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Automatic kerning refers to the kerning applied automatically by a program, as opposed to no kerning at all, or the kerning applied manually by the user. There are two types of automatic kerning: metric and optical. With metric kerning, the program directly uses the values found in the kerning tables included in the font file.
A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. [1] Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation".
One direction in metric geometry is finding purely metric ("synthetic") formulations of properties of Riemannian manifolds. For example, a Riemannian manifold is a CAT( k ) space (a synthetic condition which depends purely on the metric) if and only if its sectional curvature is bounded above by k . [ 20 ]
A key feature here is that the optical metric is not only a function of position, but also retains a dependency on . These pseudo-Finslerian optical metrics degenerate to a common, non-birefringent, pseudo-Riemannian optical metric for media that obey a curved space-time generalization of the Post conditions. [12] [6]
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
Metric geometry is a branch of geometry with metric spaces as the main object of study. It is applied mostly to Riemannian geometry and group theory Subcategories ...
The definition of an isometry requires the notion of a metric on the manifold; a manifold with a (positive-definite) metric is a Riemannian manifold, one with an indefinite metric is a pseudo-Riemannian manifold. Thus, isometries are studied in Riemannian geometry.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.