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Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
Projects the globe onto eight octants (Reuleaux triangles) with no meridians and no parallels. 1909 Cahill's butterfly map: Polyhedral Compromise Bernard Joseph Stanislaus Cahill: Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements. 1975 Cahill–Keyes projection
For example, a small circle of fixed radius (e.g., 15 degrees angular radius). [14] Sometimes spherical triangles are used. [citation needed] In the first half of the 20th century, projecting a human head onto different projections was common to show how distortion varies across one projection as compared to another. [15]
Gnomonic projection of a portion of the north hemisphere centered on the geographic North Pole The gnomonic projection with Tissot's indicatrix of deformation. A gnomonic projection, also known as a central projection or rectilinear projection, is a perspective projection of a sphere, with center of projection at the sphere's center, onto any plane not passing through the center, most commonly ...
If the normal of the viewing plane (the camera direction) is parallel to one of the primary axes (which is the x, y, or z axis), the mathematical transformation is as follows; To project the 3D point , , onto the 2D point , using an orthographic projection parallel to the y axis (where positive y represents forward direction - profile view ...
The original circle in the above example had a radius of 1, but when dealing with a Tissot indicatrix, one deals with ellipses of infinitesimal radius. Even though the radii of the original circle and its distortion ellipse will all be infinitesimal, by employing differential calculus the ratios between them can still be meaningfully calculated ...
The Madison Square Garden (MSG) Sphere at the Venetian Resort in Las Vegas has LED lights that can create these large-scale projections. It has been filmed projecting the image of a gigantic ...
If the sphere is isometrically embedded in Euclidean space, the sphere's intersection with a plane is a circle, which can be interpreted extrinsically to the sphere as a Euclidean circle: a locus of points in the plane at a constant Euclidean distance (the extrinsic radius) from a point in the plane (the extrinsic center). A great circle lies ...