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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.
Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, once the concept is translated into projective geometry's terms. Again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing.
The projection of the point C itself is not defined. The projection parallel to a direction D, onto a plane or parallel projection: The image of a point P is the intersection of the plane with the line parallel to D passing through P. See Affine space § Projection for an accurate definition, generalized to any dimension. [citation needed]
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.
Parallel projection corresponds to a perspective projection with a hypothetical viewpoint; i.e. one where the camera lies an infinite distance away from the object and has an infinite focal length, or "zoom". In parallel projection, the lines of sight from the object to the projection plane are parallel to each other. Thus, lines that are ...
The point ¯ is the projection of a point = (,,) onto the projection plane Π. The foreshortenings are v x {\displaystyle v_{x}} , v y {\displaystyle v_{y}} and v z {\displaystyle v_{z}} . Pohlke's theorem is the basis for the following procedure to construct a scaled parallel projection of a three-dimensional object: [ 1 ] [ 2 ]
An orthogonal projection is a projection ... by the properties of the dot product of parallel and perpendicular vectors ... In Riemannian geometry, ...
Drawings of the finite projective planes of orders 2 (the Fano plane) and 3, in grid layout, showing a method of creating such drawings for prime orders These parallel lines appear to intersect in the vanishing point "at infinity". In a projective plane this is actually true.