之前也有一篇笔记，都比较简单，做个记录，方便速查。
C++&OpenCV：三角形插值、线面的交点_六月的翅膀的博客-CSDN博客
目录
1、向量的模
2、两点间距离（两点间的向量模）
3、求线段中某点坐标
4、叉乘，平面法向量
5、线面交点
6、空间点到直线的距离
7、平面方程
1、向量的模
int main(){Vec3f A = Vec3f(10, 10, 1);cout << "向量A的模 = " << norm(A) << endl;Vec3f B = Vec3f(3, 3, 1);cout << "向量B的模 = " << norm(B) << endl;return 0;}
2、两点间距离（两点间的向量模）
int main(){Vec3f A = Vec3f(10, 10, 1);Vec3f B = Vec3f(3, 3, 1);cout << "线段AB的长度为 = " << norm(A - B) << endl;//结果为6*根2return 0;}
3、求线段中某点坐标
int main(){Vec3f A = Vec3f(0, 10, 0);Vec3f B = Vec3f(0, 0, 0);Vec3f C = Vec3f(10, 0, 0);Vec3f M = Vec3f(3, 0, 0);float t = norm(M - C) / norm(B - C);Vec3f N = C + (A - C) * t;cout << "N点坐标为：" << N << endl;return 0;}
4、叉乘，平面法向量
5、线面交点
int main(){//需要知道直线上一点和其方向向量，平面一点及其法向量Vec3f A=Vec3f(0, 1, 1);Vec3f B=Vec3f(1, 0, 1);Vec3f O=Vec3f(0, 0, 0);Vec3f M=Vec3f(1, 1, 0);Vec3f N=Vec3f(0, 0, 1);Vec3f line = M-N;//线方向向量，这里谁减谁都行Vec3f plane = (A - O).cross(B - O);//平面两个向量叉乘就是法向量float den = plane.dot(line);//面法向量乘线方向向量float t = plane.dot(A - N) / den;//A是面上一点，用B也可以Vec3f p0 = N + line * t;//这里线上的点用的N，也可以用M，只要上面求t的时候也是用的M就可以cout << p0 << endl;return 0;}
6、空间点到直线的距离
/// <summary>/// /// </summary>/// <param name="P">线外一点</param>/// <param name="A">线上点</param>/// <param name="B">线上点</param>/// <returns></returns>float getDist_P2L(Vec3f P, Vec3f A, Vec3f B){Vec3f PA = P - A;//线外点到线上一点的向量Vec3f Ldir = B - A;//直线的方向向量Vec3f Pnorm = PA.cross(Ldir);float S1 = norm(Ldir);float S2 = norm(Pnorm);return S2 / S1;}int main(){Vec3f A = Vec3f(1.0, 0, 0);Vec3f B = Vec3f(0.0, 1.0, 0);Vec3f P = Vec3f(0.5, 0.5, 3);float dis = getDist_P2L(P, A, B);cout << dis << endl;}
7、平面方程
vector<Vec3f> input;vector<float> coeffi;void GetPanelEquation(vector<Vec3f>& point3fArray){if (point3fArray.size() < 3){cerr << "GetPanelEquation(...)函数中输入点的数量小于3." << endl;}float a,b,c,d;a = (point3fArray[1][1] - point3fArray[0][1])*(point3fArray[2][2] - point3fArray[0][2]) -(point3fArray[1][2] - point3fArray[0][2])*(point3fArray[2][1] - point3fArray[0][1]);b = (point3fArray[1][2] - point3fArray[0][2])*(point3fArray[2][0] - point3fArray[0][0]) -(point3fArray[1][0] - point3fArray[0][0])*(point3fArray[2][2] - point3fArray[0][2]);c = (point3fArray[1][0] - point3fArray[0][0])*(point3fArray[2][1] - point3fArray[0][1]) -(point3fArray[1][1] - point3fArray[0][1])*(point3fArray[2][0] - point3fArray[0][0]);d = 0 - (a * point3fArray[0][0] + b*point3fArray[0][1] + c*point3fArray[0][2]);coeffi.push_back(a);coeffi.push_back(b);coeffi.push_back(c);coeffi.push_back(d);}int main(){input.push_back(Vec3f(100, 0, 0));input.push_back(Vec3f(0, 100, 0));input.push_back(Vec3f(0, 0, 3));GetPanelEquation(input);cout << "平面方程为："<< endl << coeffi[0] << " X + " << coeffi[1] << " Y + " << coeffi[2] << " Z + " << coeffi[3] << " = 0" << endl;if (abs(coeffi[3])>1e-6){cout << "平面方程为：" << endl << -coeffi[0] / coeffi[3] << " X + " << -coeffi[1] / coeffi[3] << " Y + " << -coeffi[2] / coeffi[3] << " Z = 1" << endl;}return 1;}
8、两直线的交点
double r_xy12 = PointOnLine[0].x * PointOnLine[1].y - PointOnLine[1].x * PointOnLine[0].y;double r_x12 = PointOnLine[0].x - PointOnLine[1].x;double r_xy34 = PointOnLine[2].x * PointOnLine[3].y - PointOnLine[3].x * PointOnLine[2].y;double r_x34 = PointOnLine[2].x - PointOnLine[3].x;double r_y12 = PointOnLine[0].y - PointOnLine[1].y;double r_y34 = PointOnLine[2].y - PointOnLine[3].y;double fenmu = r_x12 * r_y34 - r_y12 * r_x34;GridPoint[i].x = (r_xy12 * r_x34 - r_x12 * r_xy34) / fenmu;GridPoint[i].y = (r_xy12 * r_y34 - r_y12 * r_xy34) / fenmu;
struct LinePara{float k;float b;};// 获取直线参数 void getLinePara(float& x1, float& y1, float& x2, float& y2, LinePara& LP){double m = 0;// 计算分子 m = x2 - x1;if (0 == m){LP.k = 10000.0;LP.b = y1 - LP.k * x1;}else{LP.k = (y2 - y1) / (x2 - x1);LP.b = y1 - LP.k * x1;}}// 获取交点 bool getCross(Point2f& p1, Point2f& p2, Point2f& p3, Point2f& p4, Point2f& pt) {LinePara para1, para2;getLinePara(p1.x, p1.y, p2.x, p2.y, para1);getLinePara(p3.x, p3.y, p4.x, p4.y, para2);pt.x = (para2.b - para1.b) / (para1.k - para2.k);pt.y = para1.k * pt.x + para1.b;// 判断是否平行 if (abs(para1.k - para2.k) > 0.5){pt.x = (para2.b - para1.b) / (para1.k - para2.k);pt.y = para1.k * pt.x + para1.b;return true;}else{return false;}}
