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. Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points.

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 $q \equiv (x, y, f)$ be a point lying on the image plane, where $f$ is the focal length (of the camera associated with the image), and let $v q \equiv (x / h, y / h, f / h)$ be the unit vector associated with $q$ , where $h = \sqrt x 2 + y 2 + f 2$ . If we consider a straight line in space $S$ with the unit vector $n s \equiv (n x, n y, n z)$ and its vanishing point $v s$ , the unit vector associated with $v s$ is equal to $n s$ , assuming both are assumed to point towards the image plane.

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