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**Chapter 2: The vec3 Class** Almost all graphics programs have some class(es) for storing geometric vectors and colors. In many systems these vectors are 4D (3D plus a homogeneous coordinate for geometry, and RGB plus an alpha transparency channel for colors). For our purposes, three coordinates suffices. We’ll use the same class `vec3` for colors, locations, directions, offsets, whatever. Some people don’t like this because it doesn’t prevent you from doing something silly, like adding a color to a location. They have a good point, but we’re going to always take the “less code” route when not obviously wrong. Here’s the top part of my vec3 class: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ #include #include #include class vec3 { public: vec3() {} vec3(float e0, float e1, float e2) { e[0] = e0; e[1] = e1; e[2] = e2; } inline float x() const { return e[0]; } inline float y() const { return e[1]; } inline float z() const { return e[2]; } inline float r() const { return e[0]; } inline float g() const { return e[1]; } inline float b() const { return e[2]; } inline const vec3& operator+() const { return *this; } inline vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); } inline float operator[](int i) const { return e[i]; } inline float& operator[](int i) { return e[i]; } inline vec3& operator+=(const vec3 &v2); inline vec3& operator-=(const vec3 &v2); inline vec3& operator*=(const vec3 &v2); inline vec3& operator/=(const vec3 &v2); inline vec3& operator*=(const float t); inline vec3& operator/=(const float t); inline float length() const { return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]); } inline float squared_length() const { return e[0]*e[0] + e[1]*e[1] + e[2]*e[2]; } inline void make_unit_vector(); float e[3]; }; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I use floats here, but in some ray tracers I have used doubles. Neither is correct -- follow your own tastes. Everything is in the header file, and later on in the file are lots of vector operations: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ inline std::istream& operator>>(std::istream &is, vec3 &t) { is >> t.e[0] >> t.e[1] >> t.e[2]; return is; } inline std::ostream& operator<<(std::ostream &os, const vec3 &t) { os << t.e[0] << " " << t.e[1] << " " << t.e[2]; return os; } inline void vec3::make_unit_vector() { float k = 1.0 / sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]); e[0] *= k; e[1] *= k; e[2] *= k; } inline vec3 operator+(const vec3 &v1, const vec3 &v2) { return vec3(v1.e[0] + v2.e[0], v1.e[1] + v2.e[1], v1.e[2] + v2.e[2]); } inline vec3 operator-(const vec3 &v1, const vec3 &v2) { return vec3(v1.e[0] - v2.e[0], v1.e[1] - v2.e[1], v1.e[2] - v2.e[2]); } inline vec3 operator*(const vec3 &v1, const vec3 &v2) { return vec3(v1.e[0] * v2.e[0], v1.e[1] * v2.e[1], v1.e[2] * v2.e[2]); } inline vec3 operator/(const vec3 &v1, const vec3 &v2) { return vec3(v1.e[0] / v2.e[0], v1.e[1] / v2.e[1], v1.e[2] / v2.e[2]); } inline vec3 operator*(float t, const vec3 &v) { return vec3(t*v.e[0], t*v.e[1], t*v.e[2]); } inline vec3 operator/(vec3 v, float t) { return vec3(v.e[0]/t, v.e[1]/t, v.e[2]/t); } inline vec3 operator*(const vec3 &v, float t) { return vec3(t*v.e[0], t*v.e[1], t*v.e[2]); } inline float dot(const vec3 &v1, const vec3 &v2) { return v1.e[0] *v2.e[0] + v1.e[1] *v2.e[1] + v1.e[2] *v2.e[2]; } inline vec3 cross(const vec3 &v1, const vec3 &v2) { return vec3(v1.e[1] * v2.e[2] - v1.e[2] * v2.e[1], v1.e[2] * v2.e[0] - v1.e[0] * v2.e[2], v1.e[0] * v2.e[1] - v1.e[1] * v2.e[0]); } inline vec3& vec3::operator+=(const vec3 &v){ e[0] += v.e[0]; e[1] += v.e[1]; e[2] += v.e[2]; return *this; } inline vec3& vec3::operator*=(const vec3 &v){ e[0] *= v.e[0]; e[1] *= v.e[1]; e[2] *= v.e[2]; return *this; } inline vec3& vec3::operator/=(const vec3 &v){ e[0] /= v.e[0]; e[1] /= v.e[1]; e[2] /= v.e[2]; return *this; } inline vec3& vec3::operator-=(const vec3& v) { e[0] -= v.e[0]; e[1] -= v.e[1]; e[2] -= v.e[2]; return *this; } inline vec3& vec3::operator*=(const float t) { e[0] *= t; e[1] *= t; e[2] *= t; return *this; } inline vec3& vec3::operator/=(const float t) { float k = 1.0/t; e[0] *= k; e[1] *= k; e[2] *= k; return *this; } inline vec3 unit_vector(vec3 v) { return v / v.length(); } ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Now we can change our main to use this: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ #include #include "vec3.h" int main() { int nx = 200; int ny = 100; std::cout << "P3\n" << nx << " " << ny << "\n255\n"; for (int j = ny-1; j >= 0; j--) { for (int i = 0; i < nx; i++) { vec3 col(float(i) / float(nx), float(j) / float(ny), 0.2); int ir = int(255.99*col[0]); int ig = int(255.99*col[1]); int ib = int(255.99*col[2]); std::cout << ir << " " << ig << " " << ib << "\n"; } } } ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~