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。 .
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Current File : //usr/include/OpenEXR/ImathVecAlgo.h
///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
// 
// 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.
// *       Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following disclaimer
// in the documentation and/or other materials provided with the
// distribution.
// *       Neither the name of Industrial Light & Magic nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
///////////////////////////////////////////////////////////////////////////



#ifndef INCLUDED_IMATHVECALGO_H
#define INCLUDED_IMATHVECALGO_H

//-------------------------------------------------------------------------
//
//      This file contains algorithms applied to or in conjunction
//      with points (Imath::Vec2 and Imath::Vec3).
//      The assumption made is that these functions are called much
//      less often than the basic point functions or these functions
//      require more support classes.
//
//-------------------------------------------------------------------------

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

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER


//-----------------------------------------------------------------
// Find the projection of vector t onto vector s (Vec2, Vec3, Vec4)
//-----------------------------------------------------------------

template <class Vec> Vec        project (const Vec &s, const Vec &t);


//------------------------------------------------
// Find a vector that is perpendicular to s and
// in the same plane as s and t (Vec2, Vec3, Vec4)
//------------------------------------------------

template <class Vec> Vec        orthogonal (const Vec &s, const Vec &t);


//-----------------------------------------------
// Find the direction of a ray s after reflection
// off a plane with normal t (Vec2, Vec3, Vec4)
//-----------------------------------------------

template <class Vec> Vec        reflect (const Vec &s, const Vec &t);


//--------------------------------------------------------------------
// Find the vertex of triangle (v0, v1, v2) that is closest to point p
// (Vec2, Vec3, Vec4)
//--------------------------------------------------------------------

template <class Vec> Vec        closestVertex (const Vec &v0,
                                               const Vec &v1,
                                               const Vec &v2, 
                                               const Vec &p);

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

template <class Vec>
Vec
project (const Vec &s, const Vec &t)
{
    Vec sNormalized = s.normalized();
    return sNormalized * (sNormalized ^ t);
}

template <class Vec>
Vec
orthogonal (const Vec &s, const Vec &t)
{
    return t - project (s, t);
}

template <class Vec>
Vec
reflect (const Vec &s, const Vec &t)
{
    return s - typename Vec::BaseType(2) * (s - project(t, s));
}

template <class Vec>
Vec
closestVertex(const Vec &v0,
              const Vec &v1,
              const Vec &v2, 
              const Vec &p)
{
    Vec nearest = v0;
    typename Vec::BaseType neardot = (v0 - p).length2();
    typename Vec::BaseType tmp     = (v1 - p).length2();

    if (tmp < neardot)
    {
        neardot = tmp;
        nearest = v1;
    }

    tmp = (v2 - p).length2();

    if (tmp < neardot)
    {
        neardot = tmp;
        nearest = v2;
    }

    return nearest;
}


IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHVECALGO_H

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