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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Vincent Barichard <Vincent.Barichard@univ-angers.fr>
*
* Copyright:
* Vincent Barichard, 2012
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <gecode/driver.hh>
#include <gecode/minimodel.hh>
#include <gecode/float.hh>
using namespace Gecode;
/**
* \brief %Example: Golden spiral
*
* The Golden Spiral is a logarithmic spiral whose growth factor
* is the golden ratio \f$\phi=1,618\f$.
*
* It is defined by the polar equation:
* \f[
* r = ae^{b\theta}
* \f]
* where
* \f[
* \operatorname{abs}(b) = \frac{\operatorname{ln}(\phi)}{\frac{\pi}{2}}
* \f]
*
* To get cartesian coordinates, it can be solved for \f$x\f$
* and \f$y\f$ in terms of \f$r\f$ and \f$\theta\f$.
* By setting \f$a=1\f$, it yields to the equation:
*
* \f[
* r = e^{0.30649\times\theta}
* \f]
* with
* \f[
* x=r\operatorname{cos}(\theta), \quad y=r\operatorname{sin}(\theta)
* \f]
*
* The tuple \f$(r,\theta)\f$ is related to the position for
* \f$x\f$ and \f$y\f$ on the curve. \f$r\f$ and \f$\theta\f$
* are positive numbers.
*
* To get reasonable interval starting sizes, \f$x\f$ and \f$y\f$
* are restricted to \f$[-20;20]\f$.
*
* \ingroup Example
*/
class GoldenSpiral : public FloatMaximizeScript {
protected:
/// The numbers
FloatVarArray f;
public:
/// Actual model
GoldenSpiral(const Options& opt)
: FloatMaximizeScript(opt), f(*this,4,-20,20) {
// Post equation
FloatVar theta = f[0];
FloatVar r = f[3];
FloatVar x = f[1];
FloatVar y = f[2];
rel(*this, theta >= 0);
rel(*this, r >= 0);
rel(*this, r*cos(theta) == x);
rel(*this, r*sin(theta) == y);
rel(*this, exp(0.30649*theta) == r);
branch(*this,theta,FLOAT_VAL_SPLIT_MIN());
}
/// Constructor for cloning \a p
GoldenSpiral(GoldenSpiral& p)
: FloatMaximizeScript(p) {
f.update(*this, p.f);
}
/// Copy during cloning
virtual Space* copy(void) {
return new GoldenSpiral(*this);
}
/// Cost function
virtual FloatVar cost(void) const {
return f[0];
}
/// Print solution coordinates
virtual void print(std::ostream& os) const {
os << "XY " << f[1].med() << " " << f[2].med()
<< std::endl;
}
};
/** \brief Main-function
* \relates GoldenSpiral
*/
int main(int argc, char* argv[]) {
Options opt("GoldenSpiral");
opt.solutions(0);
opt.step(0.1);
opt.parse(argc,argv);
FloatMaximizeScript::run<GoldenSpiral,BAB,Options>(opt);
return 0;
}
// STATISTICS: example-any
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