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Each cell of the rectilinear grid has one scalar value from low (bright blue) to high (bright red) assigned to it. The grid's memory footprint is indicated in the lower line. The implicit max kd-tree's predefined memory footprint needs one scalar value less than that. The storing of the node's max values is indicated in the upper line.
Head and cerebral structures (hidden) extracted from 150 MRI slices using marching cubes (about 150,000 triangles). Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, [1] for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels).
An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
Fig.15 scalar cell at an exit boundary In fully developed flow no changes occurs in flow direction, gradient of all variables except pressure are zero in flow direction The equations are solved for cells up to NI-1, outside the domain values of flow variables are determined by extrapolation from the interior by assuming zero gradients at the ...
A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
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.
A scalar in physics and other areas of science is also a scalar in mathematics, as an element of a mathematical field used to define a vector space.For example, the magnitude (or length) of an electric field vector is calculated as the square root of its absolute square (the inner product of the electric field with itself); so, the inner product's result is an element of the mathematical field ...
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography (ECC). The literature presents this operation as scalar multiplication , as written in Hessian form of an elliptic curve .