Blame Imath/ImathFrustum.h

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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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// 
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// All rights reserved.
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// 
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// *       Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// *       Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// *       Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission. 
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// 
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHFRUSTUM_H
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#define INCLUDED_IMATHFRUSTUM_H
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#include "ImathVec.h"
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#include "ImathPlane.h"
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#include "ImathLine.h"
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#include "ImathMatrix.h"
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#include "ImathLimits.h"
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#include "ImathFun.h"
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#include "ImathNamespace.h"
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#include "IexMathExc.h"
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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//
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//  template class Frustum<T>
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//
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//  The frustum is always located with the eye point at the
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//  origin facing down -Z. This makes the Frustum class
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//  compatable with OpenGL (or anything that assumes a camera
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//  looks down -Z, hence with a right-handed coordinate system)
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//  but not with RenderMan which assumes the camera looks down
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//  +Z. Additional functions are provided for conversion from
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//  and from various camera coordinate spaces.
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//
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//  nearPlane/farPlane: near/far are keywords used by Microsoft's
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//  compiler, so we use nearPlane/farPlane instead to avoid
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//  issues.
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template<class T>
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class Frustum
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{
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  public:
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    Frustum();
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    Frustum(const Frustum &);
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    Frustum(T nearPlane, T farPlane, T left, T right, T top, T bottom, bool ortho=false);
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    Frustum(T nearPlane, T farPlane, T fovx, T fovy, T aspect);
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    virtual ~Frustum();
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    //--------------------
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    // Assignment operator
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    //--------------------
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    const Frustum &     operator = (const Frustum &);
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    //--------------------
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    //  Operators:  ==, !=
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    //--------------------
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    bool                operator == (const Frustum<T> &src) const;
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    bool                operator != (const Frustum<T> &src) const;
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    //--------------------------------------------------------
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    //  Set functions change the entire state of the Frustum
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    //--------------------------------------------------------
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    void                set(T nearPlane, T farPlane,
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                            T left, T right,
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                            T top, T bottom,
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                            bool ortho=false);
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    void                set(T nearPlane, T farPlane, T fovx, T fovy, T aspect);
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    //------------------------------------------------------
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    //	These functions modify an already valid frustum state
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    //------------------------------------------------------
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    void                modifyNearAndFar(T nearPlane, T farPlane);
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    void                setOrthographic(bool);
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    //--------------
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    //  Access
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    //--------------
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    bool                orthographic() const  { return _orthographic; }
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    T                   nearPlane() const     { return _nearPlane;    }
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    T                   hither() const        { return _nearPlane;    }
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    T                   farPlane() const      { return _farPlane;     }
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    T                   yon() const           { return _farPlane;     }
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    T                   left() const          { return _left;         }
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    T                   right() const         { return _right;        }
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    T                   bottom() const        { return _bottom;       }
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    T                   top() const           { return _top;          }
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    //-----------------------------------------------------------------------
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    //  Sets the planes in p to be the six bounding planes of the frustum, in
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    //  the following order: top, right, bottom, left, near, far.
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    //  Note that the planes have normals that point out of the frustum.
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    //  The version of this routine that takes a matrix applies that matrix
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    //  to transform the frustum before setting the planes.
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    //-----------------------------------------------------------------------
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    void                planes(Plane3<T> p[6]) const;
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    void                planes(Plane3<T> p[6], const Matrix44<T> &M) const;
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    //----------------------
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    //  Derived Quantities
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    //----------------------
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    T                   fovx() const;
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    T                   fovy() const;
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    T                   aspect() const;
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    Matrix44<T>         projectionMatrix() const;
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    bool                degenerate() const;
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    //-----------------------------------------------------------------------
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    //  Takes a rectangle in the screen space (i.e., -1 <= left <= right <= 1 
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    //  and -1 <= bottom <= top <= 1) of this Frustum, and returns a new
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    //  Frustum whose near clipping-plane window is that rectangle in local
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    //  space.  
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    //-----------------------------------------------------------------------
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    Frustum<T>          window(T left, T right, T top, T bottom) const;
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    //----------------------------------------------------------
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    // Projection is in screen space / Conversion from Z-Buffer
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    //----------------------------------------------------------
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    Line3<T>            projectScreenToRay( const Vec2<T> & ) const;
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    Vec2<T>             projectPointToScreen( const Vec3<T> & ) const;
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    T                   ZToDepth(long zval, long min, long max) const;
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    T                   normalizedZToDepth(T zval) const;
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    long                DepthToZ(T depth, long zmin, long zmax) const;
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    T                   worldRadius(const Vec3<T> &p, T radius) const;
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    T                   screenRadius(const Vec3<T> &p, T radius) const;
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  protected:
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    Vec2<T>             screenToLocal( const Vec2<T> & ) const;
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    Vec2<T>             localToScreen( const Vec2<T> & ) const;
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  protected:
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    T                   _nearPlane;
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    T                   _farPlane;
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    T                   _left;
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    T                   _right;
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    T                   _top;
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    T                   _bottom;
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    bool                _orthographic;
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};
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template<class T>
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inline Frustum<T>::Frustum()
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{
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    set(T (0.1),
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        T (1000.0),
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        T (-1.0),
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        T (1.0),
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        T (1.0),
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        T (-1.0),
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        false);
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}
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template<class T>
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inline Frustum<T>::Frustum(const Frustum &f)
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{
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    *this = f;
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}
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template<class T>
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inline Frustum<T>::Frustum(T n, T f, T l, T r, T t, T b, bool o)
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{
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    set(n,f,l,r,t,b,o);
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}
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template<class T>
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inline Frustum<T>::Frustum(T nearPlane, T farPlane, T fovx, T fovy, T aspect)
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{
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    set(nearPlane,farPlane,fovx,fovy,aspect);
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}
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template<class T>
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Frustum<T>::~Frustum()
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{
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}
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template<class T>
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const Frustum<T> &
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Frustum<T>::operator = (const Frustum &f)
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{
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    _nearPlane    = f._nearPlane;
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    _farPlane     = f._farPlane;
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    _left         = f._left;
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    _right        = f._right;
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    _top          = f._top;
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    _bottom       = f._bottom;
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    _orthographic = f._orthographic;
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    return *this;
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}
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template <class T>
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bool
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Frustum<T>::operator == (const Frustum<T> &src) const
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{
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    return
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        _nearPlane    == src._nearPlane   &&
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        _farPlane     == src._farPlane    &&
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        _left         == src._left   &&
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        _right        == src._right  &&
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        _top          == src._top    &&
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        _bottom       == src._bottom &&
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        _orthographic == src._orthographic;
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}
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template <class T>
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inline bool
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Frustum<T>::operator != (const Frustum<T> &src) const
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{
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    return !operator== (src);
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}
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template<class T>
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void Frustum<T>::set(T n, T f, T l, T r, T t, T b, bool o)
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{
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    _nearPlane      = n;
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    _farPlane       = f;
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    _left           = l;
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    _right          = r;
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    _bottom         = b;
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    _top            = t;
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    _orthographic   = o;
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}
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template<class T>
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void Frustum<T>::modifyNearAndFar(T n, T f)
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{
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    if ( _orthographic )
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    {
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        _nearPlane = n;
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    }
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    else
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    {
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        Line3<T>  lowerLeft( Vec3<T>(0,0,0), Vec3<T>(_left,_bottom,-_nearPlane) );
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        Line3<T> upperRight( Vec3<T>(0,0,0), Vec3<T>(_right,_top,-_nearPlane) );
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        Plane3<T> nearPlane( Vec3<T>(0,0,-1), n );
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        Vec3<T> ll,ur;
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        nearPlane.intersect(lowerLeft,ll);
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        nearPlane.intersect(upperRight,ur);
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        _left      = ll.x;
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        _right     = ur.x;
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        _top       = ur.y;
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        _bottom    = ll.y;
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        _nearPlane = n;
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        _farPlane  = f;
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    }
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    _farPlane = f;
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}
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template<class T>
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void Frustum<T>::setOrthographic(bool ortho)
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{
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    _orthographic   = ortho;
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}
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template<class T>
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void Frustum<T>::set(T nearPlane, T farPlane, T fovx, T fovy, T aspect)
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{
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    if (fovx != 0 && fovy != 0)
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        throw IEX_NAMESPACE::ArgExc ("fovx and fovy cannot both be non-zero.");
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    const T two = static_cast<T>(2);
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    if (fovx != 0)
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    {
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        _right    = nearPlane * Math<T>::tan(fovx / two);
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        _left     = -_right;
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        _top      = ((_right - _left) / aspect) / two;
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        _bottom   = -_top;
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    }
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    else
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    {
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        _top      = nearPlane * Math<T>::tan(fovy / two);
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        _bottom   = -_top;
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        _right    = (_top - _bottom) * aspect / two;
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        _left     = -_right;
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    }
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    _nearPlane    = nearPlane;
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    _farPlane     = farPlane;
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    _orthographic = false;
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}
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template<class T>
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T Frustum<T>::fovx() const
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{
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    return Math<T>::atan2(_right,_nearPlane) - Math<T>::atan2(_left,_nearPlane);
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}
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template<class T>
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T Frustum<T>::fovy() const
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{
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    return Math<T>::atan2(_top,_nearPlane) - Math<T>::atan2(_bottom,_nearPlane);
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}
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template<class T>
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T Frustum<T>::aspect() const
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{
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    T rightMinusLeft = _right-_left;
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    T topMinusBottom = _top-_bottom;
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    if (abs(topMinusBottom) < 1 &&
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        abs(rightMinusLeft) > limits<T>::max() * abs(topMinusBottom))
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    {
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        throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
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                               "aspect ratio cannot be computed.");
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    }
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    return rightMinusLeft / topMinusBottom;
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}
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template<class T>
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Matrix44<T> Frustum<T>::projectionMatrix() const
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{
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    T rightPlusLeft  = _right+_left;
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    T rightMinusLeft = _right-_left;
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    T topPlusBottom  = _top+_bottom;
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    T topMinusBottom = _top-_bottom;
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    T farPlusNear    = _farPlane+_nearPlane;
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    T farMinusNear   = _farPlane-_nearPlane;
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    if ((abs(rightMinusLeft) < 1 &&
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         abs(rightPlusLeft) > limits<T>::max() * abs(rightMinusLeft)) ||
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        (abs(topMinusBottom) < 1 &&
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         abs(topPlusBottom) > limits<T>::max() * abs(topMinusBottom)) ||
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        (abs(farMinusNear) < 1 &&
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         abs(farPlusNear) > limits<T>::max() * abs(farMinusNear)))
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    {
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        throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
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                                                 "projection matrix cannot be computed.");
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    }
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    if ( _orthographic )
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    {
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        T tx = -rightPlusLeft / rightMinusLeft;
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        T ty = -topPlusBottom / topMinusBottom;
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        T tz = -farPlusNear   / farMinusNear;
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        if ((abs(rightMinusLeft) < 1 &&
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             2 > limits<T>::max() * abs(rightMinusLeft)) ||
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            (abs(topMinusBottom) < 1 &&
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             2 > limits<T>::max() * abs(topMinusBottom)) ||
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            (abs(farMinusNear) < 1 &&
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             2 > limits<T>::max() * abs(farMinusNear)))
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        {
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            throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
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                                                         "projection matrix cannot be computed.");
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        }
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        T A  =  2 / rightMinusLeft;
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        T B  =  2 / topMinusBottom;
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        T C  = -2 / farMinusNear;
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        return Matrix44<T>( A,  0,  0,  0,
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                            0,  B,  0,  0,
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                            0,  0,  C,  0,
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                            tx, ty, tz, 1.f );
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    }
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    else
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    {
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        T A =  rightPlusLeft / rightMinusLeft;
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        T B =  topPlusBottom / topMinusBottom;
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        T C = -farPlusNear   / farMinusNear;
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        T farTimesNear = -2 * _farPlane * _nearPlane;
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        if (abs(farMinusNear) < 1 &&
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            abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
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        {
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            throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
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                                                         "projection matrix cannot be computed.");
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        }
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        T D = farTimesNear / farMinusNear;
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        T twoTimesNear = 2 * _nearPlane;
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        if ((abs(rightMinusLeft) < 1 &&
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             abs(twoTimesNear) > limits<T>::max() * abs(rightMinusLeft)) ||
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            (abs(topMinusBottom) < 1 &&
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             abs(twoTimesNear) > limits<T>::max() * abs(topMinusBottom)))
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        {
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            throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
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                                                         "projection matrix cannot be computed.");
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        }
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        T E = twoTimesNear / rightMinusLeft;
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        T F = twoTimesNear / topMinusBottom;
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        return Matrix44<T>( E,  0,  0,  0,
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                            0,  F,  0,  0,
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                            A,  B,  C, -1,
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                            0,  0,  D,  0 );
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    }
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}
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template<class T>
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bool Frustum<T>::degenerate() const
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{
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    return (_nearPlane == _farPlane) ||
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           (_left == _right) ||
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           (_top == _bottom);
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}
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template<class T>
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Frustum<T> Frustum<T>::window(T l, T r, T t, T b) const
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{
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    // move it to 0->1 space
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    Vec2<T> bl = screenToLocal( Vec2<T>(l,b) );
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    Vec2<T> tr = screenToLocal( Vec2<T>(r,t) );
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    return Frustum<T>(_nearPlane, _farPlane, bl.x, tr.x, tr.y, bl.y, _orthographic);
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}
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template<class T>
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Vec2<T> Frustum<T>::screenToLocal(const Vec2<T> &s) const
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{
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    return Vec2<T>( _left + (_right-_left) * (1.f+s.x) / 2.f,
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                    _bottom + (_top-_bottom) * (1.f+s.y) / 2.f );
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}
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template<class T>
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Vec2<T> Frustum<T>::localToScreen(const Vec2<T> &p) const
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{
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    T leftPlusRight  = _left - T (2) * p.x + _right;
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    T leftMinusRight = _left-_right;
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    T bottomPlusTop  = _bottom - T (2) * p.y + _top;
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    T bottomMinusTop = _bottom-_top;
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    if ((abs(leftMinusRight) < T (1) &&
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         abs(leftPlusRight) > limits<T>::max() * abs(leftMinusRight)) ||
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        (abs(bottomMinusTop) < T (1) &&
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         abs(bottomPlusTop) > limits<T>::max() * abs(bottomMinusTop)))
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    {
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        throw IEX_NAMESPACE::DivzeroExc
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            ("Bad viewing frustum: "
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             "local-to-screen transformation cannot be computed");
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    }
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    return Vec2<T>( leftPlusRight / leftMinusRight,
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                    bottomPlusTop / bottomMinusTop );
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}
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template<class T>
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Line3<T> Frustum<T>::projectScreenToRay(const Vec2<T> &p) const
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{
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    Vec2<T> point = screenToLocal(p);
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    if (orthographic())
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        return Line3<T>( Vec3<T>(point.x,point.y, 0.0),
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                         Vec3<T>(point.x,point.y,-1.0));
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    else
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        return Line3<T>( Vec3<T>(0, 0, 0), Vec3<T>(point.x,point.y,-_nearPlane));
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}
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template<class T>
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Vec2<T> Frustum<T>::projectPointToScreen(const Vec3<T> &point) const
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{
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    if (orthographic() || point.z == T (0))
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        return localToScreen( Vec2<T>( point.x, point.y ) );
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    else
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        return localToScreen( Vec2<T>( point.x * _nearPlane / -point.z,
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                                       point.y * _nearPlane / -point.z ) );
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}
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template<class T>
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T Frustum<T>::ZToDepth(long zval,long zmin,long zmax) const
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{
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    int zdiff = zmax - zmin;
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    if (zdiff == 0)
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    {
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        throw IEX_NAMESPACE::DivzeroExc
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            ("Bad call to Frustum::ZToDepth: zmax == zmin");
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    }
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    if ( zval > zmax+1 ) zval -= zdiff;
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    T fzval = (T(zval) - T(zmin)) / T(zdiff);
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    return normalizedZToDepth(fzval);
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}
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template<class T>
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T Frustum<T>::normalizedZToDepth(T zval) const
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{
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    T Zp = zval * 2.0 - 1;
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    if ( _orthographic )
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    {
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        return   -(Zp*(_farPlane-_nearPlane) + (_farPlane+_nearPlane))/2;
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    }
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    else 
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    {
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        T farTimesNear = 2 * _farPlane * _nearPlane;
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        T farMinusNear = Zp * (_farPlane - _nearPlane) - _farPlane - _nearPlane;
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        if (abs(farMinusNear) < 1 &&
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            abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
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        {
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            throw IEX_NAMESPACE::DivzeroExc
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                ("Frustum::normalizedZToDepth cannot be computed.  The "
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                 "near and far clipping planes of the viewing frustum "
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                 "may be too close to each other");
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        }
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        return farTimesNear / farMinusNear;
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    }
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}
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template<class T>
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long Frustum<T>::DepthToZ(T depth,long zmin,long zmax) const
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{
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    long zdiff     = zmax - zmin;
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    T farMinusNear = _farPlane-_nearPlane;
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    if ( _orthographic )
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    {
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        T farPlusNear = 2*depth + _farPlane + _nearPlane;
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        if (abs(farMinusNear) < 1 &&
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            abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
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        {
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            throw IEX_NAMESPACE::DivzeroExc
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                ("Bad viewing frustum: near and far clipping planes "
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                 "are too close to each other");
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        }
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        T Zp = -farPlusNear/farMinusNear;
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        return long(0.5*(Zp+1)*zdiff) + zmin;
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    }
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    else 
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    { 
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        // Perspective
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        T farTimesNear = 2*_farPlane*_nearPlane;
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        if (abs(depth) < 1 &&
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            abs(farTimesNear) > limits<T>::max() * abs(depth))
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        {
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            throw IEX_NAMESPACE::DivzeroExc
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                ("Bad call to DepthToZ function: value of `depth' "
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                 "is too small");
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        }
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        T farPlusNear = farTimesNear/depth + _farPlane + _nearPlane;
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        if (abs(farMinusNear) < 1 &&
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            abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
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        {
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            throw IEX_NAMESPACE::DivzeroExc
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                ("Bad viewing frustum: near and far clipping planes "
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                 "are too close to each other");
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        }
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        T Zp = farPlusNear/farMinusNear;
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        return long(0.5*(Zp+1)*zdiff) + zmin;
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    }
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}
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template<class T>
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T Frustum<T>::screenRadius(const Vec3<T> &p, T radius) const
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{
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    // Derivation:
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    // Consider X-Z plane.
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    // X coord of projection of p = xp = p.x * (-_nearPlane / p.z)
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    // Let q be p + (radius, 0, 0).
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    // X coord of projection of q = xq = (p.x - radius)  * (-_nearPlane / p.z)
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    // X coord of projection of segment from p to q = r = xp - xq
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    //         = radius * (-_nearPlane / p.z)
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    // A similar analysis holds in the Y-Z plane.
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    // So r is the quantity we want to return.
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    if (abs(p.z) > 1 || abs(-_nearPlane) < limits<T>::max() * abs(p.z))
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    {
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        return radius * (-_nearPlane / p.z);
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    }
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    else
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    {
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        throw IEX_NAMESPACE::DivzeroExc
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            ("Bad call to Frustum::screenRadius: the magnitude of `p' "
Packit 8dc392
             "is too small");
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    }
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    return radius * (-_nearPlane / p.z);
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}
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template<class T>
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T Frustum<T>::worldRadius(const Vec3<T> &p, T radius) const
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{
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    if (abs(-_nearPlane) > 1 || abs(p.z) < limits<T>::max() * abs(-_nearPlane))
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    {
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        return radius * (p.z / -_nearPlane);
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    }
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    else
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    {
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        throw IEX_NAMESPACE::DivzeroExc
Packit 8dc392
            ("Bad viewing frustum: the near clipping plane is too "
Packit 8dc392
             "close to zero");
Packit 8dc392
    }
Packit 8dc392
}
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template<class T>
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void Frustum<T>::planes(Plane3<T> p[6]) const
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{
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    //
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    //        Plane order: Top, Right, Bottom, Left, Near, Far.
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    //  Normals point outwards.
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    //
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    if (! _orthographic)
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    {
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        Vec3<T> a( _left,  _bottom, -_nearPlane);
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        Vec3<T> b( _left,  _top,    -_nearPlane);
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        Vec3<T> c( _right, _top,    -_nearPlane);
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        Vec3<T> d( _right, _bottom, -_nearPlane);
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        Vec3<T> o(0,0,0);
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        p[0].set( o, c, b );
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        p[1].set( o, d, c );
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        p[2].set( o, a, d );
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        p[3].set( o, b, a );
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    }
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    else
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    {
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        p[0].set( Vec3<T>( 0, 1, 0), _top );
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        p[1].set( Vec3<T>( 1, 0, 0), _right );
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        p[2].set( Vec3<T>( 0,-1, 0),-_bottom );
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        p[3].set( Vec3<T>(-1, 0, 0),-_left );
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    }
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    p[4].set( Vec3<T>(0, 0, 1), -_nearPlane );
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    p[5].set( Vec3<T>(0, 0,-1), _farPlane );
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}
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template<class T>
Packit 8dc392
void Frustum<T>::planes(Plane3<T> p[6], const Matrix44<T> &M) const
Packit 8dc392
{
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    //
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    //  Plane order: Top, Right, Bottom, Left, Near, Far.
Packit 8dc392
    //  Normals point outwards.
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    //
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Packit 8dc392
    Vec3<T> a   = Vec3<T>( _left,  _bottom, -_nearPlane) * M;
Packit 8dc392
    Vec3<T> b   = Vec3<T>( _left,  _top,    -_nearPlane) * M;
Packit 8dc392
    Vec3<T> c   = Vec3<T>( _right, _top,    -_nearPlane) * M;
Packit 8dc392
    Vec3<T> d   = Vec3<T>( _right, _bottom, -_nearPlane) * M;
Packit 8dc392
    if (! _orthographic)
Packit 8dc392
    {
Packit 8dc392
        double s    = _farPlane / double(_nearPlane);
Packit 8dc392
        T farLeft   = (T) (s * _left);
Packit 8dc392
        T farRight  = (T) (s * _right);
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        T farTop    = (T) (s * _top);
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        T farBottom = (T) (s * _bottom);
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        Vec3<T> e   = Vec3<T>( farLeft,  farBottom, -_farPlane) * M;
Packit 8dc392
        Vec3<T> f   = Vec3<T>( farLeft,  farTop,    -_farPlane) * M;
Packit 8dc392
        Vec3<T> g   = Vec3<T>( farRight, farTop,    -_farPlane) * M;
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        Vec3<T> o   = Vec3<T>(0,0,0) * M;
Packit 8dc392
        p[0].set( o, c, b );
Packit 8dc392
        p[1].set( o, d, c );
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        p[2].set( o, a, d );
Packit 8dc392
        p[3].set( o, b, a );
Packit 8dc392
        p[4].set( a, d, c );
Packit 8dc392
        p[5].set( e, f, g );
Packit 8dc392
     }
Packit 8dc392
    else
Packit 8dc392
    {
Packit 8dc392
        Vec3<T> e   = Vec3<T>( _left,  _bottom, -_farPlane) * M;
Packit 8dc392
        Vec3<T> f   = Vec3<T>( _left,  _top,    -_farPlane) * M;
Packit 8dc392
        Vec3<T> g   = Vec3<T>( _right, _top,    -_farPlane) * M;
Packit 8dc392
        Vec3<T> h   = Vec3<T>( _right, _bottom, -_farPlane) * M;
Packit 8dc392
        p[0].set( c, g, f );
Packit 8dc392
        p[1].set( d, h, g );
Packit 8dc392
        p[2].set( a, e, h );
Packit 8dc392
        p[3].set( b, f, e );
Packit 8dc392
        p[4].set( a, d, c );
Packit 8dc392
        p[5].set( e, f, g );
Packit 8dc392
    }
Packit 8dc392
}
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Packit 8dc392
typedef Frustum<float>  Frustumf;
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typedef Frustum<double> Frustumd;
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IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
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Packit 8dc392
Packit 8dc392
#if defined _WIN32 || defined _WIN64
Packit 8dc392
    #ifdef _redef_near
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        #define near
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    #endif
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    #ifdef _redef_far
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        #define far
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    #endif
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#endif
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#endif // INCLUDED_IMATHFRUSTUM_H