[Date Index]
[Thread Index]
[Author Index]
Re: Resolve/Reduce is taking forever
 To: mathgroup at smc.vnet.net
 Subject: [mg67237] Re: Resolve/Reduce is taking forever
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Wed, 14 Jun 2006 06:28:41 0400 (EDT)
 Organization: Uni Leipzig
 References: <e6lhfd$nd3$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
a) a line and a polynom of third order *must* have
a crossing
some where in the plane, so a infinite line
will never stay
left of the curve, except a3 is zero
b) you can search for the solutions a3×t^3 +
a2×t^2 + a1×t + a0==b1×t + b0
and look if there is a real solution and if the
real solution
is in the range 0 <= t <= 1
c) when you found no valid real solution you can
just calculate
Integrate[b1×t + b0(a3×t^3 + a2×t^2 + a1×t +
a0),{t,0,1}]
when the value is positive than the line is
above (left) the polynom
and otherwiese it its below (right) the polynom
Regards
Jens
"Bonny Banerjee" <banerjee at cse.ohiostate.edu>
schrieb im Newsbeitrag
news:e6lhfd$nd3$1 at smc.vnet.net...
I am trying to write a simple function that
determines the conditions for a
 curve to be on the left of a straight line. A
curve is to the left of a
 straight line if each point on the curve is to
the left of the straight
 line. The curve is specified using parametric
equations:

 x > a3×t^3 + a2×t^2 + a1×t + a0
 y > b1×t + b0

 where t is the parameter, 0<=t<=1, and {a0, a1,
a2, a3, b0, b1} are real
 coefficients. The straight line is specified
using two points {x1,y1} and
 {x2,y2}.

 Here is the function:

 isLeftofLine[{x1_, y1_}, {x2_, y2_}, {a0_, a1_,
a2_, a3_, b0_, b1_}] =
 Resolve[
 ForAll[t, 0 <= t <= 1 => fxy[{x1, y1}, {x2,
y2}, {a3×t^3 + a2×t^2 +
 a1×t + a0, b1×t + b0}] <= 0],
 {a0, a1, a2, a3, b0, b1}, Reals]

 where

 fxy[{x1_, y1_}, {x2_, y2_}, {x_, y_}] =
 (x  x1)×(y2  y1)  (y  y1)×(x2  x1)

 I tried Resolve and Reduce but both are taking
forever. I waited for more
 than 4 hours but could not get any result from
any of them. Considering this
 is a simple logical expression with only one
universal quantifier, I am
 surprised at what might be taking so long.

 Any insights would be very helpful. Also, any
alternative method for solving
 the same problem, such as using any other
function in place of
 Reduce/Resolve or using a different
representation for the curve or straight
 line, would be nice to know. I preferred using
parametric equations for
 representing the curve as the curve is finite.

 Thanks,
 Bonny.



Prev by Date:
Getting the (correct) roots of a polynomial
Next by Date:
Re: .NET/Link and twodimensional strings
Previous by thread:
Re: Re: Re: Resolve/Reduce is taking forever
Next by thread:
RE: Resolve/Reduce is taking forever
 