vector3.h

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// Copyright © 2008-2023 Pioneer Developers. See AUTHORS.txt for details
// Licensed under the terms of the GPL v3. See licenses/GPL-3.txt
 
#ifndef _VECTOR3_H
#define _VECTOR3_H
 
#include "FloatComparison.h"
#include "vector2.h"
#include <math.h>
#include <stdio.h>
 
// Need this pragma due to operator[] implementation.
#pragma pack(4)
 
template <typename T>
class alignas(sizeof(T)) vector3 {
public:
    T x, y, z;
 
    // Constructor definitions are outside class declaration to enforce that
    // only float and double versions are possible.
    vector3() = default;
    vector3(const vector2f &v, T t);
    explicit vector3(const T vals[3]);
    explicit vector3(T val);
    vector3(T _x, T _y, T _z);
 
    // disallow implicit conversion between floating point sizes
    explicit vector3(const vector3<typename other_floating_type<T>::type> &v);
    explicit vector3(const typename other_floating_type<T>::type vals[3]);
 
    const T &operator[](const size_t i) const { return (const_cast<const T *>(&x))[i]; }
    T &operator[](const size_t i) { return (&x)[i]; }
 
    vector3 operator+(const vector3 &a) const { return vector3(a.x + x, a.y + y, a.z + z); }
    vector3 &operator+=(const vector3 &a)
    {
        x += a.x;
        y += a.y;
        z += a.z;
        return *this;
    }
    vector3 &operator-=(const vector3 &a)
    {
        x -= a.x;
        y -= a.y;
        z -= a.z;
        return *this;
    }
    vector3 &operator*=(const float a)
    {
        x *= a;
        y *= a;
        z *= a;
        return *this;
    }
    vector3 &operator*=(const double a)
    {
        x *= a;
        y *= a;
        z *= a;
        return *this;
    }
    vector3 &operator/=(const float a)
    {
        const T inva = T(1.0 / a);
        x *= inva;
        y *= inva;
        z *= inva;
        return *this;
    }
    vector3 &operator/=(const double a)
    {
        const T inva = T(1.0 / a);
        x *= inva;
        y *= inva;
        z *= inva;
        return *this;
    }
    vector3 operator-(const vector3 &a) const { return vector3(x - a.x, y - a.y, z - a.z); }
    vector3 operator-() const { return vector3(-x, -y, -z); }
 
    bool operator==(const vector3 &a) const
    {
        return is_equal_exact(a.x, x) && is_equal_exact(a.y, y) && is_equal_exact(a.z, z);
    }
    bool ExactlyEqual(const vector3 &a) const
    {
        return is_equal_exact(a.x, x) && is_equal_exact(a.y, y) && is_equal_exact(a.z, z);
    }
 
    friend vector3 operator+(const vector3 &a, const T &scalar) { return vector3(a.x + scalar, a.y + scalar, a.z + scalar); }
    friend vector3 operator+(const T scalar, const vector3 &a) { return a + scalar; }
    friend vector3 operator-(const vector3 &a, const T &scalar) { return vector3(a.x - scalar, a.y - scalar, a.z - scalar); }
    friend vector3 operator-(const T scalar, const vector3 &a) { return a - scalar; }
 
    friend vector3 operator*(const vector3 &a, const vector3 &b) { return vector3(T(a.x * b.x), T(a.y * b.y), T(a.z * b.z)); }
    friend vector3 operator*(const vector3 &a, const T scalar) { return vector3(T(a.x * scalar), T(a.y * scalar), T(a.z * scalar)); }
    //friend vector3 operator*(const vector3 &a, const double scalar) { return vector3(T(a.x*scalar), T(a.y*scalar), T(a.z*scalar)); }
    friend vector3 operator*(const T scalar, const vector3 &a) { return a * scalar; }
    //friend vector3 operator*(const double scalar, const vector3 &a) { return a*scalar; }
    friend vector3 operator/(const vector3 &a, const float scalar)
    {
        const T inv = 1.0 / scalar;
        return vector3(a.x * inv, a.y * inv, a.z * inv);
    }
    friend vector3 operator/(const vector3 &a, const double scalar)
    {
        const T inv = 1.0 / scalar;
        return vector3(a.x * inv, a.y * inv, a.z * inv);
    }
    friend vector3 operator/(const T scalar, const vector3 &a)
    {
        return vector3(scalar / a.x, scalar / a.y, scalar / a.z);
    }
 
    vector3 Cross(const vector3 &b) const { return vector3(y * b.z - z * b.y, z * b.x - x * b.z, x * b.y - y * b.x); }
    T Dot(const vector3 &b) const { return x * b.x + y * b.y + z * b.z; }
    T Length() const { return sqrt(x * x + y * y + z * z); }
    T LengthSqr() const { return x * x + y * y + z * z; }
    vector3 Lerp(const vector3 &b, const double percent) const
    {
        return *this + percent * (b - *this);
    }
    vector3 Normalized() const
    {
        const T l = 1.0f / sqrt(x * x + y * y + z * z);
        return vector3(x * l, y * l, z * l);
    }
    vector3 NormalizedSafe() const
    {
        const T lenSqr = x * x + y * y + z * z;
        if (lenSqr < 1e-18) // sqrt(lenSqr) < 1e-9
            return vector3(1, 0, 0);
        else {
            const T l = sqrt(lenSqr);
            return vector3(x / l, y / l, z / l);
        }
    }
 
    void Print() const { printf("v(%f,%f,%f)\n", x, y, z); }
 
    /* Rotate this vector about point o, in axis defined by v. */
    void ArbRotateAroundPoint(const vector3 &o, const vector3 &__v, T ang)
    {
        vector3 t;
        T a = o.x;
        T b = o.y;
        T c = o.z;
        T u = __v.x;
        T v = __v.y;
        T w = __v.z;
        T cos_a = cos(ang);
        T sin_a = sin(ang);
        T inv_poo = 1.0f / (u * u + v * v + w * w);
        t.x = a * (v * v + w * w) + u * (-b * v - c * w + u * x + v * y + w * z) + (-a * (v * v + w * w) + u * (b * v + c * w - v * y - w * z) + (v * v + w * w) * x) * cos_a +
            sqrtf(u * u + v * v + w * w) * (-c * v + b * w - w * y + v * z) * sin_a;
        t.x *= inv_poo;
        t.y = b * (u * u + w * w) + v * (-a * u - c * w + u * x + v * y + w * z) + (-b * (u * u + w * w) + v * (a * u + c * w - u * x - w * z) + (u * u + w * w) * y) * cos_a +
            sqrtf(u * u + v * v + w * w) * (-c * u - a * w + w * x - u * z) * sin_a;
        t.y *= inv_poo;
        t.z = c * (u * u + v * v) + w * (-a * u + b * v + u * x + v * y + w * z) + (-c * (u * u + v * v) + w * (a * u + b * v - u * x - v * y) + (u * u + v * v) * z) * cos_a +
            sqrtf(u * u + v * v + w * w) * (-b * u + a * v - v * x + u * y) * sin_a;
        t.z *= inv_poo;
        *this = t;
    }
 
    /* Rotate this vector about origin, in axis defined by v. */
    void ArbRotate(const vector3 &__v, T ang)
    {
        vector3 t;
        T u = __v.x;
        T v = __v.y;
        T w = __v.z;
        T cos_a = cos(ang);
        T sin_a = sin(ang);
        T inv_poo = 1.0f / (u * u + v * v + w * w);
        t.x = u * (u * x + v * y + w * z) + (u * (-v * y - w * z) + (v * v + w * w) * x) * cos_a +
            sqrtf(u * u + v * v + w * w) * (-w * y + v * z) * sin_a;
        t.x *= inv_poo;
        t.y = v * (u * x + v * y + w * z) + (v * (-u * x - w * z) + (u * u + w * w) * y) * cos_a +
            sqrtf(u * u + v * v + w * w) * (w * x - u * z) * sin_a;
        t.y *= inv_poo;
        t.z = w * (u * x + v * y + w * z) + (w * (-u * x - v * y) + (u * u + v * v) * z) * cos_a +
            sqrtf(u * u + v * v + w * w) * (-v * x + u * y) * sin_a;
        t.z *= inv_poo;
        *this = t;
    }
 
    void xy(const vector2<T> &v2)
    {
        x = v2.x;
        y = v2.y;
    }
    void xz(const vector2<T> &v2)
    {
        x = v2.x;
        z = v2.y;
    }
    void yz(const vector2<T> &v2)
    {
        y = v2.x;
        z = v2.y;
    }
 
    vector2<T> xy() { return vector2<T>(x, y); }
    vector2<T> xz() { return vector2<T>(x, z); }
    vector2<T> yz() { return vector2<T>(y, z); }
    vector2<T> yx() { return vector2<T>(y, x); }
    vector2<T> zx() { return vector2<T>(z, x); }
};
 
// These are here in this manner to enforce that only float and double versions are possible.
template <>
inline vector3<float>::vector3(const vector2f &v, float t) :
    x(v.x),
    y(v.y),
    z(t)
{}
template <>
inline vector3<float>::vector3(const vector3<double> &v) :
    x(float(v.x)),
    y(float(v.y)),
    z(float(v.z))
{}
template <>
inline vector3<double>::vector3(const vector3<float> &v) :
    x(v.x),
    y(v.y),
    z(v.z)
{}
template <>
inline vector3<double>::vector3(const vector2f &v, double t) :
    x(v.x),
    y(v.y),
    z(t)
{}
template <>
inline vector3<float>::vector3(float val) :
    x(val),
    y(val),
    z(val)
{}
template <>
inline vector3<double>::vector3(double val) :
    x(val),
    y(val),
    z(val)
{}
template <>
inline vector3<float>::vector3(float _x, float _y, float _z) :
    x(_x),
    y(_y),
    z(_z)
{}
template <>
inline vector3<double>::vector3(double _x, double _y, double _z) :
    x(_x),
    y(_y),
    z(_z)
{}
template <>
inline vector3<float>::vector3(const float vals[3]) :
    x(vals[0]),
    y(vals[1]),
    z(vals[2])
{}
template <>
inline vector3<float>::vector3(const double vals[3]) :
    x(float(vals[0])),
    y(float(vals[1])),
    z(float(vals[2]))
{}
template <>
inline vector3<double>::vector3(const float vals[3]) :
    x(vals[0]),
    y(vals[1]),
    z(vals[2])
{}
template <>
inline vector3<double>::vector3(const double vals[3]) :
    x(vals[0]),
    y(vals[1]),
    z(vals[2])
{}
 
#pragma pack()
 
typedef vector3<float> vector3f;
typedef vector3<double> vector3d;
 
// ensure both packing and structure alignment match the constraints we have set
static_assert(alignof(vector3d) == 8);
static_assert(offsetof(vector3d, y) == 8);
static_assert(offsetof(vector3d, z) == 16);
 
static_assert(alignof(vector3f) == 4);
static_assert(offsetof(vector3f, y) == 4);
static_assert(offsetof(vector3f, z) == 8);
 
#endif /* _VECTOR3_H */