human bodies as canvases, this projection mapping created the illusion of ink forming into tattoos right before the audience's eyes. (business.com)
Projection mapping is frequently used in Disney theme parks. (business.com)
The costs of projection mapping tend to vary based on the size of the projection space and the quality and features of the media content. (business.com)
According to ON Services, the average cost of a mapping projection is $10,000 per minute. (business.com)
Consider these factors when estimating the costs of projection mapping for your business. (business.com)
This study introduces the design details of a tool to create interactive projection-mapping content in a convenient manner. (techscience.com)
Moreover, the projection accuracy was analyzed at different depth positions, and the projection-mapping accuracy was verified with the use of the proposed method. (techscience.com)
SAR is a projection-mapping technique that enables multiple users to experience virtual content simultaneously, without the need to wear specific gear. (techscience.com)
The projection-mapping technique is extensively applied in the field of media arts to show colorful displays, e.g., advertisements, exhibitions, and performances. (techscience.com)
Moreover, dynamic projection mapping that traces and projects onto a moving object, has been highlighted extensively compared with the static version that is projected onto a still object [ 8 - 11 ]. (techscience.com)
However, creating the dynamic projection-mapping content can be challenging, as explained below. (techscience.com)
Third, unlike the static projection-mapping content, which can be easily created by a user, dynamic projection-mapping content requires a complicated programming process because there are no commercialized content-creation tools. (techscience.com)
Owing to these problems, it is difficult for media producers and artists who have little knowledge of programming to create dynamic projection-mapping contents without any other assistance. (techscience.com)
In addition, it uses text-based configuration files to allow nontechnical users to create projection-mapping content without any other assistance. (techscience.com)

This color-coded map in Robinson projection displays a progression of changing global surface temperature anomalies from 1880 through 2018. (nasa.gov)

This results in substantial distortion at the poles even when re-projecting onto the sphere. (ogleearth.com)

Deproject a point from the plane to the sphere. (nasa.gov)
The input position in the projection plane. (nasa.gov)
The polygons are small 3D parts of a quasi sphere centered in the origin and a solution that works in the plane can easily be made to work in this world. (stackexchange.com)
My general question concerns what we can learn about an arbitrary, three-dimensional convex polytope (or convex hull of an arbitrary polytope) strictly from the surface areas of its two-dimensional projections on a plane as it 'tumbles' in 3-space (i.e. as it rotates along an arbitrary, shifting axis). (mathoverflow.net)

The point of view rotates around the sphere in the course of the simulation. (imaginary.org)
Prices have risen by an extra percentage point above the projections. (stlouisfed.org)
Trading at $23 a share, the declining earnings estimates point to more volatility and downside risk ahead for Sphere stock. (yahoo.com)
noun The foot of the perpendicular from a point to a straight line is the projection of the point upon the line. (wordnik.com)
A map projection is needed for going from a three-dimensional location on Earth to a two dimensional point on a map. (uber.com)
Do we gain anything by watching the evolution of the convex polytopes shadow as it tumbles (part of the point for the physical example), as opposed to an unordered collection of two-dimensional projections? (mathoverflow.net)

noun A perspective or central projection in which the center is at infinity. (wordnik.com)

This is a projection method that manipulates video and images in synchronization with something else, like music. (business.com)
The underlying projection and registration of images in Sky is based on the technology used in Google Earth. (ogleearth.com)
Aligns and transforms the images as if they were mapped to the inside of a sphere. (adobe.com)

Felix Klein used central projection in his study of the finite groups of rotations in three dimensions [ 6 , p.3-30]. (maa.org)
Do you know which rotations of the polytope gave you particular projection areas? (mathoverflow.net)

Gall-Peters projection does the opposite, showing accurate surface area with distorted ("awful") shapes. (explainxkcd.com)
Update - Nurdin Takenov (and Sergei Ivanov in later comments) nicely points out that we can use the average surface area of the two-dimensional projection to find the surface area of the tumbling convex polygon. (mathoverflow.net)

You can position it in the 360° sphere, but it always appears thin, like a piece of paper with a photograph of a 3D title on it. (apple.com)

Solution of the wave equation on a sphere. (imaginary.org)
The simulation shows a solution of the wave equation on a sphere, obtained by a finite difference scheme. (imaginary.org)

Integrators take the camera rays from the projection and return shaded results to the renderer. (pixar.com)
results in fine, minute projections (papillae), giving the tarsal conjunctiva a velvety appearance. (msdmanuals.com)

Is arcball sphere in screen space? (speakerdeck.com)
For example, you can build a Glass Bead Projection Screen . (makezine.com)
Once the 2D positions on the screen have been chosen to sample, the camera projection turns them into 3D rays in the camera space. (pixar.com)

noun A parallelogrammatic or square map-projection. (wordnik.com)

But maybe such projections are used for statistical or economic maps, as you suggest. (maptools.org)
This map-projection, invented by the French mathematician Postel in the sixteenth century, is frequently employed for star-maps, etc. (wordnik.com)

This paper describes a study about occupational projections with juveniles marked by gender, aiming at contributing with practices of vocational guidance. (bvsalud.org)

Figure 6 depicts the central projection of a dodecahedron onto the sphere. (maa.org)
Figure 6 with linked animation: Central projection. (maa.org)
noun The central equivalent projection. (wordnik.com)
First, a median line and a line touching the vestibular portions of the projections of the maxillary central incisors were drawn. (bvsalud.org)

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). (wordnik.com)

Anatomy101

Organisms15

Diseases1

Chemicals and Drugs34

Analytical, Diagnostic and Therapeutic Techniques and Equipment52

Psychiatry and Psychology5

Phenomena and Processes40

Disciplines and Occupations5

Anthropology, Education, Sociology and Social Phenomena1

Technology, Industry, Agriculture6

Information Science16

Health Care6

Mercator3

Stereographic projection4

Spherical3

Geometry7

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Immersive1

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Equirectangular3

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Cartography1

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Radius3

Inverse1

Vertices2

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Dome1

Cylinder1

Parameters1

20241

Image2

Mathbb2

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Snyder3

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Discusses1

Unit2

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Mapping23

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Point6

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