plane_3d_cartesian.inl

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
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#ifndef LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_CARTESIAN_INL
#define LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_CARTESIAN_INL

#include "../prim_common.h"
#include "plane_3d_cartesian.h"

namespace lass
{
namespace prim
{
namespace impl
{

// --- public --------------------------------------------------------------------------------------

/** initializes to an invalid state.
 */
template<typename T, class NP>
Plane3DCartesian<T, NP>::Plane3DCartesian():
    normal_(),
    d_(TNumTraits::zero)
{
    LASS_ASSERT(!isValid());
}



/** Construct a plane through three points.
 *  - normal vector N is given by the cross product N = U x V.
 *  - value d is choosen so that the support point is indeed a point of the plane.
 */
template<typename T, class NP>
Plane3DCartesian<T, NP>::Plane3DCartesian(const TPoint& iSupport,
                                          const TPoint& iPointU,
                                          const TPoint& iPointV)
{
    Plane3DImplDetail::generateCartesian(iSupport, iPointU - iSupport, iPointV - iSupport,
                                         normal_, d_);
    NP::normalizeAndScale(normal_, d_);
}



/** construct a plane through a support point and by two direction vectors..
 *  - normal vector N is given by the cross product N = U x V.
 *  - value d is choosen so that the support point is indeed a point of the plane.
 */
template<typename T, class NP>
Plane3DCartesian<T, NP>::Plane3DCartesian(const TPoint& iSupport,
                                          const TVector& iDirectionU,
                                          const TVector& iDirectionV)
{
    Plane3DImplDetail::generateCartesian(iSupport, iDirectionU, iDirectionV, normal_, d_);
    NP::normalizeAndScale(normal_, d_);
}



/** Construct a plane through a support point and by a normal vector.
 *  - normal vector N is given by the vector iNormal.
 *  - value d is choosen so that the support point is indeed a point of the plane.
 */
template<typename T, class NP>
Plane3DCartesian<T, NP>::Plane3DCartesian(const TVector& iNormal, const TPoint& iSupport):
    normal_(iNormal),
    d_(-dot(iNormal, iSupport.position()))
{
    NP::normalizeAndScale(normal_, d_);
}



/** Construct a plane by a cartesian equation N.P + d == 0.
 *  - normal vector N is given by the vector iNormal.
 *  - value d is given by the value iD.
 */
template<typename T, class NP>
Plane3DCartesian<T, NP>::Plane3DCartesian(const TVector& iNormal, TParam iD):
    normal_(iNormal),
    d_(iD)
{
    NP::normalizeAndScale(normal_, d_);
}



/** return support point.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TPoint Plane3DCartesian<T, NP>::support() const
{
    return TPoint(-d_ * normal_);
}



/** return U and V direction vectors
 */
template<typename T, class NP>
void Plane3DCartesian<T, NP>::getDirections(TVector& oDirectionU, TVector& oDirectionV) const
{
    Plane3DImplDetail::generateDirections(normal_, oDirectionU, oDirectionV);
    NP::normalize(oDirectionU);
    NP::normalize(oDirectionV);
}



/** return U direction vector.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector Plane3DCartesian<T, NP>::directionU() const
{
    TVector directionU;
    TVector directionV;
    getDirections(directionU, directionV);
    return directionU;
}



/** return V direction vector.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector Plane3DCartesian<T, NP>::directionV() const
{
    TVector directionU;
    TVector directionV;
    getDirections(directionU, directionV);
    return directionV;
}



/** return reciprocal vectors for U and V direction vectors
 */
template<typename T, class NP>
void Plane3DCartesian<T, NP>::getReciprocals(TVector& oReciprocalU,
                                             TVector& oReciprocalV) const
{
    TVector directionU;
    TVector directionV;
    getDirections(directionU, directionV);
    Plane3DImplDetail::generateReciprocal(directionU, directionV, oReciprocalU, oReciprocalV);
}



/** return reciprocal for U direction vector.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector Plane3DCartesian<T, NP>::reciprocalU() const
{
    TVector reciprocalU;
    TVector reciprocalV;
    getReciprocals(reciprocalU, reciprocalV);
    return reciprocalU;
}



/** return reciprocal for V direction vector.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector Plane3DCartesian<T, NP>::reciprocalV() const
{
    TVector reciprocalU;
    TVector reciprocalV;
    getReciprocals(reciprocalU, reciprocalV);
    return reciprocalV;
}



template<typename T, class NP>
void Plane3DCartesian<T, NP>::getCartesian(TVector& oNormal, TReference oD) const
{
    oNormal = normal_;
    oD = d_;
}



template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector& Plane3DCartesian<T, NP>::normal() const
{
    return normal_;
}



template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TParam Plane3DCartesian<T, NP>::d() const
{
    return d_;
}



/** Return value of point in equation.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TValue
Plane3DCartesian<T, NP>::equation(const TPoint& iPoint) const
{
    return dot(iPoint.position(), normal_) + d_;
}



/** Return value of point in equation.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TValue
Plane3DCartesian<T, NP>::equation(const TPoint& iPoint, TParam iRelativeTolerance) const
{
    const TValue a = dot(iPoint.position(), normal_);
    return num::almostEqual(a, -d_, iRelativeTolerance) ? TNumTraits::zero : (a + d_);
}



/** return the vector that, if added to the PROJECTION of iPoint, you get iPoint again.
 *  iPoint == (almost) project(iPoint) + reject(iPoint)
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector
Plane3DCartesian<T, NP>::reject(const TPoint& iPoint) const
{
    return normal_ * NP::divideBySquaredNorm(equation(iPoint), normal_);
}



/** return the part of iVector that is orthogonal to the plane.
 *  it's the vector that, if added to the PROJECTION of iVector, you get iVector again.
 *  iVector == (almost) project(iVector) + reject(iVector).
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector
Plane3DCartesian<T, NP>::reject(const TVector& iVector) const
{
    return normal_ * NP::divideBySquaredNorm(dot(normal_, iVector), normal_);
}



/** project a point orthogonally onto the plane
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TPoint
Plane3DCartesian<T, NP>::project(const TPoint& iPoint) const
{
    return iPoint - reject(iPoint);
}



/** project a vector orthogonally onto the plane
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector
Plane3DCartesian<T, NP>::project(const TVector& iVector) const
{
    return iVector - reject(iVector);
}



/** reflect a point orthogonally into the plane.
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TPoint
Plane3DCartesian<T, NP>::reflect(const TPoint& iPoint) const
{
    return iPoint - 2 * reject(iPoint);
}



/** reflect a vector orthogonally into the plane
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TVector
Plane3DCartesian<T, NP>::reflect(const TVector& iVector) const
{
    return iVector - 2 * reject(iVector);
}



/** return point by filling in the parametric equation: P(u, v) = S + u * U + v * V
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TPoint
Plane3DCartesian<T, NP>::point(TParam iU, TParam iV) const
{
    return point(TIndex(iU, iV));
}



/** return point by filling in the parametric equation: P(u, v) = S + u * U + v * V
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TPoint
Plane3DCartesian<T, NP>::point(const TUV& iUV) const
{
    TVector directionU;
    TVector directionV;
    getDirections(directionU, directionV);
    return support() + iUV.x * directionU + iUV.y * directionV;
}



/** return UV pair of parameters
 */
template<typename T, class NP>
const typename Plane3DCartesian<T, NP>::TUV
Plane3DCartesian<T, NP>::uv(const TPoint& iPoint) const
{
    TVector reciprocalU;
    TVector reciprocalV;
    getReciprocals(reciprocalU, reciprocalV);
    const TVector relative = iPoint - support();
    return TUV(dot(relative, reciprocalU), dot(relative, reciprocalV));
}



template <typename T, class NP>
void Plane3DCartesian<T, NP>::flip()
{
    normal_ = -normal_;
    d_ = -d_;
}



/** return true if plane is a valid plane (no normal or direction vectors that are zero).
 */
template<typename T, class NP>
const bool Plane3DCartesian<T, NP>::isValid() const
{
    return !normal_.isZero();
}




// --- protected -----------------------------------------------------------------------------------



// --- private -------------------------------------------------------------------------------------



// --- free ----------------------------------------------------------------------------------------

template<typename T, class NP>
std::ostream& operator<<(std::ostream& ioOStream, const Plane3DCartesian<T, NP>& iPlane)
{
    LASS_ENFORCE(ioOStream) << "{N=" << iPlane.normal() << ", d=" << iPlane.d() << "}";
    return ioOStream;
}



}

}

}

#endif

// EOF