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//
// Created by Keuin on 2022/4/11.
//
#include <cmath>
static inline bool eq(int a, int b) {
return a == b;
}
static inline bool eq(double a, double b) {
// FIXME broken on large values
// https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
// https://stackoverflow.com/a/253874/14332799
const double c = a - b;
return c <= 1e-14 && c >= -1e-14;
}
// 3-dim vector
template<typename T>
struct vec3 {
T x;
T y;
T z;
vec3 operator+(vec3 &b) const {
return vec3{.x=x + b.x, .y=y + b.y, .z=z + b.z};
}
vec3 operator-() const {
return vec3{.x = -x, .y = -y, .z = -z};
}
vec3 operator-(vec3 &b) const {
return vec3{.x=x - b.x, .y=y - b.y, .z=z - b.z};
}
// cross product
vec3 operator*(vec3 &b) const {
return vec3{.x=y * b.z - z * b.y, .y=x * b.z - z * b.x, .z=x * b.y - y * b.x};
}
bool operator==(vec3 b) const {
return eq(x, b.x) && eq(y, b.y) && eq(z, b.z);
}
// dot product
int dot(vec3 &b) const {
return x * b.x + y * b.y + z * b.z;
}
// norm value
int norm(int level = 2) const {
if (level == 2) {
return std::abs(x * x + y * y + z * z);
} else if (level == 1) {
return std::abs(x + y + z);
} else {
return (int) std::abs(powl(x, level) + powl(y, level) + powl(z, level));
}
}
};
// 3-dim vector (int)
using vec3i = vec3<int>;
// 3-dim vector (long long)
using vec3l = vec3<long long>;
// 3-dim vector (float)
using vec3f = vec3<float>;
// 3-dim vector (double)
using vec3d = vec3<double>;
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