计算几何(判断四边形形状) - Determine the Shape - UVA 11800
题意:
给 定 四 个 点 坐 标 , 判 断 四 边 形 形 状 。 给定四个点坐标,判断四边形形状。给定四个点坐标,判断四边形形状。
输入:
T 组 测 试 数 据 , T组测试数据,T组测试数据,
每 组 包 括 四 个 点 的 坐 标 。 每组包括四个点的坐标。每组包括四个点的坐标。
输出:
四 边 形 形 状 。 四边形形状。四边形形状。
Sample Input
6
0 0
2 0
2 2
0 2
0 0
3 0
3 2
0 2
0 0
8 4
5 0
3 4
0 0
2 0
3 2
1 2
0 0
5 0
4 3
1 3
0 0
5 0
4 3
1 4
Sample Output
Case 1: Square
Case 2: Rectangle
Case 3: Rhombus
Case 4: Parallelogram
Case 5: Trapezium
Case 6: Ordinary Quadrilateral
代码:
#include<iostream>
#include<cmath>
#include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const double eps=1e-10;
const double pi=acos(-1.0);
struct Point
{
double x,y;
Point(double x=0,double y=0) : x(x), y(y) {}
};
//点与向量
typedef Point Vector;
Vector operator + (Vector A,Vector B) { return Vector(A.x+B.x,A.y+B.y); }
Vector operator - (Point A,Point B) { return Vector(A.x-B.x,A.y-B.y); }
Vector operator * (Vector A,double p) { return Vector(A.x*p,A.y*p); }
Vector operator / (Vector A,double p) { return Vector(A.x/p,A.y/p); }
bool operator < (const Point &a,const Point &b)
{
return a.x<b.x || (a.x==b.x && a.y<b.y);
}
int dcmp(double x)
{
if(fabs(x)<eps) return 0;
else return x<0 ? -1 : 1;
}
bool operator == (const Point &a, const Point &b)
{
return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;
}
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)); } //A和B夹角
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; } //若A到B逆时针则为正,否则为负
double Area2(Point A,Point B,Point C) { return Cross(B-A,C-A); } //三角形ABC的面积的两倍(有方向)
//点和直线
struct Line
{//直线定义
Point v, p;
Vector dir;
double ang;
Line() { } //构造函数
Line(const Line& L): p(L.p), dir(L.dir), ang(L.ang) { }
Line(Point v, Point p):v(v), p(p){ dir=p-v; ang=atan2(dir.y,dir.x); }
bool operator < (const Line& L) const //极角排序
{
return ang < L.ang;
}
Point point(double t)
{//返回点P = v + (p - v)*t
return v + dir*t;
}
};
typedef vector<Point> Polygon;
//平行四边形的判定(保证四边形顶点按顺序给出)
bool isParallelogram(Polygon p) {
if (dcmp(Length(p[0]-p[1]) - Length(p[2]-p[3])) || dcmp(Length(p[0]-p[3]) - Length(p[2]-p[1]))) return false;
Line a = Line(p[0], p[1]);
Line b = Line(p[1], p[2]);
Line c = Line(p[3], p[2]);
Line d = Line(p[0], p[3]);
return dcmp(a.ang - c.ang) == 0 && dcmp(b.ang - d.ang) == 0;
}
//梯形的判定
bool isTrapezium(Polygon p) {
Line a = Line(p[0], p[1]);
Line b = Line(p[1], p[2]);
Line c = Line(p[3], p[2]);
Line d = Line(p[0], p[3]);
return (dcmp(a.ang - c.ang) == 0 && dcmp(b.ang - d.ang)) || (dcmp(a.ang - c.ang) && dcmp(b.ang - d.ang) == 0);
}
//菱形的判定
bool isRhombus(Polygon p) {
if (!isParallelogram(p)) return false;
return dcmp(Length(p[1]-p[0]) - Length(p[2]-p[1])) == 0;
}
//矩形的判定
bool isRectangle(Polygon p) {
if (!isParallelogram(p)) return false;
return dcmp(Length(p[2]-p[0]) - Length(p[3]-p[1])) == 0;
}
//正方形的判定
bool isSquare(Polygon p) {
return isRectangle(p) && isRhombus(p);
}
int check(Polygon p)
{
if(isSquare(p)) return 1;
else if(isRectangle(p)) return 2;
else if(isRhombus(p)) return 3;
else if(isParallelogram(p)) return 4;
else if(isTrapezium(p)) return 5;
else return 6;
}
int main()
{
int T;
scanf("%d",&T);
for(int C=1;C<=T;C++)
{
Polygon p;
Point tmp;
for(int i=0;i<4;i++) {scanf("%lf%lf",&tmp.x,&tmp.y); p.push_back(tmp);}
int t=check(p);//V[0],V[1],V[2],V[3];
swap(p[1],p[2]);
t=min(t,check(p));//V[0],V[2],V[1],V[3];
swap(p[1],p[2]);
swap(p[2],p[3]);
t=min(t,check(p));//V[0],V[1],V[3],V[2];
printf("Case %d: ",C);
if(t==1) puts("Square");
else if(t==2) puts("Rectangle");
else if(t==3) puts("Rhombus");
else if(t==4) puts("Parallelogram");
else if(t==5) puts("Trapezium");
else puts("Ordinary Quadrilateral");
}
return 0;
}