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vanishing point
In graphical perspective, a vanishing point is a point in the picture plane that is the intersection of the projections (or drawings) of a set of parallel lines in space on to the picture plane. When the set of parallels is perpendicular to the picture plane, the construction is known as one-point perspective and their vanishing point corresponds to the oculus or eye point from which the image should be viewed for correct perspective geometry.〔Kirsti Andersen (2007) ''Geometry of an Art'', p. xxx, Springer, ISBN 0-387-25961-9〕 Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points.
== Vector notation ==
The vanishing point may also be referred to as the “direction point”, as lines having the same directional vector, say D, will have the same vanishing point or converge at the same vanishing points. Mathematically, let q Ξ (x, y, f) be a point lying on the image plane, where f is the focal length (of the camera associated with the image), and let vq Ξ (x/h, y/h, f/h) be the unit vector associated with q, where h = (x2+ y2+ f2)1/2. If we consider a straight line in space S with the unit vector ns Ξ (nx, ny, nz) and its vanishing point vs, the unit vector associated with vs is equal to ns, assuming both are assumed to point towards the image plane. 〔B. Caprile, V. Torre () "Using Vanishing Points for Camera Calibration", International Journal of Computer Vision, Volume 4, Issue 2, pp. 127-139, March 1990 〕
When the image plane is parallel to two world-coordinate axes, lines parallel to the axis which is cut by this image plane will meet at infinity i.e. at the vanishing point. Lines parallel to the other two axes will not form vanishing points as they are parallel to the image plane. This is one-point perspective. Similarly, when the image plane intersects two world-coordinate axes, lines parallel to those planes will meet at infinity and form two vanishing points. This is called two-point perspective. In three-point perspective the image plane intersects the x, y, and z axes and therefore lines parallel to these axes intersect, resulting in three different vanishing points.
See also: Property 1 below.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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