ViewDesignEngine
ac5011091d
- foundation/interval.h: 双精度区间算术（+ - * / sqrt） - orient_2d_verified: 区间验证 orient2d 结果可靠性 - cmp/overlaps: 确定性比较 - curves/nurbs_curve.cpp: 改写为解析导数 - 基于 quotient rule 的精确导数公式 - 支持任意阶导数（非有限差分） - curves/bezier_surface.cpp: de Casteljau 解析导数 - derivative_u/v 使用差分控制点 + de Casteljau
95 lines
3.2 KiB
C++
95 lines
3.2 KiB
C++
#pragma once
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#include <cmath>
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#include <limits>
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#include <algorithm>
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namespace vde::foundation {
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/// 双精度区间算术：存储 [lo, hi] 边界，用于验证计算结果可靠性
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class Interval {
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public:
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double lo, hi;
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Interval() : lo(0), hi(0) {}
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Interval(double v) : lo(v), hi(v) {}
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Interval(double l, double h) : lo(std::min(l,h)), hi(std::max(l,h)) {}
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/// 区间中点
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[[nodiscard]] double mid() const { return (lo + hi) * 0.5; }
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/// 区间宽度
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[[nodiscard]] double width() const { return hi - lo; }
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/// 区间是否包含值
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[[nodiscard]] bool contains(double v) const { return lo <= v && v <= hi; }
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/// 是否精确（宽度 < eps）
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[[nodiscard]] bool is_exact(double eps = 1e-12) const { return width() < eps; }
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/// 区间是否与另一个区间重叠
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[[nodiscard]] bool overlaps(const Interval& o) const {
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return !(hi < o.lo || o.hi < lo);
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}
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/// 确定性比较
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[[nodiscard]] int cmp(const Interval& o) const {
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if (hi < o.lo) return -1; // 确定 this < o
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if (lo > o.hi) return 1; // 确定 this > o
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return 0; // 不确定（区间重叠）
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}
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// ── 算术运算 ──
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Interval operator+(const Interval& o) const {
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return {lo + o.lo, hi + o.hi};
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}
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Interval operator-(const Interval& o) const {
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return {lo - o.hi, hi - o.lo};
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}
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Interval operator*(const Interval& o) const {
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double a = lo*o.lo, b = lo*o.hi, c = hi*o.lo, d = hi*o.hi;
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return {std::min({a,b,c,d}), std::max({a,b,c,d})};
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}
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Interval operator/(const Interval& o) const {
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if (o.lo <= 0 && o.hi >= 0) return {-std::numeric_limits<double>::max(),
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std::numeric_limits<double>::max()};
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double a = lo/o.lo, b = lo/o.hi, c = hi/o.lo, d = hi/o.hi;
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return {std::min({a,b,c,d}), std::max({a,b,c,d})};
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}
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Interval operator-() const { return {-hi, -lo}; }
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// ── 数学函数（保守区间）──
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[[nodiscard]] Interval sqrt() const {
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return {std::sqrt(std::max(0.0, lo)), std::sqrt(std::max(0.0, hi))};
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}
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/// 从 double 创建区间（含舍入误差）
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static Interval from_double(double v, double error = 0) {
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return {v - error, v + error};
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}
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/// 将 double 表示的坐标转为区间（含 ULP 误差）
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static Interval from_coord(double v) {
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double eps = std::abs(v) * 2.22e-16 + 1e-300;
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return {v - eps, v + eps};
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}
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};
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/// 行列式的区间验证
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inline Interval orient_2d_interval(double ax, double ay, double bx, double by, double cx, double cy) {
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Interval acx = Interval::from_coord(ax - cx);
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Interval acy = Interval::from_coord(ay - cy);
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Interval bcx = Interval::from_coord(bx - cx);
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Interval bcy = Interval::from_coord(by - cy);
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return acx * bcy - acy * bcx;
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}
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/// 使用区间算术验证 orient_2d 结果
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/// 返回: -1(CW), 0(无法确定), 1(CCW)
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inline int orient_2d_verified(double ax, double ay, double bx, double by, double cx, double cy) {
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Interval det = orient_2d_interval(ax, ay, bx, by, cx, cy);
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return det.cmp(Interval(0.0));
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}
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} // namespace vde::foundation
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