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A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
Usually clipped near 80°N/S. Standard world projection of the NGS in 1922–1988. c. 150: Equidistant conic = simple conic: Conic Equidistant Based on Ptolemy's 1st Projection Distances along meridians are conserved, as is distance along one or two standard parallels. [3] 1772 Lambert conformal conic: Conic Conformal Johann Heinrich Lambert
If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may be any shape [2] and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base). Contrasted with right ...
The term "conic projection" is used to refer to any projection in which meridians are mapped to equally spaced lines radiating out from the apex and circles of latitude (parallels) are mapped to circular arcs centered on the apex. [31] When making a conic map, the map maker arbitrarily picks two standard parallels.
Lambert conformal conic projection. Oblique conformal conic projection (This projection is sometimes used for long-shaped regions, like as continents of Americas or Japanese archipelago.) Stereographic projection (Conformal azimuthal projection. Every circle on the earth is drawn as a circle or a straight line on the map.)
In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section ( ellipse , parabola , or hyperbola ) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of ...
In Euclidean and projective geometry, five points determine a conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines.
More generally, when the directrix is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of , one obtains an elliptic cone [4] (also called a conical quadric or quadratic cone), [5] which is a special case of a quadric surface. [4] [5]