# Thread: Not Able to Understand Perspective Projection Equations

1. Hi,
The perspective equations are:
x' = x - xu
y' = y - yu
z' = z - (z- zprp)u

I cant understand these equations. According to book
Parameter u takes values from 0 to 1 and coordinate position (x', y', z') represents any point along the projection line. When u=0, we are at position P = (x, y, z). At the other end of the line u=1, and we have the projection reference point coordinates (0, 0, zprp)

I cant understand how we get the above eq and how (0,0,zprp).

I got the following image from a web site:
Perspective Projection.jpg
Somebody plz guide me.

Zulfi.

2. My experience is two years of manual technical drawing in HS. So I am simply trying to help.

The x and y are the length of lines parallel to the drawing surface. x is horizontal and y vertical.
x' and y' are the same orientation but deeper, farther into the background of the drawing. As such a 1 meter line would appear shorter as the vanishing point is approached.
The u is factor that shrinks the line, a gradient like factor. I guess it is calculated based upon the vanishing points location with respect to the observers pov.

In perspective drawing the lines going from the observer into the background are not parallel, instead the converge on one or two vanishing points often located on a horizon. Think of walls, railways, fences disasappearing into the distance.
This explains the more complicated relationship between z and z'.

3. Hi,
Thanks for sharing your practical knowledge. Its very useful that you explained me the theoretical background of the variables used. But still I don't know how to evaluate x', y' and z' mathematically.
Somebody plz guide me.
Zulfi.

4. Use a value of u that is appropriate for the perspective effect you want.
I presume that u = zero gives no reduction of size with distance. There is no vanishing point.
A u that is large would reduce the size steeply.

Perspective (graphical) - Wikipedia, the free encyclopedia

5. Hi,
Thanks for help. But I cant understand this because x', y' and z' are not in the diagram. Plz tell me how can i get the above equations when the diagram does not show them.

Zulfi.

6. This is not easy stuff. Do not expect to learn this completely in a few minutes with just thinking about it.
This requires a few hours of lecture, tutorials and problem solving.

Mathematics of Perspective Drawing

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