Path: chuka.playstation.co.uk!news
From: "Nathan Miller" <millerbosnia@hotmail.com>
Newsgroups: scee.yaroze.programming.3d_graphics
Subject: The ultimate 3d->2d problem
Date: Sat, 2 Jan 1999 13:57:01 +0200
Organization: PlayStation Net Yaroze (SCEE)
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To all the math inclined-

I have a BIG problem that I cannot seem to figure out.  I have been thinking
about it for the past few days, but I just cannot seem to figure it out.  It
involves the process of converting 3d to 2d.  I am writing my own polygon
rasterizer for a specific type of polygon.  I have to convert the points of
the polygon myself from 3d to 2d.  The polygon is forced to be a
quadrilateral.  Once the polygon has been converted to 2d screen space the
output is always either a quadrilateral or a parallelagram.  I then
calculate 2 points based on their z components to be the side I want to
start drawing from.  The other two points are the side I want to draw to.
My loop has to determine whether or not it is drawing top to bottom or side
to side.  This is the point that becomes a problem.  I cannot seem to figure
out how to determine which side I am drawing based on the two points that
the algorithm found.  Before I try and clarify the problem with a visual, I
am not doing standard texture mapping (if you couldn't tell)  I am doing a
special :-) texture mapping that requires me to draw back to front (in the z
direction).  I can find the rear of my 2d polygon based on its converted z
component.  Here is the visual and why it is a problem (remember it has to
be as fast as possible):


                                     p1->  x----------x  <-p2
                                               /             /
                                              /             /
                                             /             /
                                            /             /
                                 p3-> x----------x <-p4

p1 and p2 define the edge I want to draw from and p3 and p4 define the edge
I want to draw to.  This case is easy, but what happens when it looks like
this:

                                            p1->  x----------x  <-p2

                             p3-> x---------x <-p4

now p3 and p4's x values are left so the algoritm may make a mistake and
think it is drawing side to side instead of top to bottom.

Is it a lot easier than I am thinking it is or is it an impossible problem?

Your help will be appreciated,

Nathan Miller