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#include <iostream>
#include <cassert>
#include <cmath>
#include <array>
#include <algorithm>
#include <numeric>
#include <initializer_list>
template<typename T, std::size_t d>
struct basic_vec : public std::array<T, d> {
static constexpr std::size_t dimensions = d;
static constexpr T null_element = static_cast<T>(0);
static constexpr T unit_element = static_cast<T>(1);
static constexpr T unit_additive_inverse_element = static_cast<T>(-1);
basic_vec();
basic_vec(const std::initializer_list<T> l);
template<std::size_t n> basic_vec(const basic_vec<T, n>& other);
T length() const;
};
template<typename T, std::size_t d>
basic_vec<T, d>::basic_vec() : std::array<T, d>() {
this->fill(basic_vec<T,d>::null_element);
}
template<typename T, std::size_t d>
basic_vec<T, d>::basic_vec(const std::initializer_list<T> l) {
basic_vec();
// why can't this sh*t be a constexpr with static_assert???
assert(l.size() <= d);
std::copy(l.begin(), l.end(), this->begin());
}
template<typename T, std::size_t d>
template<std::size_t n>
basic_vec<T, d>::basic_vec(const basic_vec<T, n>& other) {
basic_vec();
static_assert(d >= n);
for (std::size_t i = 0; i < n; i++) {
this->at(i) = other.at(i);
}
}
template<typename T, std::size_t d>
T basic_vec<T, d>::length() const {
T res = basic_vec<T, d>::null_element;
for (const T& val : *this) {
res += val * val;
}
return res;
}
template<typename T, std::size_t d>
basic_vec<T, d> operator+(const basic_vec<T, d>& rhs, const basic_vec<T, d>& lhs) {
basic_vec<T, d> out;
std::transform(rhs.begin(), rhs.end(), lhs.begin(), out.begin(),
[](const T& r, const T& l) -> T {
return r + l;
}
);
return out;
}
template<typename T, std::size_t d>
basic_vec<T, d> operator*(const T& rhs, const basic_vec<T, d>& lhs) {
basic_vec<T, d> out;
std::transform(lhs.begin(), lhs.end(), out.begin(),
[rhs](const T& t) -> T {
return t * rhs;
});
return out;
}
template<typename T, std::size_t d>
basic_vec<T, d> operator-(const basic_vec<T, d>& rhs, const basic_vec<T, d>& lhs) {
return rhs + basic_vec<T, d>::unit_additive_inverse_element * lhs;
}
template<typename T, std::size_t d>
T operator*(const basic_vec<T, d>& rhs, const basic_vec<T, d>& lhs) {
return std::inner_product(rhs.begin(), rhs.end(), lhs.begin(), 0);
}
template<typename T, std::size_t d>
std::ostream& operator<<(std::ostream& os, const basic_vec<T, d>& v) {
os << "<";
for (std::size_t i = 0; i < d -1; i++) {
os << v[i] << ", ";
}
os << v[d-1] << ">";
return os;
}
template<typename T, std::size_t d>
class vec: public basic_vec<T, d> {
public:
vec(std::initializer_list<T> l) : basic_vec<T, d>(l) {}
template<std::size_t n>
vec(const basic_vec<T, n>& other) : basic_vec<T, d>(other) {}
};
template<typename T>
class vec3 : public basic_vec<T, 3> {
public:
vec3(std::initializer_list<T> l) : basic_vec<T, 3>(l) {}
template<std::size_t n>
vec3(const basic_vec<T, n>& other) : basic_vec<T, 3>(other) {}
static vec3<T> cross(const vec3<T>& rhs, const vec3<T>& lhs);
};
template<typename T>
vec3<T> vec3<T>::cross(const vec3<T>& rhs, const vec3<T>& lhs) {
vec3<T> res;
res[0] = (rhs[1] * lhs[2]) - (rhs[2] * lhs[1]);
res[1] = (rhs[2] * lhs[0]) - (rhs[0] * lhs[2]);
res[2] = (rhs[0] * lhs[1]) - (rhs[1] * lhs[0]);
return res;
}
template<typename T>
class vec2: public basic_vec<T, 2> {
public:
vec2(std::initializer_list<T> l) : basic_vec<T, 2>(l) {}
template<std::size_t n>
vec2(const basic_vec<T, n>& other) : basic_vec<T, 2>(other) {}
T polar();
static vec3<T> cross(const vec2<T>& rhs, const vec2<T>& lhs);
};
template<typename T>
T vec2<T>::polar() {
return std::atan2(this->at(0), this->at(1));
}
template<typename T>
vec3<T> vec2<T>::cross(const vec2<T>& rhs, const vec2<T>& lhs) {
return vec3<T>::cross(vec3<T>(rhs), vec3<T>(lhs));
}
int main(int argc, char *argv[]) {
vec3<double> v{1, 2, 3};
vec3<double> u{3, 4, 5};
std::cout << v << std::endl;
std::cout << v.length() << std::endl;
std::cout << v + u << std::endl;
std::cout << v - u << std::endl;
std::cout << 2.0 * u << std::endl;
std::cout << v * u << std::endl;
return 0;
}
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