Consider at line segment AB in the Figure k, parallel to the z-axis along with end points A (3, 2, 4) and B (3, 2, 8). Perform a perspective projection on the z = 0 plane from the center of projection at E (0, 0, - 2). Also determine vanishing point.
![1121_Perform a perspective projection on the plane.png](https://www.expertsmind.com/CMSImages/1121_Perform%20a%20perspective%20projection%20on%20the%20plane.png)
Figure: (k)
Solution. We know about the Equation (1) shows the center of particular point perspective transformation: of a point P (x, y, z) on z = 0 plane; where (0, 0, - d) is center of projection provided by:
![2082_Perform a perspective projection on the plane 1.png](https://www.expertsmind.com/CMSImages/2082_Perform%20a%20perspective%20projection%20on%20the%20plane%201.png)
P'n = Pn. Pper,z ------------------------(I)
Frequently the perspective transformation of provided line AB to A* B* along with d = 2 are as:
V'n = Vn. Pper,z
![1138_Perform a perspective projection on the plane 2.png](https://www.expertsmind.com/CMSImages/1138_Perform%20a%20perspective%20projection%20on%20the%20plane%202.png)
Thus, the projected points of a provided line AB are:
A* = (1, 0.667, 0) B* = (0.6, 0.4, 0)
The vanishing point is given as (0, 0, 0).