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问题描述
给定n条线段，要求根据它们的交点将线段打断，生成新的线段集合。
定义结构：
代码如下：

typedef struct tagStruVertex
{double x;double y;tagStruVertex(double x = 0, double y = 0) : x(x), y(y) {}// 重载运算符，用于排序和去重bool operator<(const tagStruVertex& other) const {if (x != other.x) return x < other.x;return y < other.y;}bool operator==(const tagStruVertex& other) const {return fabs(x - other.x) < 1e-9 && fabs(y - other.y) < 1e-9;}bool operator!=(const tagStruVertex& other) const {if (x != other.x || y != other.y) return true;return false;}double distanceTo(
const tagStruVertex& point) const{double disX = x - point.x;double disY = y - point.y;return sqrt(disX * disX + disY * disY);}
}Vertex;
typedef struct tagStruSegment
{Vertex start, end;tagStruSegment(Vertex p1, Vertex p2) : start(p1), end(p2) {}tagStruSegment() {}// 重载运算符，用于 set 去重bool operator<(const tagStruSegment& other) const {if (start == other.start) return end < other.end;return start < other.start;}bool operator==(const tagStruSegment& other) const {if ((start == other.start && end == other.end) || (start == other.end && end == other.start))return true;elsereturn false;}
}Segment;

判断交点
使用线段相交的几何算法来检测两条线段是否相交。计算交点坐标，如果相交，则返回交点。
代码如下：

// 计算叉积
double cross(const Vertex& o, const Vertex& a, const Vertex& b) {return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x);
}//判断点是否在线段上
bool IsPointOnSegment(const Vertex& p, const Segment& seg) {double crossProd = cross(seg.start, seg.end, p);if (fabs(crossProd) > 1e-9) return false; // 不在直线上double minX = min(seg.start.x, seg.end.x);double maxX = max(seg.start.x, seg.end.x);double minY = min(seg.start.y, seg.end.y);double maxY = max(seg.start.y, seg.end.y);return (p.x >= minX - 1e-9 && p.x <= maxX + 1e-9) &&
(p.y >= minY - 1e-9 && p.y <= maxY + 1e-9);
}//判断两条线段是否相交：
bool IsCross(const Segment& seg1, const Segment& seg2, Vertex& intersect) {Vertex a = seg1.start, b = seg1.end;Vertex c = seg2.start, d = seg2.end;double cross1 = cross(a, b, c);double cross2 = cross(a, b, d);double cross3 = cross(c, d, a);double cross4 = cross(c, d, b);// 判断是否相交if (((cross1 * cross2) < 0) && ((cross3 * cross4) < 0)) {// 计算交点double t = cross3 / (cross3 - cross4);intersect.x = a.x + t * (b.x - a.x);intersect.y = a.y + t * (b.y - a.y);return true;}// 处理共线情况if (fabs(cross1) < 1e-9 && IsPointOnSegment(c, seg1)) { intersect = c; return true; }if (fabs(cross2) < 1e-9 && IsPointOnSegment(d, seg1)) { intersect = d; return true; }if (fabs(cross3) < 1e-9 && IsPointOnSegment(a, seg2)) { intersect = a; return true; }if (fabs(cross4) < 1e-9 && IsPointOnSegment(b, seg2)) { intersect = b; return true; }return false;
}

线段根据交点打断后生成新的线段
代码如下：

// 打断线段
vector<Segment> AdjustSegment(const Segment& seg, const set<Vertex>& intersections) {vector<Segment> vecSegments;vector<Vertex> points;// 将起点和终点加入points.push_back(seg.start);for (const auto& p : intersections) {if (IsPointOnSegment(p, seg)) {points.push_back(p);}}points.push_back(seg.end);// 按x坐标排序（或按y坐标，取决于线段方向）sort(points.begin(), points.end());// 生成小线段for (size_t i = 1; i < points.size(); ++i) {vecSegments.push_back(Segment(points[i - 1], points[i]));}return vecSegments;
}vector<Segment> AdjustSegments(const vector<Segment>& segments) {vector<Segment> vecSegments;for (size_t i = 0; i < segments.size(); ++i) {set<Vertex> intersections;// 查找当前线段与其他线段的交点for (size_t j = 0; j < segments.size(); ++j) {if (i == j) continue;Vertex intersect;if (IsCross(segments[i], segments[j], intersect)) {intersections.insert(intersect);}}// 打断当前线段vector<Segment> lines = AdjustSegment(segments[i], intersections);vecSegments.insert(vecSegments.end(), lines.begin(), lines.end());}// 使用 set 去重set<Segment> uniqueSegments(vecSegments.begin(), vecSegments.end());return vector<Segment>(uniqueSegments.begin(), uniqueSegments.end());
}

调用测试
代码如下：

vector<Segment> segments = {Segment(Vertex(0, 0), Vertex(30, 0)),Segment(Vertex(0, 10), Vertex(30, 10)),Segment(Vertex(0, 20), Vertex(30, 20)),Segment(Vertex(0, 30), Vertex(30, 30)),Segment(Vertex(0, 0), Vertex(0, 30)),Segment(Vertex(10, 0), Vertex(10, 30)),Segment(Vertex(20, 0), Vertex(20, 30)),Segment(Vertex(30, 0), Vertex(30, 30))
};
vector<Segment> vecSegments = AdjustSegments(segments);
//过滤掉长度为0的线段
for (auto it = vecSegments.begin(); it != vecSegments.end(); ) {if (it->start.distanceTo(it->end) == 0)it = vecSegments.erase(it);  // 如果匹配，删除元素并更新迭代器else ++it;  // 如果不匹配，继续遍历}
//处理完成最终vecSegments里边的结果即为打断后的所有小线段

处理完得到小线段的数量为24条小线段。结果与预期一致。