ImathLine.h

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//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
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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"

namespace Imath {


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 );
}


} // namespace Imath

#endif