79 lines
2.2 KiB
C++
79 lines
2.2 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* 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
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Copyright 2016-2018 Danny Robson <danny@nerdcruft.net>
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*/
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#ifndef CRUFT_GEOM_TRI_HPP
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#define CRUFT_GEOM_TRI_HPP
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#include <cstddef>
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#include "../point.hpp"
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namespace util::geom {
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///////////////////////////////////////////////////////////////////////////
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// n-dimensional triangle area
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template <std::size_t DimensionV, typename ValueT>
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ValueT
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area (util::point<DimensionV,ValueT> a,
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util::point<DimensionV,ValueT> b,
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util::point<DimensionV,ValueT> c)
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{
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// heron's formula
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const auto ab = util::distance (a, b);
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const auto bc = util::distance (b, c);
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const auto ca = util::distance (c, a);
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const auto s = (ab + bc + ca) / 2;
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return std::sqrt (s * (s - ab) * (s - bc) * (s - ca));
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}
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//-------------------------------------------------------------------------
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// 2-dimension triangle area
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template <typename T>
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T
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area (util::point<2,T> a, util::point<2,T> b, util::point<2,T> c)
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{
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// | x1 y1 1 |
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// area = 0.5 det | x2 y2 1 |
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// | x3 y3 1 |
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return std::abs (
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-b.x * a.y
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+c.x * a.y
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+a.x * b.y
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-c.x * b.y
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-a.x * c.y
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+b.x * c.y
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) / 2;
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}
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//-------------------------------------------------------------------------
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// 3-dimension triangle area
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template <typename T>
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T
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area (util::point<3,T> a, util::point<3,T> b, util::point<3,T> c)
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{
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const auto ab = a - b;
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const auto ac = a - c;
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return norm (cross (ab, ac)) / 2;
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}
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};
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#endif
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