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Projection mapping, similar to video mapping and spatial augmented reality, is a projection technique [1] [2] used to turn objects, often irregularly shaped, into display surfaces for video projection. The objects may be complex industrial landscapes, such as buildings, small indoor objects, or theatrical stages.
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
A diagram of a pinhole camera.. The pinhole camera model describes the mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light.
The modified Rodrigues vector is a stereographic projection mapping unit quaternions from a 3-sphere onto the 3-dimensional pure-vector hyperplane. The projection of the opposite quaternion −q results in a different modified Rodrigues vector p s than the projection of the original quaternion q.
Third-angle projection: In this type of projection, the object is imagined to be in the third quadrant. Again, as the observer is normally supposed to look from the right side of the quadrant to obtain the front view, in this method, the projection plane comes in between the observer and the object.
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.
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
For example, in perspective projection, a position in space is associated with the line from it to a fixed point called the center of projection. The point is then mapped to a plane by finding the point of intersection of that plane and the line. This produces an accurate representation of how a three-dimensional object appears to the eye.