3D Computer Graphics II PART

Perspective Projection

In perspective projection, the distance from the center of projection to project plane is finite and the size of the object varies inversely with distance which looks more realistic.

The distance and angles are not preserved and parallel lines do not remain parallel. Instead, they all converge at a single point called center of projection or projection reference point. There are 3 types of perspective projections which are shown in the following chart.

One point perspective projection is simple to draw.
Two point perspective projection gives better impression of depth.
Three point perspective projection is most difficult to draw.

The following figure shows all the three types of perspective projection −

Translation

In 3D translation, we transfer the Z coordinate along with the X and Y coordinates. The process for translation in 3D is similar to 2D translation. A translation moves an object into a different position on the screen.

The following figure shows the effect of translation −

A point can be translated in 3D by adding translation coordinate (tx,ty,tz)

to the original coordinate (X, Y, Z) to get the new coordinate (X’, Y’, Z’).

T=⎡⎣⎢⎢⎢⎢100tx010ty001tz0001⎤⎦⎥⎥⎥⎥

P’ = P∙T

[X'Y'Z'1]=[XYZ1]⎡⎣⎢⎢⎢⎢100tx010ty001tz0001⎤⎦⎥⎥⎥⎥

=[X+txY+tyZ+tz1]

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