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In this context the stereographic projection is often referred to as the equal-angle lower-hemisphere projection. The equal-area lower-hemisphere projection defined by the Lambert azimuthal equal-area projection is also used, especially when the plot is to be subjected to subsequent statistical analysis such as density contouring. [21]
We take the "temperature" to be zero along the gluing 2-sphere and let one of the 3-balls be "hot" and let the other 3-ball be "cold". The "hot" 3-ball could be thought of as the "upper hemisphere" and the "cold" 3-ball could be thought of as the "lower hemisphere". The temperature is highest/lowest at the centers of the two 3-balls.
The hemisphere can then be plotted as a disk of radius √ 2 using the Lambert azimuthal projection. Thus the Lambert azimuthal projection lets us plot directions as points in a disk. Due to the equal-area property of the projection, one can integrate over regions of the real projective plane (the space of directions) by integrating over the ...
Guyou hemisphere-in-a-square projection: Other Conformal Émile Guyou: Tessellates. 1925 Adams hemisphere-in-a-square projection: Other Conformal Oscar S. Adams: 1965 Lee conformal world on a tetrahedron: Polyhedral Conformal Laurence Patrick Lee: Projects the globe onto a regular tetrahedron. Tessellates. 1514 Octant projection: Polyhedral ...
The data for an earthquake is plotted using a lower-hemisphere stereographic projection. The azimuth and take-off angle are used to plot the position of an individual seismic record. The take-off angle is the angle from the vertical of a seismic ray as it emerges from the earthquake focus.
Schmidt net, used for making plots of the Lambert azimuthal projection. The Schmidt net is a manual drafting method for the Lambert azimuthal equal-area projection using graph paper. It results in one lateral hemisphere of the Earth with the grid of parallels and meridians. The method is common in geoscience.
A skybox is a method of creating backgrounds to make a video game level appear larger than it really is. [1] When a skybox is used, the level is enclosed in a cuboid.The sky, distant mountains, distant buildings, and other unreachable objects are projected onto the cube's faces (using a technique called cube mapping), thus creating the illusion of distant three-dimensional surroundings.
2.5D (basic pronunciation two-and-a-half dimensional) perspective refers to gameplay or movement in a video game or virtual reality environment that is restricted to a two-dimensional (2D) plane with little to no access to a third dimension in a space that otherwise appears to be three-dimensional and is often simulated and rendered in a 3D digital environment.