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Stake. Gradient maps are both at the center and at the basic level of map making on Wikipedia. A simple blank map and fill with color tool are needed. To continue to build a coherent Wikipedia display, this page suggests the most suitable SVG source files together with a blue-based color ramps from academic, screen friendly, print friendly, and color-blind friendly ColorBrewer2 by cartography ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.
and an external gradient is given by: G e ( f ) = f ⊕ b − f {\displaystyle G_{e}(f)=f\oplus b-f} . The internal and external gradients are "thinner" than the gradient, but the gradient peaks are located on the edges, whereas the internal and external ones are located at each side of the edges.
Gradients are expressed as a ratio of vertical rise to horizontal distance; for example, a 1% gradient (1 in 100) means the track rises 1 vertical unit for every 100 horizontal units. On such a gradient, a locomotive can pull half (or less) of the load that it can pull on level track.
Let : be a smooth map of smooth manifolds. Given , the differential of at is a linear map : from the tangent space of at to the tangent space of at (). The image of a tangent vector under is sometimes called the pushforward of by .
The pixels with the largest gradient values in the direction of the gradient become edge pixels, and edges may be traced in the direction perpendicular to the gradient direction. One example of an edge detection algorithm that uses gradients is the Canny edge detector. Image gradients can also be used for robust feature and texture matching.
In differential geometry, the four-gradient (or 4-gradient) is the four-vector analogue of the gradient from vector calculus. In special relativity and in quantum mechanics , the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors .