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Appearance. In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity. The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point ...
v. t. e. An engineering drawing is a type of technical drawing that is used to convey information about an object. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing. Usually, a number of drawings are necessary to completely specify even a simple component.
Projective geometry. In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts.
In a projective plane this is actually true. In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect.
Projective space. In graphical perspective, parallel (horizontal) lines in the plane intersect at a vanishing point (on the horizon). In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a ...
Definitions. [edit] A projection on a vector space is a linear operator such that . When has an inner product and is complete, i.e. when is a Hilbert space, the concept of orthogonality can be used. A projection on a Hilbert space is called an orthogonal projection if it satisfies for all .
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.
Graphical projection. In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the projection plane or image plane, where the rays, known as lines of sight or projection lines, are parallel to each other.