libcruft-util/region.hpp

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/*
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* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
* Copyright 2010-2019 Danny Robson <danny@nerdcruft.net>
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*/
#pragma once
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#include "./extent.hpp"
#include "./point.hpp"
#include "./vector.hpp"
#include "./types/traits.hpp"
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#include <iosfwd>
namespace cruft {
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/**
* A two-dimensional rectangle, with size and position.
*/
template <size_t S, typename T>
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struct region {
using extent_t = cruft::extent<S,T>;
using point_t = cruft::point<S,T>;
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using value_type = T;
//---------------------------------------------------------------------
static constexpr size_t dimension = S;
static constexpr size_t elements = extent_t::elements + point_t::elements;
point_t p;
extent_t e;
//---------------------------------------------------------------------
region () = default;
explicit region (extent_t);
region (point_t, extent_t);
region (point_t, point_t);
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//---------------------------------------------------------------------
template <typename U>
constexpr region<S,U>
cast (void) const
{
return {
p.template cast<U> (),
e.template cast<U> ()
};
}
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//---------------------------------------------------------------------
constexpr T area (void) const { return e.area (); }
constexpr T diameter (void) const { return e.diameter (); }
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extent_t magnitude (void) const;
extent_t magnitude (extent_t);
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bool empty (void) const;
//---------------------------------------------------------------------
point_t base (void) const;
point_t away (void) const;
point_t centre (void) const;
point_t closest (point_t) const;
//---------------------------------------------------------------------
// exclusive of borders
bool intersects (region<S,T>) const;
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// Compute binary region combinations
region intersection (region<S,T>) const;
// Test if a region lies completely within our space
bool covers (region<S,T>) const noexcept;
/// Test if a point lies within our space. Inclusive of borders
constexpr
bool
inclusive (point<S,T> q) const noexcept
{
return all (p <= q && p + e >= q);
}
/// test if a point lies within our space, exclusive of the
/// bottom-right border
constexpr bool
exclusive (point<S,T> q) const noexcept
{
return all (p <= q && p + e > q);
}
// Move a point to be within the region bounds
point_t constrain (point_t) const noexcept;
//---------------------------------------------------------------------
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// Compute a region `mag` units into the region
region inset (T mag) const;
region inset (vector<S,T> mag) const;
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region expand (T mag) const;
region expand (vector<S,T>) const;
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// arithmetic operators
region operator+ (vector<S,T>) const;
region operator- (vector<S,T>) const;
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// Logical comparison operators
bool operator ==(region<S,T> rhs) const;
bool operator !=(region<S,T> rhs) const
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{ return !(*this == rhs); }
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// Utility constants
static constexpr region<S,T> max (void)
{
return {
cruft::point <S,T> {std::numeric_limits<T>::lowest () / 2},
cruft::extent<S,T> {std::numeric_limits<T>::max ()}
};
}
static constexpr region<S,T> unit (void)
{
return {
point_t::origin (),
extent_t {1}
};
}
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static constexpr region<S,T> zero (void)
{ return { point_t {0}, extent_t {0} }; }
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class iterator {
public:
using iterator_category = std::forward_iterator_tag;
using difference_type = std::size_t;
using value_type = point_t;
using pointer = value_type*;
using reference = value_type&;
iterator (point_t _lo, point_t _hi):
cursor (_lo),
lo (_lo),
hi (_hi)
{ ; }
iterator ()
: cursor {}
, lo {}
, hi {}
{ ; }
const point_t& operator* (void) const& { return cursor; }
iterator&
operator++ (void)
{
cursor[0] += 1;
for (size_t s = 0; s < S-1; ++s) {
if (cursor[s] < hi[s])
return *this;
cursor[s] = lo[s];
cursor[s+1]++;
}
return *this;
}
bool operator== (const iterator &rhs) const { return cursor == rhs.cursor; }
bool operator!= (const iterator &rhs) const { return cursor != rhs.cursor; }
private:
point_t cursor, lo, hi;
};
/// Returns an iterator that provides successive points across the
/// region.
///
/// The points are in the half open range [p, p+e). ie, the
/// 'bottom-right' corner will never be returned. If you need this
/// behaviour then construct a larger range.
auto step (void) const
{
point_t last = p;
last[S-1] = (p + e)[S-1];
return cruft::view {
iterator { p, p + e },
iterator { last, p + e }
};
};
void sanity (void) const;
};
///////////////////////////////////////////////////////////////////////////
/// constructs the minimal region that encompasses a region and a point.
template <typename T, size_t S>
region<S,T>
operator| (region<S,T> const r, point<S,T> const p)
{
const auto p0 = select (r.p < p, r.p, p);
const auto p1 = select (r.away () > p, r.away (), p);
return { p0, p1 };
}
//-------------------------------------------------------------------------
template <typename T, size_t S>
auto
operator| (point<S,T> const p, region<S,T> const r)
{
return r | p;
}
//-------------------------------------------------------------------------
// construct a minimal bounding region over two supplied regions
template <typename T, size_t S>
region<S,T>
operator| (region<S,T> const a, region<S,T> const b)
{
return a | b.base () | b.away ();
}
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///////////////////////////////////////////////////////////////////////////
/// Construct a region that consists of the overlapping portions of two
/// supplied regions.
///
/// The behaviour is undefined if there is no overlap. The caller should
/// test using `intersects` if required beforehand.
template <typename T, std::size_t S>
region<S,T>
intersection (region<S,T> const a, region<S,T> const b)
{
// Find the two corners of the new region.
auto const lo = cruft::max (a.base (), b.base ());
auto const hi = cruft::min (a.away (), b.away ());
CHECK (all (lo <= hi));
return { lo, hi };
}
///////////////////////////////////////////////////////////////////////////
/// returns the squared minimum distance from a region to a given point
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template <size_t S, typename T>
T
distance2 (region<S,T> r, point<S,T> p)
{
auto const clamped = cruft::max (
r.p - p,
vector<S,T> (0),
p - (r.p + r.e)
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);
return sum (clamped * clamped);
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}
///------------------------------------------------------------------------
/// returns the squared minimum distance from a region to a given point
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template <size_t S, typename T>
T
distance2 (point<S,T> p, region<S,T> r)
{
return distance2 (r, p);
}
///////////////////////////////////////////////////////////////////////////
/// returns true if the supplied point lies within the supplied region
/// inclusive of borders.
template <size_t S, typename T>
bool
intersects (cruft::region<S,T> const area,
cruft::point<S,T> const query)
{
return area.inclusive (query);
}
///------------------------------------------------------------------------
/// returns true if the supplied point lies within the supplied region
/// inclusive of borders.
template <size_t S, typename T>
bool
intersects (cruft::point<S,T> const query,
cruft::region<S,T> const area)
{
return intersects (area, query);
}
///////////////////////////////////////////////////////////////////////////
/// returns a uniformly randomly sampled point within the supplied region
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template <size_t S, typename T, typename GeneratorT>
cruft::point<S,T>
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sample (region<S,T> shape, GeneratorT &&gen)
{
return shape.p + sample (
shape.e, std::forward<GeneratorT> (gen)
).template as<cruft::vector> ();
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}
///------------------------------------------------------------------------
/// Returns a uniformly randomly sampled point within the supplied region
/// using the default thread-local generator.
template <size_t S, typename T>
decltype(auto)
sample (region<S,T> const &shape)
{
return sample (shape, cruft::random::generator ());
}
///////////////////////////////////////////////////////////////////////////
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template <typename T> using region2 = region<2,T>;
template <typename T> using region3 = region<3,T>;
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using region2u = region2<unsigned>;
using region2i = region2<int>;
using region2f = region2<float>;
using region2d = region2<double>;
///////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
std::ostream& operator<< (std::ostream&, const cruft::region<S,T>&);
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}