perform a perspective projection on the plane, Computer Graphics

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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

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

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

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).


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