150 lines
3.8 KiB
C++
150 lines
3.8 KiB
C++
/*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* Copyright 2016-2018 Danny Robson <danny@nerdcruft.net>
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*/
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#pragma once
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#include "../point.hpp"
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#include "cruft/util/geom/segment.hpp"
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#include "sample/fwd.hpp"
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#include <cstddef>
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#include <random>
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namespace cruft::geom {
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///////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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struct tri {
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tri () = default;
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tri (point<S,T> _a, point<S,T> _b, point<S,T> _c)
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: a (_a)
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, b (_b)
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, c (_c)
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{ ; }
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cruft::point<S,T> a, b, c;
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};
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template <size_t S, typename T>
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tri (point<S,T>, point<S,T>, point<S,T>) -> tri<S,T>;
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template <typename T> using tri2 = tri<2, T>;
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template <typename T> using tri3 = tri<3, T>;
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using tri2f = tri<2,float>;
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using tri3f = tri<3,float>;
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namespace sample {
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template <size_t S, typename T>
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class surface<tri<S,T>> {
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public:
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using shape_type = tri<S,T>;
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explicit surface (tri<S,T> _target):
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base (_target.a),
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v0 (_target.b - _target.a),
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v1 (_target.c - _target.a)
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{ ; }
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template <typename GeneratorT>
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cruft::point<S,T>
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operator() (GeneratorT &&gen) const noexcept
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{
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std::uniform_real_distribution<float> dist (0, 1);
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return base + dist (gen) * v0 + dist (gen) * v1;
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}
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private:
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cruft::point<S,T> base;
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cruft::vector<S,T> v0;
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cruft::vector<S,T> v1;
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};
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};
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///////////////////////////////////////////////////////////////////////////
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template <std::size_t S, typename T>
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std::array<cruft::geom::segment<S,T>, 3>
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edges (tri<S,T> const &t)
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{
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return {{
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{ t.a, t.b },
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{ t.b, t.c },
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{ t.c, t.a },
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}};
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}
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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 (tri<DimensionV,ValueT> obj)
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{
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// heron's formula
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const auto ab = cruft::distance (obj.a, obj.b);
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const auto bc = cruft::distance (obj.b, obj.c);
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const auto ca = cruft::distance (obj.c, obj.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 (tri<2,T> obj)
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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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-obj.b.x * obj.a.y
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+obj.c.x * obj.a.y
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+obj.a.x * obj.b.y
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-obj.c.x * obj.b.y
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-obj.a.x * obj.c.y
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+obj.b.x * obj.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 (tri<3,T> obj)
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{
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const auto ab = obj.a - obj.b;
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const auto ac = obj.a - obj.c;
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return norm (cross (ab, ac)) / 2;
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}
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//-------------------------------------------------------------------------
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// convenience forwarder
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template <size_t S, typename T>
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T
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area (point<S,T> a, point<S,T> b, point<S,T> c)
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{
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return area (tri (a, b, c));
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}
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//-------------------------------------------------------------------------
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template <typename T>
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bool
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inclusive (tri2<T> const &obj, point2<T> const &p);
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};
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