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dekker.one
1/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
2/*
3 * Main authors:
4 * Vincent Barichard <Vincent.Barichard@univ-angers.fr>
5 *
6 * Copyright:
7 * Vincent Barichard, 2012
8 *
9 * This file is part of Gecode, the generic constraint
10 * development environment:
11 * http://www.gecode.org
12 *
13 * Permission is hereby granted, free of charge, to any person obtaining
14 * a copy of this software and associated documentation files (the
15 * "Software"), to deal in the Software without restriction, including
16 * without limitation the rights to use, copy, modify, merge, publish,
17 * distribute, sublicense, and/or sell copies of the Software, and to
18 * permit persons to whom the Software is furnished to do so, subject to
19 * the following conditions:
20 *
21 * The above copyright notice and this permission notice shall be
22 * included in all copies or substantial portions of the Software.
23 *
24 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
25 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
26 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
27 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
28 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
29 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
30 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
31 *
32 */
33
34#include <gecode/driver.hh>
35
36#include <gecode/minimodel.hh>
37#include <gecode/float.hh>
38
39using namespace Gecode;
40
41/**
42 * \brief %Example: Cartesian Heart
43 *
44 * There are many mathematical curves that produce heart shapes.
45 * With a good solving effort, coordinates of a filled heart shape
46 * can be computed by solving the cartesian equation:
47 *
48 * \f[
49 * x^2+2\left(y-p\times\operatorname{abs}(x)^{\frac{1}{q}}\right)^2 = 1
50 * \f]
51 *
52 * By setting \f$p=0.5\f$ and \f$q=2\f$, it yields to the equation:
53 *
54 * \f[
55 * x^2+2\left(y-\frac{\operatorname{abs}(x)^{\frac{1}{2}}}{2}\right)^2 = 1
56 * \f]
57 *
58 * To get reasonable interval starting sizes, \f$x\f$ and \f$y\f$
59 * are restricted to \f$[-20;20]\f$.
60 *
61 * \ingroup Example
62 */
63class CartesianHeart : public Script {
64protected:
65 /// The numbers
66 FloatVarArray f;
67 /// Minimum distance between two solutions
68 FloatNum step;
69public:
70 /// Actual model
71 CartesianHeart(const Options& opt)
72 : Script(opt), f(*this,2,-20,20), step(opt.step()) {
73 int q = 2;
74 FloatNum p = 0.5;
75 // Post equation
76 rel(*this, sqr(f[0]) + 2*sqr(f[1]-p*nroot(abs(f[0]),q)) == 1);
77 branch(*this, f[0], FLOAT_VAL_SPLIT_MIN());
78 branch(*this, f[1], FLOAT_VAL_SPLIT_MIN());
79 }
80 /// Constructor for cloning \a p
81 CartesianHeart(CartesianHeart& p)
82 : Script(p), step(p.step) {
83 f.update(*this, p.f);
84 }
85 /// Copy during cloning
86 virtual Space* copy(void) {
87 return new CartesianHeart(*this);
88 }
89 /// Add constraints to current model to get next solution (not too close)
90 virtual void constrain(const Space& _b) {
91 const CartesianHeart& b = static_cast<const CartesianHeart&>(_b);
92 rel(*this,
93 (f[0] >= (b.f[0].max()+step)) ||
94 (f[1] >= (b.f[1].max()+step)) ||
95 (f[1] <= (b.f[1].min()-step)));
96 }
97 /// Print solution coordinates
98 virtual void print(std::ostream& os) const {
99 os << "XY " << f[0].med() << " " << f[1].med()
100 << std::endl;
101 }
102
103};
104
105/** \brief Main-function
106 * \relates CartesianHeart
107 */
108int main(int argc, char* argv[]) {
109 Options opt("CartesianHeart");
110 opt.solutions(0);
111 opt.step(0.01);
112 opt.parse(argc,argv);
113 Script::run<CartesianHeart,BAB,Options>(opt);
114 return 0;
115}
116
117// STATISTICS: example-any