这是一个可以在平面坐标系中表示
任意多边形并且计算其面积和周长的类。
不过目前只能在第一象限计算。使用时较简便，只要把多边形的各个顶点传进去就可以了
（不用按顺序）。
（其中面积的计算是参考
https://blog.csdn.net/hemmingway/article/details/7814494的公式）
程序中附带包含了point 类，line 类。
point 类：
计算点点距离的函数：
double distancebetweenpoint(const point &a, const point &b);
计算点到线距离的成员函数：
double distancetoline(const line &line)const;
line 类：
获得直线标准方程的函数：
void getStandardEquation(double &A, double &B, double &C)const;//get the standard equation of line( Ax+By+C=0)
计算直线长度的成员函数：
double length()const;判断两条直线是否相交的成员函数：
bool line::iflinemeet(const line &other)const//return a bool value represent whether this line meets the other line (1 stand for yes, 0 for no)
（第一次用不是很会排版）
以下是使用样例：
point a(3, 6), b(3, 3), c(0, 5),d(5,5),e(10,5),f(5,8),g(10,8);
point v[4] = { e,f,g,d};
polygon m(4, v);
cout << " area is " << m.area() << " perimeter is " << m.perimeter()<<endl;
area（面积）和perimeter（周长）是double类型的。
以下是头文件中类的声明等等：
#pragma once
#include<iostream>
using namespace std;
#define PI 3.1415926535
enum errortype { noside,cantcalculate };//the type in exceptions class which may occured in shape's functions
class line;
class point;
class error;
//the exception class
class error {
private:
errortype eor;
public:
error(errortype e) :eor(e) {}//constructor
const errortype what()const { return eor; }//for inquiry
};
//class point used to represent a point in a rectangular coordinate system
class point {
friend double distancebetweenpoint(const point &a, const point &b);//calculate the distance between two difference point(which isn't a member function of point)
public:
double x;
double y;
point(double setx = 0, double sety = 0) { x = setx; y = sety; }//constructor
double distancetoline(const line &line)const;//calculate the distance between this point and a line
bool operator==(const point &ro)const;//compare by the x and y of the point
void show()const { cout << "(" << x << "," << y << ")"; }//a simple output function for test
};
const point O(0, 0);//the origin in the rectangular coordinate system
//class line used to represent a line in a rectangular coordinate system
//with two different point, which may used to derive a class vector(for now, the difference between start point and end point doesn't make any sense)
class line {
friend bool compareSlope(const line &l, const line &r);//compare(>) two lines' slope( no numercially, but geometrically)
public:
point start;
point end;
line():start(0,0),end(1,0){}//default constructor which construct the line which go through (0,0) and (1,0)
line(point startpoint, point endpoint) { start = startpoint; end = endpoint; }//constructor( construct with any two point on the line)
void getStandardEquation(double &A, double &B, double &C)const;//get the standard equation of line( Ax+By+C=0)
double length()const;//return the length of line
bool iflinemeet(const line &other)const;//return a bool value represent whether this line meets the other line (1 stand for yes, 0 for no(coincide situation included))
};
//class polygon can represent arbitrary planar polygon in the rectangular coordinate system( in the first quadrant)
class polygon {
protected:
point originalvertex;//the vertex of polygon which is the closest to original point
//( if this shape doesn't have any vertex, then originalvertex is the center point of the shape
point *vertexes;//save the vertexes of the polygon( the order of the vertexes follow the anti-clockwise and begin in orginalvertex)
line *sides;//save the sides of the polygon( follow the same rule of the vertexes)
unsigned int sidenum;//the number of the polygon's sides
void setoriginalvertex(point ov);//reset the originalvertex of the polygon
public:
polygon( unsigned int numofside=0);//contructor which only set number of sides, thus its *sides and *vertexes is null pointer(originalvertex is (0,0))
polygon(point Uoriginalvertex,unsigned int numofside = 0);//contructor which set number of sides and originalvertex, thus its *sides and *vertexes is null pointer
polygon(unsigned int numofside, point vertex[]) throw(error);//contructor, whose parameter is a point array saved the vertexes of the polygon
//if numofside is 0, function will throw a exception( within the exception class is the error type "noside")
~polygon();//destructor
polygon(const polygon &obj);//copy constructor
point getoriginalvertex()const;//return the originalvertex
int getnumofsides()const;//return the sides' number of ploygon
virtual double area()const throw(error);//return polygon's area( if polygon has no vertexes, this function will throw exception( within the exception class is the error type "cantcalculate")
virtual double perimeter()const throw(error);//return polygon's perimeter( if polygon has no sides, this function will throw exception( within the exception class is the error type "cantcalculate")
virtual void show()const {//a simple output function for test
cout << "original vertex is "; originalvertex.show(); cout << " number of sides is"
<< sidenum;
}
};
bool compareSlope(const line &l, const line &r);
具体的实现文件：
#include"Shape.h"
#include<cmath>
//class point {
bool point::operator==(const point &ro)const {
if (x == ro.x&&y == ro.y) {
return true;
}
else {
return false;
}
}
double distancebetweenpoint(const point &a, const point &b)//calculate the distance between two difference point
{
double x = (a.x - b.x);
double y = (a.y - b.y);
x = pow(x, 2);
y = pow(y, 2);
double dis = sqrt(x + y);
return dis;
}
double point::distancetoline(const line &line)const//calculate the distance between this point and line
{
double A, B, C;
line.getStandardEquation(A, B, C);
C = -C;
//calculate the distance
double dis =abs( (A*x + B*y + C) / sqrt(A*A + B*B));
return dis;
}
//class line {
void line::getStandardEquation(double &A, double &B, double &C)const {
//give the line's equation
double dy1 = end.y - start.y;
double dx1 = end.x - start.x;
A = dy1; B = -dx1; C = start.y*dx1 - start.x*dy1;
C = -C;
return;
}
double line::length()const {//return the length of line
return distancebetweenpoint(start, end);
}
bool line::iflinemeet(const line &other)const//return a bool value represent whether this line meets the other line (1 stand for yes, 0 for no)
{
if (end.x<other.start.x || end.y<other.start.y || start.x>other.end.x || start.y>other.end.y)
{
return 0;
}
//get the line's equation
double A1, B1, C1;
getStandardEquation(A1, B1, C1);
//get the line's equation
double A2, B2, C2;
other.getStandardEquation(A2, B2, C2);
if ((A1 / A2) == (B1 / B2)) {
if (C1 != C2)
return 0;
else
return 1;
}
double rx, ry;//calculate the meet point
ry = (C1*A2 / A1 - C2) / (B2 - A2*B1 / A1);
rx = ((-1)*C2 + (-1)*B2*ry) / A2;
if (rx<start.x || rx<other.start.x || rx>end.x || rx>other.end.x ||
ry<start.y || ry<other.start.y || ry>end.y || ry>other.end.y) {
return 0;
}
return 1;
}
//class shape {
polygon::polygon(const polygon &obj) {
sidenum = obj.sidenum;
originalvertex = obj.originalvertex;
if (!obj.vertexes) {
vertexes = nullptr;
}
else {
vertexes = new point[obj.sidenum];
for (int i = 0; i < sidenum; i++) {
vertexes[i] = obj.vertexes[i];
}
}
if (!obj.sides) {
sides = nullptr;
}
else {
sides = new line[obj.sidenum];
for (int i = 0; i < sidenum; i++) {
sides[i] = obj.sides[i];
}
}
}
double polygon::perimeter()const {
if (!sides) {//the shape's can't be represent/calculate this way
throw error(cantcalculate);
}
double perimeter = 0;
for (int i = 0; i < sidenum; i++) {
perimeter += sides[i].length();
}
return perimeter;
}
//the way of calculate the area is refered from the website below:
//https://blog.csdn.net/hemmingway/article/details/7814494
double polygon::area()const {
if (!vertexes) {//the shape has no vertex
throw error(cantcalculate);
}
double s=0;
int n = sidenum - 1;
for (int i = 0; i <= n - 1; i++) {
s += (vertexes[i].x - vertexes[0].x)*(vertexes[i + 1].y - vertexes[0].y) - (vertexes[i].y - vertexes[0].y)*(vertexes[i + 1].x - vertexes[0].x);
}
s = abs(s) / 2;
return s;
}
void polygon::setoriginalvertex(point ov) {
originalvertex = ov;
}
int polygon::getnumofsides()const {
return sidenum;
}
point polygon::getoriginalvertex()const {
return originalvertex;
}
polygon::~polygon() {
if (vertexes != nullptr) {
delete[]vertexes;
}
if (sides != nullptr) {
delete[]sides;
}
}
polygon::polygon(point Uoriginalvertex, unsigned int numofside ):vertexes(nullptr),sides(nullptr),sidenum(numofside),originalvertex(Uoriginalvertex) {}
polygon::polygon(unsigned int numofside):sidenum(numofside),vertexes(nullptr),sides(nullptr),originalvertex(O) {}
bool compareSlope(const line &l, const line &r) {//compare(>) two lines' slope( no numercially, but geometrically)
bool flagl, flagr;
flagl = flagr = 0;
if (l.end.x == l.start.x)//whether the slope is existed
flagl = 1;
if (r.end.x == r.start.x)
flagr = 1;
if (flagl&&flagr)
return 0;
if (flagl) {
double k = (r.end.y - r.start.y) / (r.end.x - r.start.x);
if (k >= 0)
return 1;
else
return 0;
}
if (flagr) {
double k = (l.end.y - l.start.y) / (l.end.x - l.start.x);
if (k >= 0)
return 0;
else
return 1;
}
double kr = (r.end.y - r.start.y) / (r.end.x - r.start.x);
double kl = (l.end.y - l.start.y) / (l.end.x - l.start.x);
if (kl >= 0 ) {
if (kr >= 0)
return kl > kr;
else
return 0;
}
if (kl < 0) {
if (kr < 0)
return kl > kr;
else
return 1;
}
}
bool aTempCompareFunctionfor_polygonConstructor(double kl, double kr) {
if (kl >= 0) {
if (kr >= 0)
return kl > kr;
else
return 0;
}
if (kl < 0) {
if (kr < 0)
return kl > kr;
else
return 1;
}
}
polygon::polygon(unsigned int numofside, point vertex[]) {
if (numofside == 0) {
throw error(errortype(0));
}
//find the originalvertex
sidenum = numofside; double min = distancebetweenpoint(O, vertex[0]);
for (int i = 0; i < numofside; i++) {
if (distancebetweenpoint(O, vertex[i]) <= min) {
originalvertex = vertex[i];
}
}
//set the vertexes in anti-clock order( only make sense when all the vertexes are in the first quadrant )
class dot {//use a list structure to reorder
public:
point v;
double k;//the slope of the line which go through the original vertex and this point
bool flag;//whether the point is the original vertex
dot *next;
dot() = default;
dot(point vertex, point original) :v(vertex), next(nullptr), flag(0) {
if (vertex.x == original.x) {//the slope doesn't exist, so I use a really big numerical value to represent it
k = 1000000000000;
if (vertex.y == original.y)
flag = 1;
}
else {
k = (vertex.y - original.y) / (vertex.x - original.x);
}
}
dot& operator=(const dot &ro) { v = ro.v; k = ro.k; next = ro.next; flag = ro.flag; }
dot(const dot &ro) { v = ro.v; k = ro.k; next = nullptr; flag = ro.flag; }
};
typedef dot* dotp;
int i=1;
dot *head = new dot(vertex[0],originalvertex);//create the head node
while (head->flag) {
delete head;
head = new dot(vertex[i], originalvertex);
i++;
}
dot *p1, *b1; b1 = head;
for ( ; i < numofside; i++) {//create the list
p1 = new dot(vertex[i], originalvertex);
if (p1->flag) { delete p1; continue; }
b1->next = p1;
b1 = p1;
}
//the reorder operation
int num = sidenum-1;
dotp *arr = new dotp[num];
dotp b, p, *t, *todelete;
t = new dotp;//这里只是为了堵住编译器的嘴
todelete = t;
b = p = head;
for ( i = 0; i < num; i++) {
arr[i] = p;
p = p->next;
}
for (int j = 0; j<num; j++) {
double temp;
for (int i = j; i<num; i++) {
if (i == j) {
temp = arr[i]->k;
t = &arr[i];
}
if (!aTempCompareFunctionfor_polygonConstructor(arr[i]->k, temp)){
temp = arr[i]->k;
t = &arr[i];
}
}
dotp lin = arr[j];
arr[j] = *t;
*t = lin;
}
head = arr[0];
b = head;
for ( i = 1; i < num; i++) {
b->next = arr[i];
b = arr[i];
}
b->next = nullptr;
//create the polygon's vertexes and sides
vertexes = new point[sidenum];
sides = new line[sidenum];
vertexes[0] = originalvertex;
p1 = head;
for ( i = 1; i < num+1; i++) {
vertexes[i] = p1->v;
line ts(vertexes[i - 1], vertexes[i]);
sides[i-1] = ts;
p1 = p1->next;
}
line ts(vertexes[sidenum - 1], vertexes[0]);
sides[sidenum - 1] = ts;
//clean up
delete todelete;
for ( i = 0; i < num; i++) {
p = head->next;
delete head;
head = p;
}
}