Path: utzoo!utgpu!water!watmath!clyde!rutgers!mit-eddie!husc6!bbn!rochester!cornell!batcomputer!saponara
From: saponara@batcomputer.tn.cornell.edu (John Saponara)
Newsgroups: comp.graphics
Subject: Re: Simple geometric formulae.
Summary: Article & book recommendations
Message-ID: <3454@batcomputer.tn.cornell.edu>
Date: 21 Jan 88 15:48:28 GMT
References: <515@unioncs.UUCP>
Reply-To: saponara@tcgould.tn.cornell.edu (Eric Haines, actually)
Distribution: na
Organization: Cornell Theory Center, Cornell University, Ithaca NY
Lines: 62

In article <515@unioncs.UUCP> brownh@unioncs.UUCP (H. Brown) writes:
>In article <554@acornrc.UUCP> you write:
>>I'm looking for some simple geometric formulae such as
>>	distance from a point to a line segment
>>	distance from a point to a bezier
>>	distance from a point to an ellipse
>>	how to determine whether a point is inside an ellipse
>>	how to determine whether a point is inside a polygon
>>	etc.
>
>I am also interested in any references to this information, as well as
>	intersection of a line and a plane
>	intersection of a line and a sphere
>I would appreciate it if someone could forward any pointers  to 
>such info.  Thanks much in advance.
>
>Alex Brown

Alex,
	I recently posted a long, long note on the fastest test for a point
inside a polygon.  Line/plane, line/sphere, and line/quadric intersections
are covered in lots of places:  SIGGRAPH 87 "Intro to Ray Tracing" Course
Notes has them all, Kay & Kajiya's "Ray Tracing Complex Scenes" in SIGGRAPH
'86 Proceedings is about the newest in a long line of sources for ray/plane
intersection, sphere & other quadrics are in Kajiya's SIGGRAPH 83 "Tutorial
on Ray Tracing" in the "State of the Art in Image Synthesis" Course Notes.

I just received some recommendations on good books on geometry for use in
computer graphics, and will list these below (haven't checked them all out
yet, though).

"A Programmer's Geometry", A. Bowyer, J. Woodwark, Butterworths Press, 1983?
- heard about from some people at Cornell's computer graphics lab as being
fairly helpful.

A bunch of recommendations came from Jeff Goldsmith at JPL:

	    Computational Geometry for Design and Manufacture
	        Faux & Pratt
	 	--an early CAD text.  It has lots of good stuff
		on splines and 3D math.

	    Differential Geometry of Curves and Surfaces
		DoCarmo
		--A super text on classical differential geometry.
		(Not quite the same as analytic geometry.)

	    CRC Standard Math Tables
		--This has an awesome section on analytic geometry.
		Calculus, too.  Can't live without it.  It is not
		the same as the first part of the Chemistry and 
		Physics one.

	    Analytic Geometry
		Steen and Ballou
		--Once was the standard college text on the subject.
		That was a long time ago, but it is very easy to
		read and it covers the fundamentals.

That's all, folks,

Eric Haines