Orthographic projection

Orthographic projection (sometimes orthogonal projection) is a means of representing three-dimensional objects in two dimensions. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane. Orthographic projection (sometimes orthogonal projection) is a means of representing three-dimensional objects in two dimensions. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane. 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, but these are better known as multiview projections. Furthermore, when the principal planes or axes of an object in an orthographic projection are not parallel with the projection plane, but are rather tilted to reveal multiple sides of the object, the projection is called an axonometric projection. Sub-types of multiview projection include plans, elevations and sections. Sub-types of axonometric projection include isometric, dimetric and trimetric projections. A lens providing an orthographic projection is known as an object-space telecentric lens. A simple orthographic projection onto the plane z = 0 can be defined by the following matrix: For each point v = (vx, vy, vz), the transformed point Pv would be Often, it is more useful to use homogeneous coordinates. The transformation above can be represented for homogeneous coordinates as For each homogeneous vector v = (vx, vy, vz, 1), the transformed vector Pv would be In computer graphics, one of the most common matrices used for orthographic projection can be defined by a 6-tuple, (left, right, bottom, top, near, far), which defines the clipping planes. These planes form a box with the minimum corner at (left, bottom, -near) and the maximum corner at (right, top, -far).