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* \brief Simple closed interval class
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* Copyright 2007 Michael Sloan <mgsloan@gmail.com>
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* Original Rect/Range code by:
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* Lauris Kaplinski <lauris@kaplinski.com>
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* Nathan Hurst <njh@mail.csse.monash.edu.au>
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* bulia byak <buliabyak@users.sf.net>
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* MenTaLguY <mental@rydia.net>
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* This library is free software; you can redistribute it and/or
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* modify it either under the terms of the GNU Lesser General Public
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* License version 2.1 as published by the Free Software Foundation
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* (the "LGPL") or, at your option, under the terms of the Mozilla
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* Public License Version 1.1 (the "MPL"). If you do not alter this
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* notice, a recipient may use your version of this file under either
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* the MPL or the LGPL.
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* You should have received a copy of the LGPL along with this library
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* in the file COPYING-LGPL-2.1; if not, output to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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* You should have received a copy of the MPL along with this library
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* in the file COPYING-MPL-1.1
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* The contents of this file are subject to the Mozilla Public License
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* Version 1.1 (the "License"); you may not use this file except in
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* compliance with the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
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* OF ANY KIND, either express or implied. See the LGPL or the MPL for
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* the specific language governing rights and limitations.
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#ifndef LIB2GEOM_SEEN_INTERVAL_H
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#define LIB2GEOM_SEEN_INTERVAL_H
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#include <boost/none.hpp>
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#include <boost/optional.hpp>
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#include <boost/operators.hpp>
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#include <2geom/coord.h>
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#include <2geom/math-utils.h>
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#include <2geom/generic-interval.h>
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#include <2geom/int-interval.h>
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* @brief Range of real numbers that is never empty.
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* Intervals are closed ranges \f$[a, b]\f$, which means they include their endpoints.
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* To use them as open ranges, you can use the interiorContains() methods.
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: public GenericInterval<Coord>
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typedef GenericInterval<Coord> Base;
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/// @name Create intervals.
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/** @brief Create an interval that contains only zero. */
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/** @brief Create an interval that contains a single point. */
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explicit Interval(Coord u) : Base(u) {}
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/** @brief Create an interval that contains all points between @c u and @c v. */
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Interval(Coord u, Coord v) : Base(u,v) {}
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/** @brief Convert from integer interval */
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Interval(IntInterval const &i) : Base(i.min(), i.max()) {}
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Interval(Base const &b) : Base(b) {}
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/** @brief Create an interval containing a range of values.
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* The resulting interval will contain all values from the given range.
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* The return type of iterators must be convertible to Coord. The given range
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* must not be empty. For potentially empty ranges, see OptInterval.
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* @param start Beginning of the range
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* @param end End of the range
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* @return Interval that contains all values from [start, end). */
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template <typename InputIterator>
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static Interval from_range(InputIterator start, InputIterator end) {
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Interval result = Base::from_range(start, end);
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/** @brief Create an interval from a C-style array of values it should contain. */
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static Interval from_array(Coord const *c, unsigned n) {
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Interval result = from_range(c, c+n);
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/// @name Inspect contained values.
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/// Check whether both endpoints are finite.
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bool isFinite() const {
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return IS_FINITE(min()) && IS_FINITE(max());
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/** @brief Map the interval [0,1] onto this one.
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* This method simply performs 1D linear interpolation between endpoints. */
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Coord valueAt(Coord t) {
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return lerp(t, min(), max());
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/** @brief Compute a time value that maps to the given value.
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* The supplied value does not need to be in the interval for this method to work. */
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Coord timeAt(Coord v) {
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return (v - min()) / extent();
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/// Find closest time in [0,1] that maps to the given value. */
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Coord nearestTime(Coord v) {
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if (v <= min()) return 0;
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if (v >= max()) return 1;
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/// @name Test coordinates and other intervals for inclusion.
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/** @brief Check whether the interior of the interval includes this number.
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* Interior means all numbers in the interval except its ends. */
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bool interiorContains(Coord val) const { return min() < val && val < max(); }
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/** @brief Check whether the interior of the interval includes the given interval.
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* Interior means all numbers in the interval except its ends. */
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bool interiorContains(Interval const &val) const { return min() < val.min() && val.max() < max(); }
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/// Check whether the number is contained in the union of the interior and the lower boundary.
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bool lowerContains(Coord val) { return min() <= val && val < max(); }
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/// Check whether the given interval is contained in the union of the interior and the lower boundary.
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bool lowerContains(Interval const &val) const { return min() <= val.min() && val.max() < max(); }
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/// Check whether the number is contained in the union of the interior and the upper boundary.
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bool upperContains(Coord val) { return min() < val && val <= max(); }
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/// Check whether the given interval is contained in the union of the interior and the upper boundary.
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bool upperContains(Interval const &val) const { return min() < val.min() && val.max() <= max(); }
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/** @brief Check whether the interiors of the intervals have any common elements.
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* A single point in common is not considered an intersection. */
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bool interiorIntersects(Interval const &val) const {
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return std::max(min(), val.min()) < std::min(max(), val.max());
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// IMPL: ScalableConcept
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/** @brief Scale an interval */
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Interval &operator*=(Coord s) {
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if(s < 0) swap(_b[0], _b[1]);
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/** @brief Scale an interval by the inverse of the specified value */
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Interval &operator/=(Coord s) {
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if(s < 0) swap(_b[0], _b[1]);
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/** @brief Multiply two intervals.
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* Product is defined as the set of points that can be obtained by multiplying
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* any value from the second operand by any value from the first operand:
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* \f$S = \{x \in A, y \in B: x * y\}\f$ */
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Interval &operator*=(Interval const &o) {
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// TODO implement properly
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Coord mn = min(), mx = max();
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expandTo(mn * o.min());
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expandTo(mn * o.max());
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expandTo(mx * o.min());
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expandTo(mx * o.max());
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bool operator==(IntInterval const &ii) const {
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return min() == Coord(ii.min()) && max() == Coord(ii.max());
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bool operator==(Interval const &other) const {
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return Base::operator==(other);
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/// @name Rounding to integer values
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/** @brief Return the smallest integer interval which contains this one. */
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IntInterval roundOutwards() const {
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IntInterval ret(floor(min()), ceil(max()));
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/** @brief Return the largest integer interval which is contained in this one. */
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OptIntInterval roundInwards() const {
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IntCoord u = ceil(min()), v = floor(max());
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if (u > v) { OptIntInterval e; return e; }
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IntInterval ret(u, v);
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* @brief Range of real numbers that can be empty.
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* @ingroup Primitives
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: public GenericOptInterval<Coord>
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typedef GenericOptInterval<Coord> Base;
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/// @name Create optionally empty intervals.
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/** @brief Create an empty interval. */
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OptInterval() : Base() {}
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/** @brief Wrap an existing interval. */
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OptInterval(Interval const &a) : Base(a) {}
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/** @brief Create an interval containing a single point. */
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OptInterval(Coord u) : Base(u) {}
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/** @brief Create an interval containing a range of numbers. */
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OptInterval(Coord u, Coord v) : Base(u,v) {}
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OptInterval(Base const &b) : Base(b) {}
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/** @brief Promote from IntInterval. */
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OptInterval(IntInterval const &i) : Base(Interval(i)) {}
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/** @brief Promote from OptIntInterval. */
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OptInterval(OptIntInterval const &i) : Base() {
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if (i) *this = Interval(*i);
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// functions required for Python bindings
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inline Interval unify(Interval const &a, Interval const &b)
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inline OptInterval intersect(Interval const &a, Interval const &b)
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OptInterval r = a & b;
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} // end namespace Geom
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#endif //SEEN_INTERVAL_H
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c-file-style:"stroustrup"
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c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
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// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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2geom/interval.h
