Трёхкомпонентный вектор

vec3.cpp

#include <cmath>
#include <ostream>

// Трёхкомпонентный вектор
struct vec3
{
    double x, y, z;

    // Длина вектора
    double length() const {
        return std::sqrt(dot(*this));
    }

    // Нормализовать вектор
    void normalize() {
        *this *= 1 / length();
    }

    // Скалярное произведение
    double dot(const vec3& b) const {
        return x*b.x + y*b.y + z*b.z;
    }

    // Повернуть вектор вокруг b на угол t
    void turn_around(const vec3& b, const double t) {
        turn_around_sin(b, std::sin(t));
    }

    // Повернуть вектор вокруг b на угол, синус которого равен sin_t
    void turn_around_sin(vec3 b, const double sin_t) {
        const double cos_t = std::sqrt(1 - sin_t*sin_t);
        b.normalize();
        *this = {
            (cos_t+(1-cos_t)*b.x*b.x)*x + ((1-cos_t)*b.x*b.y-sin_t*b.z)*y + ((1-cos_t)*b.x*b.z+sin_t*b.y)*z,
            ((1-cos_t)*b.y*b.x+sin_t*b.z)*x + (cos_t+(1-cos_t)*b.y*b.y)*y + ((1-cos_t)*b.y*b.z-sin_t*b.x)*z,
            ((1-cos_t)*b.z*b.x-sin_t*b.y)*x + ((1-cos_t)*b.z*b.y+sin_t*b.x)*y + (cos_t+(1-cos_t)*b.z*b.z)*z
        };
    }

    // Векторное произведение
    vec3& operator*=(const vec3& b);

    // Умножение на число
    vec3& operator*=(const double n);
}; // vec3

// Произведения
vec3 operator*(const vec3& a, const vec3& b)
{
    return { a.y*b.z - b.y*a.z, a.z*b.x - b.z*a.x, a.x*b.y - b.x*a.y };
}

vec3 operator*(const vec3& a, const double n)
{
    return { a.x*n, a.y*n, a.z*n };
}

vec3& vec3::operator*=(const vec3& b)
{
    *this = *this * b;
    return *this;
}

vec3& vec3::operator*=(const double n)
{
    *this = *this * n;
    return *this;
}

// Сравнение векторов
bool operator==(const vec3& a, const vec3& b)
{
    return (a.x == b.x && a.y == b.y && a.z == b.z);
}

bool operator!=(const vec3& a, const vec3& b)
{
    return !(a == b);
}

// Вывод вектора в поток
std::ostream& operator<<(std::ostream& str, const vec3& a)
{
    str << "{ " << a.x << ", " << a.y << ", " << a.z << " }";
    return str;
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

#include <iostream>

using std::cout;
using std::endl;

void test1()
{
    cout << "TEST1:" << endl;

    vec3 a = { 0, 0, 1 };
    vec3 b = { 0.3, 0.5, 0.7 };
    b.normalize();
    cout << "a = " << a << endl;
    cout << "b = " << b << endl;

    vec3 c = a * b;
    double sin_t = c.length();
    cout << "a * b = " << c << endl;
    cout << "sin_t = " << sin_t << endl;

    a.turn_around_sin(c, sin_t);
    cout << std::fixed;
    cout << "turn a (sin_t) = " << a << endl;

    a.turn_around_sin(c, -sin_t);
    cout << "turn a (-sin_t) = " << a << endl;
}

void test2()
{
    cout << "TEST2:" << endl;

    vec3 a = { 2, 3, 4 };
    vec3 b = { 0, 0, 1 };
    vec3 b1 = { 1, 0, 0 };
//    b.normalize();
//    b1.normalize();
    cout << "a = " << a << endl;
    cout << "b = " << b << endl;
    cout << "b1 = " << b1 << endl;

    vec3 bn = b * b1;
    double sin_t = bn.length();
    cout << "b * b1 = " << bn << endl;
    cout << "sin_t = " << sin_t << endl;

    a.turn_around_sin(bn, sin_t);
    cout << std::fixed;
    cout << "turn a (sin_t) = " << a << endl;

    a.turn_around_sin(bn, -sin_t);
    cout << "turn a (-sin_t) = " << a << endl;
}


int main()
{
    test1();
    cout << endl;
    test2();
}