Re: [Algorithms] Solving a system of line equations -- Simple Version ; )

[metanet s. <met...@ya...>]

I've gotten the basic solver working, but I'm still struggling with how to deal with additional constraints, such as:

-drive r[] values towards targets (minimize ||targ[i] - r[i]||)
-enforce a minimum allowable r value (make sure r[i] > rmin)

Currently I'm adding these as additional constraints the solver has to deal with; this makes sense for enforcing the minimum allowable value, but it seems wrong to drive r[] values towards targets using constraints, since they almost always directly "fight" with the main constraints.. causing the solver to fail to converge to a solution.

Raigan



--- On Fri, 12/5/08, metanet software <met...@ya...> wrote:

> From: metanet software <met...@ya...>
> Subject: [Algorithms] Solving a system of line equations -- Simple Version ; )
> To: gda...@li...
> Received: Friday, December 5, 2008, 10:20 AM
> My first form of this question was needlessly obtuse, this
> version should be much more comprehensible! 
> 
> I have the following system:
> http://www.harveycartel.org/raigan/system.jpg
> 
> I'd like to solve for r0,r1,r2 such that s < t;
> obviously setting r0=r1=r2=0 is a trivial solution; I'm
> more interested in driving r0,r1,r2 towards target values
> r0max,r1max,r2max while maintaining the constraint s < t.
> 
> My current plan is to construct the constraint equation C =
> s - t < 0 and then solve for the r values (by calculating
> the partial derivatives of C wrt r[i] and doing a
> non-linear-least-squares fit as in
> http://www.matthiasmueller.info/publications/posBasedDyn.pdf
> ).
> 
> However even if this works, I have no idea how to
> simultaneously minimize (rmax[i] - r[i]), i.e how I should
> drive the r values towards target values while obeying C.
> 
> Sorry for the totally obfuscated initial question.. thanks
> for your time!
> 
> Raigan
> 
> p.s - Just in case it's not clear from the diagram, s
> and t are the parametric times of intersection between
> lines; each line is parallel to a segment (p[i+1] - p[i])
> and passes through the point p[i] + r[i]*Perp(p[i+1] -
> p[i])/Len(p[i+1] - p[i]).. i.e each line is just a
> linesegment offset along its normal.
> 
> 
> 
>      
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