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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: Golden spiral
43 *
44 * The Golden Spiral is a logarithmic spiral whose growth factor
45 * is the golden ratio \f$\phi=1,618\f$.
46 *
47 * It is defined by the polar equation:
48 * \f[
49 * r = ae^{b\theta}
50 * \f]
51 * where
52 * \f[
53 * \operatorname{abs}(b) = \frac{\operatorname{ln}(\phi)}{\frac{\pi}{2}}
54 * \f]
55 *
56 * To get cartesian coordinates, it can be solved for \f$x\f$
57 * and \f$y\f$ in terms of \f$r\f$ and \f$\theta\f$.
58 * By setting \f$a=1\f$, it yields to the equation:
59 *
60 * \f[
61 * r = e^{0.30649\times\theta}
62 * \f]
63 * with
64 * \f[
65 * x=r\operatorname{cos}(\theta), \quad y=r\operatorname{sin}(\theta)
66 * \f]
67 *
68 * The tuple \f$(r,\theta)\f$ is related to the position for
69 * \f$x\f$ and \f$y\f$ on the curve. \f$r\f$ and \f$\theta\f$
70 * are positive numbers.
71 *
72 * To get reasonable interval starting sizes, \f$x\f$ and \f$y\f$
73 * are restricted to \f$[-20;20]\f$.
74 *
75 * \ingroup Example
76 */
77class GoldenSpiral : public FloatMaximizeScript {
78protected:
79 /// The numbers
80 FloatVarArray f;
81public:
82 /// Actual model
83 GoldenSpiral(const Options& opt)
84 : FloatMaximizeScript(opt), f(*this,4,-20,20) {
85 // Post equation
86 FloatVar theta = f[0];
87 FloatVar r = f[3];
88 FloatVar x = f[1];
89 FloatVar y = f[2];
90 rel(*this, theta >= 0);
91 rel(*this, r >= 0);
92 rel(*this, r*cos(theta) == x);
93 rel(*this, r*sin(theta) == y);
94 rel(*this, exp(0.30649*theta) == r);
95
96 branch(*this,theta,FLOAT_VAL_SPLIT_MIN());
97 }
98 /// Constructor for cloning \a p
99 GoldenSpiral(GoldenSpiral& p)
100 : FloatMaximizeScript(p) {
101 f.update(*this, p.f);
102 }
103 /// Copy during cloning
104 virtual Space* copy(void) {
105 return new GoldenSpiral(*this);
106 }
107 /// Cost function
108 virtual FloatVar cost(void) const {
109 return f[0];
110 }
111 /// Print solution coordinates
112 virtual void print(std::ostream& os) const {
113 os << "XY " << f[1].med() << " " << f[2].med()
114 << std::endl;
115 }
116
117};
118
119/** \brief Main-function
120 * \relates GoldenSpiral
121 */
122int main(int argc, char* argv[]) {
123 Options opt("GoldenSpiral");
124 opt.solutions(0);
125 opt.step(0.1);
126 opt.parse(argc,argv);
127 FloatMaximizeScript::run<GoldenSpiral,BAB,Options>(opt);
128 return 0;
129}
130
131// STATISTICS: example-any