不规则三角网 Delaunay——TIN

http://blog.csdn.net/u010025211/article/details/25032209

开源库：http://www.cs.cmu.edu/~quake/triangle.html

下载地址： 链接：http://pan.baidu.com/s/1jIlxK6U 密码：2xgg

知识点一：平面中判断一个点是否在三角形内部。

#include <stdio.h>
//m,n表示待检测点的x,y坐标，a,b,c表示三角形的三个点
bool isInTriangle(double m,double n,double ax,double bx,double cx,double ay,double by,double cy) 
{
    double u = (m-ax)*(by-ay)-(n-ay)*(bx-ax);
    u/=(cx-ax)*(by-ay)-(cy-ay)*(bx-ax);
    double v = (m-ax)*(cy-ay)-(n-ay)*(cx-ax);
    v/=(bx-ax)*(cy-ay)-(by-ay)*(cx-ax);
    return u>0&&v>0&&(u+v)<=1;
}
int main(void) {

    bool answer = true;
    answer = isInTriangle(0.5,0.7,0,0,1,1,0,0);

    printf("%s\n", answer?"Point is in triangle.":"Points isn't in triangle.");

    answer = isInTriangle(0.5,0.3,0,0,1,1,0,0);
    printf("%s\n", answer?"Point is in triangle.":"Points isn't in triangle.");
    
}

 知识点二、判断一点是否在三角形的外接圆内

　　　　　　1、外接圆的圆心

#include <stdio.h>

void getCenterOfCircle(double &x,double &y,double x1,double x2,double x3,double y1,double y2,double y3)
{
    x=(x2*x2-x1*x1+y2*y2-y1*y1)*(y3-y1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(y2-y1);
    x/=2*(x2-x1)*(y3-y1)-2*(x3-x1)*(y2-y1);    
    y=(x2*x2-x1*x1+y2*y2-y1*y1)*(x3-x1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(x2-x1);
    y/=2*(y2-y1)*(x3-x1)-2*(y3-y1)*(x2-x1);
} 
int main(void) {

    bool answer = true;
    
    double x=0,y=0;
    getCenterOfCircle(x,y,0,3,3,4,4,0);
    
    printf("%f %f\n", x,y);
    
}

 　　　2.判断点(m,n)是否在三角形的外接圆内

#include <stdio.h>

void getCenterOfCircle(double &x,double &y,double x1,double x2,double x3,double y1,double y2,double y3)
{
    x=(x2*x2-x1*x1+y2*y2-y1*y1)*(y3-y1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(y2-y1);
    x/=2*(x2-x1)*(y3-y1)-2*(x3-x1)*(y2-y1);    
    y=(x2*x2-x1*x1+y2*y2-y1*y1)*(x3-x1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(x2-x1);
    y/=2*(y2-y1)*(x3-x1)-2*(y3-y1)*(x2-x1);
} 
bool isInCircumcircle(double m,double n,double x1,double x2,double x3,double y1,double y2,double y3)
{
    double x=0;
    double y=0;
    getCenterOfCircle(x,y,x1,x2,x3,y1,y2,y3);
    return (m-x)*(m-x)+(n-y)*(n-y)<=(x1-x)*(x1-x)+(y1-y)*(y1-y);
}
int main(void) {
    
    double x=0,y=0;
    bool answer = true;
    answer = isInCircumcircle(0,-1,0,3,3,4,4,0);    
     printf("%s\n", answer?"Point is in Circumcircle.":"Points isn't in Circumcircle.");
}