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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: Mars lander crash |
| Date | 2016-12-13 20:13 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <o2ph6u$aec$1@dont-email.me> (permalink) |
| References | (17 earlier) <13b758b6-d938-4ffd-9659-c76a0007ba62@googlegroups.com> <eb90bsF18c4U2@mid.individual.net> <bd14a6ca-b4e9-4685-abcd-22765b96acd8@googlegroups.com> <lnr35bpzs6.fsf@kst-u.example.com> <87lgvjahls.fsf@bsb.me.uk> |
On 13/12/16 18:01, Ben Bacarisse wrote: > 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. > I think you mean that the sum of the powers is at most 3, so that you have: a.x³ + b.x²y + c.xy² + d.y³ + e.x² + f.xy + g.y² + h.x + i.y + j 10 coefficients, so 9 roots (counting doubles as necessary, and including complex numbers). I don't think you you need a point at infinity. (Malcolm can say if this is more accurate or not.) > 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). >
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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
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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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