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The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
where is a reconstruction offset value in the range of 0 to 1 as a fraction of the step size. Ordinarily, 0 ≤ r k ≤ 1 2 {\displaystyle 0\leq r_{k}\leq {\tfrac {1}{2}}} when quantizing input data with a typical probability density function (PDF) that is symmetric around zero and reaches its peak value at zero (such as a Gaussian , Laplacian ...
Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
Vector extraction, or vectorization, offers another approach. Vectorization first creates a resolution-independent vector representation of the graphic to be scaled. Then the resolution-independent version is rendered as a raster image at the desired resolution. This technique is used by Adobe Illustrator, Live Trace, and Inkscape. [7]
The apparent PPI of a monitor depends upon the screen resolution (that is, the number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than does the same monitor in a 1024×768 or 1280×960 mode.
This makes it possible to calculate the resolution of a structure regardless of how it was solved (X-ray, NMR, EM, modeling, ab initio prediction). ResProx was originally designed to serve as a simple, single-number evaluation that allows straightforward comparison between the quality/resolution of X-ray structures and the quality of a given ...