libcruft-util/point.hpp

/*
 * 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
 *
 *     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.
 *
 * Copyright 2011-2016 Danny Robson <danny@nerdcruft.net>
 */

#ifndef CRUFT_UTIL_POINT_HPP
#define CRUFT_UTIL_POINT_HPP

#include "vector.hpp"
#include "coord.hpp"
#include "maths.hpp"

#include <algorithm>
#include <type_traits>

namespace util {
    /// 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;

        vector<S,T> to (point) const;
        vector<S,T> from (point) const;

        /// expand point to use homogenous coordinates of a higher dimension.
        /// ie, fill with (0,..,0,1)
        template <size_t D = 4>
        point<D,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;
        }

        ///////////////////////////////////////////////////////////////////////
        static constexpr
        auto min (void)
        {
            return point { std::numeric_limits<T>::lowest () };
        }

        //-------------------------------------------------------------------
        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;
    };

    ///////////////////////////////////////////////////////////////////////////
    // 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 (pow2 (a - b));
    }

    /// 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 = util::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) * util::min (diff);

        return axis + diag;
    }


    /// 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 util::max (abs (a - b));
    }

    // 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;
}

#endif // __UTIL_POINT_HPP