Under perspective projections, parallel straight lines appear to intersect at a point, the vanishing point.
#Calculating the Vanishing Point
Mathematical intuition: $\frac{f}{z_0}$ when $z_0 \to \infty$ = 0. This is where everything is a single point.
- Since vanishing points depend only on direction and not position, we consider the direction vector
shared by a family of parallel 3D lines.
- In projective geometry, this direction corresponds to a point at infinity.
- This point corresponds to any point on the ray
originating at the camera center.
- Projecting such a point onto the image plane yields the same image location for any $\lambda$. This location is the vanishing point of the parallel lines.
#Vanishing point in Art
The vanishing point has been used to attract viewer’s attention.
The Pinhole Camera