interval.h

浏览该文件的文档.

#pragma once
#include <cmath>
#include <limits>
#include <algorithm>
 
namespace vde::foundation {
 
class Interval {
public:
    double lo, hi;
 
    Interval() : lo(0), hi(0) {}
 
    Interval(double v) : lo(v), hi(v) {}
 
    Interval(double l, double h) : lo(std::min(l,h)), hi(std::max(l,h)) {}
 
    [[nodiscard]] double mid() const { return (lo + hi) * 0.5; }
 
    [[nodiscard]] double width() const { return hi - lo; }
 
    [[nodiscard]] bool contains(double v) const { return lo <= v && v <= hi; }
 
    [[nodiscard]] bool is_exact(double eps = 1e-12) const { return width() < eps; }
 
    [[nodiscard]] bool overlaps(const Interval& o) const {
        return !(hi < o.lo || o.hi < lo);
    }
 
    [[nodiscard]] int cmp(const Interval& o) const {
        if (hi < o.lo) return -1;  // 确定 this < o
        if (lo > o.hi) return 1;   // 确定 this > o
        return 0;                   // 不确定（区间重叠）
    }
 
    // ── 算术运算 ──
 
    Interval operator+(const Interval& o) const {
        return {lo + o.lo, hi + o.hi};
    }
 
    Interval operator-(const Interval& o) const {
        return {lo - o.hi, hi - o.lo};
    }
 
    Interval operator*(const Interval& o) const {
        double a = lo*o.lo, b = lo*o.hi, c = hi*o.lo, d = hi*o.hi;
        return {std::min({a,b,c,d}), std::max({a,b,c,d})};
    }
 
    Interval operator/(const Interval& o) const {
        if (o.lo <= 0 && o.hi >= 0) return {-std::numeric_limits<double>::max(),
                                             std::numeric_limits<double>::max()};
        double a = lo/o.lo, b = lo/o.hi, c = hi/o.lo, d = hi/o.hi;
        return {std::min({a,b,c,d}), std::max({a,b,c,d})};
    }
 
    Interval operator-() const { return {-hi, -lo}; }
 
    // ── 数学函数（保守区间）──
 
    [[nodiscard]] Interval sqrt() const {
        return {std::sqrt(std::max(0.0, lo)), std::sqrt(std::max(0.0, hi))};
    }
 
    static Interval from_double(double v, double error = 0) {
        return {v - error, v + error};
    }
 
    static Interval from_coord(double v) {
        double eps = std::abs(v) * 2.22e-16 + 1e-300;
        return {v - eps, v + eps};
    }
};
 
inline Interval orient_2d_interval(double ax, double ay, double bx, double by, double cx, double cy) {
    Interval acx = Interval::from_coord(ax - cx);
    Interval acy = Interval::from_coord(ay - cy);
    Interval bcx = Interval::from_coord(bx - cx);
    Interval bcy = Interval::from_coord(by - cy);
    return acx * bcy - acy * bcx;
}
 
inline int orient_2d_verified(double ax, double ay, double bx, double by, double cx, double cy) {
    Interval det = orient_2d_interval(ax, ay, bx, by, cx, cy);
    return det.cmp(Interval(0.0));
}
 
}  // namespace vde::foundation