imathfrustum.h

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// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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#ifndef INCLUDED_IMATHFRUSTUM_H
#define INCLUDED_IMATHFRUSTUM_H


#include "ImathVec.h"
#include "ImathPlane.h"
#include "ImathLine.h"
#include "ImathMatrix.h"
#include "ImathLimits.h"
#include "ImathFun.h"
#include "IexMathExc.h"

#if defined _WIN32 || defined _WIN64
    #ifdef near
        #undef near
    #endif
    #ifdef far
        #undef far
    #endif
#endif

namespace Imath {

//
//	template class Frustum<T>
//
//	The frustum is always located with the eye point at the
//	origin facing down -Z. This makes the Frustum class 
//	compatable with OpenGL (or anything that assumes a camera
//	looks down -Z, hence with a right-handed coordinate system) 
//	but not with RenderMan which assumes the camera looks down
//	+Z. Additional functions are provided for conversion from
//	and from various camera coordinate spaces.
//


template<class T>
class Frustum
{
  public:
    Frustum();
    Frustum(const Frustum &);
    Frustum(T near, T far, T left, T right, T top, T bottom, bool ortho=false);
    Frustum(T near, T far, T fovx, T fovy, T aspect);
    virtual ~Frustum();

    //--------------------
    // Assignment operator
    //--------------------

    const Frustum &operator	= (const Frustum &);

    //--------------------
    //  Operators:  ==, !=
    //--------------------
    
    bool                        operator == (const Frustum<T> &src) const;
    bool                        operator != (const Frustum<T> &src) const;

    //--------------------------------------------------------
    //  Set functions change the entire state of the Frustum
    //--------------------------------------------------------

    void		set(T near, T far, 
			    T left, T right, 
			    T top, T bottom, 
			    bool ortho=false);

    void		set(T near, T far, T fovx, T fovy, T aspect);

    //------------------------------------------------------
    //	These functions modify an already valid frustum state
    //------------------------------------------------------

    void		modifyNearAndFar(T near, T far);
    void		setOrthographic(bool);

    //--------------
    //  Access
    //--------------

    bool		orthographic() const	{ return _orthographic; }
    T			near() const		{ return _near;		}
    T			far() const		{ return _far;		}
    T			left() const		{ return _left;		}
    T			right() const		{ return _right;	}
    T			bottom() const		{ return _bottom;	}
    T			top() const		{ return _top;		}

    //-----------------------------------------------------------------------
    //  Sets the planes in p to be the six bounding planes of the frustum, in
    //  the following order: top, right, bottom, left, near, far.
    //  Note that the planes have normals that point out of the frustum.
    //  The version of this routine that takes a matrix applies that matrix
    //  to transform the frustum before setting the planes.
    //-----------------------------------------------------------------------

    void		planes(Plane3<T> p[6]);
    void		planes(Plane3<T> p[6], const Matrix44<T> &M);

    //----------------------
    //  Derived Quantities
    //----------------------

    T			fovx() const;
    T			fovy() const;
    T			aspect() const;
    Matrix44<T>		projectionMatrix() const;

    //-----------------------------------------------------------------------
    //  Takes a rectangle in the screen space (i.e., -1 <= left <= right <= 1 
    //  and -1 <= bottom <= top <= 1) of this Frustum, and returns a new
    //  Frustum whose near clipping-plane window is that rectangle in local
    //  space.  
    //-----------------------------------------------------------------------

    Frustum<T>		window(T left, T right, T top, T bottom) const;

    //----------------------------------------------------------
    // Projection is in screen space / Conversion from Z-Buffer
    //----------------------------------------------------------

    Line3<T>		projectScreenToRay( const Vec2<T> & ) const;
    Vec2<T>		projectPointToScreen( const Vec3<T> & ) const;

    T			ZToDepth(long zval, long min, long max) const;
    T			normalizedZToDepth(T zval) const;
    long		DepthToZ(T depth, long zmin, long zmax) const;

    T			worldRadius(const Vec3<T> &p, T radius) const;
    T			screenRadius(const Vec3<T> &p, T radius) const;


  protected:

    Vec2<T>		screenToLocal( const Vec2<T> & ) const;
    Vec2<T>		localToScreen( const Vec2<T> & ) const;

  protected:
    T			_near;
    T			_far;
    T			_left;
    T			_right;
    T			_top;
    T			_bottom;
    bool		_orthographic;
};


template<class T>
inline Frustum<T>::Frustum()
{
    set(T (0.1),
	T (1000.0),
	T (-1.0),
	T (1.0),
	T (1.0),
	T (-1.0),
	false);
}

template<class T>
inline Frustum<T>::Frustum(const Frustum &f)
{
    *this = f;
}

template<class T>
inline Frustum<T>::Frustum(T n, T f, T l, T r, T t, T b, bool o)
{
    set(n,f,l,r,t,b,o);
}

template<class T>
inline Frustum<T>::Frustum(T near, T far, T fovx, T fovy, T aspect)
{
    set(near,far,fovx,fovy,aspect);
}

template<class T>
Frustum<T>::~Frustum()
{
}

template<class T>
const Frustum<T> &
Frustum<T>::operator = (const Frustum &f)
{
    _near         = f._near;
    _far          = f._far;
    _left         = f._left;
    _right        = f._right;
    _top          = f._top;
    _bottom       = f._bottom;
    _orthographic = f._orthographic;

    return *this;
}

template <class T>
bool
Frustum<T>::operator == (const Frustum<T> &src) const
{
    return
        _near         == src._near   &&
        _far          == src._far    &&
        _left         == src._left   &&
        _right        == src._right  &&
        _top          == src._top    &&
        _bottom       == src._bottom &&
        _orthographic == src._orthographic;
}

template <class T>
inline bool
Frustum<T>::operator != (const Frustum<T> &src) const
{
    return !operator== (src);
}

template<class T>
void Frustum<T>::set(T n, T f, T l, T r, T t, T b, bool o)
{
    _near	    = n;
    _far	    = f;
    _left	    = l;
    _right	    = r;
    _bottom	    = b;
    _top	    = t;
    _orthographic   = o;
}

template<class T>
void Frustum<T>::modifyNearAndFar(T n, T f)
{
    if ( _orthographic )
    {
	_near = n;
    }
    else
    {
	Line3<T>  lowerLeft( Vec3<T>(0,0,0), Vec3<T>(_left,_bottom,-_near) );
	Line3<T> upperRight( Vec3<T>(0,0,0), Vec3<T>(_right,_top,-_near) );
	Plane3<T> nearPlane( Vec3<T>(0,0,-1), n );

	Vec3<T> ll,ur;
	nearPlane.intersect(lowerLeft,ll);
	nearPlane.intersect(upperRight,ur);

	_left	= ll.x;
	_right	= ur.x;
	_top	= ur.y;
	_bottom	= ll.y;
	_near	= n;
	_far	= f;
    }

    _far = f;
}

template<class T>
void Frustum<T>::setOrthographic(bool ortho)
{
    _orthographic   = ortho;
}

template<class T>
void Frustum<T>::set(T near, T far, T fovx, T fovy, T aspect)
{
    if (fovx != 0 && fovy != 0)
	throw Iex::ArgExc ("fovx and fovy cannot both be non-zero.");

    if (fovx != 0)
    {
	_right	    = near * Math<T>::tan(fovx/2.0);
	_left	    = -_right;
	_top	    = ((_right - _left)/aspect)/2.0;
	_bottom	    = -_top;
    }
    else
    {
	_top	    = near * Math<T>::tan(fovy/2.0);
	_bottom	    = -_top;
	_right	    = (_top - _bottom) * aspect / 2.0;
	_left	    = -_right;
    }
    _near	    = near;
    _far	    = far;
    _orthographic   = false;
}

template<class T>
T Frustum<T>::fovx() const
{
    return Math<T>::atan2(_right,_near) - Math<T>::atan2(_left,_near);
}

template<class T>
T Frustum<T>::fovy() const
{
    return Math<T>::atan2(_top,_near) - Math<T>::atan2(_bottom,_near);
}

template<class T>
T Frustum<T>::aspect() const
{
    T rightMinusLeft = _right-_left;
    T topMinusBottom = _top-_bottom;

    if (abs(topMinusBottom) < 1 &&
	abs(rightMinusLeft) > limits<T>::max() * abs(topMinusBottom))
    {
	throw Iex::DivzeroExc ("Bad viewing frustum: "
			       "aspect ratio cannot be computed.");
    }

    return rightMinusLeft / topMinusBottom;
}

template<class T>
Matrix44<T> Frustum<T>::projectionMatrix() const
{
    T rightPlusLeft  = _right+_left;
    T rightMinusLeft = _right-_left;

    T topPlusBottom  = _top+_bottom;