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#pragma once
#include <algorithm>
#include <initializer_list>
#include <type_traits>
namespace {
// last param to fool SFINAE into overloading
template<int i, int j, int ignored>
struct equals
{
enum { value = i == j };
};
template<int i, int j, int min>
struct maybe_add_swizzle
{
enum { value = (i == 1 || j == 1) && (i >= min || j >= min) };
};
template<int i1, int j1, int i2, int j2>
struct is_vector_pair
{
enum { value = i1 == i2 && j1 == 1 && j2 == 1 || j1 == j2 && i1 == 1 && i2 == 1 };
};
template<int i, int j>
struct vector_len
{
enum { value = i > j ? i : j };
};
template<int a, int b, int c, int d>
struct is_dim3
{
enum { value = a == 1 && c == 1 && b == 3 && d == 3 || a == 3 && c == 3 && b == 1 && d == 1 };
enum { P = a == 1 ? 1 : 3 };
enum { Q = a == 1 ? 3 : 1 };
};
}
template<typename num, int h_, int w_>
struct Mat
{
num data[h_][w_];
template<int Q = w_> typename std::enable_if<equals<Q, 1, 0>::value, num>::type
__inline operator()(int i) const { return data[i][0]; }
template<int P = h_> typename std::enable_if<equals<P, 1, 1>::value, num>::type
__inline operator()(int i) const { return data[0][i]; }
template<int Q = w_> typename std::enable_if<equals<Q, 1, 2>::value, num&>::type
__inline operator()(int i) { return data[i][0]; }
template<int P = h_> typename std::enable_if<equals<P, 1, 3>::value, num&>::type
__inline operator()(int i) { return data[0][i]; }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 1>::value, num>::type
__inline x() const { return operator()(0); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 2>::value, num>::type
__inline y() const { return operator()(1); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 3>::value, num>::type
__inline z() const { return operator()(2); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 4>::value, num>::type
__inline w() const { return operator()(3); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 1>::value, num&>::type
__inline x() { return operator()(0); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 2>::value, num&>::type
__inline y() { return operator()(1); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 3>::value, num&>::type
__inline z() { return operator()(2); }
template<int P = h_, int Q = w_> typename std::enable_if<maybe_add_swizzle<P, Q, 4>::value, num&>::type
__inline w() { return operator()(3); }
template<int R, int S, int P = h_, int Q = w_>
typename std::enable_if<is_vector_pair<R, S, P, Q>::value, num>::type
__inline dot(const Mat<num, R, S>& p2) const {
num ret = 0;
constexpr int len = vector_len<R, S>::value;
for (int i = 0; i < len; i++)
ret += operator()(i) * p2.operator ()(i);
return ret;
}
template<int R, int S, int P = h_, int Q = w_>
typename std::enable_if<is_dim3<P, Q, R, S>::value, Mat<num, is_dim3<P, Q, R, S>::P, is_dim3<P, Q, R, S>::Q>>::type
__inline cross(const Mat<num, R, S>& p2) const
{
return Mat<num, R, S>({y() * p2.z() - p2.y() * z(),
p2.x() * z() - x() * p2.z(),
x() * p2.y() - y() * p2.x()});
}
Mat<num, h_, w_> operator+(const Mat<num, h_, w_>& other) const
{
Mat<num, h_, w_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w; i++)
ret(j, i) = this->operator ()(j, i) + other(j, i);
return ret;
}
Mat<num, h_, w_> operator-(const Mat<num, h_, w_>& other) const
{
Mat<num, h_, w_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
ret(j, i) = this->operator ()(j, i) - other(j, i);
return ret;
}
Mat<num, h_, w_> operator+(const num& other) const
{
Mat<num, h_, w_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w; i++)
ret(j, i) = this->operator ()(j, i) + other;
return ret;
}
Mat<num, h_, w_> operator-(const num& other) const
{
Mat<num, h_, w_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
ret(j, i) = this->operator ()(j, i) - other;
return ret;
}
Mat<num, w_, h_> operator*(const num& other) const
{
Mat<num, h_, w_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
ret(j, i) = operator()(j, i) * other;
return ret;
}
template<int p>
Mat<num, w_, p> operator*(const Mat<num, w_, p>& other) const
{
Mat<num, w_, p> ret;
for (int j = 0; j < w_; j++)
for (int i = 0; i < p; i++)
{
num sum = num(0);
for (int k = 0; k < h_; k++)
sum += data[j][k]*other.data[k][i];
ret.data[j][i] = sum;
}
return ret;
}
__inline num operator()(int j, int i) const { return data[j][i]; }
__inline num& operator()(int j, int i) { return data[j][i]; }
Mat(std::initializer_list<num>&& list)
{
auto iter = list.begin();
for (int i = 0; i < h_; i++)
for (int j = 0; j < w_; j++)
data[i][j] = *iter++;
}
Mat()
{
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
data[j][i] = 0;
}
Mat(const num* mem)
{
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
data[j][i] = mem[i*h_+j];
}
// XXX add more operators as needed, third-party dependencies mostly
// not needed merely for matrix algebra -sh 20141030
static Mat<num, h_, h_> eye()
{
Mat<num, h_, h_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
ret.data[j][i] = 0;
for (int i = 0; i < h_; i++)
ret.data[i][i] = 1;
return ret;
}
Mat<num, w_, h_> t() const
{
Mat<num, w_, h_> ret;
for (int j = 0; j < h_; j++)
for (int i = 0; i < w_; i++)
ret.data[i][j] = data[j][i];
return ret;
}
template<int h__, int w__> using dmat = Mat<double, h__, w__>;
// http://stackoverflow.com/a/18436193
static dmat<3, 1> rmat_to_euler(const dmat<3, 3>& R)
{
static constexpr double pi = 3.141592653;
const double up = 90 * pi / 180.;
static constexpr double bound = 1. - 2e-4;
if (R(0, 2) > bound)
{
double roll = atan(R(1, 0) / R(2, 0));
return dmat<3, 1>({0., up, roll});
}
if (R(0, 2) < -bound)
{
double roll = atan(R(1, 0) / R(2, 0));
return dmat<3, 1>({0., -up, roll});
}
double pitch = asin(-R(0, 2));
double roll = atan2(R(1, 2), R(2, 2));
double yaw = atan2(R(0, 1), R(0, 0));
return dmat<3, 1>({yaw, pitch, roll});
}
// tait-bryan angles, not euler
static dmat<3, 3> euler_to_rmat(const double* input)
{
static constexpr double pi = 3.141592653;
auto H = input[0] * pi / 180;
auto P = input[1] * pi / 180;
auto B = input[2] * pi / 180;
const auto c1 = cos(H);
const auto s1 = sin(H);
const auto c2 = cos(P);
const auto s2 = sin(P);
const auto c3 = cos(B);
const auto s3 = sin(B);
double foo[] = {
// z
c1 * c2,
c1 * s2 * s3 - c3 * s1,
s1 * s3 + c1 * c3 * s2,
// y
c2 * s1,
c1 * c3 + s1 * s2 * s3,
c3 * s1 * s2 - c1 * s3,
// x
-s2,
c2 * s3,
c2 * c3
};
return dmat<3, 3>(foo);
}
};
template<int h_, int w_> using dmat = Mat<double, h_, w_>;
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