Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!iuvax!ndcheg!uceng!achhabra
From: achhabra@uceng.UC.EDU (atul k chhabra)
Newsgroups: comp.graphics
Subject: ray/bounding box intersection
Keywords: ray tracing, bounding box
Message-ID: <857@uceng.UC.EDU>
Date: 11 Apr 89 21:30:37 GMT
Distribution: na
Organization: Univ. of Cincinnati, College of Engg.
Lines: 70


I have a question about checking for ray/bounding box intersection in ray
tracing. Rogers ("Procedural Elements for Computer Graphics," 1985,
pp. 299) suggests a transformation comprising of translation and rotations
about the coordinate axes, in order to make the ray coincident with the 
z-axis. This transformation is applied to both the ray and the bounding
box. Rogers goes on to say that the ray intersects the box if, in the
translated and rotated coordinate system, the signs of x_min and x_max 
AND of y_min and y_max are opposite. He illustrates this with a ray-box
configuration which, after aligning the ray with the z-axis, looks as 
shown below.
		       ^ y
		       |
		       |
		 ------|------
		 |     |     |
		 |     |     |     x
             ----------------------->
		 |     |     |
		 |     |     |      (z-axis perpendicular to the screen)
		 ------|------
		       |
		       |

But what if the transformation leads to a configuration as shown below?
In this case, you cannot infer anything about the ray/bounding box 
intersection from the values of x_min, x_max, y_min, and y_max. 
x_min and x_max have opposite signs. Also, y_min and y_max have opposite
signs. Yet the ray (z-axis) does not intersect the bounding box (cube).

		       ^
		       | y
                       |        ------------------
		       |       /                / \
		       |     /                /     \      x
                  -----|---/----------------/---------\------>
		       | /                /             \
		       |                /                 \
		     / |              /                     \
		    ---|--------------                      
		     \ |              \                     /
		       |                \                 /
		       | \                \             /
		       |   \                \         /
		       |     \                \     /
			       \                \ /
				------------------
                                  (z-axis perpendicular to the screen)

                 (Say, a unit cube first translated, then rotated about
		 the x-axis and next rotated about the y-axis, such that
		 the same transformation makes the ray lie on the z-axis).

Could some ray tracing guru clarify this? Am I using the right kind of
transformations? In addition to determining whether the ray intersects the
bounding box, I am also interested in computing the coordinates of the 
point of intersection closest to the origin of the ray. Could some kind soul
email me a piece of code that does the computations for ray/bounding box
intersection?

Thanks,
  Atul
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Atul K. Chhabra                        INTERNET: achhabra@ucesp1.ece.uc.edu
811J Rhodes Hall, ML 030                                   (129.137.33.114)
Dept. of Electrical &                            OR   achhabra@uceng.uc.edu
     Computer Engineering                                    (129.137.33.1)
University of Cincinnati
Cincinnati, OH 45221-0030              Phone: (513)556-4766
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