libcruft-util/geom/tri.hpp

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/*
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* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* 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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#ifndef CRUFT_GEOM_TRI_HPP
#define CRUFT_GEOM_TRI_HPP
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#include "../point.hpp"
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#include "sample.hpp"
#include <cstddef>
#include <random>
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namespace cruft::geom {
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///////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
struct tri {
tri () = default;
tri (point<S,T> _a, point<S,T> _b, point<S,T> _c):
a (_a), b (_b), c (_c)
{ ; }
cruft::point<S,T> a, b, c;
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};
template <size_t S, typename T>
tri (point<S,T>, point<S,T>, point<S,T>) -> tri<S,T>;
using tri3f = tri<3,float>;
namespace surface {
template <size_t S, typename T>
class sampler<tri<S,T>> {
public:
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sampler (tri<S,T> _target):
base (_target.a),
v0 (_target.b - _target.a),
v1 (_target.c - _target.a)
{ ; }
template <typename GeneratorT>
cruft::point<S,T>
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operator() (GeneratorT &&gen) const noexcept
{
std::uniform_real_distribution<float> dist (0, 1);
return base + dist (gen) * v0 + dist (gen) * v1;
}
private:
cruft::point<S,T> base;
cruft::vector<S,T> v0, v1;
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};
};
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///////////////////////////////////////////////////////////////////////////
// n-dimensional triangle area
template <std::size_t DimensionV, typename ValueT>
ValueT
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area (tri<DimensionV,ValueT> obj)
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{
// heron's formula
const auto ab = cruft::distance (obj.a, obj.b);
const auto bc = cruft::distance (obj.b, obj.c);
const auto ca = cruft::distance (obj.c, obj.a);
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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
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area (tri<2,T> obj)
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{
// | x1 y1 1 |
// area = 0.5 det | x2 y2 1 |
// | x3 y3 1 |
return std::abs (
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-obj.b.x * obj.a.y
+obj.c.x * obj.a.y
+obj.a.x * obj.b.y
-obj.c.x * obj.b.y
-obj.a.x * obj.c.y
+obj.b.x * obj.c.y
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) / 2;
}
//-------------------------------------------------------------------------
// 3-dimension triangle area
template <typename T>
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;
const auto ac = obj.a - obj.c;
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return norm (cross (ab, ac)) / 2;
}
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//-------------------------------------------------------------------------
// convenience forwarder
template <size_t S, typename T>
T
area (point<S,T> a, point<S,T> b, point<S,T> c)
{
return area (tri (a, b, c));
}
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};
#endif