plane_3d_impl_detail.h

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
 *  *** BEGIN LICENSE INFORMATION ***
 *  
 *  The contents of this file are subject to the Common Public Attribution License 
 *  Version 1.0 (the "License"); you may not use this file except in compliance with 
 *  the License. You may obtain a copy of the License at 
 *  http://lass.sourceforge.net/cpal-license. The License is based on the 
 *  Mozilla Public License Version 1.1 but Sections 14 and 15 have been added to cover 
 *  use of software over a computer network and provide for limited attribution for 
 *  the Original Developer. In addition, Exhibit A has been modified to be consistent 
 *  with Exhibit B.
 *  
 *  Software distributed under the License is distributed on an "AS IS" basis, WITHOUT 
 *  WARRANTY OF ANY KIND, either express or implied. See the License for the specific 
 *  language governing rights and limitations under the License.
 *  
 *  The Original Code is LASS - Library of Assembled Shared Sources.
 *  
 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
 *  The Original Developer is the Initial Developer.
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/** @class lass::prim::impl::Plane3DImplDetail
 *  @brief common implementation stuff for Plane3D implementations.
 *  @author Bram de Greve [BdG]
 *
 *  Here are some common generator functions gahtered, that are used to generate some values
 *  automatically from others.
 */

#ifndef LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_IMPL_DETAIL_H
#define LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_IMPL_DETAIL_H

#include "../prim_common.h"
#include "../../num/floating_point_comparison.h"

namespace lass
{
namespace prim
{
namespace impl
{

struct Plane3DImplDetail
{
    /** Generate cartesian equation out of parametric equation.
     *  Generate normal vector N and value d of cartesian equaition N.P + d == 0,
     *  given support point S and direction vectors U and V of parametric
     *  equation P = S + x*U + y*V.
     */
    template <typename T>
    static void generateCartesian(const Point3D<T>& iSupport,
                                  const Vector3D<T>& iDirU,
                                  const Vector3D<T>& iDirV,
                                  Vector3D<T>& oNormal,
                                  T& oD)
    {
        oNormal = cross(iDirU, iDirV);
        oD = -dot(oNormal, iSupport.position());
    }

    /** Generate directions vectors U and V of parametric equation P = S + x*U + y*V,
     *  based on the normal vector N of the cartesian equation N.P + S == 0.
     */
    template <typename T>
    static void generateDirections(const Vector3D<T>& iNormal,
                                   Vector3D<T>& oDirU,
                                   Vector3D<T>& oDirV)
    {
        typedef Vector3D<T> TVector;
        typedef typename TVector::TValue TValue;
        typedef typename TVector::TNumTraits TNumTraits;

        const TValue absX = num::abs(iNormal.x);
        const TValue absY = num::abs(iNormal.y);
        const TValue absZ = num::abs(iNormal.z);

        if (absZ > absX && absZ > absY)
        {
            const TVector j(TNumTraits::zero, TNumTraits::one, TNumTraits::zero);
            oDirU = cross(j, iNormal);
            oDirV = cross(iNormal, oDirU);
        }
        else if (absX > absY)
        {
            const TVector k(TNumTraits::zero, TNumTraits::zero, TNumTraits::one);
            oDirU = cross(k, iNormal);
            oDirV = cross(iNormal, oDirU);
        }
        else
        {
            const TVector i(TNumTraits::one, TNumTraits::zero, TNumTraits::zero);
            oDirU = cross(i, iNormal);
            oDirV = cross(iNormal, oDirU);
        }
    }

    /** generate reciprocal direction vectors Ur and Vr given directions U and V.
     *  Reciprocal vectors can be used to find the values x and y in A=x*U+y*V,
     *  given A, U and V.  With Ur and Vr, they can be found by x=A.Ur and y=A.Vr.
     */
    template <typename T>
    static void generateReciprocal(const Vector3D<T>& iDirU,
                                   const Vector3D<T>& iDirV,
                                   Vector3D<T>& oReciprocalDirU,
                                   Vector3D<T>& oReciprocalDirV)
    {
        const typename Vector3D<T>::TValue dotUV = dot(iDirU, iDirV);
        oReciprocalDirU = iDirU - iDirV * (dotUV / iDirV.squaredNorm());
        oReciprocalDirV = iDirV - iDirU * (dotUV / iDirU.squaredNorm());
        oReciprocalDirU /= dot(oReciprocalDirU, iDirU);
        oReciprocalDirV /= dot(oReciprocalDirV, iDirV);
    }

};



}

}

}

#endif

// EOF