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Re: Mars lander crash

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups comp.lang.c
Subject Re: Mars lander crash
Date 2016-12-13 17:01 +0000
Organization A noiseless patient Spider
Message-ID <87lgvjahls.fsf@bsb.me.uk> (permalink)
References (16 earlier) <eb8bj5F18c4U1@mid.individual.net> <13b758b6-d938-4ffd-9659-c76a0007ba62@googlegroups.com> <eb90bsF18c4U2@mid.individual.net> <bd14a6ca-b4e9-4685-abcd-22765b96acd8@googlegroups.com> <lnr35bpzs6.fsf@kst-u.example.com>

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Keith Thompson <kst-u@mib.org> writes:

> Malcolm McLean <malcolm.mclean5@btinternet.com> writes:
> [...]
>> One way of solving the curve intersection problem is to build
>> a root finder which will solve equations with nine roots.
>> If the root finder works for all representable values of
>> coefficients, then great. But what if it doesn't? Is to going
>> to be good enough, (2 cubics can intersect nine times, but
>> almost always they intersect only once or twice on the interval
>> you are interested in)?  
>
> Two cubics can intersect nine times?  I don't think so.
>
> A cubic is an equation of the form ax^3 + bx^2 + cx + d = 0.
> It can have up to three roots (values of x for which it's true).
> The intersections of two cubics are the solutions of the difference
> between the two cubics -- which is itself a cubic, which have no
> more than three solutions.
>
> Is there a confusion about terminology?

I think so.  Malcolm is almost certainly talking about a cubic curve
rather than a cubic equation in one variable.  A cubic curve is a
polynomial equation in /two/ variables p(x, y) = 0 where the maximum
degree of any term in x or y is 3.

AFAIK, if you solve them in the right field (C extended with point at
infinity), two cubic cures always intersect in nine points but you must
count multiple coincident points as separate ones.

The default meaning of cubic is certainly the one you assumed, but in
the context of graphics algorithms I think cubic curve is the more
natural meaning (though I'd try to keep saying "cubic curve" just to be
clear).

-- 
Ben.

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Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 13:26 +0100
  Re: Mars lander crash Richard Heathfield <rjh@cpax.org.uk> - 2016-12-09 12:44 +0000
    Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 14:53 +0100
      Re: Mars lander crash already5chosen@yahoo.com - 2016-12-09 05:58 -0800
        Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 15:11 +0100
        Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 16:56 +0100
          Re: Mars lander crash supercat@casperkitty.com - 2016-12-09 08:51 -0800
          Re: Mars lander crash already5chosen@yahoo.com - 2016-12-11 02:23 -0800
            Re: Mars lander crash Gareth Owen <gwowen@gmail.com> - 2016-12-11 10:57 +0000
          Re: Mars lander crash "James R. Kuyper" <jameskuyper@verizon.net> - 2016-12-11 12:34 -0500
            Re: Mars lander crash Robert Wessel <robertwessel2@yahoo.com> - 2016-12-11 23:33 -0600
      Re: Mars lander crash Richard Heathfield <rjh@cpax.org.uk> - 2016-12-09 14:22 +0000
        Re: Mars lander crash asetofsymbols@gmail.com - 2016-12-09 06:30 -0800
          Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 15:48 +0100
        Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 15:46 +0100
          Re: Mars lander crash Richard Heathfield <rjh@cpax.org.uk> - 2016-12-09 14:55 +0000
            Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 16:08 +0100
              Re: Mars lander crash Richard Heathfield <rjh@cpax.org.uk> - 2016-12-09 15:52 +0000
          Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 17:35 +0100
            Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 18:35 +0100
              Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 19:10 +0100
                Re: Mars lander crash "James R. Kuyper" <jameskuyper@verizon.net> - 2016-12-09 19:18 -0500
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-09 16:49 -0800
                Re: Mars lander crash "J. Clarke" <j.clarke.873638@gmail.com> - 2016-12-20 20:03 -0500
                Re: Mars lander crash <william@wilbur.25thandClement.com> - 2016-12-09 22:04 -0800
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-10 10:59 -0800
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-11 13:22 +0100
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 14:18 +0100
                Re: Mars lander crash already5chosen@yahoo.com - 2016-12-11 06:03 -0800
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 15:08 +0100
                Re: Mars lander crash already5chosen@yahoo.com - 2016-12-11 06:20 -0800
                Re: Mars lander crash luser droog <luser.droog@gmail.com> - 2016-12-11 07:08 -0800
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-11 11:56 -0800
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 21:05 +0100
                Re: Mars lander crash jameskuyper@verizon.net - 2016-12-11 12:57 -0800
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-11 21:26 +0000
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-11 09:23 -0800
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-11 14:01 +0000
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 15:11 +0100
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-11 18:57 +0100
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 19:23 +0100
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-11 19:55 +0100
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 20:52 +0100
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-11 23:37 +0100
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-11 16:10 -0800
                Re: Mars lander crash BartC <bc@freeuk.com> - 2016-12-12 01:13 +0000
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-12 09:53 +0100
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-12 08:30 -0800
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-12 09:25 +0100
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-11 10:36 -0800
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-11 18:46 +0000
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-11 09:12 -0800
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 18:53 +0100
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-11 12:09 -0800
                Re: Mars lander crash Jean-Marc Bourguet <jm@bourguet.org> - 2016-12-11 21:30 +0100
                Re: Mars lander crash Lew Pitcher <lew.pitcher@digitalfreehold.ca> - 2016-12-11 15:50 -0500
                Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-11 23:02 +0100
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-11 18:29 -0800
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-11 12:03 -0800
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-11 11:55 -0800
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-11 23:42 +0100
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-11 14:53 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-12 17:09 +1300
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-12 10:00 +0100
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-12 22:20 +1300
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-12 01:28 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-12 22:38 +1300
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-12 02:43 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-13 08:20 +1300
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-12 12:57 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-13 14:14 +1300
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-13 01:19 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-13 22:56 +1300
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-13 05:16 -0800
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-14 18:05 +1300
                Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-13 08:19 -0800
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-13 17:01 +0000
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-13 10:48 -0800
                Re: Mars lander crash Geoff <geoff@invalid.invalid> - 2016-12-13 11:56 -0800
                Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-13 13:37 -0800
                Re: Mars lander crash Geoff <geoff@invalid.invalid> - 2016-12-13 19:11 -0800
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-13 20:13 +0100
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-13 11:45 -0800
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-13 23:10 +0000
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-14 10:18 +0100
                Re: Mars lander crash Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-14 12:37 +0000
                Re: Mars lander crash Tim Rentsch <txr@alumni.caltech.edu> - 2016-12-14 21:31 -0800
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-15 13:26 +0100
                Re: Mars lander crash Ian Collins <ian-news@hotmail.com> - 2016-12-12 22:40 +1300
                Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-12 13:22 +0100
                Re: Mars lander crash supercat@casperkitty.com - 2016-12-12 08:35 -0800
        Re: Mars lander crash supercat@casperkitty.com - 2016-12-09 08:43 -0800
      Re: Mars lander crash Jerry Stuckle <jstucklex@attglobal.net> - 2016-12-09 09:47 -0500
        Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 16:11 +0100
          Re: Mars lander crash Jerry Stuckle <jstucklex@attglobal.net> - 2016-12-09 10:49 -0500
  Re: Mars lander crash already5chosen@yahoo.com - 2016-12-09 05:53 -0800
    Re: Mars lander crash asetofsymbols@gmail.com - 2016-12-09 06:04 -0800
      Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 15:09 +0100
        Re: Mars lander crash Jerry Stuckle <jstucklex@attglobal.net> - 2016-12-09 10:06 -0500
          Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 16:32 +0100
    Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 17:30 +0100
      Re: Mars lander crash BartC <bc@freeuk.com> - 2016-12-09 16:42 +0000
      Re: Mars lander crash Lew Pitcher <lew.pitcher@digitalfreehold.ca> - 2016-12-09 11:43 -0500
      Re: Mars lander crash Keith Thompson <kst-u@mib.org> - 2016-12-09 08:59 -0800
      Re: Mars lander crash "J. Clarke" <j.clarke.873638@gmail.com> - 2016-12-20 19:36 -0500
  Re: Mars lander crash "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2016-12-09 06:46 -0800
    Re: Mars lander crash Richard Heathfield <rjh@cpax.org.uk> - 2016-12-09 14:57 +0000
      Re: Mars lander crash Noob <root@127.0.0.1> - 2016-12-09 16:07 +0100
    Re: Mars lander crash David Brown <david.brown@hesbynett.no> - 2016-12-09 16:03 +0100
      Re: Mars lander crash "James R. Kuyper" <jameskuyper@verizon.net> - 2016-12-09 12:41 -0500
    Re: Mars lander crash Jerry Stuckle <jstucklex@attglobal.net> - 2016-12-09 10:52 -0500
      Re: Mars lander crash jameskuyper@verizon.net - 2016-12-09 12:13 -0800
        Re: Mars lander crash jacobnavia <jacob@jacob.remcomp.fr> - 2016-12-09 21:56 +0100
          Re: Mars lander crash jameskuyper@verizon.net - 2016-12-09 14:11 -0800
        Re: Mars lander crash Jerry Stuckle <jstucklex@attglobal.net> - 2016-12-09 22:46 -0500
          Re: Mars lander crash <william@wilbur.25thandClement.com> - 2016-12-09 22:34 -0800
          Re: Mars lander crash James Kuyper <jameskuyper@verizon.net> - 2016-12-10 18:38 -0500
      Re: Mars lander crash Malcolm McLean <malcolm.mclean5@btinternet.com> - 2016-12-11 06:06 -0800
  Re: Mars lander crash "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-10 01:17 +0800
  Re: Mars lander crash Ken Brody <kenbrody@spamcop.net> - 2016-12-13 14:28 -0500
  Re: Mars lander crash Ken Brody <kenbrody@spamcop.net> - 2016-12-13 14:30 -0500

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