求面积问题,请大家来帮忙讨论!

queena 2003-10-20 11:46:24

问题是:求多边型的面积;
1.先给出顶点数N;
2.然后按顺序给出每一个顶点:
3.判断是否是多边型,是,输出;不是,输出不是.
如
N=5
(0,0)(0,1)(1,1)(0.5,0.5)(1,0)注意这里的点是按顺序输入的;
那么输出:
是多边型;面积是:0.75
如
N=4
(0,0)(1,0)(0,1)(1,1)
那么输出不是多边型

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queena 2003-10-22

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对于凹多边型我的想法是:
任取一点作为寻找起点,按照起点开始顺序走;
对每相邻的俩条线如果它们的夹角是小于180度
那么就计算接下去的两条;
如果大于的话就把第二条的起点与本次寻找的起点相连
形成凸边型计算;
那么就把凹多边型分成几个凸多边型进行计算.
谢谢zhang21cnboy(事了抚衣去，不留身与名)
的代码

zhang21cnboy 2003-10-22

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凹多边形的我也有，不过呢，这个东东就不给你了！不然人家说我泄漏秘密哦！

queena 2003-10-22

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呵呵还是谢谢了

zhang21cnboy 2003-10-21

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上代码：
package com.kefa.zhang.math;

import java.awt.Point;
import java.lang.Math;
import java.util.Vector;
/**
* <p>描述：计算两点之间的距离，计算多边形的面积</p>
*
* */
public class MeasureMath {
public MeasureMath() {
}

/**
* 计算两点之间的距离
* */
public static double distBetween2Dots(Point point1,Point point2){
double res = Math.sqrt((point2.getX()-point1.getX()) * (point2.getX()-point1.getX())
+ (point2.getY()-point1.getY()) * (point2.getY()-point1.getY()));
return res;
}

/**
* 按顺序计算各点之间的距离之和,带方向
* **/
public static double distAmongNDots(Vector points){
int j=0;
double res1 = 0.0;
for (int i=0;i<points.size();i++){
Point p1 = (Point)points.get(j);
Point p2 = (Point)points.get(i);
res1 += MeasureMath.distBetween2Dots(p1,p2);
j = i;
}
return res1;
}

/**
* 计算三角形的面积
* */
public double getAreaOf3Angels(Point p1,Point p2,Point p3){
double a = MeasureMath.distBetween2Dots(p1,p2);
double b = MeasureMath.distBetween2Dots(p2,p3);
double c = MeasureMath.distBetween2Dots(p1,p3);

double all = 0.5*(a+b+c);

return Math.sqrt(all*(all-a)*(all-b)*(all-c));
}

//判断是否是凸多边形
public boolean validateAngels(Vector points){
boolean rt = true;

int j = 0;
int z = 0;
boolean left=false,right = false;
for(int i=0;i<points.size();i++){

j = (i+1)%points.size();
z = (i+2)%points.size();

Point p1 = (Point)points.get(i);
Point p2 = (Point)points.get(j);
Point p3 = (Point)points.get(z);

Point ft1 = new Point();
ft1.setLocation(p2.getX()-p1.getX(),p2.getY()-p1.getY());

Point ft2 = new Point();
ft2.setLocation(p3.getX()-p1.getX(),p3.getY()-p1.getY());

//求叉积

double cj = ft1.getX()*ft2.getY() - ft1.getY()*ft2.getX();

if (cj < 0) //左边
left = true;
else //右边
right = true;

if((left == true) && (right == true)){//如果有左边，也有右边，则一定不是凸多边形
rt = false;
break;
}
// i++;
j++;
z++;

}
return rt;
}
/**
* 计算多边形面积
* */
public double getAreaOfNAngels(Vector points)throws Exception{

if(!this.validateAngels(points)){
throw new StyleError("计算面积不允许凹多边形");
}
double rts = this.calculArea(points);
return rts;

}

private double calculArea(Vector points){
double rs = 0.0;

Point p1 = (Point)points.get(0);
Point p2 = (Point)points.get(1);
Point p3 = (Point)points.get(2);

rs = this.getAreaOf3Angels(p1,p2,p3);
Vector new1 = points;
new1.remove(1);
if (new1.size() >=3)
return rs + calculArea(new1);
else
return rs;
}

public static void main(String[] args) {
MeasureMath measureMath1 = new MeasureMath();
}

}

class StyleError extends Exception {
String ErrorMsg = null;
public StyleError(String msg) {

ErrorMsg = msg;
}

public String toString() {
return ErrorMsg;
}
}

zhang21cnboy 2003-10-21