libcruft-util/point.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 2011-2018 Danny Robson <danny@nerdcruft.net>
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*/
#ifndef CRUFT_UTIL_POINT_HPP
#define CRUFT_UTIL_POINT_HPP
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#include "vector.hpp"
#include "coord.hpp"
#include "maths.hpp"
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#include "view.hpp"
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#include <type_traits>
namespace cruft {
/// An n-dimensional position in space.
///
/// \tparam S number of dimensions
/// \tparam T the underlying per-dimension datatype
template <size_t S, typename T>
struct point : public coord::base<S,T,point<S,T>>
{
using coord::base<S,T,point<S,T>>::base;
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// use a forwarding assignment operator so that we can let the base
// take care of the many different types of parameters. otherwise we
// have to deal with scalar, vector, initializer_list, ad nauseum.
template <typename Arg>
point&
operator= (Arg&&arg)
{
coord::base<S,T,point<S,T>>::operator=(std::forward<Arg> (arg));
return *this;
}
vector<S,T> to (point dst) const { return dst - *this; }
vector<S,T> from (point src) const { return *this - src; }
/// expand point to use homogenous coordinates of a higher dimension.
/// ie, fill with (0,..,0,1)
point<S+1,T>
homog (void) const
{
return this->template redim<S+1> (1);
}
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///////////////////////////////////////////////////////////////////////
static constexpr
auto min (void)
{
return point { std::numeric_limits<T>::lowest () };
}
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//-------------------------------------------------------------------
static constexpr
auto max (void)
{
return point { std::numeric_limits<T>::max () };
}
//-------------------------------------------------------------------
static constexpr
point<S,T> origin (void)
{
return point<S,T> {0};
}
///////////////////////////////////////////////////////////////////////
void sanity (void) const;
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};
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// Convenience typedefs
template <typename T> using point1 = point<1,T>;
template <typename T> using point2 = point<2,T>;
template <typename T> using point3 = point<3,T>;
template <typename T> using point4 = point<4,T>;
template <size_t S> using pointi = point<S,int>;
template <size_t S> using pointf = point<S,float>;
typedef point1<float> point1f;
typedef point2<float> point2f;
typedef point3<float> point3f;
typedef point4<float> point4f;
typedef point2<double> point2d;
typedef point3<double> point3d;
typedef point4<double> point4d;
typedef point1<unsigned> point1u;
typedef point2<unsigned> point2u;
typedef point3<unsigned> point3u;
typedef point4<unsigned> point4u;
typedef point2<int> point2i;
typedef point3<int> point3i;
typedef point4<int> point4i;
///////////////////////////////////////////////////////////////////////////
// distance operators
/// computes the exact euclidean distance between two points.
template <size_t S, typename T, typename U>
typename std::common_type<T,U>::type
distance (point<S,T> a, point<S,U> b)
{
using type_t = typename std::common_type<T,U>::type;
static_assert (std::is_floating_point<type_t>::value,
"sqrt likely requires fractional types");
return std::sqrt (distance2 (a, b));
}
/// computes the squared euclidean distance between two points.
///
/// useful if you just need to compare distances because it avoids a sqrt
/// operation.
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
distance2 (point<S,T> a, point<S,U> b)
{
return sum (pow (a - b, 2));
}
/// computes the octile distance between two points. that is, the shortest
/// distance between `a' and `b' where travel is only allowed beween the 8
/// grid neighbours and cost for diagonals is proportionally larger than
/// cardinal movement. see also: chebyshev.
template <typename T, typename U>
typename std::common_type<T,U>::type
octile (point<2,T> a, point<2,U> b)
{
using type_t = typename std::common_type<T,U>::type;
static_assert (!std::is_integral<type_t>::value,
"octile requires more than integer precision");
const type_t D1 = 1;
const type_t D2 = std::sqrt (type_t {2});
auto diff = cruft::abs (a - b);
// distance for axis-aligned walks
auto axis = D1 * (diff.x + diff.y);
// the savings from diagonal walks
auto diag = (D2 - 2 * D1) * cruft::min (diff);
return axis + diag;
}
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/// computes the manhattan distance between two points. that is, the
/// distance where travel is only allowed along cardinal directions.
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
manhattan (point<S,T> a, point<S,U> b)
{
return sum (abs (a - b));
}
/// computes the cheyvshev distance between two points. that is, the
/// shortest distance between `a' and `b' where travel is only allowed
/// between the 8 grid neighbours and cost for diagonals is the same as
/// cardinal movement. see also: octile.
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
chebyshev (point<S,T> a, point<S,U> b)
{
return cruft::max (abs (a - b));
}
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///////////////////////////////////////////////////////////////////////////
// returns the most distant pair of points in a set
//
// performance has no guarantees. in fact it's probably spectacularly slow.
//
// especially given we have nothing to accelerate lookups with. if you
// want it to be fast it may be an idea to construct a bounding volume and
// pass those vertices instead.
template <size_t S, typename T>
std::pair<
cruft::point<S,T>,
cruft::point<S,T>
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>
furthest (cruft::view<const cruft::point<S,T>*>);
///////////////////////////////////////////////////////////////////////////
/// computes the mean point across a view of points
template <typename InputT>
auto
center (cruft::view<InputT> points)
{
CHECK_NEZ (points.size ());
using point_type = typename std::iterator_traits<InputT>::value_type;
using value_type = typename point_type::value_type;
cruft::vector<point_type::elements,value_type> accum = 0;
for (auto const &i: points)
accum += i.template as<cruft::vector> ();
return (accum / points.size ()).template as<cruft::point> ();
}
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}
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#endif // __UTIL_POINT_HPP