libcruft-util/geom/tri.hpp

79 lines
2.2 KiB
C++

/*
* 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