homework issue
David Norris
those who post their homework, especially when
the subject is something like, "please hurry!".
In these cases, creative repremands or non-responses
I think are appropriate. However, people don't
always post their h/w even though it looks like it.
Example: I am an engineer for the R&D acoustics company
BBN and am working on an sound reverberation model. I
needed a solution for the specularly reflected angle
in 3-space, so I posted the problem ("SPACE ANAYLTIC
GEOMERTY question"). No response, so I narrowed the
problem down to a simple theoretical problem ("three
lines forming a plane"), thinking I would get a
better response. Success! The responses I got were
excellent and solved my problem, but, as some thought,
it wasn't homework :)
David Norris
Richard Carr
:Date: Wed, 19 Apr 2000 15:34:19 GMT
:From: David Norris <dno...@bbn.com>
:Newsgroups: sci.math
:Subject: homework issue
:
:I support people's frustration/annoyance with
Of course, you might just be a creative student fabricating a cunning
story to make everyone think that you are not asking homework questions
when, in fact, you are. : )
:
:David Norris
:
ne...@my-deja.com
for homework help. These are people who are have a passion for math just
like everyone else here. So what if they need some help on a homework
problem. If YOU don't want to help them then don't, you don't have to rip on
them (which by the way, takes just as long as answering them, and more time
then ignoring them). And by the way, how exactly is it different to ask for
homework help then it is to ask for help at work. So what I'm looking for is
you to tell me why someone who is having a hard time with an integral or
setting up a series or whatever for school, shouldn't be allowed to ask on a
public messege board while, you can ask for help on an engineering problem at
work, I guess you're just better then the rest of us college students. (BTW
I assuming that you NEVER asked for help on a single homework problem while
you went through school.) I bow down to you oh great genius. Goodbye, this
shall be the last time I pose here, I will be finding a new newsgroup to help
with my calculus homework, one that will actually help and not treat me like
dirt.
In article <38FDD1AE...@bbn.com>,
dno...@bbn.com wrote:
> I support people's frustration/annoyance with
> those who post their homework, especially when
> the subject is something like, "please hurry!".
>
> In these cases, creative repremands or non-responses
> I think are appropriate. However, people don't
> always post their h/w even though it looks like it.
>
> Example: I am an engineer for the R&D acoustics company
> BBN and am working on an sound reverberation model. I
> needed a solution for the specularly reflected angle
> in 3-space, so I posted the problem ("SPACE ANAYLTIC
> GEOMERTY question"). No response, so I narrowed the
> problem down to a simple theoretical problem ("three
> lines forming a plane"), thinking I would get a
> better response. Success! The responses I got were
> excellent and solved my problem, but, as some thought,
> it wasn't homework :)
>
> David Norris
>
Sent via Deja.com http://www.deja.com/
Before you buy.
ne...@my-deja.com
Richard Carr
I'm replying to this, even though it wasn't directed to me.
On Wed, 19 Apr 2000 ne...@my-deja.com wrote:
:Date: Wed, 19 Apr 2000 18:43:46 GMT
:From: ne...@my-deja.com
:Newsgroups: sci.math
:Subject: Re: homework issue
:
:I think you're a real fucking asshole for saying that. So what if people ask
You wonder why you don't get very far asking for help?
:for homework help. These are people who are have a passion for math just
People often get at least part of their final grade based on their
homework (at least in the US)- thus it is quite a big deal, in fact.
:like everyone else here. So what if they need some help on a homework
Sometimes, sometimes not. Very often students haven't done any work for
themselves at all- including not reading the very text that they are doing
questions from. Often it is a matter of flipping back two pages from where
the question occurs in the book and pointing them to the equation
underlined and in a box.
:problem. If YOU don't want to help them then don't, you don't have to rip on
:them (which by the way, takes just as long as answering them, and more time
:then ignoring them). And by the way, how exactly is it different to ask for
:homework help then it is to ask for help at work. So what I'm looking for is
You are getting a certificate to say that you are competent, arguably.
:you to tell me why someone who is having a hard time with an integral or
:setting up a series or whatever for school, shouldn't be allowed to ask on a
:public messege board while, you can ask for help on an engineering problem at
Sure, but it helps if they give some indication of what they have done or,
if they are really clueless about a problem, the concept they don't
understand. Helping people with 1 problem or just plain giving them the
answer will not help them with future problems.
:work, I guess you're just better then the rest of us college students. (BTW
For the most part, mathematically speaking, that is not saying very much,
unfortunately. In many other ways, the students are probably very much
better.
:I assuming that you NEVER asked for help on a single homework problem while
:you went through school.) I bow down to you oh great genius. Goodbye, this
No. At any rate, our degree was exam-based. The latter part there is
ridiculous.
:shall be the last time I pose here, I will be finding a new newsgroup to help
:with my calculus homework, one that will actually help and not treat me like
:dirt.
:
You probably have a teacher who is paid to teach you. You could ask
them. If your grade is in any way dependent on your homework then people
are less likely to be willing to give help. If you had any idea what it is
like to grade your own work several times a week (which is sometimes a
corollary of working in a help room) or copied work or the solutions
manual or whatever, you might understand this.
:
:In article <38FDD1AE...@bbn.com>,
:
Richard Carr
Having looked at your particular previous posts, it looks like you have
got somewhere, so I will give you some hints (assuming that what you've
got so far is correct):
a) the integration one (surface of revolution)- (almost) always try to
simplify the most horrible looking expression in the integrand. In this
case sqrt(1+(cos(x))^2). The sin(x) bit should take care of itself, so you
should subsitute something like v=f(x) where f(x) is related to what is
under the square root sign (not necessarily v=1+cos^2(x), but something
along those lines).
b) 1000n=n*(1+1/2+1/3+...+1/n). If this equation is right, then divide by
n to get 1000=1+1/2+1/3+...+1/n. You can't get an exact equality because
1+1/2+1/3+...+1/n is never an integer if n>1. On the other hand, since the
right hand side diverges as n tends to infinity there will be an n such
that it is greater than 1000 (and an n where it is less than 1000). The n
at which this first happens will be extremely large, though.
(You could still do with being more polite.)
G. A. Edgar
it looks like homework.)
--
Gerald A. Edgar ed...@math.ohio-state.edu
dann...@here.com
>I think you're a real fucking asshole for saying that.
I think you're a university student. Oh, right, you are. I also
think you won't get too far with that attitude. Right on both counts.
Dan.
dann...@here.com
wrotf:
>The responses I got were excellent and solved my problem, but, as some thought,
>it wasn't homework :)
Aw shucks. A simple "Thank you." would have done. Some *do* ask
directly, or under some pretense, for homework done for them. If I,
for one, suspect at all, I simply don't reply. If I recall, you did
get a reply. A simple solution is to post your effort so far as you
could and *then* ask for help.
Remember: nobody here owes you anything.
Dan.
Doug Norris
>I think you're a real fucking asshole for saying that.
And I don't recall anyone asking you what you thought. Wanker.
Doug
Richard Carr
:Date: Wed, 19 Apr 2000 19:00:43 GMT
:From: dann...@here.com
:Newsgroups: sci.math
:Subject: Re: homework issue
:
:On Wed, 19 Apr 2000 15:34:19 GMT, David Norris <dno...@bbn.com>
Maybe. Maybe somebody does owe him something. After all, didn't JSH once
owe somebody some money over a bet or something (which I understand he
later paid) so it is not beyond the realm of possibility that somebody
here owes him something.
Remember: you have to be very careful and precise when writing to a
mathematical newsgroup. : )
:
:Dan.
:
Erik Max Francis
> Maybe. Maybe somebody does owe him something. After all, didn't JSH
> once
> owe somebody some money over a bet or something (which I understand he
> later paid) so it is not beyond the realm of possibility that somebody
> here owes him something.
He bet $500 that his proof was wrong, admitted defeat, and (since nobody
complained) apparently paid the debt.
But he also bet someone that if he was wrong he'd take out an ad in a
newspaper or somesuch and admit defeat. He very clearly attempted to
weasel his way out of that one by saying that there weren't any time
constraints, and since now he has given up the fight, it's safe to say
that he is reneging on that agreement (then again, it was pretty clear
at the time when he was backpedalling).
--
Erik Max Francis | email m...@alcyone.com | icq 16063900
Alcyone Systems | web http://www.alcyone.com/max/ | q3a Product
San Jose, CA | languages en, eo | icbm 37 20 07 N 121 53 38 W
USA | 970.333 Ms p.L. | 256 days left | &tSftDotIotE
__
/ \ Some mistakes we must carry with us.
\__/ Speaker-to-Animals
Richard Carr
:Date: Wed, 19 Apr 2000 13:44:26 -0700
:From: Erik Max Francis <m...@alcyone.com>
:Newsgroups: sci.math
:Subject: Re: homework issue
:
:Richard Carr wrote:
:
:> Maybe. Maybe somebody does owe him something. After all, didn't JSH
:> once
:> owe somebody some money over a bet or something (which I understand he
:> later paid) so it is not beyond the realm of possibility that somebody
:> here owes him something.
:
:He bet $500 that his proof was wrong, admitted defeat, and (since nobody
:complained) apparently paid the debt.
:
:But he also bet someone that if he was wrong he'd take out an ad in a
:newspaper or somesuch and admit defeat. He very clearly attempted to
I never really meant to hold him to that anyway.
:weasel his way out of that one by saying that there weren't any time
:
Erik Max Francis
> I never really meant to hold him to that anyway.
Ah, was it you who made the agreement with him? Still, it show what his
word was worth.
Erik Max Francis
> Why are you silent, when good mathematicians, like
> Kovarik or Chapman, try to weasel out from their defeats?
Kovarik never entered in any challenge with you, so he by definition
cannot be defeated.
And Chapman's bet with you was restricted to a time frame, which you
failed to meet (by your own admission). Thus you were defeated, not
Chapman. (Of course you just ignore this because it makes you look
stupid.)
> Are these defeats trivially clear? To you? To everybody? Why
> is it non-interesting, when good mathematicians are defeated?
Because they weren't defeated. Your pathetic ego demands that you
engage in self-aggrandization at every opportunity.
Randy Poe
>I think you're a real fucking asshole for saying that. So what if people ask
>for homework help. These are people who are have a passion for math just
>like everyone else here. So what if they need some help on a homework
>problem.
Those who ask for help on homework problems generally get help. The
form likely to get a response is this:
"This is a homework problem:
[verbatim copy of problem]
I'm having trouble with [something]. Here's what I've got so far
[partial solution, or thoughts]. Can anyone [show me where I've gone
wrong, give me a hint, etc?]"
Here are the forms which make people mad or unresponsive:
a. "[verbatim copy of problem]"
b. "[verbatim copy of problem]. Solution needed urgently!! E-mail me
by Monday!"
c. "[verbatim copy of problem]. What is the answer to this?"
d. "This is a problem which came up at work/ a friend and I have a bet
on this/ I was wondering about this, any of you geniuses know how to
solve [verbatim copy of problem]."
Can you see the difference? Lots of people want to help. But they
don't want to do all the work. Showing evidence of your own work and
asking specific questions other than "Help! Complete answer please!"
triggers the inner teacher in many people here. I find a. and c
particularly irritating, especially when the words typed in include a
phrase like "draw a diagram" or "show all your work."
> If YOU don't want to help them then don't, you don't have to rip on
>them (which by the way, takes just as long as answering them, and more time
>then ignoring them).
Yes it does. But people actually do want to help, which is why they
take the time to respond, even negatively. And it only takes a little
bit of encouragement, as I said, to trigger the helpful mode. The
responses you find "ripping" or "unhelpful" are often saying "you will
get help if you show some of your thinking". And they mean it. Such an
exchange happened just in the last couple of days. The poster
published his problem, got shot down. Added a few words of what he had
done already, and got 4 or 5 detailed responses within hours.
> And by the way, how exactly is it different to ask for
>homework help then it is to ask for help at work.
It isn't. And when you take the approach at work of just dumping your
problem in other people's lap with no effort on your part, then taking
their solutions and presenting them as their own, eventually you get a
bad reputation and people stop helping you. It's been done. It even
succeeds for a while. Longer if you structure it so people don't get a
chance to compare notes.
> So what I'm looking for is
>you to tell me why someone who is having a hard time with an integral or
>setting up a series or whatever for school, shouldn't be allowed to ask on a
>public messege board while, you can ask for help on an engineering problem at
>work, I guess you're just better then the rest of us college students.
People do ask in both of these situations, and they get responses. The
difference that is escaping you is between "help me do it" and "do it
for me."
>I assuming that you NEVER asked for help on a single homework problem while
>you went through school.)
As I said, you don't have to look far back in this newsgroup to see
actual help. Maybe 1-2 days.
> I bow down to you oh great genius. Goodbye, this
>shall be the last time I pose here, I will be finding a new newsgroup to help
>with my calculus homework, one that will actually help and not treat me like
>dirt.
You'll find the reluctance to do homework for you occurs elsewhere in
the world as well, not just on newsgroups. And it occurs in
non-technical newsgroup.
And yes, this response took a long time to compose. Why did I do it?
Because I like to be helpful. This process of education is, in my
opinion, helpful.
Have YOU ever taught someone how to do something you knew how to do?
Wouldn't it be quicker to just push them out of the way and do it
yourself? Yet in teaching, you let them make fumbling attempts, and
only offer small course corrections here and there. Why? Because,
instinctively, we (most people) know this is the best way to teach.
And we (again, most people) like to teach.
- Randy
Richard Carr
:Date: Wed, 19 Apr 2000 22:09:20 GMT
:From: Randy Poe <ran...@visionplace.com>
:Newsgroups: sci.math
:Subject: Re: homework issue
:
:Can you see the difference? Lots of people want to help. But they
:don't want to do all the work. Showing evidence of your own work and
:asking specific questions other than "Help! Complete answer please!"
:triggers the inner teacher in many people here. I find a. and c
:particularly irritating, especially when the words typed in include a
:phrase like "draw a diagram" or "show all your work."
:
You left out the one where the problem is posted as an attachment that
people may not be able to read- and the subsequent urges (OK, so this part
hasn't happened... yet... as far as I know) "Well, you go and buy the
software that enables you to read my attachment! It's not my problem
that you can't read it. etc. etc. (I already wrote the problem into
software X! Do I have to do everything?)"
Erik Max Francis
> Kovarik did post a solution, on Mar 29, to his own problem
> of Mar 24.
And Kovarik and indeed you yourself admit that there was no "challenge,"
so there is no way he could have been defeated.
> Chapman set out rules to his challenge of proving his theorems.
> The rules could be interpreted in two ways. Chapman was not
> a winner, unambiguously, on the basis of his schedules. Thus,
> Chapman did not manage to win his own challenge. See
Except that you have explicitly pointed out in the past that you
deliberately reinterpret what people say in order to put yourself in the
most favorable light. In other words, you'll weasel out of any
agreement or misinterpret or misquote what other people say in order to
"win" a "challenge," when in fact there is no challenge, and all you are
doing is shouting that you're best.
You're a waste of space. No. One. Cares.
> The bottom line is this: Who knows best the mathematical topic
> discussed. Your opinion is unprofessional, if you arrive at some
> other name than Lounesto.
"If you don't admit I'm best, you're unprofessional?" That sentiment is
about as unprofessional as you can get, Lounesto. Man, are you loopy.
--
Erik Max Francis | email m...@alcyone.com | icq 16063900
Alcyone Systems | web http://www.alcyone.com/max/ | q3a Product
San Jose, CA | languages en, eo | icbm 37 20 07 N 121 53 38 W
USA | 970.348 Ms p.L. | 256 days left | &tSftDotIotE
__
/ \ Love is like war: easy to begin but very hard to stop.
\__/ H.L. Mencken
Data
>> Chapman set out rules to his challenge of proving his theorems.
>> The rules could be interpreted in two ways. Chapman was not
>> a winner, unambiguously, on the basis of his schedules. Thus,
>> Chapman did not manage to win his own challenge.
<snip>
Lounesto, would you please give some references for professional, non-online
mathematical journals where your name is mentioned?
Thanks.
Pertti Lounesto
> But he also bet someone that if he was wrong he'd take out an ad in a
> newspaper or somesuch and admit defeat. He very clearly attempted to
> weasel his way out of that one by saying that there weren't any time
> constraints, and since now he has given up the fight, it's safe to say
> that he is reneging on that agreement (then again, it was pretty clear
> at the time when he was backpedalling).
Why is it important that somebody, who is not a mathematician,
admits his defeat, in proving something or presenting some math
methods? Why are you silent, when good mathematicians, like
Kovarik or Chapman, try to weasel out from their defeats? See
http://www.hit.fi/~lounesto/Robin.Chapman
http://www.hit.fi/~lounesto/Zdislav.Kovarik
Pertti Lounesto
> Pertti Lounesto wrote:
>
> > Why are you silent, when good mathematicians, like
> > Kovarik or Chapman, try to weasel out from their defeats?
>
> Kovarik never entered in any challenge with you, so he by
> definition cannot be defeated.
Kovarik did post a solution, on Mar 29, to his own problem
of Mar 24. I showed that his solution was incomplete, as
did Giffen and Feldmann. More important than Kovarik's
defeat is his poor method, which does not allow profound
understanding of the problem. For details, see
http://www.hit.fi/~lounesto/Zdislav.Kovarik
> And Chapman's bet with you was restricted to a time frame, which you
> failed to meet (by your own admission). Thus you were defeated, not
> Chapman. (Of course you just ignore this because it makes you look
> stupid.)
Chapman set out rules to his challenge of proving his theorems.
The rules could be interpreted in two ways. Chapman was not
a winner, unambiguously, on the basis of his schedules. Thus,
Chapman did not manage to win his own challenge. See
http://www.hit.fi/~lounesto/Robin.Chapman
> Because they weren't defeated. Your pathetic ego demands that you
> engage in self-aggrandization at every opportunity.
The bottom line is this: Who knows best the mathematical topic
dann...@here.com
>Lounesto, would you please give some references for professional, non-online
>mathematical journals where your name is mentioned?
I can understand the creep crepping into a conversation and turning it
into his personal thread. What I don't understand is intelligent
people constantly feeding him.
Dan.
Pertti Lounesto
Being feeded, I give, on behest, references to professional, non-online
mathematical journals, evaluating the last one of my 4 books:
P. Lounesto: Clifford algebras and spinors, Cambridge University Press,
1997/98 (2nd print). ISBN: 0 521 59916 4.
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
1. Monatshefte für Mathematik:
"The author gives a consice but thorough introduction to
spinors and Clifford algebras ... A very recommendable book
for everyone interested in this field."
2. Zentralblatt f"ur Mathematik:
"This book serves a very wide audience, from a first course
lectures to recent research. It provides a comprehensible and
pedagogical introduction to Clifford algebra ... This book sets
standards in the field quality and careful notation. It is highly
recommended to teachers and reserachers."
3. Mathematical Reviews:
"This is certainly one of the best book written about Clifford
algebras and spinors."
4. European Mathematical Society:
"This is a remarkable book. It is centered around Clifford algebras
and its main aim is to present applications of Clifford algebras in
physics, geometry and analysis. ... The author starts at a very low
level. ... Before defining a notion, he presents a motivation which
justifies its introduction and then usually presents many different
aspects and applications of this notion. These are well chosen
and interesting applications. The presentation is complete ...
It is worth mentioining that the author brings also quite recent
results. ... this book will be of interest to any mathematician ...
From the formal point of view tha book is perfectly presented.
The author tries to make the text as interesting as possible and
also tries to help the reader as much as possible. At the end of
almost every chapter you find a historical survey, questions and
answers to them, exercises and hints or solutions to them, and
usually a vast bibliography."
David C. Ullrich
>I think you're a real fucking asshole for saying that.
Golly, I'm glad it wasn't _me_ who said it.
> So what if people ask
>for homework help. These are people who are have a passion for math just
>like everyone else here.
In the typical case being discussed that's not so;
we're talking about the guys who couldn't care less why the
answer is what it is, they just want the right answer. By
Monday.
A person can usually tell the difference (except
when he can't): The person with an interest in the
mathematics has something to _say_ about the problem,
for example.
David Norris
my post. I first want to apologize to any students
I may have offended. I have the upmost respect for
both students and professors (even though my degree
has taken me into business rather than academia), and
I do not wish to make either's vocation more difficult.
I found Richard Carr and Randy Poe's comments particularly
articulate. Echoing much of the same ideas, I think the
keys for anyone posting is:
1) Be straightforward. Don't lie or be vague in your motives.
2) Show you are trying. Don't leave it up to the sci.math
contributors to assume so.
3) Please be polite (vulgar language makes it difficult
to respect someone).
In my previous posts, I think I passed 1) and 3), but failed 2).
Maybe I could have written:
Given three lines that share a common point,
can you give the conditions under which they
all are in the same plane?
Thanks for any help,
David Norris
Background (just added info you may read if interested):
I'm an research acoustician working on a ray-traced based reverberation
model in
3-space (I work for BBN). I'm stuck on characterizing the specularly
reflected
ray off of a plane. I have a feeling this is a simple problem but I'm
stuck.
I know the direction vector of the incoming ray and the normal vector of
the plane,
and need the direction vector of the outgoing ray. Soooo, I have three
unknowns (vx,vy,vz of outgoing ray) and therefore need three equations.
The angle constraints (specular: angle of incident ray with plane =
that for outgoing ray) gives me the first two. I figured the "three
lines
in a plane" condition would give me the third. Then all I have is a
simple
problem that can be sovlved with one line of matlab code:
Ax = B -> x = A\B, where
x is unknowns [3x1],
A is coefficent matrix [3x3] and B is [3x1].
Of course, eqns. must be linearly independent, i.e., A is non-singular.
David Norris wrote:
>
> I support people's frustration/annoyance with
> those who post their homework, especially when
> the subject is something like, "please hurry!".
>
> In these cases, creative repremands or non-responses
> I think are appropriate. However, people don't
> always post their h/w even though it looks like it.
>
> Example: I am an engineer for the R&D acoustics company
> BBN and am working on an sound reverberation model. I
> needed a solution for the specularly reflected angle
> in 3-space, so I posted the problem ("SPACE ANAYLTIC
> GEOMERTY question"). No response, so I narrowed the
> problem down to a simple theoretical problem ("three
> lines forming a plane"), thinking I would get a
> better response. Success! The responses I got were
> excellent and solved my problem, but, as some thought,
> it wasn't homework :)
>
> David Norris
bri...@eisner.decus.org
> I'm an research acoustician working on a ray-traced based reverberation
> model in
> 3-space (I work for BBN). I'm stuck on characterizing the specularly
> reflected
> ray off of a plane. I have a feeling this is a simple problem but I'm
> stuck.
> I know the direction vector of the incoming ray and the normal vector of
> the plane,
> and need the direction vector of the outgoing ray.
Off the top of my head (turns out there is an easier way -- skip ahead):
Take incident vector cross the plane normal vector. If this is zero
then you are done. Reflection vector = - incident vector.
This gives you a non-zero vector that is in the plane and is
orthogonal to both the incident ray and to the normal vector.
Cross this vector with the normal vector.
This gives you a non-zero vector that is in the original plane and is
also in the plane defined by the incident ray and the normal vector.
Normalize this vector so that its magnitude is 1.
Now, take the incoming ray, dot it with this vector and multiply
it by this vector.
This gives you the component of the outbound direction vector orthogonal
to the plane normal vector.
Take the incoming ray, dot it with the plane normal vector, multiply
by the plane normal vector and negate. (You may have to normalize the
plane normal vector to a unit vector before taking this step).
This gives you the component of the outbound direction vector parallel
to the plane normal vector.
Add the two components.
Voila.
Alternatively: (Here is the easy way)
Take incident vector dot normal vector times normal vector (assume normal
is a unit vector).
This is the component of the incident ray parallel to the normal vector.
Subtract this from the incident vector
This is the component of the incident ray in the plane of reflection.
Negate the parallel component, add to the orthogonal component.
Voila -- the reflected vector.
John Briggs bri...@eisner.decus.org
David Norris
I love your solution! Very elegant.
Mine was quite sloppy, especially as
I was needlessly doing numerical
trig evaluations, which of course are
approximations, whereas your solution
is exact.
Thanks for the post. I've really enjoyed
looking at this!
David
Virgil
>Given three lines that share a common point,
>can you give the conditions under which they
>all are in the same plane?
Probably the simplest test is to take three vectors, say u,v and w,
along the lines and form the triple scalar product "u dot(v cross w)"
If this is zero the lines are coplanar, otherwise not.
Direction cosines will serve as components of vectors along the lines.
The determinant of the 3 by 3 matrix formed by the components of the
three vectors is another form of the triple scalar product.
--
Virgil
vm...@frii.com
Ron Bloom
> --
> Virgil
> vm...@frii.com
A practical question, I have forgotten how to asnwer,
but this issue reminded me to ask all the same:
If our vectors and matrices consist of components which
are floating point numbers,
how do we decide when a cross-product is "zero",
or when a determinant is zero, for that matter.
How close to machine "epsilon" must a number be
before we say, "aha: the result is zero!"
Pertti Lounesto
This is a problem we encountered when developing CLICAL,
a computer program for Clifford algebra calculations, see
http://www.hit.fi/~lounesto/CLICAL.htm. We thought that
the zeroness of a cross product might depend on absolute
values of the factors: if the absolute value of the cross
product is considerably smaller than the absolute values of
the factors, then the cross product is zero. However, in
computations, where the cross product is only a medium
result, in particular, when considering limits and derivatives,
such zeroing proved a bad idea. Therefore, we decided
that the cross product is never zero, unless it goes under
the epsilon of the machine. However, in Clifford
algebras a cross product might be a term in a sum, like in
ab = a.b + axb.
In such cases, we decided that the cross product is zero,
if its absolute value is considerably smaller than absolute
value of the largest term.
David Franklin
David Norris <dno...@bbn.com> wrote in message news:390062C9...@bbn.com...
> John,
>
> I love your solution! Very elegant.
> Mine was quite sloppy, especially as
> I was needlessly doing numerical
> trig evaluations, which of course are
> approximations, whereas your solution
> is exact.
David - I'm not really sure *why* you want
to solve it using the 3 lines condition. If the
normal to the plane is N, and the incident
vector V, then the reflected vector is simply
V - 2 * (N.V) N
There's a *lot* of literature on raytracing
around these days - you may find getting
a book (I quite like Glassner's one) saves
you a lot of time.
Dave
Virgil
>but this issue reminded me to ask all the same:
>
> If our vectors and matrices consist of components which
>are floating point numbers,
> how do we decide when a cross-product is "zero",
>or when a determinant is zero, for that matter.
>How close to machine "epsilon" must a number be
>before we say, "aha: the result is zero!"
If you are using direction cosines, so that each vector has length 1.
and are doing n significant digit accuracy calculations in floating
point, the epsilon should probably be between 1/(10^(n-1)) and
1/(10^(n-3)). You might have to experiment a bit to find an acceptable
epsilon in that range.
If the direction cosines are derived from other calculations, you might
want to estimate their accuracy based on the calculation types and the
accuracy of your raw data. The less accurate the direction cosines are,
of course, the larger epsilon you will want.
--
Virgil
vm...@frii.com
Charles H. Giffen
>
[snip]
(BTW
> I assuming that you NEVER asked for help on a single homework problem while
> you went through school.)
Believe it or not there ARE some who NEVER asked for help on a single
homework problem while they went through school.
I bow down to you oh great genius. Goodbye, this
> shall be the last time I pose here, I will be finding a new newsgroup to help
Hopefully, you will be more modest and won't try to pose in the nude, as
you seem to be trying to do here.
> with my calculus homework, one that will actually help and not treat me like
> dirt.
>
[snip]
--Chuck Giffen
Pertti Lounesto
> I assuming that you NEVER asked for help on a single
> homework problem while you went through school.
At school, I solved the homework problems on my way
to the blackboard, when the teacher asked for model
solutions in the case that no other student could solve
the problems. It happened that some of my teachers
NEVER asked for my help to solve homework problems,
although they presented false solutions to the problems.