libcruft-util/vector.cpp
Danny Robson 7b083df977 maths: tighten up type requirements for almost_equal
almost_equal only operates on two reals, or two integers (and even then
only on the same signedness).
2015-11-13 17:18:10 +11:00

330 lines
8.9 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 2011 Danny Robson <danny@nerdcruft.net>
*/
#include "vector.hpp"
#include "debug.hpp"
#include "maths.hpp"
#include "random.hpp"
#include <algorithm>
#include <cmath>
#include <limits>
#include <numeric>
using util::vector;
using util::vector3f;
using util::vector3d;
///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
T
util::vector<S,T>::magnitude (void) const
{
// TODO: this should not truncate for integral types
return static_cast<T> (std::sqrt (magnitude2 ()));
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
T
util::vector<S,T>::magnitude2 (void) const
{
T total { 0 };
for (size_t i = 0; i < S; ++i)
total += pow2 (this->data[i]);
return total;
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
T
util::vector<S,T>::difference (vector<S,T> rhs) const
{
// TODO: change the signature to ensure it does not truncate
return static_cast<T> (std::sqrt (difference2 (rhs)));
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
T
util::vector<S,T>::difference2 (vector<S,T> rhs) const
{
T sum {0};
for (size_t i = 0; i < S; ++i)
sum += pow2 (this->data[i] - rhs.data[i]);
return sum;
}
///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
bool
vector<S,T>::is_normalised (void) const
{
return almost_equal (magnitude2 (), T{1});
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
util::vector<S,T>&
util::vector<S,T>::normalise (void)
{
T mag = magnitude ();
for (size_t i = 0; i < S; ++i)
this->data[i] /= mag;
return *this;
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
util::vector<S,T>
util::vector<S,T>::normalised (void) const
{
T mag = magnitude ();
util::vector<S,T> out;
for (size_t i = 0; i < S; ++i)
out.data[i] = this->data[i] / mag;
return out;
}
///////////////////////////////////////////////////////////////////////////////
template <typename T>
vector<2,T>
util::polar_to_cartesian (vector<2,T> v)
{
return util::vector<2,T> {
v[0] * std::cos (v[1]),
v[0] * std::sin (v[1])
};
}
//-----------------------------------------------------------------------------
template <typename T>
vector<2,T>
util::cartesian_to_polar (vector<2,T> v)
{
return util::vector<2,T> {
std::hypot (v.x, v.y),
std::atan2 (v.y, v.x)
};
}
///////////////////////////////////////////////////////////////////////////////
template <typename T>
vector<3,T>
util::from_euler (vector<2,T> euler)
{
return {
std::sin (euler.x) * std::cos (euler.y),
std::cos (euler.x),
-std::sin (euler.x) * std::sin (euler.y),
};
}
template util::vector3f util::from_euler (util::vector2f);
template util::vector3d util::from_euler (util::vector2d);
//-----------------------------------------------------------------------------
template <typename T>
vector<2,T>
util::to_euler (vector<3,T> vec)
{
vec.normalise ();
return {
std::acos (vec.y / vec.magnitude ()),
-std::atan2 (vec.z, vec.x),
};
}
template util::vector2f util::to_euler (util::vector3f);
template util::vector2d util::to_euler (util::vector3d);
///////////////////////////////////////////////////////////////////////////////
template <typename T>
vector<3,T>
util::cross (vector<3,T> a,
vector<3,T> b)
{
return util::vector<3,T> {
a.y * b.z - a.z * b.y,
a.z * b.x - a.x * b.z,
a.x * b.y - a.y * b.x
};
}
template vector3f util::cross(vector3f, vector3f);
template vector3d util::cross(vector3d, vector3d);
//-----------------------------------------------------------------------------
template <typename T>
vector<3,T>
util::spherical_to_cartesian (vector<3,T> s)
{
return vector<3,T> {
s.x * sin (s.y) * cos (s.z),
s.x * sin (s.y) * sin (s.z),
s.x * cos (s.y),
};
}
//-----------------------------------------------------------------------------
template <typename T>
vector<3,T>
util::cartesian_to_spherical (vector<3,T> c)
{
T mag = c.magnitude ();
return vector<3,T> {
mag,
acos (c.z / mag),
atan2 (c.y, c.x)
};
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
bool
util::vector<S,T>::is_zero (void) const
{
return std::all_of (std::begin (this->data),
std::end (this->data),
[] (T i) { return almost_zero (i); });
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
const util::vector<S,T>
util::vector<S,T>::UNIT (T{1});
template <size_t S, typename T>
const util::vector<S,T>
util::vector<S,T>::ZERO (T{0});
//-----------------------------------------------------------------------------
template <size_t S, typename T>
void
util::vector<S,T>::sanity (void) const
{
CHECK (std::all_of (std::begin (this->data),
std::end (this->data),
[] (T i) { return !std::isnan (i); }));
}
///////////////////////////////////////////////////////////////////////////////
// ostream
template <size_t S, typename T>
std::ostream&
util::operator<< (std::ostream &os, util::vector<S,T> v)
{
os << "vec" << S << "(" << v.data[0];
for (size_t i = 1; i < S; ++i)
os << ", " << v.data[i];
os << ")";
return os;
}
//-----------------------------------------------------------------------------
template <size_t S, typename T>
const json::tree::node&
util::operator>> (const json::tree::node &node, util::vector<S,T> &v)
{
const json::tree::array &array = node.as_array ();
if (array.size () != S)
throw std::runtime_error ("Invalid dimensionality for json-to-vector");
// XXX: This used to be a std::transform but gcc 4.9.0 hit an internal
// compiler error at this point in release mode, so we dumb it down a
// little.
for (size_t i = 0; i < array.size (); ++i)
v.data[i] = static_cast<T> (array[i].as_number ().native ());
return node;
}
//-----------------------------------------------------------------------------
#define INSTANTIATE_S_T(S,T) \
template struct util::vector<S,T>; \
template std::ostream& util::operator<< (std::ostream&, util::vector<S,T> v); \
template const json::tree::node& util::operator>> (const json::tree::node&, util::vector<S,T>&);
#define INSTANTIATE(T) \
INSTANTIATE_S_T(1,T) \
INSTANTIATE_S_T(2,T) \
INSTANTIATE_S_T(3,T) \
INSTANTIATE_S_T(4,T)
INSTANTIATE(uint32_t)
INSTANTIATE(int32_t)
INSTANTIATE(uint64_t)
INSTANTIATE(int64_t)
INSTANTIATE(float)
INSTANTIATE(double)
//-----------------------------------------------------------------------------
namespace util {
template vector<2,float> polar_to_cartesian (util::vector<2,float>);
template vector<2,float> cartesian_to_polar (util::vector<2,float>);
template <> vector<1,float> random (void) { util::vector<1,float> out; randomise (out.data); return out; }
template <> vector<2,float> random (void) { util::vector<2,float> out; randomise (out.data); return out; }
template <> vector<3,float> random (void) { util::vector<3,float> out; randomise (out.data); return out; }
template <> vector<4,float> random (void) { util::vector<4,float> out; randomise (out.data); return out; }
template <> vector<1,double> random (void) { util::vector<1,double> out; randomise (out.data); return out; }
template <> vector<2,double> random (void) { util::vector<2,double> out; randomise (out.data); return out; }
template <> vector<3,double> random (void) { util::vector<3,double> out; randomise (out.data); return out; }
template <> vector<4,double> random (void) { util::vector<4,double> out; randomise (out.data); return out; }
}
template <>
bool
almost_equal [[gnu::pure]] (const util::vector2f &a, const util::vector2f &b)
{
bool (*comparator) (const float&, const float&) = almost_equal;
return std::equal (a.begin (), a.end (), b.begin (), comparator);
}