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Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.
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").
In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (radians), or one of the vectors is zero. [4] Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension.
(In cases where such a view is useful, e.g. a ceiling viewed from above, a reflected view is used, which is a mirror image of the true orthographic view.) Monge's original formulation uses two planes only and obtains the top and front views only. The addition of a third plane to show a side view (either left or right) is a modern extension.
In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle). A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles , for instance in inversive geometry , then an ...
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 ...
In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain , the bilinear form may be the integral of the product of functions over the interval:
A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .