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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.
Plane orthogonal to line L and including the origin. Point B is the origin. Line L passes through point D and is orthogonal to the plane of the picture. The two planes pass through CD and DE and are both orthogonal to the plane of the picture.
(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
Two flat planes and of a Euclidean four-dimensional space are called completely orthogonal if and only if every line in is orthogonal to every line in . [7] In that case the planes A {\displaystyle A} and B {\displaystyle B} intersect at a single point O {\displaystyle O} , so that if a line in A {\displaystyle A} intersects with a line in B ...
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").
The term orthographic is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are also parallel with the projection plane (or the paper on which the orthographic or parallel projection is drawn). However, the term primary view is also used.
One solution is to start from the (x, y) projection plane and construct the image from the values defined in (λ, φ) by using the inverse formulas of the orthographic projection. See References for an ellipsoidal version of the orthographic map projection. [3]
For example, the three-dimensional Cartesian coordinates (x, y, z) is an orthogonal coordinate system, since its coordinate surfaces x = constant, y = constant, and z = constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.