Vanishing Point in Computer Graphics

Vanishing Point:

Perspective projection produces realistic views but it doesn’t preserve relative proportions of object dimensions. Projection of distant objects is smaller than the projection of objects of the same size that after projection certain sets of parallel lines appear to meet at some point on the projection plane. These points are called Vanishing Point.

Computing Vanishing Point:

The vanishing point for a set of parallel lines (AB & CD parallel to vector U) for perspective projection on a plane defined by normal vector N=n₁i+n₂j+n₃k and in-plane reference point R₀(x₀, y₀, z₀), the centre projection being C_p(a,b,c).

Principal Vanishing Point:

Principal Vanishing Point corresponds to the vector direction parallel to the three principal axes directions. There are three principal vanishing point P_VP1, P_VP2 and P_VP3.

For U=i, P_VP = P_VP1
For U=j, P_VP = P_VP2
For U=k, P_VP = P_VP3

This is true only if the vector direction isn’t parallel to the plane of projection.