Planar projection

	Part of a series on:
	Graphical projection
	Planar Perspective Linear perspective One-point perspective; Two-point perspective; Three-point perspective; Zero-point perspective; ; Curvilinear perspective; Reverse perspective; ; Parallel Orthographic projection Multiviews Plan, or floor plan; Section; Elevation; ; Auxiliary view; Axonometric projection Isometric projection; Dimetric projection; Trimetric projection; ; ; Oblique projection Cavalier perspective; Cabinet projection; ; ;
	Other 3D projection; Stereographic projection; Anamorphic projection;
	Views Bird's-eye view/Aerial view; Detail view; 3/4 perspective; Exploded view drawing; Fisheye; Fixed 3D; Panorama; Top-down perspective; Worm's-eye view; Zoom;
	Topics Computer graphics; Computer-aided design; Descriptive geometry; Engineering drawing; Foreshortening; Map projection; Projective geometry; Technical drawing; Vanishing point;
	v • d • e

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two-dimensional projection plane. The projected point on the plane is chosen such that it is collinear with the corresponding three dimensional point and the centre of projection. The lines connecting these points are commonly referred to as projectors.

The centre of projection can be thought of as the location of the observer while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed (e.g., photographic negative, photographic print, computer monitor). When the centre of projection is at a finite distance from the projection plane, a perspective projection is obtained. When the centre of projection is at infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections.

[edit] Mathematical formulation

Mathematically, planar projections are linear transformations acting on a point in three dimensional space $\mathbf{a}_{x,y,z}$ to give a point $\mathbf{b}_{u,v}$ on the projection plane. These transformations consist of various compositions of the five transformations: orthographic projection, rotation, shear, translation and perspective.