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Give the number of principal vanishing point(s) along with their direction for the standard prospective transformation:

  1. Only one in the direction K
  2. Two in the directions i and j
  3. Three in the directions I, J and K
  4. Only two in the directions J and K
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ans is A

In this case the view plane normal N is vector K. since N.I =0 and N.J=0, so there are no vanishing points in the direction I and J. on the other hand N.K = K.K = 1. thus there is only one principal vanishing point and it is in K direction

STANDARD PERSPECTIVE PROJECTION


A perspective transformation is the transformation from one three space in to another three space. In contrast to the parallel transformation , in perspective transformations parallel lines converge, object size is reduced with increasing distance from the center of projection, and non uniform foreshortening of lines in the object as a function of orientation and the distance of the object from the center of projection occurs. All of these effects laid the depth perception of the human visual system., but the shape of the object is not preserved. Perspective drawings are characterized by perspective foreshortening and vanishing points .Perspective foreshortening is the illusion that object and lengths appear smaller as there distance from the center of projection increases. The illusion that certain sets of parallel lines appear to meet at a point is another feature of perspective drawings. These points are called vanishing points .Principal vanishing points are formed by the apparent intersection of lines parallel to one of the three x,y or z axis. The number of principal vanishing points is determined by the number of principal axes interested by the view plane

Perspective Anomalies

1.Perspective foreshortening- The farther an object is from the center of projection ,the smaller it appears

2.vanishing Points- Projections of lines that are not parallel to the view plane (i.e. lines that are not perpendicular to the view plane normal) appear to meet at some point on the view plane. This point is called the vanishing point. A vanishing point corresponds to every set of parallel lines. Vanishing points corresponding to the three principle directions are referred to as "Principle Vanishing Points (PVPs)". We can thus have at most three PVPs. If one or more of these are at infinity (that is parallel lines in that direction continue to appear parallel on the projection plane), we get 1 or 2 PVP perspective projection

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