#include "stdafx.h" #include "PublicFunctions.h" #include "Clipper/clipperhandler.h" #include #include #ifndef ZERO6 #define ZERO6 1e-6 #endif #ifndef ZERO #define ZERO 1e-8 #endif using namespace NClipperLib; using namespace std; //#ifndef RHO //#define RHO 57.295779513082320876798154814105 //#endif CPublicFunctions::CPublicFunctions() { } CPublicFunctions::~CPublicFunctions() { } void CPublicFunctions::GetGravityCenter(double* xx, double* yy, int num, double& x0, double& y0) { if (num < 2) return; if (num == 2) { x0 = (xx[0] + xx[1]) / 2.0; y0 = (yy[0] + yy[1]) / 2.0; return; } double x[3], y[3]; memcpy(x, xx, sizeof(double) * 3); memcpy(y, yy, sizeof(double) * 3); double sum_x = 0; double sum_y = 0; double sum_area = 0; double area = 0; for (int i = 2; i < num; i++) { x[1] = xx[i - 1]; y[1] = yy[i - 1]; x[2] = xx[i]; y[2] = yy[i]; area = GetAreaTrue(3, x, y); sum_area += area; sum_x += (x[0] + x[1] + x[2])*area; sum_y += (y[0] + y[1] + y[2])*area; } x0 = sum_x / sum_area / 3.0; y0 = sum_y / sum_area / 3.0; } double CPublicFunctions::GetAreaTrue(int num, double* x, double* y) { int i; double s; s = (y[0] + y[num - 1]) * (x[0] - x[num - 1]); for (i = 0; i < num - 1; ++i) s += (y[i + 1] + y[i]) * (x[i + 1] - x[i]); return s * 0.5; } double CPublicFunctions::LinearInterpolate(double x1, double y1, double x2, double y2, double x0) { if (fabs(x1 - x2) < ZERO6) return (y1 + y2) / 2.0; if (fabs(x1 - x0) < ZERO6) return y1; if (fabs(x2 - x0) < ZERO6) return y2; double y0 = 0; double k = (x0 - x1) / (x2 - x1); y0 = y1 + k*(y2 - y1); return y0; } void CPublicFunctions::Trim(string& line) { if (line.size() < 1) return; size_t idx1 = line.find_first_not_of(' '); size_t idx2 = line.find_last_not_of(' '); if (idx1 > idx2) { line.clear(); return; } line = line.substr(idx1, idx2 - idx1 + 1); } double CPublicFunctions::Area(int num, double * x, double * y) { int i; double s; s = (y[0] + y[num - 1]) * (x[0] - x[num - 1]); for (i = 0; i < num - 1; ++i) s += (y[i + 1] + y[i]) * (x[i + 1] - x[i]); return fabs(s * 0.5); } //判断两条线段(x1,y1)-(x2,y2) ,(x3,y3)-(x4,y4)是否相交 int CPublicFunctions::IsSegmentCross(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) { //矩形快速排斥实验 double xmin1 = min(x1, x2); double ymin1 = min(y1, y2); double xmax1 = max(x1, x2); double ymax1 = max(y1, y2); double xmin2 = min(x3, x4); double ymin2 = min(y3, y4); double xmax2 = max(x3, x4); double ymax2 = max(y3, y4); if (xmin1 > xmax2 + ZERO6 || xmax1 + ZERO6 < xmin2) return 0; if (ymin1 > ymax2 + ZERO6 || ymin2 > ymax1 + ZERO6) return 0; //跨立实验 double x12 = x2 - x1; //向量 double y12 = y2 - y1; double x23 = x3 - x2; double y23 = y3 - y2; double x34 = x4 - x3; double y34 = y4 - y3; double x13 = x3 - x1; double y13 = y3 - y1; double x14 = x4 - x1; double y14 = y4 - y1; //判定3,4点是否跨立1-2向量 if (CrossProduct(x12, y12, x13, y13) * CrossProduct(x12, y12, x14, y14) > 0) return 0; //点3,4在 1-2线段同侧 if (CrossProduct(x34, y34, x13, y13) * CrossProduct(x34, y34, x23, y23) > 0) return 0; //点1,2在 3-4线段同侧 //判断是否共线 if (fabs(CrossProduct(x12, y12, x34, y34)) < 1e-8) return 2; return 1; } bool CPublicFunctions::IsEqual(double x, double y, double esp) { if (fabs(x - y) < esp) return true; return false; } //两向量A(x1,y1),B(x2,y2)的叉积(外积) double CPublicFunctions::CrossProduct(double x1, double y1, double x2, double y2) { return (x1*y2 - x2*y1); } double CPublicFunctions::CrossProduct(double x1, double y1, double x2, double y2, double ptX, double ptY) { return (x2 - x1) * (ptY - y1) - (y2 - y1) * (ptX - x1); } int CPublicFunctions::IsInsidePolygon(double x0, double y0, double * x, double * y, int m) { if (m < 3) return 0; double x1 = x0; double y1 = y0; double x2 = x0 - 1e10; double y2 = y0; const double zero8 = 1e-8; int crossNum = 0; int iprev; int inext; for (int i = 0; i < m - 1; i++) { if (fabs(x[i] - x[i + 1]) < zero8 && fabs(y[i] - y[i + 1]) < 1e-8) continue; if (fabs(y[i + 1] - y0) < zero8 && x[i + 1] < x0) continue; if (fabs(y[i] - y0) < zero8 && x[i] < x0) { if (0 == i) { iprev = m - 1; while (IsEqual(x[iprev], x[i], zero8) && IsEqual(y[iprev], y[i], zero8)) iprev--; } else iprev = i - 1; inext = i + 1; if (((y0 - y[iprev]) > -1e-8 && (y[inext] - y0) > -1e-8) || (((y0 - y[iprev]) < -1e-8 && (y[inext] - y0)< -1e-8)) ) crossNum++; } else if (IsSegmentCross(x1, y1, x2, y2, x[i], y[i], x[i + 1], y[i + 1])) crossNum++; } //末尾点如果不等于起点 if (fabs(x[0] - x[m - 1]) > zero8 || fabs(y[0] - y[m - 1]) > zero8) { if (fabs(y[0] - y0) > zero8 || x[0] > x0) { if (fabs(y[m - 1] - y0) < zero8 && x[m - 1] < x0) { int i = m - 1; if (((y0 - y[i - 1]) > -1e-8 && (y[0] - y0) > -1e-8) || (((y0 - y[i - 1]) < -1e-8 && (y[0] - y0)< -1e-8)) ) crossNum++; } else if (IsSegmentCross(x1, y1, x2, y2, x[0], y[0], x[m - 1], y[m - 1])) crossNum++; } } if (crossNum % 2 == 0) //外部 return 0; return 1; } double CPublicFunctions::Distance(double x1, double y1, double x2, double y2) { double dist = sqrt((x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1)); return dist; } int CPublicFunctions::LineCrossPoint(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4, double& x0, double& y0) { double k1 = 1e11; double k2 = 1e11; if (fabs(x2-x1) > ZERO) k1 = (y2 - y1) / (x2 - x1); if (fabs(x4 - x3) > ZERO) k2 = (y4 - y3) / (x4 - x3); return LineCrossPoint(x1, y1, k1, x3, y3, k2, x0, y0); } //两条直线的交点,k1,k2为两条直线的斜率，若k值 > 1e10 表示垂直于x轴返回0表示无交点，返回1表示存在唯一交点，返回2表示两直线重合 int CPublicFunctions::LineCrossPoint(double x1, double y1, double k1, double x2, double y2, double k2, double& x0, double& y0) { if (fabs(k1) > 1e10 && fabs(k2) > 1e10) //同时垂直于x轴 { if (fabs(x2 - x1) < ZERO6) //两线重合 { x0 = x1; y0 = y1; return 2; } return 0; } //若平行 if (fabs(k1 - k2) < ZERO) { //两点x相等 if (fabs(x2 - x1) < ZERO) return 0; double k = (y2 - y1) / (x2 - x1); if (fabs(k1 - k) < 1e-10) // 斜率相等共线 { x0 = x1; y0 = y1; return 2; } return 0; } //若斜率不等 if (fabs(x2 - x1) < ZERO && fabs(y2 - y1) < ZERO) { x0 = x1; y0 = y1; return 1; } //线1垂直x轴 if (fabs(k1) > 1e10) { if (fabs(x2 - x1) < ZERO) { x0 = x2; y0 = y2; return 1; } x0 = x1; y0 = y2 - k2*(x2 - x0); return 1; } //线2垂直x轴 if (fabs(k2) > 1e10) { if (fabs(x2 - x1) < ZERO) { x0 = x1; y0 = y1; return 1; } x0 = x2; y0 = y1 - k1*(x1 - x0); return 1; } //都不垂直于x轴 x0 = -(y1 - y2 - k1*x1 + k2*x2) / (k1 - k2); y0 = y1 - k1*(x1 - x0); return 1; } //获取角度 -pi/2 ~pi/2 double CPublicFunctions::GetAngle180(double x1, double y1, double x2, double y2) { if (fabs(x1 - x2) < ZERO) return PI / 2; return atan((y2 - y1) / (x2 - x1)); } //获取角度 -pi ~ pi double CPublicFunctions::GetAngle360(double x1, double y1, double x2, double y2) { return atan2(y2 - y1, x2 - x1); } void CPublicFunctions::Rotate(double &x0, double &y0, double radians, int directionFlag) { Rotate(x0, y0, cos(radians), sin(radians), directionFlag); //double xp,yp; //xp=x0; //yp=y0; //x0=yp*sin(angle)+xp*cos(angle); //y0=yp*cos(angle)-xp*sin(angle); } void CPublicFunctions::Rotate(double &x, double &y, double cosa, double sina, int directionFlag) { if (directionFlag == 1) { double tx, ty; tx = x * cosa + y * sina; ty = y * cosa - x * sina; x = tx; y = ty; } // 断层标注用到的算法 else { double tx, ty; tx = x * cosa - y * sina; ty = x * sina + y * cosa; x = tx; y = ty; } } void CPublicFunctions::Rotate(double& x0, double& y0, double xs, double ys, double radian) { double tx = x0 - xs; double ty = y0 - ys; Rotate(tx, ty, radian); x0 = tx + xs; y0 = ty + ys; } void CPublicFunctions::Rotate(double& x0, double& y0, double xs, double ys, double cosa, double sina) { double tx = x0 - xs; double ty = y0 - ys; Rotate(tx, ty, cosa,sina); x0 = tx + xs; y0 = ty + ys; } // 判断点在直线的哪侧 1-- 左侧 0--线上 2---右侧 ///////////////////////////////////////////////////////////////////////// int CPublicFunctions::PointInLine(double x0, double y0, double x1, double y1, double x2, double y2) { double r = (x1 - x0) * (y2 - y0) - (y1 - y0) * (x2 - x0); if (fabs(r) < ZERO6) return 0; else if (r > 0.0) return 1; else return 2; } bool CPublicFunctions::IsPointOnsegment(double x0, double y0, double x1, double y1, double x2, double y2) { if (x0 < min(x1, x2) - ZERO6) return false; if (x0 > max(x1, x2) + ZERO6) return false; if (y0 < min(y1, y2) - ZERO6) return false; if (y0 > max(y1, y2) + ZERO6) return false; if (0 == PointInLine(x0, y0, x1, y1, x2, y2)) return true; return false; } double CPublicFunctions::PointLineDistance(double x0, double y0, double k, double b) { if (fabs(k) > 1e30) return x0 - b; return (y0 - k * x0 - b) / sqrt(1.0 + k * k); } //获得两直线之间的夹角 double CPublicFunctions::GetAngle(double x1, double y1, double x2, double y2, double x3, double y3, int directionFlag) { double RHO = 57.295779513082320876798154814105; double tx, ty; tx = x2 - x1; ty = y2 - y1; double angle = 90; if (fabs(tx) < 1e-10) //防止被0除 { if (ty > 1e-10)angle = 90.0; else angle = -90.0; } else angle = atan2(ty, tx); tx = x3 - x2; ty = y3 - y2; Rotate(tx, ty, angle, directionFlag); if (fabs(tx) < 1e-10) { if (ty > 1e-10) return 90.0; else return -90.0; } return atan2(ty, tx) * RHO; } int CPublicFunctions::BinarySearch(double key, std::vector& x) { int i1, i2, i; int num = (int)x.size(); i1 = 0; i2 = num - 1; if (x[i2] - x[i1] > 1e-10) { if (key > x[i2])return num + 100; if (key < x[i1])return -100; } else if (x[i2] < x[i1]) { if (key < x[i2])return num + 100; if (key > x[i1])return -100; } if (fabs(key - x[i1]) < 1e-10)return 0; if (fabs(key - x[i2]) < 1e-10)return i2 - 1; while (i2 - i1 > 1) { if (fabs(x[i2] - x[i1]) < 1e-10)break; i = (i1 + i2) / 2; if ((key - x[i]) * (key - x[i2]) > 1e-10) i2 = i; else i1 = i; } return i1; }