Path: utzoo!attcan!uunet!bellcore!rutgers!mcnc!thorin!homer!leech
From: leech@homer.cs.unc.edu (Jonathan Leech)
Newsgroups: comp.graphics
Subject: Re: Blinn's article
Message-ID: <18068@thorin.cs.unc.edu>
Date: 11 Dec 90 22:03:51 GMT
References: <1990Dec7.105837.19722@funet.fi>
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Reply-To: leech@homer.cs.unc.edu (Jonathan Leech)
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In article <1990Dec7.105837.19722@funet.fi> jk87377@tut.fi (Kouhia Juhana Krister) writes:
>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)

    The transformation as specified has at least two uses.  First, to
allow additional clipping planes at Znear and Zfar in addition to the
normal viewport clipping planes (this is the reason he cited when I
took and later TAed his graphics class at Caltech).  Second, to
compress Z values in the range in a nonlinear fashion suitable for
depth-buffering, providing greater precision of transformed Z values
close to the eye.

    The actual Z value after perspective is

       Zfar	Z - Znear
       ---- * ------------     [Znear,Zfar] -> [0,1]
	Z     Zfar - Znear

    which as you observe degenerates to a constant if Znear = 0.  The
solution is simply to specify a nonzero Znear, prererably reasonably
large.

    If you are using the direct-quadric rendering algorithm Blinn
describes elsewhere in conjunction with this perspective matrix, you
definitely want a large Znear; otherwise, large relative errors can
creep into normal vectors and points on the surface back-transformed
into object space for texturing.
--
    Jon Leech (leech@cs.unc.edu)    __@/
    "Why do you suppose we only feel compelled to chase the ones who run away?"
    "Immaturity."
	_Dangerous Liasons_