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/* vector.hpp
* Part of Mathematical library built (ab)using Modern C++ 17 abstractions.
*
* This library is not intended to be _performant_, it does not contain
* hand written SMID / SSE / AVX optimizations. It is instead an example
* of highly abstracted code, where Vectors can contain any data type.
*
* As a challenge, the vector data structure has been built on a container
* of static capacity. But if a dynamic base container is needed, the code
* should be easily modifiable to add further abstraction, by templating
* the container, and by consequence the allocator.
*
* Naoki Pross <naopross@thearcway.org>
* 2018 ~ 2019
*/
#include <iostream>
#include <cassert>
#include <cmath>
#include <array>
#include <algorithm>
#include <numeric>
#include <complex>
#include <initializer_list>
namespace mm {
// generic implementation
template<typename T, std::size_t d>
struct basic_vec;
// usable specializations
template<typename T, std::size_t d>
struct vec;
template<typename T>
struct vec3;
template<typename T>
struct vec2;
}
template<typename T, std::size_t d>
struct mm::basic_vec : public std::array<T, d> {
using type = T;
static constexpr std::size_t dimensions = d;
// TODO: template away these
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>
mm::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>
mm::basic_vec<T, d>::basic_vec(const std::initializer_list<T> l) {
// construct with empty values
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>
mm::basic_vec<T, d>::basic_vec(const mm::basic_vec<T, n>& other) {
// construct with empty values
basic_vec();
static_assert(
d >= n,
"cannot copy higher dimensional vector into a smaller one"
);
std::copy(other.begin(), other.end(), this->begin());
}
template<typename T, std::size_t d>
T mm::basic_vec<T, d>::length() const {
return std::sqrt(std::accumulate(this->begin(), this->end(),
basic_vec<T, d>::null_element,
[](const T& init, const T& val) -> T {
return init + val * val;
}
));
}
template<typename T, std::size_t d>
mm::basic_vec<T, d> operator+(const mm::basic_vec<T, d>& rhs, const mm::basic_vec<T, d>& lhs) {
mm::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>
mm::basic_vec<T, d> operator*(const mm::basic_vec<T, d>& rhs, const T& lhs) {
return lhs * rhs;
}
template<typename T, std::size_t d>
mm::basic_vec<T, d> operator*(const T& rhs, const mm::basic_vec<T, d>& lhs) {
mm::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>
mm::basic_vec<T, d> operator-(const mm::basic_vec<T, d>& rhs, const mm::basic_vec<T, d>& lhs) {
return rhs + mm::basic_vec<T, d>::unit_additive_inverse_element * lhs;
}
template<typename T, std::size_t d>
T operator*(const mm::basic_vec<T, d>& rhs, const mm::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 mm::basic_vec<T, d>& v) {
os << "<";
std::for_each(v.begin(), v.end() -1, [&](const T& el) {
os << el << ", ";
});
os << v.back() << ">";
return os;
}
// actual classes to use in your code
template<typename T, std::size_t d>
class mm::vec: public mm::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) {}
};
// three dimensional specialization with a static cross product
template<typename T>
class mm::vec3 : public mm::basic_vec<T, 3> {
public:
vec3() : basic_vec<T, 3>() {}
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) {}
T& x() { return this->at(0); }
T& y() { return this->at(1); }
T& z() { return this->at(2); }
const T& x() const { return this->at(0); }
const T& y() const { return this->at(1); }
const T& z() const { return this->at(2); }
T zenith() const;
T azimuth() const;
vec3<T> spherical() const;
static vec3<T> cross(const vec3<T>& rhs, const vec3<T>& lhs);
};
template<typename T>
T mm::vec3<T>::zenith() const {
return std::acos(this->z() / this->length());
}
template<typename T>
T mm::vec3<T>::azimuth() const {
return std::atan(this->y() / this->x());
}
template<typename T>
mm::vec3<T> mm::vec3<T>::spherical() const {
return mm::vec3<T> {
this->length(),
this->zenith(),
this->azimuth(),
};
}
template<typename T>
mm::vec3<T> mm::vec3<T>::cross(const vec3<T>& rhs, const vec3<T>& lhs) {
mm::vec3<T> res;
res.x() = (rhs.y() * lhs.z()) - (rhs.z() * lhs.y());
res.y() = (rhs.z() * lhs.x()) - (rhs.x() * lhs.z());
res.z() = (rhs.x() * lhs.y()) - (rhs.y() * lhs.x());
return res;
}
// two dimensional specialization with a polar conversion
template<typename T>
class mm::vec2: public mm::basic_vec<T, 2> {
public:
vec2() : basic_vec<T, 2>() {}
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& x() { return this->at(0); }
T& y() { return this->at(1); }
const T& x() const { return this->at(0); }
const T& y() const { return this->at(1); }
T angle() const;
vec2<T> polar() const;
static vec3<T> cross(const vec2<T>& rhs, const vec2<T>& lhs);
};
template<typename T>
T mm::vec2<T>::angle() const {
return std::atan(this->y() / this->x());
}
template<typename T>
mm::vec2<T> mm::vec2<T>::polar() const {
return mm::vec2 {
this->length(),
this->angle()
};
}
template<typename T>
mm::vec3<T> mm::vec2<T>::cross(const mm::vec2<T>& rhs, const mm::vec2<T>& lhs) {
return mm::vec3<T>::cross(mm::vec3<T>(rhs), mm::vec3<T>(lhs));
}
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