libcruft-util/vector.hpp

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/*
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* 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
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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
* 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.
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*
* Copyright 2011-2017 Danny Robson <danny@nerdcruft.net>
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*/
#ifndef CRUFT_UTIL_VECTOR_HPP
#define CRUFT_UTIL_VECTOR_HPP
#include "./coord/fwd.hpp"
#include "./coord.hpp"
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#include "maths.hpp"
#include "json/fwd.hpp"
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#include <cstddef>
#include <cmath>
///////////////////////////////////////////////////////////////////////////////
namespace util {
template <size_t S, typename T>
struct vector : public coord::base<S,T,vector<S,T>>
{
using coord::base<S,T,vector<S,T>>::base;
// use a forwarding assignment operator so that we can let the base
// take care of the many different types of parameters. otherwise we
// have to deal with scalar, vector, initializer_list, ad nauseum.
template <typename Arg>
vector&
operator= (Arg&&arg)
{
coord::base<S,T,vector<S,T>>::operator=(std::forward<Arg> (arg));
return *this;
}
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// representations
template <size_t D = 4>
vector<D,T> homog (void) const
{
static_assert (D > S, "reducing size loses data");
return (*this).template redim<D> (0.f);
}
// constants
static constexpr vector<S,T> ones (void) { return vector<S,T> {1}; }
static constexpr vector<S,T> zeros (void) { return vector<S,T> {0}; }
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};
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template <typename T>
constexpr vector<3,T>
cross (vector<3,T> a, vector<3,T> b)
{
return {
a.y * b.z - a.z * b.y,
a.z * b.x - a.x * b.z,
a.x * b.y - a.y * b.x
};
}
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template <typename T>
constexpr
T
cross (vector<2,T> a, vector<2,T> b)
{
return a[0] * b[1] - a[1] * b[0];
}
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//-------------------------------------------------------------------------
// given a vector find two vectors which produce an orthonormal basis.
//
// we use frisvad's method, avoids explicit normalisation. a good
// alternative is hughes-moeller, but the paper is hard to find.
template <typename T>
std::pair<
util::vector<3,T>,
util::vector<3,T>
>
make_basis (const util::vector<3,T> n)
{
// avoid a singularity
if (n.z < -T(0.9999999)) {
return {
{ 0, -1, 0 },
{ -1, -1, 0 }
};
}
const T a = 1 / (1 + n.z);
const T b = -n.x * n.y * a;
return {
{ 1 - n.x * n.x * a, b, -n.x },
{ b, 1 - n.y * n.y * a, -n.y }
};
}
// polar/cartesian conversions; assumes (mag, angle) form.
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template <typename T> vector<2,T> polar_to_cartesian (vector<2,T>);
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template <typename T> vector<2,T> cartesian_to_polar (vector<2,T>);
// convert vector in spherical coordinates (r,theta,phi) with theta
// inclination and phi azimuth to cartesian coordinates (x,y,z)
template <typename T>
constexpr vector<3,T>
spherical_to_cartesian (const vector<3,T> s)
{
return {
s.x * std::sin (s.y) * std::cos (s.z),
s.x * std::sin (s.y) * std::sin (s.z),
s.x * std::cos (s.y)
};
}
// convert vector in cartesian coordinates (x,y,z) to spherical
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// coordinates (using ISO convention: r,inclination,azimuth) with theta
// inclination and phi azimuth.
template <typename T>
constexpr vector<3,T>
cartesian_to_spherical (vector<3,T> c)
{
auto r = norm (c);
return {
r,
std::acos (c.z / r),
std::atan2 (c.y, c.x)
};
}
template <typename T>
constexpr vector<3,T>
canonical_spherical (vector<3,T> s)
{
if (s.x < 0) {
s.x = -s.x;
s.y += util::pi<T>;
}
if (s.y < 0) {
s.y = -s.y;
s.z += util::pi<T>;
}
s.y = std::fmod (s.y, util::pi<T>);
s.z = std::fmod (s.z, util::pi<T>);
return s;
}
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template <typename T> vector<2,T> to_euler (vector<3,T>);
template <typename T> vector<3,T> from_euler (vector<2,T>);
// output and serialisation operators
template <size_t S, typename T>
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const json::tree::node&
operator>> (const json::tree::node&, vector<S,T>&);
template <typename T> using vector1 = vector<1,T>;
template <typename T> using vector2 = vector<2,T>;
template <typename T> using vector3 = vector<3,T>;
template <typename T> using vector4 = vector<4,T>;
template <size_t S> using vectoru = vector<S,unsigned>;
template <size_t S> using vectori = vector<S,int>;
template <size_t S> using vectorf = vector<S,float>;
template <std::size_t S> using vectorb = vector<S,bool>;
using vector2u = vector2<unsigned>;
using vector3u = vector3<unsigned>;
using vector4u = vector4<unsigned>;
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using vector2i = vector2<int>;
using vector3i = vector3<int>;
using vector4i = vector4<int>;
using vector1f = vector1<float>;
using vector2f = vector2<float>;
using vector3f = vector3<float>;
using vector4f = vector4<float>;
using vector2d = vector2<double>;
using vector3d = vector3<double>;
using vector4d = vector4<double>;
using vector2b = vector2<bool>;
using vector3b = vector3<bool>;
using vector4b = vector4<bool>;
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}
#endif