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 *                                                                       *
 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
 * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
 *                                                                       *
 * This library is free software; you can redistribute it and/or         *
 * modify it under the terms of EITHER:                                  *
 *   (1) The GNU Lesser General Public License as published by the Free  *
 *       Software Foundation; either version 2.1 of the License, or (at  *
 *       your option) any later version. The text of the GNU Lesser      *
 *       General Public License is included with this library in the     *
 *       file LICENSE.TXT.                                               *
 *   (2) The BSD-style license that is included with this library in     *
 *       the file LICENSE-BSD.TXT.                                       *
 *                                                                       *
 * This library is distributed in the hope that it will be useful,       *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
 *                                                                       *


given (A,b,lo,hi), solve the LCP problem: A*x = b+w, where each x(i),w(i)
satisfies one of
      (1) x = lo, w >= 0
      (2) x = hi, w <= 0
      (3) lo < x < hi, w = 0
A is a matrix of dimension n*n, everything else is a vector of size n*1.
lo and hi can be +/- dInfinity as needed. the first `nub' variables are
unbounded, i.e. hi and lo are assumed to be +/- dInfinity.

we restrict lo(i) <= 0 and hi(i) >= 0.

the original data (A,b) may be modified by this function.

if the `findex' (friction index) parameter is nonzero, it points to an array
of index values. in this case constraints that have findex[i] >= 0 are
special. all non-special constraints are solved for, then the lo and hi values
for the special constraints are set:
  hi[i] = abs( hi[i] * x[findex[i]] )
  lo[i] = -hi[i]
and the solution continues. this mechanism allows a friction approximation
to be implemented.


#ifndef _ODE_LCP_H_
#define _ODE_LCP_H_

void dSolveLCP (int n, dReal *A, dReal *x, dReal *b, dReal *w,
            int nub, dReal *lo, dReal *hi, int *findex);


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