C++20 Euclidean Vector Library

Header-only C++20 library for Euclidean vectors in n-dimensions

General Overview

• Supports basic Euclidean vector operations
• Type flexibility, using C++20 concepts to check for valid scalar types
• Dimension flexibility in favor of performance
• Supports compile-time calculations with constexpr
• Built on std::array
• Heavy use of standard library functions

Example Usage

test.cpp:

#include <complex>
#include <iostream>

#include "euclidean_vector.hpp"

// Overloads the output stream operator to print a Euclidean vector.
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &os, const EucVec<T, N> &vec) {
    os << '<';
    for (auto it = vec.begin(); it != vec.end(); ++it) {
        if (it != vec.begin()) {
            os << ", ";
        }
        os << *it;
    }
    os << '>';

    return os;
}

int main() {
    // Real-valued vectors
    constexpr EucVec<double, 3> v1{1.5, 2.5, 3.5};
    constexpr EucVec<double, 3> v2{4.5, 5.5, 6.5};
    constexpr double s1 = 3.0;

    std::cout << v1 << " + " << v2 << " = " << v1 + v2 << '\n';
    std::cout << v1 << " - " << v2 << " = " << v1 - v2 << '\n';
    std::cout << v1 << " x " << v2 << " = " << v1.cross(v2) << '\n';
    std::cout << v1 << " . " << v2 << " = " << v1.dot(v2) << '\n';
    std::cout << v1 << " * " << s1 << " = " << v1 * s1 << '\n';
    std::cout << "Euclidean norm of " << v1 << ": " << v1.norm() << '\n';
    std::cout << "3-norm of " << v1 << ": " << v1.norm<3>() << '\n';
    std::cout << "Normalized vector " << v1 << ": " << v1.normalize<3>()
              << '\n';
    std::cout << "Distance between " << v1 << " and " << v2 << ": "
              << v1.dist_to(v2) << '\n';
    std::cout << "Angle between " << v1 << " and " << v2 << ": "
              << v1.radians_between(v2) << " radians" << '\n';
    std::cout << "Projection of " << v1 << " onto " << v2 << ": "
              << v1.project_onto(v2) << '\n';

    // Complex-valued vectors
    using namespace std::complex_literals;
    constexpr EucVec<std::complex<double>, 3> v3{
        std::complex<double>(1.0, 1.0), std::complex<double>(2.0, 2.0),
        std::complex<double>(3.0, 3.0)};
    constexpr EucVec<std::complex<double>, 3> v4{
        std::complex<double>(4.0, 4.0), std::complex<double>(5.0, 5.0),
        std::complex<double>(6.0, 6.0)};
    constexpr std::complex<double> s2{3, 3};

    std::cout << v3 << " + " << v4 << " = " << v3 + v4 << '\n';
    std::cout << v3 << " - " << v4 << " = " << v3 - v4 << '\n';
    std::cout << v3 << " x " << v4 << " = " << v3.cross(v4) << '\n';
    std::cout << v3 << " . " << v4 << " = " << v3.dot(v4) << '\n';
    std::cout << v3 << " * " << s2 << " = " << v3 * s2 << '\n';
    std::cout << "Euclidean norm of " << v3 << ": " << v3.norm() << '\n';

    return 0;
}

Output:

<1.5, 2.5, 3.5> + <4.5, 5.5, 6.5> = <6, 8, 10>
<1.5, 2.5, 3.5> - <4.5, 5.5, 6.5> = <-3, -3, -3>
<1.5, 2.5, 3.5> x <4.5, 5.5, 6.5> = <-3, 6, -3>
<1.5, 2.5, 3.5> . <4.5, 5.5, 6.5> = 43.25
<1.5, 2.5, 3.5> * 3 = <4.5, 7.5, 10.5>
Euclidean norm of <1.5, 2.5, 3.5>: 4.55522
3-norm of <1.5, 2.5, 3.5>: 3.95523
Normalized vector <1.5, 2.5, 3.5>: <0.379245, 0.632075, 0.884904>
Distance between <1.5, 2.5, 3.5> and <4.5, 5.5, 6.5>: 5.19615
Angle between <1.5, 2.5, 3.5> and <4.5, 5.5, 6.5>: 0.1683 radians
Projection of <1.5, 2.5, 3.5> onto <4.5, 5.5, 6.5>: <2.09838, 2.56469, 3.031>
<(1,1), (2,2), (3,3)> + <(4,4), (5,5), (6,6)> = <(5,5), (7,7), (9,9)>
<(1,1), (2,2), (3,3)> - <(4,4), (5,5), (6,6)> = <(-3,-3), (-3,-3), (-3,-3)>
<(1,1), (2,2), (3,3)> x <(4,4), (5,5), (6,6)> = <(0,-6), (0,12), (0,-6)>
<(1,1), (2,2), (3,3)> . <(4,4), (5,5), (6,6)> = (0,64)
<(1,1), (2,2), (3,3)> * (3,3) = <(0,6), (0,12), (0,18)>

License

Licensed under the MIT license.