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From: jk87377@tavi.tut.fi (Kouhia Juhana Krister)
Newsgroups: comp.graphics
Subject: Blinn's article
Message-ID: <1990Dec7.105837.19722@funet.fi>
Date: 7 Dec 90 10:58:37 GMT
Sender: news@funet.fi (#News )
Reply-To: jk87377@tut.fi (Kouhia Juhana Krister)
Organization: Tampere University of Technology, Finland
Lines: 74



Hi,

In IEEE CG&A has an article written by Jim Blinn:
Nested Transformations and Blobby Man
October 1987

I have problem with Jim Blinn's perspective projection matrix

c 0 0   0
0 c 0   0
0 0 Q   s
0 0 -Qn 0

where Q = s/(1-n/f)
      c = cos(viewing angle/2)
      s = sin(viewing angle/2)
      n = depth of the near clipping plane
      f = depth of the far clipping plane
      eye point is (0,0,0)

If I set n = 0 and f = +oo matrix is:

c 0 0 0
0 c 0 0
0 0 s s
0 0 0 0

I have 3d point (x,y,z); same point is (x,y,z,1) in homogeneous
coordinates.
I multibly it by matrix and I get (cx/sz, cy/sz, sz/sz)
= (cx/sz, cy/sz, 1)

QUESTION:
---------
If I have polygon in 3d space, how I calculate the depth by
interpolation?
At every vertex there's z = 1.


While go I looked at the another paper, where eye point is (0,0,-1)
and perspective projection matrix is

1 0 0 0
0 1 0 0
0 0 1 1
0 0 0 1

Now we have the point (x,y,z) --> (x/(z+1), y/(z+1), z/(z+1))
Now there's a little sense exists.
If I now interpolate depth between vertexes I got everything right,
though.

QUESTION:
---------
Have I found an error from Jim Blinn's nested transformations article?


I have suggestion for the new matrix (eye point is (0,0,0) as in
article, n = 0, f = +oo):

c 0  0 0
0 c  0 0
0 0  s s
0 0 -1 0

Now the result point is (cx/sz, cy/sz, (sz-1)/sz)
I tested this and it's ok, though.

I found an another weierd thing from this article, but that's is
an another story.

Juhana Kouhia
jk87377@tut.fi