libcruft-util/point.ipp

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/*
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* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
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*
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* Copyright 2014-2015 Danny Robson <danny@nerdcruft.net>
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*/
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#include "maths.hpp"
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#include <algorithm>
///////////////////////////////////////////////////////////////////////////////
/// expand point to use homogenous coordinates of a higher dimension.
/// ie, fill with (0,..,0,1)
template <size_t S, typename T>
template <size_t D>
util::point<D,T>
util::point<S,T>::homog (void) const
{
static_assert (D > S, "homog will not overwrite data");
point<D,T> out;
// Copy the existing data
auto c = std::copy (this->begin (),
this->end (),
out.begin ());
// Fill until the second last element with zeros
auto f = std::fill_n (c, D - S - 1, T{0});
// Last element should be one
*f = T{1};
return out;
}
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///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
constexpr
util::point<S,T>
util::point<S,T>::origin (void)
{
return point<S,T> {0};
}
///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T, typename U>
typename std::common_type<T,U>::type
util::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");
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return std::sqrt (distance2 (a, b));
}
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///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
util::distance2 (point<S,T> a, point<S,U> b)
{
typename std::common_type<T,U>::type sum {0};
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for (size_t i = 0; i < S; ++i)
sum += pow2 (a.data[i] - b.data[i]);
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return sum;
}
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///////////////////////////////////////////////////////////////////////////////
template <typename T, typename U>
typename std::common_type<T,U>::type
util::octile (point2<T> a, point2<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");
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const type_t D1 = 1;
const type_t D2 = std::sqrt (type_t {2});
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auto diff = util::abs (a - b);
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// distance for axis-aligned walks
auto axis = D1 * (diff.x + diff.y);
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// the savings from diagonal walks
auto diag = (D2 - 2 * D1) * util::min (diff);
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return axis + diag;
}
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///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
util::manhattan (point<S,T> a, point<S,U> b)
{
typename std::common_type<T,U>::type sum {0};
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for (size_t i = 0; i < S; ++i)
sum += util::abs (a.data[i] - b.data[i]);
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return sum;
}
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///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T, typename U>
constexpr typename std::common_type<T,U>::type
util::chebyshev(point<S,T> a, point<S,U> b)
{
return util::max (abs (a - b));
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}