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In uniform scaling with a non-zero scale factor, all non-zero vectors retain their direction (as seen from the origin), or all have the direction reversed, depending on the sign of the scaling factor. In non-uniform scaling only the vectors that belong to an eigenspace will retain their direction. A vector that is the sum of two or more non ...
An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".
When composing multiple linear transformations, it is possible to create a shear/skew by composing a parent transform with a non-uniform scale, and a child transform with a rotation. Therefore, in situations where shear/skew is not allowed, transformation matrices must also have uniform scale in order to prevent a shear/skew from appearing as ...
Scaling (geometry) a similar notion in vector spaces Homothetic center , the center of a homothetic transformation taking one of a pair of shapes into the other The Hadwiger conjecture on the number of strictly smaller homothetic copies of a convex body that may be needed to cover it
Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.
Graphical scale bar in combination with a scale expressed as a ratio and a conversion help. The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building ...
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A Procrustes transformation is a geometric transformation that involves only translation, rotation, uniform scaling, or a combination of these transformations.Hence, it may change the size, position, and orientation of a geometric object, but not its shape.