0.根据a（x1，y1），b（x2，y2）求直线方程:
根据两点式(x-x1)/(x2-x1)=(y-y1)/(y2-y1)，可知
A=y2-y1 ，B=x1-x2 ，
C=(y1-y2)*x1 + (x2-x1)*y1
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8//已知 double x1=10,y1=10; double x2=15,y2=20; //求直线方程 double A=y2-y1; double B=x1-x2; double C=(y1-y2)*x1 + (x2-x1)*y1
1.两条直线叉乘，计算交点
二维向量叉乘公式
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a（x_1，y_1），b（x_2，y_2），则a×b＝（x_1y_2－x_2y_1）
a（x1，y1），b（x2，y2），则a×b＝（x1y2－x2y1）
假设两直线方程为
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F0(x) = a_0*x + b_0*y + c_0 = 0\ F1(x) = a_1*x + b_1*y + c_1 = 0
F0(x)=a0∗x+b0∗y+c0=0F1(x)=a1∗x+b1∗y+c1=0
那么两条直线的交点应该满足
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a_0*x + b_0*y +c_0 = a_1*x + b_1*y + c_1
a0∗x+b0∗y+c0=a1∗x+b1∗y+c1
由此可推出
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x = (b_0*c_1 – b_1*c_0)/D \ y = (a_1*c_0 – a_0*c_1)/D \ D = a_0*b_1 – a_1*b_0
x=(b0∗c1–b1∗c0)/Dy=(a1∗c0–a0∗c1)/DD=a0∗b1–a1∗b0 (D为0时，表示两直线平行)
实际上就是叉积应用
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12//得到直线方程 double A1,B1,C1; double A2,B2,C2; double D=(A1*B2-A2*B1); //计算交点 cv::Point crossPoint; if(D!=0) { crossPoint.x=(B1*C2-B2*C1)/D; crossPoint.Y=(A2*C1-A1*C2)/D; }
2. 根据两条直线的方向向量，以及直线上的两点计算交点
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43double deltaX_X1 = endPoint.x - orgin.x; double deltaY_X1 = endPoint.y -orgin.y; double deltaX_X2 = endPoint.x - orgin.x; double deltaY_X2 = endPoint.y - orgin.y; double lineLengthX1 = sqrt(deltaX_X1*deltaX_X1+deltaY_X1*deltaY_X1); double lineLengthX2 = sqrt(deltaX_X2*deltaX_X2+deltaY_X2*deltaY_X2); X1DirectionVector.push_back(deltaX_X1/lineLengthX1); X1DirectionVector.push_back(deltaY_X1/lineLengthX1); X2DirectionVector.push_back(deltaX_X2/lineLengthX2); X2DirectionVector.push_back(deltaY_X2/lineLengthX2); //交点计算函数 cv::Point intersectionPointCalculate(std::vector<double> X1DirectionVec,cv::Point point1, std::vector<double> X2DirectionVec,cv::Point point2) { cv::Point crossPoint(9999,9999); if((X1DirectionVec.at(0)!=0) && X2DirectionVec.at(0)!=0) { double ka = X1DirectionVec.at(1)/X1DirectionVec.at(0); double kb = X2DirectionVec.at(1)/X2DirectionVec.at(0); double x = ((-1)*kb*double(point2.x)+double(point2.y)+ka*double(point1.x)-double(point1.y)) / (ka - kb); crossPoint.x = int(x); crossPoint.y = ka*(x-double(point1.x))+double(point1.y); //std::cout<<"point1: "<<point1<<" point2: "<<point2<<" ka: "<<ka<<" kb "<<kb<<" crossPoint: "<<crossPoint<<std::endl; } if((X1DirectionVec.at(0)==0) && X2DirectionVec.at(0)==0) { //std::cout<<"tensioner coordinate calculate error!"<<std::endl; } if((X1DirectionVec.at(0)==0) && X2DirectionVec.at(0)!=0) { double kb = X2DirectionVec.at(1)/X2DirectionVec.at(0); crossPoint.x = point1.x; crossPoint.y = kb*(crossPoint.x-point2.x)+point2.y; } if((X1DirectionVec.at(0)!=0) && X2DirectionVec.at(0)==0) { double ka = X1DirectionVec.at(1)/X1DirectionVec.at(0); crossPoint.x = point2.x; crossPoint.y = ka*(crossPoint.x-point1.x)+point1.y; } return crossPoint; }
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