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One implication of that is the "isotropy of scale factors", which means that the point scale factor is independent of direction, so that small shapes are preserved by the projection. This implies that the vertical scale factor, h, equals the horizontal scale factor, k. Since k = sec φ, so must h.
Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
The Medieval and Early Modern Nautical Chart: Birth, Evolution and Use, Lisbon-based ERC-funded academic project. They develop and maintain the MEDEA-CHART Database, a sophisticated search engine and aggregator of early nautical charts data. Online version of Chart No.1 with "Symbols, Abbreviations and Terms" used in nautical charts
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
The point scale factor is independent of direction. It is a function of y on the projection. (On the sphere it depends on latitude only.) The scale is true on the equator. • The point scale factor is independent of direction. It is a function of x on the projection. (On the sphere it depends on both latitude and longitude.)
Programs on the nautical chart, directions, coastal navigation and beacons, nautical publications. The astronomical navigation section includes the resolution of the position triangle, the usefulness of a height line, the recognition of stars and the determinant of the height line, in addition to other topics of interest in nautical: tides, naval kinematics, meteorology and hurricanes, and ...
A contour chart of scale factors of GS50 projection Maps reflecting directions, such as a nautical chart or an aeronautical chart , are projected by conformal projections. Maps treating values whose gradients are important, such as a weather map with atmospheric pressure , are also projected by conformal projections.
The Helmert transform is a seven-parameter transform with three translation (shift) parameters ,,, three rotation parameters ,, and one scaling (dilation) parameter . The Helmert transform is an approximate method that is accurate when the transform parameters are small relative to the magnitudes of the ECEF vectors.