点到线段所在直线垂足(perpendicular).txt

vc++中的点和直线之间的各种几何算法...对c++初学者或者ACM编程者有很大帮助

/* 判断点与线段的关系,用途很广泛 
本函数是根据下面的公式写的，P是点C到线段AB所在直线的垂足 

  AC dot AB 
  r =     --------- 
  ||AB||^2 
  (Cx-Ax)(Bx-Ax) + (Cy-Ay)(By-Ay) 
  = ------------------------------- 
  L^2 
  
    r has the following meaning: 
	
	  r=0      P = A 
	  r=1      P = B 
	  r<0 P is on the backward extension of AB 
	  r>1      P is on the forward extension of AB 
	  0<r<1 P is interior to AB 
*/ 

double relation(POINT p,LINESEG l) 
{ 
	LINESEG tl; 
	tl.s=l.s; 
	tl.e=p; 
	return dotmultiply(tl.e,l.e,l.s)/(dist(l.s,l.e)*dist(l.s,l.e)); 
} 

// 求点C到线段AB所在直线的垂足 P 
POINT perpendicular(POINT p,LINESEG l) 
{ 
	double r=relation(p,l); 
	POINT tp; 
	tp.x=l.s.x+r*(l.e.x-l.s.x); 
	tp.y=l.s.y+r*(l.e.y-l.s.y); 
	return tp; 
}