要求
用面向对象的思维设计相关类，从而实现直线与直线、直线与圆、直线与矩形的交点
思路
设计直线，圆，矩形的类，运用数学定义来判断是否有交点，并计算出交点的坐标。
代码示例：（使用 VS Code 运行）
/*file: robocup2d2cd.h
brief:各个类的定义:直线类，圆形类，矩形类*/
class MyCircle2D {
public:
MyCircle2D(double x, double y, double r);
double getCirX();
double getCirY();
double getCirR();
private:
double x;
double y; //圆心坐标
double r; //半径
};
class MyRectangle2D {
public:
MyRectangle2D(double xLeftB,
double yLeftB,
double xRightT,
double yRightT);
double getRecXL();
double getRecYL();
double getRecXR();
double getRecYR();
private:
double xLeftB;
double yLeftB;
double xRightT;
double yRightT; //分别代表矩形左下角和右上角的坐标
};
class MyLine2D {
public:
MyLine2D(double a, double b, double c);
void PointOfIntersection(MyLine2D &line);
void PointOfIntersection(MyCircle2D &circle);
void PointOfIntersection(MyRectangle2D &rectangle);//求交点
double getLineA();
double getLineB();
double getLineC();
private:
double a;
double b;
double c; //ax + by + c = 0;
};
/*file:robocup2d2cd.cpp
compiler: VS Code
function: 求直线与直线、直线与圆、直线与矩形的交点
*/
#include<iostream>
#include<math.h>
#include"robocup2d2cd.h"
using namespace std;
MyLine2D::MyLine2D(double a, double b, double c){
this->a = a;
this->b = b;
this->c = c;
}
double MyLine2D::getLineA(){
return this->a;
}
double MyLine2D::getLineB(){
return this->b;
}
double MyLine2D::getLineC(){
return this->c;
}
void MyLine2D::PointOfIntersection(MyLine2D &line){
//直线与另一条直线的交点
if((this->a==0 && line.a==0) || (this->b==0 && line.b==0)){
cout<<"wrong line!"<<endl;
}
if((this->a)*(line.b) != (this->b)*(line.a)){
//两直线相交
cout<<"两直线相交,交点：("
<<((this->b)*(line.c) - (this->c)*(line.b))/((this->a)*(line.b) - (this->b)*(line.a))
<<","
<<((this->c)*(line.a) - (this->a)*(line.c))/((this->a)*(line.b) - (this->b)*(line.a))
<<")"<<endl;
}else {
if(this->a!=0 && line.a!=0){
if((this->a)/(line.a) == (this->c)/(line.c)) {
cout<<"两直线重合,有无数交点"<<endl;
}else {
cout<<"两直线平行--无交点"<<endl;
}
}else if(this->b!=0 && line.b!=0){
if((this->b)/(line.b) == (this->c)/(line.c)) {
cout<<"两直线重合,有无数交点"<<endl;
}else {
cout<<"两直线平行,无交点"<<endl;
}
}
}
}
void MyLine2D::PointOfIntersection(MyCircle2D &circle){
if(this->a==0 && this->b==0){
cout<<"wrong line!"<<endl;
}
double dist; //圆心到直线的距离
double k;
double d;
double f;
dist = fabs((this->a)*(circle.getCirX()) + (this->b)*(circle.getCirY()) + this->c)
/sqrt((this->a)*(this->a) + (this->b)*(this->b));
if(this->b != 0){
//斜率存在时,转化
k = (-1)*this->a/this->b;
d = (-1)*this->c/this->b; //截距
f = sqrt((k*k+1)*circle.getCirR()*circle.getCirR()
- circle.getCirX()*circle.getCirX()*k*k
+ 2*k*(circle.getCirX()*circle.getCirY()+d*circle.getCirX())
- circle.getCirY()*circle.getCirY()-2*d*circle.getCirY()-d*d);
}
if(dist == circle.getCirR()){
cout<<"直线与圆相切，一个交点，交点：";
if(this->a == 0){
cout<<"("<<circle.getCirX()<<","<<(-1)*(this->c/this->b)<<")"<<endl;
}else if(this->b == 0){
cout<<"("<<(-1)*(this->c/this->a)<<","<<circle.getCirY()<<")"<<endl;
}else {
cout<<"("<<((-1)*f+(circle.getCirY()+d)*k+circle.getCirX())/(k*k+1)<<","
<<((-1)*(k*(f+circle.getCirX())+circle.getCirY()*k*k-d)/(k*k+1))<<")"<<endl;
}
}else if(dist > circle.getCirR()){
cout<<"直线与圆相离，无交点"<<endl;
}else {
cout<<"直线与圆相交，两个交点，交点：";
double f1 = sqrt(circle.getCirR()*circle.getCirR()-(dist/2)*(dist/2));
if(this->a == 0){
cout<<"("<<circle.getCirX()-f1<<","<<d<<"),"
<<"("<<circle.getCirX()+f1<<","<<d<<")"<<endl;
}else if(this->b == 0){
cout<<"("<<(-1)*this->c/this->a<<","<<circle.getCirY()-f1<<"),"
<<"("<<(-1)*this->c/this->a<<","<<circle.getCirY()+f1<<")"<<endl;
}else{
cout<<"("<<((-1)*f+(circle.getCirY()+d)*k+circle.getCirX())/(k*k+1)<<","
<<((-1)*(k*(f+circle.getCirX())+circle.getCirY()*k*k-d)/(k*k+1))<<")"
<<","
<<"("<<(f+(-1)*(circle.getCirY()+d)*k-circle.getCirX())/(k*k+1)<<","
<<k*((f+(-1)*(circle.getCirY()+d)*k-circle.getCirX())/(k*k+1))+d<<")"<<endl;
}
}
}
void MyLine2D::PointOfIntersection(MyRectangle2D &rec){
if(this->a==0 && this->b==0){
cout<<"wrong line!"<<endl;
}
//假设矩形的边平行于坐标轴
double kRec;
double bRec; //矩形对角线所在的直线的斜率，截距
double kLine; //直线斜率存在时的斜率，截距
double bLine;
kRec = tan((rec.getRecYR()-rec.getRecYL())/(rec.getRecXR()-rec.getRecXL()));
bRec = rec.getRecYL() - kRec*rec.getRecXL();
if(this->b != 0){
//直线斜率存在
kLine = (-1)*this->a/this->b;
bLine = (-1)*this->c/this->b;
double y1 = kLine*rec.getRecXL()+bLine;
double y2 = kLine*rec.getRecXR()+bLine;
//矩形顶点到对角线的距离
double dist = (rec.getRecXR()-rec.getRecXL())*(rec.getRecYR()-rec.getRecYL())
/sqrt((rec.getRecXR()-rec.getRecXL())*(rec.getRecXR()-rec.getRecXL())+
(rec.getRecYR()-rec.getRecYL())*(rec.getRecYR()-rec.getRecYL()));
//矩形的左下角点到直线距离
double dist1 = fabs(this->a*rec.getRecXL()+this->b*rec.getRecYL()+this->c)
/sqrt(this->a*this->a + this->b*this->b);
//矩形的右上角点到直线距离
double dist2 = fabs(this->a*rec.getRecXR()+this->b*rec.getRecYR()+this->c)
/sqrt(this->a*this->a + this->b*this->b);
//对角线段（除去端点）与直线相交
if((rec.getRecYL()<y1 && rec.getRecYR()>y2) || (rec.getRecYL()>y1 && rec.getRecYR()<y2)){
cout<<"直线与矩形有两个交点:";
if(kLine > 0){
if(kLine > kRec){
cout<<"("<<(rec.getRecYL()-bLine)/kLine<<","<<rec.getRecYL()<<")"
<<"("<<(rec.getRecYR()-bLine)/kLine<<","<<rec.getRecYR()<<")"<<endl;
}else {
cout<<"("<<rec.getRecXL()<<","<<kLine*rec.getRecXL()<<"),"
<<"("<<rec.getRecXR()<<","<<kLine*rec.getRecXR()<<")"<<endl;
}
}else if(kLine < 0){
if(kLine*rec.getRecXR()+bLine > rec.getRecYL()){
if(kLine*rec.getRecXL()+bLine < rec.getRecYL()){
cout<<"("<<rec.getRecXL()<<","<<kLine*rec.getRecXL()<<"),"
<<"("<<rec.getRecXR()<<","<<kLine*rec.getRecXR()<<")"<<endl;
}else{
cout<<"("<<(rec.getRecYR()-bLine)/kLine<<","<<rec.getRecYR()<<")"
<<"("<<rec.getRecXR()<<","<<rec.getRecXR()*kLine+bLine<<")"<<endl;
}
}else {
cout<<"("<<(rec.getRecYL()-bLine)/kLine<<","<<rec.getRecYL()<<")"
<<"("<<rec.getRecXL()<<","<<rec.getRecXL()*kLine+bLine<<")"<<endl;
}
}
}else if(rec.getRecYL()<y1 && rec.getRecYR()<y2){
//两点在直线的下方
if(kLine*rec.getRecXL()+bLine > rec.getRecYR()){
cout<<"直线与矩形没有交点"<<endl;
}else if(kLine*rec.getRecXL()+bLine == rec.getRecYR()){
cout<<"直线与矩形有一个交点:";
cout<<"("<<rec.getRecXL()<<","<<rec.getRecYR()<<")"<<endl;
}else {
cout<<"直线与矩形有两个交点:";
cout<<"("<<rec.getRecXL()<<","<<kLine*rec.getRecXL()+bLine<<"),"
<<"("<<(rec.getRecYR()-bLine)/kLine<<","<<rec.getRecYR()<<")"<<endl;
}
}else if(rec.getRecYL()>y1 && rec.getRecYR()>y2){
//两点在直线的上方
if(kLine*rec.getRecXR()+bLine < rec.getRecYL()){
cout<<"直线与矩形没有交点"<<endl;
}else if(kLine*rec.getRecXR()+bLine == rec.getRecYL()){
cout<<"直线与矩形有一个交点:";
cout<<"("<<rec.getRecXR()<<","<<rec.getRecYL()<<endl;
}else {
cout<<"直线与矩形有两个交点:";
cout<<"("<<(rec.getRecYL()-bLine)/kLine<<","<<rec.getRecYL()<<"),"
<<"("<<rec.getRecXR()<<","<<kLine*rec.getRecXR()+bLine<<")"<<endl;
}
}
}else{
bLine = (-1)*this->a/this->c;
if(bLine>rec.getRecXR() || bLine<rec.getRecXL()){
cout<<"直线与矩形没有交点"<<endl;
}else if(bLine<rec.getRecXR() || bLine>rec.getRecXL()){
cout<<"直线与矩形有两个交点:";
cout<<"("<<bLine<<","<<rec.getRecYL()<<"),"
<<"("<<bLine<<","<<rec.getRecYR()<<")"<<endl;
}else{
cout<<"直线与矩形一条边重合，有无数交点"<<endl;
}
}
}
MyCircle2D::MyCircle2D(double x, double y, double r){
this->x = x;
this->y = y;
this->r = r;
}
double MyCircle2D::getCirX(){
return this->x;
}
double MyCircle2D::getCirY(){
return this->y;
}
double MyCircle2D::getCirR(){
return this->r;
}
MyRectangle2D::MyRectangle2D(double x1, double y1,
double x2, double y2){
this->xLeftB = x1;
this->yLeftB = y1;
this->xRightT = x2;
this->yRightT = y2;
}
double MyRectangle2D::getRecXL(){
return this->xLeftB;
}
double MyRectangle2D::getRecYL(){
return this->yLeftB;
}
double MyRectangle2D::getRecXR(){
return this->xRightT;
}
double MyRectangle2D::getRecYR(){
return this->yRightT;
}
int main(){
MyLine2D line1(2.0, 3.0, 1.0);
MyLine2D line2(1.0, 4.0, 8.0);
MyLine2D line3(4.0, -2.0, 3.0);
MyLine2D line4(0.0, 3.0, 8.0);
MyCircle2D circle(2.0, 2.0, 2.0);
MyRectangle2D rec(-4.0, 0.0, 0.0, 3.0);
line1.PointOfIntersection(line2);
line1.PointOfIntersection(circle);
line1.PointOfIntersection(rec);
line2.PointOfIntersection(line3);
line2.PointOfIntersection(circle);
line2.PointOfIntersection(rec);
line3.PointOfIntersection(line4);
line3.PointOfIntersection(circle);
line3.PointOfIntersection(rec);
return 0;
}
运行结果示例：
PS：关于直线与矩形的交点问题并没有全面完整的解决。