3D projection in the context of Perspective projection

Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.

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.

In 3D computer graphics, the image plane is that plane in the world which is identified with the plane of the display monitor used to view the image that is being rendered. It is also referred to as screen space. If one makes the analogy of taking a photograph to rendering a 3D image, the surface of the film is the image plane. In this case, the viewing transformation is a projection that maps the world onto the image plane. A rectangular region of this plane, called the viewing window or viewport, maps to the monitor. This establishes the mapping between pixels on the monitor and points (or rather, rays) in the 3D world. The plane is not usually an actual geometric object in a 3D scene, but instead is usually a collection of target coordinates or dimensions that are used during the rasterization process so the final output can be displayed as intended on the physical screen.

In optics, the image plane is the plane that contains the object's projected image, and lies beyond the back focal plane.

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. It is a basic tool in descriptive geometry. The projection is called orthographic if the rays are perpendicular (orthogonal) to the image plane, and oblique or skew if they are not.

In scientific visualization, a maximum intensity projection (MIP) is a method for 3D data that projects in the visualization plane the voxels with maximum intensity that fall in the way of parallel rays traced from the viewpoint to the plane of projection. This implies that two MIP renderings from opposite viewpoints are symmetrical images if they are rendered using orthographic projection.

MIP is used for the detection of lung nodules in lung cancer screening programs which use computed tomography scans. MIP enhances the 3D nature of these nodules, making them stand out from pulmonary bronchi and vasculature. MIP imaging is also used routinely by physicians in interpreting Positron Emission Tomography (PET) or Magnetic Resonance Angiography studies.