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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: Cartesian Heart
*
* There are many mathematical curves that produce heart shapes.
* With a good solving effort, coordinates of a filled heart shape
* can be computed by solving the cartesian equation:
*
* \f[
* x^2+2\left(y-p\times\operatorname{abs}(x)^{\frac{1}{q}}\right)^2 = 1
* \f]
*
* By setting \f$p=0.5\f$ and \f$q=2\f$, it yields to the equation:
*
* \f[
* x^2+2\left(y-\frac{\operatorname{abs}(x)^{\frac{1}{2}}}{2}\right)^2 = 1
* \f]
*
* To get reasonable interval starting sizes, \f$x\f$ and \f$y\f$
* are restricted to \f$[-20;20]\f$.
*
* \ingroup Example
*/
class CartesianHeart : public Script {
protected:
/// The numbers
FloatVarArray f;
/// Minimum distance between two solutions
FloatNum step;
public:
/// Actual model
CartesianHeart(const Options& opt)
: Script(opt), f(*this,2,-20,20), step(opt.step()) {
int q = 2;
FloatNum p = 0.5;
// Post equation
rel(*this, sqr(f[0]) + 2*sqr(f[1]-p*nroot(abs(f[0]),q)) == 1);
branch(*this, f[0], FLOAT_VAL_SPLIT_MIN());
branch(*this, f[1], FLOAT_VAL_SPLIT_MIN());
}
/// Constructor for cloning \a p
CartesianHeart(CartesianHeart& p)
: Script(p), step(p.step) {
f.update(*this, p.f);
}
/// Copy during cloning
virtual Space* copy(void) {
return new CartesianHeart(*this);
}
/// Add constraints to current model to get next solution (not too close)
virtual void constrain(const Space& _b) {
const CartesianHeart& b = static_cast<const CartesianHeart&>(_b);
rel(*this,
(f[0] >= (b.f[0].max()+step)) ||
(f[1] >= (b.f[1].max()+step)) ||
(f[1] <= (b.f[1].min()-step)));
}
/// Print solution coordinates
virtual void print(std::ostream& os) const {
os << "XY " << f[0].med() << " " << f[1].med()
<< std::endl;
}
};
/** \brief Main-function
* \relates CartesianHeart
*/
int main(int argc, char* argv[]) {
Options opt("CartesianHeart");
opt.solutions(0);
opt.step(0.01);
opt.parse(argc,argv);
Script::run<CartesianHeart,BAB,Options>(opt);
return 0;
}
// STATISTICS: example-any
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