2條線段的最短距離

float DistanceLineToLine( const osg::Vec3d& p1,const osg::Vec3d& p2,const osg::Vec3d& p3,const osg::Vec3d& p4 )
	{
		float distance;
		float x1 = p1.x(); //A點座標（x1,y1,z1）
		float y1 = p1.y();
		float z1 = p1.z();
		float x2 = p2.x(); //B點座標（x2,y2,z2）
		float y2 = p2.y();
		float z2 = p2.z();
		float x3 = p3.x(); //C點座標（x3,y3,z3）
		float y3 = p3.y();
		float z3 = p3.z();
		float x4 = p4.x(); //D點座標（x4,y4,z4）
		float y4 = p4.y();
		float z4 = p4.z();

		float a = (x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)+(z2-z1)*(z2-z1);
		float b = -((x2-x1)*(x4-x3)+(y2-y1)*(y4-y3)+(z2-z1)*(z4-z3));
		float c = -((x1-x2)*(x1-x3)+(y1-y2)*(y1-y3)+(z1-z2)*(z1-z3));

		float d = -((x2-x1)*(x4-x3)+(y2-y1)*(y4-y3)+(z2-z1)*(z4-z3));
		float e = (x4-x3)*(x4-x3)+(y4-y3)*(y4-y3)+(z4-z3)*(z4-z3);
		float f = -((x1-x3)*(x4-x3)+(y1-y3)*(y4-y3)+(z1-z3)*(z4-z3));

		if ((a*e-b*d)==0&&(b*d-a*e)==0) //平行
		{
			float d1 = (p1-p3).length();
			float d2 = (p1-p4).length();
			distance = (d1<d2)?d1:d2;
			return distance;
		}

		float s = (b*f-e*c)/(a*e-b*d);
		float t = (a*f-d*c)/(b*d-a*e);

		if(0<=s&&s<=1&&0<=t&&t<=1) //說明P點落線上段AB上,Q點落線上段CD上
		{
			//2條線段的公垂線段PQ;
			//P點座標
			float X = x1+s*(x2-x1);
			float Y = y1+s*(y2-y1);
			float Z = z1+s*(z2-z1);
			//Q點座標
			float U = x3+t*(x4-x3);
			float V = y3+t*(y4-y3);
			float W = z3+t*(z4-z3);
			osg::Vec3d P(X,Y,Z);
			osg::Vec3d Q(U,V,W);
			distance = (P-Q).length();
		}
		else
		{
			float d1 = DistancePointToLine(p3,p4,p1);
			float d2 = DistancePointToLine(p3,p4,p2);
			float d3 = DistancePointToLine(p1,p2,p3);
			float d4 = DistancePointToLine(p1,p2,p4);
			distance = (d1<d2)?d1:d2;
			distance = (distance<d3)?distance:d3;
			distance = (distance<d4)?distance:d4;
		}
		return distance;
	}
 

空間中一個點到空間中一條線段的最短距離

float DistancePointToLine( const osg::Vec3d& star, const osg::Vec3d& end,const osg::Vec3d& center )
{
float distance;
float x0 = center.x();//P點座標（x0,y0,z0）
float y0 = center.y();
float z0 = center.z();
float x1 = star.x(); //A點座標（x1,y1,z1）
float y1 = star.y();
float z1 = star.z();
float x2 = end.x();//B點座標（x2,y2,z2）
float y2 = end.y();
float z2 = end.z();
float t = ((x1-x0)*(x1-x2)+(y1-y0)*(y1-y2)+(z1-z0)*(z1-z2))
      /((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)+(z1-z2)*(z1-z2));
if (0<=t&&t<=1)//垂足Q點落線上段AB上
{
float X = x1+t*(x2-x1);
float Y = y1+t*(y2-y1);
float Z = z1+t*(z2-z1);
osg::Vec3d Q(X,Y,Z);
distance = (Q-center).length();
}
if (t<0) //垂足Q點不落線上段AB上，而是落在BA的延長線上
{
distance = (star-center).length();
}
if (t>1) //垂足Q點不落線上段AB上，而是落在AB的延長線上
{
distance = (end-center).length();
}
return distance;
}