c 空间点到直线的垂足及距离计算

已知条件：

已知空间一个点的坐标a(x0,y0,z0)，已知空间的另外两个点的坐标b（x1,y1,z1），c(x2,y2,z2),求a点到 b，c两点所在直线的 距离最近的点的坐标 可以说是a点到 过b，c点直线垂足的坐标。并且求出a点到直线的距离。

 

#include <stdio.h>
#include <conio.h>
#include <math.h>

typedef struct{
double x,y,z;
}point;

typedef struct{
point p1,p2;
}line;

main()
{
line lne;
point points[3],point_Q;
int initpoint(point *a,double x,double y,double z);
int printpoint(point a);
int initline(line *l,point a,point b);
int point2line(line l,point a,point *b);
double p2p(point a,point b);

/*初始化三个点,其中前两个点用来做直线的*/
initpoint(&points[0],1,2,3);
initpoint(&points[1],-1,4,6);
initpoint(&points[2],0,0,0);
initline(&lne,points[0],points[1]); /*前两个点做线*/



/*求垂足*/
point2line(lne,points[2],&point_Q);

printpoint(point_Q);/*输出垂足*/
printf("dist=%lf/n",p2p(points[2],point_Q));
getch();
}




int initpoint(point *a,double x,double y,double z)
{
a->x=x;
a->y=y;
a->z=z;
return 1;
}


int printpoint(point a)
{
printf("x=%lf y=%lf z=%lf/n",a.x,a.y,a.z);
}

int initline(line *l,point a,point b)
{
l->p1.x=a.x;
l->p1.y=a.y;
l->p1.z=a.z;

l->p2.x=b.x;
l->p2.y=b.y;
l->p2.z=b.z;
return 1;
}


int point2line(line l,point p,point *Q)
{
double a,b,c;
double A,B,C;

a=l.p2.x-l.p1.x;
b=l.p2.y-l.p1.y;
c=l.p2.z-l.p1.z;

A=a*p.x+b*p.y+c*p.z;
B=b*l.p1.x-a*l.p1.y;
C=c*l.p1.x-a*l.p1.z;

if (a!=0)
{
  Q->x=(A*a+B*b+C*c)/(a*a+b*b+c*c);
  Q->y=(b*Q->x-B)/a;
  Q->z=(c*Q->x-C)/a;
}
else
{
  double D,temp;
  D=c*l.p1.y-b*l.p1.z;
  temp=b*b+c*c;
  Q->y=(A*b+D*c)/temp;
  Q->z=(A*c-D*b)/temp;
  Q->x=(B+a*Q->y)/b;
}
 
return 1;
}


double p2p(point a,point b)
{
double dx,dy,dz;
dx=a.x-b.x;
dy=a.y-b.y;
dz=a.z-b.z;
return sqrt(dx*dx+dy*dy+dz*dz);
}