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If the length of the line segment connecting two projected points on the plane is proportional to the geodesic (shortest surface) distance between the two unprojected points on the globe, then we say that distance has been preserved between those two points. An equidistant projection preserves distances from one or two special points to all ...
A map of Africa using the Chamberlin trimetric projection. The three red dots indicate the selected "base" locations: (22°N, 0°), (22°N, 45°E), (22°S, 22.5°E). 10° graticule. The Chamberlin trimetric projection is a map projection where three points are fixed on the globe and the points on the sphere are mapped onto a plane by triangulation.
The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points. c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
The true distance between two points on a meridian can be measured on the map as the vertical distance between the parallels that intersect the meridian at those points. With no distortion along the central meridian and the equator, distances along those lines are correct, as are the angles of intersection of other lines with those two lines ...
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar ...
To get an end view of SU, projection 4 is drawn with hinge line H 3,4 perpendicular to S 3 U 3. The perpendicular distance d gives the shortest distance between PR and SU. To get points Q and T on these lines giving this shortest distance, projection 5 is drawn with hinge line H 4,5 parallel to P 4 R 4, making both P 5 R 5 and S 5 U 5 true ...
The lines connecting these points are commonly referred to as projectors. The centre of projection can be thought of as the location of the observer, while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed (e.g., photographic negative, photographic print ...
Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line segment parallel to the projection plane remains unchanged. The length of any line segment is shortened ...
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