/*
 * 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 2016-2018 Danny Robson <danny@nerdcruft.net>
 */

#ifndef CRUFT_GEOM_TRI_HPP
#define CRUFT_GEOM_TRI_HPP

#include <cstddef>

#include "../point.hpp"

namespace util::geom {
    ///////////////////////////////////////////////////////////////////////////
    // n-dimensional triangle area
    template <std::size_t DimensionV, typename ValueT>
    ValueT
    area (util::point<DimensionV,ValueT> a,
          util::point<DimensionV,ValueT> b,
          util::point<DimensionV,ValueT> c)
    {
        // heron's formula
        const auto ab = util::distance (a, b);
        const auto bc = util::distance (b, c);
        const auto ca = util::distance (c, a);

        const auto s = (ab + bc + ca) / 2;

        return std::sqrt (s * (s - ab) * (s - bc) * (s - ca));
    }


    //-------------------------------------------------------------------------
    // 2-dimension triangle area
    template <typename T>
    T
    area (util::point<2,T> a, util::point<2,T> b, util::point<2,T> c)
    {
        //                | x1 y1 1 |
        // area = 0.5 det | x2 y2 1 |
        //                | x3 y3 1 |

        return std::abs (
            -b.x * a.y
            +c.x * a.y
            +a.x * b.y
            -c.x * b.y
            -a.x * c.y
            +b.x * c.y
        ) / 2;
    }


    //-------------------------------------------------------------------------
    // 3-dimension triangle area
    template <typename T>
    T
    area (util::point<3,T> a, util::point<3,T> b, util::point<3,T> c)
    {
        const auto ab = a - b;
        const auto ac = a - c;

        return norm (cross (ab, ac)) / 2;
    }
};

#endif