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///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
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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 "ImathNamespace.h"
#include "IexMathExc.h"
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
//
// 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.
//
// nearPlane/farPlane: near/far are keywords used by Microsoft's
// compiler, so we use nearPlane/farPlane instead to avoid
// issues.
template<class T>
class Frustum
{
public:
Frustum();
Frustum(const Frustum &);
Frustum(T nearPlane, T farPlane, T left, T right, T top, T bottom, bool ortho=false);
Frustum(T nearPlane, T farPlane, 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 nearPlane, T farPlane,
T left, T right,
T top, T bottom,
bool ortho=false);
void set(T nearPlane, T farPlane, T fovx, T fovy, T aspect);
//------------------------------------------------------
// These functions modify an already valid frustum state
//------------------------------------------------------
void modifyNearAndFar(T nearPlane, T farPlane);
void setOrthographic(bool);
//--------------
// Access
//--------------
bool orthographic() const { return _orthographic; }
T nearPlane() const { return _nearPlane; }
T hither() const { return _nearPlane; }
T farPlane() const { return _farPlane; }
T yon() const { return _farPlane; }
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]) const;
void planes(Plane3<T> p[6], const Matrix44<T> &M) const;
//----------------------
// Derived Quantities
//----------------------
T fovx() const;
T fovy() const;
T aspect() const;
Matrix44<T> projectionMatrix() const;
bool degenerate() 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 _nearPlane;
T _farPlane;
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 nearPlane, T farPlane, T fovx, T fovy, T aspect)
{
set(nearPlane,farPlane,fovx,fovy,aspect);
}
template<class T>
Frustum<T>::~Frustum()
{
}
template<class T>
const Frustum<T> &
Frustum<T>::operator = (const Frustum &f)
{
_nearPlane = f._nearPlane;
_farPlane = f._farPlane;
_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
_nearPlane == src._nearPlane &&
_farPlane == src._farPlane &&
_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)
{
_nearPlane = n;
_farPlane = f;
_left = l;
_right = r;
_bottom = b;
_top = t;
_orthographic = o;
}
template<class T>
void Frustum<T>::modifyNearAndFar(T n, T f)
{
if ( _orthographic )
{
_nearPlane = n;
}
else
{
Line3<T> lowerLeft( Vec3<T>(0,0,0), Vec3<T>(_left,_bottom,-_nearPlane) );
Line3<T> upperRight( Vec3<T>(0,0,0), Vec3<T>(_right,_top,-_nearPlane) );
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;
_nearPlane = n;
_farPlane = f;
}
_farPlane = f;
}
template<class T>
void Frustum<T>::setOrthographic(bool ortho)
{
_orthographic = ortho;
}
template<class T>
void Frustum<T>::set(T nearPlane, T farPlane, T fovx, T fovy, T aspect)
{
if (fovx != 0 && fovy != 0)
throw IEX_NAMESPACE::ArgExc ("fovx and fovy cannot both be non-zero.");
const T two = static_cast<T>(2);
if (fovx != 0)
{
_right = nearPlane * Math<T>::tan(fovx / two);
_left = -_right;
_top = ((_right - _left) / aspect) / two;
_bottom = -_top;
}
else
{
_top = nearPlane * Math<T>::tan(fovy / two);
_bottom = -_top;
_right = (_top - _bottom) * aspect / two;
_left = -_right;
}
_nearPlane = nearPlane;
_farPlane = farPlane;
_orthographic = false;
}
template<class T>
T Frustum<T>::fovx() const
{
return Math<T>::atan2(_right,_nearPlane) - Math<T>::atan2(_left,_nearPlane);
}
template<class T>
T Frustum<T>::fovy() const
{
return Math<T>::atan2(_top,_nearPlane) - Math<T>::atan2(_bottom,_nearPlane);
}
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_NAMESPACE::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;
T topMinusBottom = _top-_bottom;
T farPlusNear = _farPlane+_nearPlane;
T farMinusNear = _farPlane-_nearPlane;
if ((abs(rightMinusLeft) < 1 &&
abs(rightPlusLeft) > limits<T>::max() * abs(rightMinusLeft)) ||
(abs(topMinusBottom) < 1 &&
abs(topPlusBottom) > limits<T>::max() * abs(topMinusBottom)) ||
(abs(farMinusNear) < 1 &&
abs(farPlusNear) > limits<T>::max() * abs(farMinusNear)))
{
throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
"projection matrix cannot be computed.");
}
if ( _orthographic )
{
T tx = -rightPlusLeft / rightMinusLeft;
T ty = -topPlusBottom / topMinusBottom;
T tz = -farPlusNear / farMinusNear;
if ((abs(rightMinusLeft) < 1 &&
2 > limits<T>::max() * abs(rightMinusLeft)) ||
(abs(topMinusBottom) < 1 &&
2 > limits<T>::max() * abs(topMinusBottom)) ||
(abs(farMinusNear) < 1 &&
2 > limits<T>::max() * abs(farMinusNear)))
{
throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
"projection matrix cannot be computed.");
}
T A = 2 / rightMinusLeft;
T B = 2 / topMinusBottom;
T C = -2 / farMinusNear;
return Matrix44<T>( A, 0, 0, 0,
0, B, 0, 0,
0, 0, C, 0,
tx, ty, tz, 1.f );
}
else
{
T A = rightPlusLeft / rightMinusLeft;
T B = topPlusBottom / topMinusBottom;
T C = -farPlusNear / farMinusNear;
T farTimesNear = -2 * _farPlane * _nearPlane;
if (abs(farMinusNear) < 1 &&
abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
{
throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
"projection matrix cannot be computed.");
}
T D = farTimesNear / farMinusNear;
T twoTimesNear = 2 * _nearPlane;
if ((abs(rightMinusLeft) < 1 &&
abs(twoTimesNear) > limits<T>::max() * abs(rightMinusLeft)) ||
(abs(topMinusBottom) < 1 &&
abs(twoTimesNear) > limits<T>::max() * abs(topMinusBottom)))
{
throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
"projection matrix cannot be computed.");
}
T E = twoTimesNear / rightMinusLeft;
T F = twoTimesNear / topMinusBottom;
return Matrix44<T>( E, 0, 0, 0,
0, F, 0, 0,
A, B, C, -1,
0, 0, D, 0 );
}
}
template<class T>
bool Frustum<T>::degenerate() const
{
return (_nearPlane == _farPlane) ||
(_left == _right) ||
(_top == _bottom);
}
template<class T>
Frustum<T> Frustum<T>::window(T l, T r, T t, T b) const
{
// move it to 0->1 space
Vec2<T> bl = screenToLocal( Vec2<T>(l,b) );
Vec2<T> tr = screenToLocal( Vec2<T>(r,t) );
return Frustum<T>(_nearPlane, _farPlane, bl.x, tr.x, tr.y, bl.y, _orthographic);
}
template<class T>
Vec2<T> Frustum<T>::screenToLocal(const Vec2<T> &s) const
{
return Vec2<T>( _left + (_right-_left) * (1.f+s.x) / 2.f,
_bottom + (_top-_bottom) * (1.f+s.y) / 2.f );
}
template<class T>
Vec2<T> Frustum<T>::localToScreen(const Vec2<T> &p) const
{
T leftPlusRight = _left - T (2) * p.x + _right;
T leftMinusRight = _left-_right;
T bottomPlusTop = _bottom - T (2) * p.y + _top;
T bottomMinusTop = _bottom-_top;
if ((abs(leftMinusRight) < T (1) &&
abs(leftPlusRight) > limits<T>::max() * abs(leftMinusRight)) ||
(abs(bottomMinusTop) < T (1) &&
abs(bottomPlusTop) > limits<T>::max() * abs(bottomMinusTop)))
{
throw IEX_NAMESPACE::DivzeroExc
("Bad viewing frustum: "
"local-to-screen transformation cannot be computed");
}
return Vec2<T>( leftPlusRight / leftMinusRight,
bottomPlusTop / bottomMinusTop );
}
template<class T>
Line3<T> Frustum<T>::projectScreenToRay(const Vec2<T> &p) const
{
Vec2<T> point = screenToLocal(p);
if (orthographic())
return Line3<T>( Vec3<T>(point.x,point.y, 0.0),
Vec3<T>(point.x,point.y,-1.0));
else
return Line3<T>( Vec3<T>(0, 0, 0), Vec3<T>(point.x,point.y,-_nearPlane));
}
template<class T>
Vec2<T> Frustum<T>::projectPointToScreen(const Vec3<T> &point) const
{
if (orthographic() || point.z == T (0))
return localToScreen( Vec2<T>( point.x, point.y ) );
else
return localToScreen( Vec2<T>( point.x * _nearPlane / -point.z,
point.y * _nearPlane / -point.z ) );
}
template<class T>
T Frustum<T>::ZToDepth(long zval,long zmin,long zmax) const
{
int zdiff = zmax - zmin;
if (zdiff == 0)
{
throw IEX_NAMESPACE::DivzeroExc
("Bad call to Frustum::ZToDepth: zmax == zmin");
}
if ( zval > zmax+1 ) zval -= zdiff;
T fzval = (T(zval) - T(zmin)) / T(zdiff);
return normalizedZToDepth(fzval);
}
template<class T>
T Frustum<T>::normalizedZToDepth(T zval) const
{
T Zp = zval * 2.0 - 1;
if ( _orthographic )
{
return -(Zp*(_farPlane-_nearPlane) + (_farPlane+_nearPlane))/2;
}
else
{
T farTimesNear = 2 * _farPlane * _nearPlane;
T farMinusNear = Zp * (_farPlane - _nearPlane) - _farPlane - _nearPlane;
if (abs(farMinusNear) < 1 &&
abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
{
throw IEX_NAMESPACE::DivzeroExc
("Frustum::normalizedZToDepth cannot be computed. The "
"near and far clipping planes of the viewing frustum "
"may be too close to each other");
}
return farTimesNear / farMinusNear;
}
}
template<class T>
long Frustum<T>::DepthToZ(T depth,long zmin,long zmax) const
{
long zdiff = zmax - zmin;
T farMinusNear = _farPlane-_nearPlane;
if ( _orthographic )
{
T farPlusNear = 2*depth + _farPlane + _nearPlane;
if (abs(farMinusNear) < 1 &&
abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
{
throw IEX_NAMESPACE::DivzeroExc
("Bad viewing frustum: near and far clipping planes "
"are too close to each other");
}
T Zp = -farPlusNear/farMinusNear;
return long(0.5*(Zp+1)*zdiff) + zmin;
}
else
{
// Perspective
T farTimesNear = 2*_farPlane*_nearPlane;
if (abs(depth) < 1 &&
abs(farTimesNear) > limits<T>::max() * abs(depth))
{
throw IEX_NAMESPACE::DivzeroExc
("Bad call to DepthToZ function: value of `depth' "
"is too small");
}
T farPlusNear = farTimesNear/depth + _farPlane + _nearPlane;
if (abs(farMinusNear) < 1 &&
abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
{
throw IEX_NAMESPACE::DivzeroExc
("Bad viewing frustum: near and far clipping planes "
"are too close to each other");
}
T Zp = farPlusNear/farMinusNear;
return long(0.5*(Zp+1)*zdiff) + zmin;
}
}
template<class T>
T Frustum<T>::screenRadius(const Vec3<T> &p, T radius) const
{
// Derivation:
// Consider X-Z plane.
// X coord of projection of p = xp = p.x * (-_nearPlane / p.z)
// Let q be p + (radius, 0, 0).
// X coord of projection of q = xq = (p.x - radius) * (-_nearPlane / p.z)
// X coord of projection of segment from p to q = r = xp - xq
// = radius * (-_nearPlane / p.z)
// A similar analysis holds in the Y-Z plane.
// So r is the quantity we want to return.
if (abs(p.z) > 1 || abs(-_nearPlane) < limits<T>::max() * abs(p.z))
{
return radius * (-_nearPlane / p.z);
}
else
{
throw IEX_NAMESPACE::DivzeroExc
("Bad call to Frustum::screenRadius: the magnitude of `p' "
"is too small");
}
return radius * (-_nearPlane / p.z);
}
template<class T>
T Frustum<T>::worldRadius(const Vec3<T> &p, T radius) const
{
if (abs(-_nearPlane) > 1 || abs(p.z) < limits<T>::max() * abs(-_nearPlane))
{
return radius * (p.z / -_nearPlane);
}
else
{
throw IEX_NAMESPACE::DivzeroExc
("Bad viewing frustum: the near clipping plane is too "
"close to zero");
}
}
template<class T>
void Frustum<T>::planes(Plane3<T> p[6]) const
{
//
// Plane order: Top, Right, Bottom, Left, Near, Far.
// Normals point outwards.
//
if (! _orthographic)
{
Vec3<T> a( _left, _bottom, -_nearPlane);
Vec3<T> b( _left, _top, -_nearPlane);
Vec3<T> c( _right, _top, -_nearPlane);
Vec3<T> d( _right, _bottom, -_nearPlane);
Vec3<T> o(0,0,0);
p[0].set( o, c, b );
p[1].set( o, d, c );
p[2].set( o, a, d );
p[3].set( o, b, a );
}
else
{
p[0].set( Vec3<T>( 0, 1, 0), _top );
p[1].set( Vec3<T>( 1, 0, 0), _right );
p[2].set( Vec3<T>( 0,-1, 0),-_bottom );
p[3].set( Vec3<T>(-1, 0, 0),-_left );
}
p[4].set( Vec3<T>(0, 0, 1), -_nearPlane );
p[5].set( Vec3<T>(0, 0,-1), _farPlane );
}
template<class T>
void Frustum<T>::planes(Plane3<T> p[6], const Matrix44<T> &M) const
{
//
// Plane order: Top, Right, Bottom, Left, Near, Far.
// Normals point outwards.
//
Vec3<T> a = Vec3<T>( _left, _bottom, -_nearPlane) * M;
Vec3<T> b = Vec3<T>( _left, _top, -_nearPlane) * M;
Vec3<T> c = Vec3<T>( _right, _top, -_nearPlane) * M;
Vec3<T> d = Vec3<T>( _right, _bottom, -_nearPlane) * M;
if (! _orthographic)
{
double s = _farPlane / double(_nearPlane);
T farLeft = (T) (s * _left);
T farRight = (T) (s * _right);
T farTop = (T) (s * _top);
T farBottom = (T) (s * _bottom);
Vec3<T> e = Vec3<T>( farLeft, farBottom, -_farPlane) * M;
Vec3<T> f = Vec3<T>( farLeft, farTop, -_farPlane) * M;
Vec3<T> g = Vec3<T>( farRight, farTop, -_farPlane) * M;
Vec3<T> o = Vec3<T>(0,0,0) * M;
p[0].set( o, c, b );
p[1].set( o, d, c );
p[2].set( o, a, d );
p[3].set( o, b, a );
p[4].set( a, d, c );
p[5].set( e, f, g );
}
else
{
Vec3<T> e = Vec3<T>( _left, _bottom, -_farPlane) * M;
Vec3<T> f = Vec3<T>( _left, _top, -_farPlane) * M;
Vec3<T> g = Vec3<T>( _right, _top, -_farPlane) * M;
Vec3<T> h = Vec3<T>( _right, _bottom, -_farPlane) * M;
p[0].set( c, g, f );
p[1].set( d, h, g );
p[2].set( a, e, h );
p[3].set( b, f, e );
p[4].set( a, d, c );
p[5].set( e, f, g );
}
}
typedef Frustum<float> Frustumf;
typedef Frustum<double> Frustumd;
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
#if defined _WIN32 || defined _WIN64
#ifdef _redef_near
#define near
#endif
#ifdef _redef_far
#define far
#endif
#endif
#endif // INCLUDED_IMATHFRUSTUM_H
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