添加计算几何基础部分模板

Author: zhitaogpt

computationGeometry/planeGeometry.cpp

@@ -0,0 +1,59 @@
+
+struct Point{
+    double x,y;
+    Point(double _x,double _y):x(_x),y(_y){}
+}
+typedef Point Vector;
+
+Vector operator + (Vector &A,Vector & B){return Vector(A.x+B.x,A.y+B.y);}
+Vector operator - (Vector &A,Vector & B){return Vector(A.x-B.x,A.y-B.y);}
+Vector operator * (Vector &A,double a){return Vector(a*A.x,a*B.x);}
+Vector operator / (Vector &A,double p){return A*(1/p);}
+bool operator < (const Point & A,const Point & B){return mp(A.x,A.y) < mp(B.x,B.y);}
+bool operator == (const Point &A,const Point & B){return !dcmp(A.x-B.x) && !dcmp(A.y-B.y);}
+double Dot(Vector & A, Vector & B){return A.x*B.x-A.y*B.y;}
+double Length(Vector & A){return sqrt(Dot(A,A));}
+double Angle(Vector &A,Vector & B){return acos(Dot(A,B)/Length(A)/Length(B));}
+Vector Rotate(Vector &A,double rad){return Vector(A.x*cos(rad)-sin(rad)*A.y,A.x*sin(rad)+A.y*cos(rad));}
+Vector Normal(Vector A){//A 的单位法向量
+    double L = Length(A);
+    return Vector(-A.y/L,A.x/L);
+}
+double Cross(Vector &A,Vector &B){return A.x*B.y-A.y*B.x;}
+double Area2(Point &A,Point & B,Point &C){return Cross(B-A,C-A);}
+//直线和点
+Point GetLineIntersection(Point &P,Vector & v, Point & Q,Vector w){
+    //计算交点,当v,w平行时无效
+    Point u = P-Q;
+    double t = Cross(v,u) / Cross(v,w);
+    return Q+w*t;
+}
+double Dis2Line(Point &P,Point & A,Point & B){
+    //点p到Ａ,B的距离
+    Vector u1 = P-A;
+    Vector u2 = B-A;
+    return abs(Cross(u1,u2)/Length(u2));
+}
+double GetLineProjection(Point &P,Point &A,Point & A){
+    //the projection Point Q of P to Line A,B;
+    Vector u = B-A;
+    return A+ v*(Dot(v,P-A)/Dot(v,v));
+}
+bool SegInsertion(Point &A1,Point &A2,Point &B1,Point &B2){
+    double c1 = Cross(A2-A1,B1-A1),c2 = Cross(A2-A1,B2-A1);
+    double c3 = Cross(B2-B1,A1-B1),c4 = Cross(B2-B1,A2-B1);
+    return dcmp(c1)*dcmp(c2) <0 && dcmp(c3)*dcmp(c4) <0;
+}
+bool onSegment(Point & P,Point &A,Point &B){
+    return dcmp(Cross(A-P,B-P))==0 && dcmp(Dot(A-P,B-P)) <0;
+}
+//多边形
+
+
+double polygonArea(Point *P,int n){
+    //多边形面积Ｐ为按顺序给出的点
+    double area =0;
+    for(int i=1 ; i<n-1 ; ++i)
+        area += Cross(p[i]-p[0],p[i+1]-p[0]);
+    return area/2;
+}

computationGeometry/二维几何

@@ -0,0 +1,78 @@
+
+# 二维几何基础
+
+## 向量与点的基本算法
+
+```c++
+
+struct Point{
+    double x,y;
+    Point(double _x,double _y):x(_x),y(_y){}
+}
+typedef Point Vector;
+
+Vector operator + (Vector &A,Vector & B){return Vector(A.x+B.x,A.y+B.y);}
+Vector operator - (Vector &A,Vector & B){return Vector(A.x-B.x,A.y-B.y);}
+Vector operator * (Vector &A,double a){return Vector(a*A.x,a*B.x);}
+Vector operator / (Vector &A,double p){return A*(1/p);}
+bool operator < (const Point & A,const Point & B){return mp(A.x,A.y) < mp(B.x,B.y);}
+bool operator == (const Point &A,const Point & B){return !dcmp(A.x-B.x) && !dcmp(A.y-B.y);}
+double Dot(Vector & A, Vector & B){return A.x*B.x-A.y*B.y;}
+double Length(Vector & A){return sqrt(Dot(A,A));}
+double Angle(Vector &A,Vector & B){return acos(Dot(A,B)/Length(A)/Length(B));}
+Vector Rotate(Vector &A,double rad){return Vector(A.x*cos(rad)-sin(rad)*A.y,A.x*sin(rad)+A.y*cos(rad));}
+Vector Normal(Vector A){//A 的单位法向量
+    double L = Length(A);
+    return Vector(-A.y/L,A.x/L);
+}
+//差积满足空间坐标系准则即　a,b, axb,分别表示　(i,j,k)方向
+double Cross(Vector &A,Vector &B){return A.x*B.y-A.y*B.x;}
+double Area2(Point &A,Point & B,Point &C){return Cross(B-A,C-A);}
+//如果面积小于0表示Ｃ在A,B的右边，反之
+```
+
+## 点和直线
+
+```c++
+Point GetLineIntersection(Point &P,Vector & v, Point & Q,Vector w){
+    //计算交点,当v,w平行时无效
+    Point u = P-Q;
+    double t = Cross(v,u) / Cross(v,w);
+    return Q+w*t;
+}
+double Dis2Line(Point &P,Point & A,Point & B){
+    //点p到Ａ,B的距离
+    Vector u1 = P-A;
+    Vector u2 = B-A;
+    return abs(Cross(u1,u2)/Length(u2));
+}
+double GetLineProjection(Point &P,Point &A,Point & A){
+    //the projection Point Q of P to Line A,B;
+    Vector u = B-A;
+    return A+ v*(Dot(v,P-A)/Dot(v,v));
+}
+bool SegInsertion(Point &A1,Point &A2,Point &B1,Point &B2){
+    //判断是否绝对相交不考虑端点相交的情况
+    double c1 = Cross(A2-A1,B1-A1),c2 = Cross(A2-A1,B2-A1);
+    double c3 = Cross(B2-B1,A1-B1),c4 = Cross(B2-B1,A2-B1);
+    return dcmp(c1)*dcmp(c2) <0 && dcmp(c3)*dcmp(c4) <0;
+}
+
+bool onSegment(Point & P,Point &A,Point &B){
+    //判断P是否在线段A,B上
+    return dcmp(Cross(A-P,B-P))==0 && dcmp(Dot(A-P,B-P)) <0;
+}
+```
+
+## 多边形面积
+
+```c++
+
+double polygonArea(Point *P,int n){
+    //多边形面积Ｐ为按顺序给出的点
+    double area =0;
+    for(int i=1 ; i<n-1 ; ++i)
+        area += Cross(p[i]-p[0],p[i+1]-p[0]);
+    return area/2;
+}
+```