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　晋太元中，武陵人捕鱼为业。缘溪行，忘路之远近。忽逢桃花林，夹岸数百步，中无杂树，芳草鲜美，落英缤纷。渔人甚异之，复前行，欲穷其林。　　林尽水源，便得一山，山有小口，仿佛若有光。便舍船，从口入。初极狭，才通人。复行数十步，豁然开朗。土地平旷，屋舍俨然，有良田、美池、桑竹之属。阡陌交通，鸡犬相闻。其中往来种作，男女衣着，悉如外人。黄发垂髫，并怡然自乐。　　见渔人，乃大惊，问所从来。具答之。便要还家，设酒杀鸡作食。村中闻有此人，咸来问讯。自云先世避秦时乱，率妻子邑人来此绝境，不复出焉，遂与外人间隔。问今是何世，乃不知有汉，无论魏晋。此人一一为具言所闻，皆叹惋。余人各复延至其家，皆出酒食。停数日，辞去。此中人语云：“不足为外人道也。”(间隔一作：隔绝) 　　既出，得其船，便扶向路，处处志之。及郡下，诣太守，说如此。太守即遣人随其往，寻向所志，遂迷，不复得路。　　南阳刘子骥，高尚士也，闻之，欣然规往。未果，寻病终。后遂无问津者。 . Prv8 Shell

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///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
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// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
// *       Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
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// copyright notice, this list of conditions and the following disclaimer
// in the documentation and/or other materials provided with the
// distribution.
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// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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///////////////////////////////////////////////////////////////////////////



#ifndef INCLUDED_IMATHLINE_H
#define INCLUDED_IMATHLINE_H

//-------------------------------------
//
//	A 3D line class template
//
//-------------------------------------

#include "ImathVec.h"
#include "ImathLimits.h"
#include "ImathMatrix.h"
#include "ImathNamespace.h"

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER


template <class T>
class Line3
{
  public:

    Vec3<T>			pos;
    Vec3<T>			dir;
    
    //-------------------------------------------------------------
    //	Constructors - default is normalized units along direction
    //-------------------------------------------------------------

    Line3() {}
    Line3(const Vec3<T>& point1, const Vec3<T>& point2);

    //------------------
    //	State Query/Set
    //------------------

    void			set(const Vec3<T>& point1, 
				    const Vec3<T>& point2);

    //-------
    //	F(t)
    //-------

    Vec3<T>			operator() (T parameter) const;

    //---------
    //	Query
    //---------

    T				distanceTo(const Vec3<T>& point) const;
    T				distanceTo(const Line3<T>& line) const;
    Vec3<T>			closestPointTo(const Vec3<T>& point) const;
    Vec3<T>			closestPointTo(const Line3<T>& line) const;
};


//--------------------
// Convenient typedefs
//--------------------

typedef Line3<float> Line3f;
typedef Line3<double> Line3d;


//---------------
// Implementation
//---------------

template <class T>
inline Line3<T>::Line3(const Vec3<T> &p0, const Vec3<T> &p1)
{
    set(p0,p1);
}

template <class T>
inline void Line3<T>::set(const Vec3<T> &p0, const Vec3<T> &p1)
{
    pos = p0; dir = p1-p0;
    dir.normalize();
}

template <class T>
inline Vec3<T> Line3<T>::operator()(T parameter) const
{
    return pos + dir * parameter;
}

template <class T>
inline T Line3<T>::distanceTo(const Vec3<T>& point) const
{
    return (closestPointTo(point)-point).length();
}

template <class T>
inline Vec3<T> Line3<T>::closestPointTo(const Vec3<T>& point) const
{
    return ((point - pos) ^ dir) * dir + pos;
}

template <class T>
inline T Line3<T>::distanceTo(const Line3<T>& line) const
{
    T d = (dir % line.dir) ^ (line.pos - pos);
    return (d >= 0)? d: -d;
}

template <class T>
inline Vec3<T> 
Line3<T>::closestPointTo(const Line3<T>& line) const
{
    // Assumes the lines are normalized

    Vec3<T> posLpos = pos - line.pos ;
    T c = dir ^ posLpos;
    T a = line.dir ^ dir;
    T f = line.dir ^ posLpos ;
    T num = c - a * f;

    T denom = a*a - 1;

    T absDenom = ((denom >= 0)? denom: -denom);

    if (absDenom < 1)
    {
	T absNum = ((num >= 0)? num: -num);

	if (absNum >= absDenom * limits<T>::max())
	    return pos;
    }

    return pos + dir * (num / denom);
}

template<class T>
std::ostream& operator<< (std::ostream &o, const Line3<T> &line)
{
    return o << "(" << line.pos << ", " << line.dir << ")";
}

template<class S, class T>
inline Line3<S> operator * (const Line3<S> &line, const Matrix44<T> &M)
{
    return Line3<S>( line.pos * M, (line.pos + line.dir) * M );
}


IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHLINE_H

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