#pragma once
#include <math.hfa>
#include <iostream.hfa>

struct vec2 {
    float x, y;
};

// Constructors

void ?{}( vec2 & v, float x, float y) {
    v.[x, y] = [x, y];
}
void ?{}(vec2& vec, zero_t) with (vec) {
    x = y = 0;
}
void ?{}(vec2& vec, float val) with (vec) {
    x = y = val;
}
void ?{}(vec2& vec, vec2& other) with (vec) {
    [x,y] = other.[x,y];
}

// Assignment
void ?=?(vec2& vec, const vec2& other) with (vec) {
    [x,y] = other.[x,y];
}

// Primitive mathematical operations

// Subtraction
vec2 ?-?(const vec2& u, const vec2& v) {
    return [u.x - v.x, u.y - v.y];
}
vec2& ?-=?(vec2& u, const vec2& v) {
    u = u - v;
    return u;
}
vec2 -?(const vec2& v) with (v) {
    return [-x, -y];
}

// Addition
vec2 ?+?(const vec2& u, const vec2& v) {
    return [u.x + v.x, u.y + v.y];
}
vec2& ?+=?(vec2& u, const vec2& v) {
    u = u + v;
    return u;
}

// Scalar Multiplication
vec2 ?*?(const vec2& v, float scalar) with (v) {
    return [x * scalar, y * scalar];
}
vec2& ?*=?(vec2& v, float scalar) with (v) {
    v = v * scalar;
    return v;
}
vec2 ?*?(float scalar, const vec2& v) {
    return v * scalar;
}


// Scalar Division
vec2 ?/?(const vec2& v, float scalar) with (v) {
    return [x / scalar, y / scalar];
}
vec2& ?/=?(vec2& v, float scalar) with (v) {
    v = v / scalar;
    return v;
}

// Relational Operators
bool ?==?(const vec2& u, const vec2& v) with (u) {
    return x == v.x && y == v.y;
}
bool ?!=?(const vec2& u, const vec2& v) {
    return !(u == v);
}

// Printing the vector (ostream)
forall( dtype ostype | ostream( ostype ) ) {
    ostype & ?|?( ostype & os, const vec2& v) with (v) {
        if ( sepPrt( os ) ) fmt( os, "%s", sepGetCur( os ) );
        fmt( os, "<%g,%g>", x, y);
        return os;
    }
    void ?|?( ostype & os, const vec2& v ) {
        (ostype &)(os | v); ends( os );
    }
}

/* //---------------------- Geometric Functions ---------------------- */
/* // These functions implement the Geometric Functions section of GLSL for 2D vectors*/

static inline float dot(const vec2& u, const vec2& v) {
    return u.x * v.x + u.y * v.y;
}

static inline float length(const vec2& v) {
   return sqrt(dot(v, v));
}

static inline float distance(const vec2& v1, const vec2& v2) {
    return length(v1 - v2);
}

static inline vec2 normalize(const vec2& v) {
    return v / sqrt(dot(v, v));
}

// Project vector u onto vector v
static inline vec2 project(const vec2& u, const vec2& v) {
    vec2 v_norm = normalize(v);
    return v_norm * dot(u, v_norm);
}

// Reflect incident vector v with respect to surface with normal n
static inline vec2 reflect(const vec2& v, const vec2& n) {
    return v - 2 * project(v, n);
}

// Refract incident vector v with respect to surface with normal n
// eta is the ratio of indices of refraction between starting material and
// entering material (i.e., from air to water, eta = 1/1.33)
static inline vec2 refract(const vec2& v, const vec2& n, float eta) {
    float dotValue = dot(n, v);
    float k = 1 - eta * eta * (1 - dotValue * dotValue);
    if (k < 0) {
        return 0;
    }
    return eta * v - (eta * dotValue + sqrt(k)) * n;
}

// Used to render perturbed surfaces by ensuring that a perturbed normal
// is pointing in the same direction as the geometric normal of the
// surface.
// n is the perturbed vector that we want to align
// i is the incident vector
// ng is the geometric normal of the surface
static inline vec2 faceforward(const vec2& n, const vec2& i, float ng) {
    return dot(n, i) < 0 ? ng : -ng;
}