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Fig.2 Orthogonal Grids Fig.3 Non-Orthogonal Grids. a) Structured curvilinear grid arrangements (vertices having similar neighborhood). b) Unstructured grid arrangements (vertices having variation in neighborhood). Structured curvilinear grids. 1) Grid points are identified at the intersection of coordinate line.
A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...
In urban planning, the grid plan, grid street plan, or gridiron plan is a type of city plan in which streets run at right angles to each other, forming a grid. [ 1 ] Two inherent characteristics of the grid plan, frequent intersections and orthogonal geometry, facilitate movement.
An orthonormal basis is a basis whose vectors are both orthogonal and normalized (they are unit vectors). A conformal linear transformation preserves angles and distance ratios, meaning that transforming orthogonal vectors by the same conformal linear transformation will keep those vectors orthogonal.
Orthogonal coordinates: coordinate surfaces meet at right angles; Skew coordinates: coordinate surfaces are not orthogonal; The log-polar coordinate system represents a point in the plane by the logarithm of the distance from the origin and an angle measured from a reference line intersecting the origin.
Given a smooth manifold of dimension n, an orthogonal web (also called orthogonal grid or Ricci’s grid) on a Riemannian manifold (M,g) is a set [3] = (, …,) of n pairwise transversal and orthogonal foliations of connected submanifolds of dimension 1.