Graphics & neural rendering

#include <cmath>
#include <print>

struct vec3 { float x = 0, y = 0, z = 0; };

constexpr vec3 operator-(vec3 a, vec3 b) { return {a.x - b.x, a.y - b.y, a.z - b.z}; }
constexpr vec3 operator/(vec3 a, float s) { return {a.x / s, a.y / s, a.z / s}; }
constexpr float dot(vec3 a, vec3 b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
constexpr vec3 cross(vec3 a, vec3 b) {
    return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
}
inline vec3 normalize(vec3 a) {
    float len = std::sqrt(dot(a, a));
    return len > 0.0f ? a / len : vec3{};   // zero stays zero: no NaN
}

static_assert(cross({1, 0, 0}, {0, 1, 0}).z == 1.0f);   // right-handed

int main() {
    // Triangle normal: counter-clockwise vertices seen from the front.
    vec3 p0{0, 0, 0}, p1{1, 0, 0}, p2{0, 1, 0};
    vec3 n = normalize(cross(p1 - p0, p2 - p0));
    std::println("n = ({}, {}, {})", n.x, n.y, n.z);
    // A degenerate (zero-area) triangle:
    vec3 d = normalize(cross(p1 - p0, p1 - p0));
    std::println("degenerate = ({}, {}, {})", d.x, d.y, d.z);
}