Subject:
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RE: Quad intersections
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Newsgroups:
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lugnet.cad.dev
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Date:
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Mon, 5 Apr 1999 21:47:42 GMT
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Viewed:
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758 times
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By all means. I can't really claim that it's original since most of the
material I used to derive the results came from my Calculus Text, which, if
anybody cares was:
Calculus with Analytical Geometry, 3rd edition
by Howard E. Campbell and Paul F. Dierker (from the University of Idaho)
I used the sections titled: "The Cross Product", and "Equations of Lines and
Planes".
---
Dave Hylands Email: DHylands@creo.com 3700 Gilmore Way
Principal Software Developer Tel: (604) 451-2700 x2329 Burnaby B.C.
Creo Products Inc. Fax: (604) 437-9891 Canada V5G 4M1
-----Original Message-----
From: blisses@worldnet.att.net
To: lugnet.cad.dev@lugnet.com
Sent: 4/5/99 6:57 AM
Subject: Re: Quad intersections
Dave,
Thank you very much! This will help me on some parts-work I was
avoiding,
just because I didn't want to figure out these intersections.
I'm planning on uploading a spreadsheet with some basic interpolation
and
intersection templates. Do you mind if I include your results in that
file?
Steve
On Mon, 5 Apr 1999 07:25:41 GMT, Dave Hylands <DHylands@creo.com> wrote:
> Hi Steve,
>
> I've been lurking for a while and thought your post was interesting • enough
> to figure it out. I brushed off my Calculus text book, and after a page • and
> a half of algebra, and remembering what determinants and cross products • are
> all about I believe that I have the answer.
>
> The formula for a plane can be expressed as:
>
> ax + by + cz = d, where a, b, c, and d are all constants.
>
> Given 3 points (x0, y0, z0) (x1, y1, z1) (x2, y2, z2)
>
> a = y0*z1 - y0*z2 - y1*z0 + y1*z2 + y2*z0 - y2*z1
> b = - x0*z1 + x0*z2 + x1*z0 - x1*z2 - x2*z0 + x2*z1
> c = x0*y1 - x0*y2 - x1*y0 + x1*y2 + x2*y0 - x2*y1
> d = a*x0 + b*y0 + c*z0
>
> Note for d you can substitue any of the 3 points (by definition they • all
> have to give the same answer).
>
> Now that you know a, b, c, d and assuming that you're given x and z, • then:
>
> by = d - ax - cz
>
> and
>
> y = d/b - ax/b - cz/b
>
> The fourth point on the quad is redundant, although you can check it by
> plugging it into the formula for the plane and verifying that ax3 + by3 • +
> cz3 is within some small epsilon of d (the small epsilon is to account • for
> floating point round off errors).
>
> Of course, now that you've found y, you probably need to verify that • (x, y,
> z) actually falls within the given quad (as they say in the textbooks, • this
> is an exercise left for the reader).
>
> If anyone is interested in a more detailed derivation, I'd be happy to • share
> the gory details.
>
> ---
> Dave Hylands Email: DHylands@creo.com 3700 Gilmore • Way
> Principal Software Developer Tel: (604) 451-2700 x2329 Burnaby B.C.
> Creo Products Inc. Fax: (604) 437-9891 Canada V5G 4M1
>
>
> -----Original Message-----
> From: blisses@worldnet.att.net [mailto:blisses@worldnet.att.net]
> Sent: Friday, April 02, 1999 7:16 PM
> To: lugnet.cad.dev@lugnet.com
> Subject: Quad intersections
>
>
> Can anyone explain how to intersect a quad? I'm sure I can figure it • out
> on my own, but if someone knows of some straightforward formulae, I'd • be
> very appreciative.
>
> Since this is for LDraw, I've got the following situation:
>
> Conditions:
> - Four points to make a quad (or, to be simpler, 3 points to make a
> triangle).
> - Two components for another point (probably X and Z, but it doesn't • really
> matter which two).
>
> Needed:
> - Value for third component.
>
> TIA for any help!
> Steve
>
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