plane_3d_combined.inl

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/** @file
 *  @author Bram de Greve (bram@cocamware.com)
 *  @author Tom De Muer (tom@cocamware.com)
 *
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 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
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#ifndef LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_COMBINED_INL
#define LASS_GUARDIAN_OF_INCLUSION_PRIM_IMPL_PLANE_3D_COMBINED_INL
 
#include "../prim_common.h"
#include "plane_3d_combined.h"
 
namespace lass
{
namespace prim
{
namespace impl
{
 
// --- public --------------------------------------------------------------------------------------
 
/** initializes to an invalid state.
 */
template<typename T, class NP>
Plane3DCombined<T, NP>::Plane3DCombined():
    support_(),
    directionU_(),
    directionV_(),
    reciprocalU_(),
    reciprocalV_(),
    normal_(),
    d_(TNumTraits::zero)
{
    LASS_ASSERT(!isValid());
}
 
 
 
/** Construct a plane through three points.
 *  - support point S is given by the first point iSupport.
 *  - direction vectors U and V are choosen from iSupport to iPointU and iPointV respectively
 *    (U = iPointU - iSupport, V = iPointV - iSupport).
 *  - 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>
Plane3DCombined<T, NP>::Plane3DCombined(const TPoint& iSupport,
                                        const TPoint& iPointU,
                                        const TPoint& iPointV):
    support_(iSupport),
    directionU_(iPointU - iSupport),
    directionV_(iPointV - iSupport)
{
    Plane3DImplDetail::generateCartesian(support_, directionU_, directionV_, normal_, d_);
    NP::normalize(directionU_);
    NP::normalize(directionV_);
    NP::normalizeAndScale(normal_, d_);
    Plane3DImplDetail::generateReciprocal(directionU_, directionV_, reciprocalU_, reciprocalV_);
}
 
 
 
/** construct a plane through a support point and by two direction vectors..
 *  - support point S is given by the point iSupport.
 *  - direction vectors U and V are given by iDirectionU and iDirectionV.
 *  - 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>
Plane3DCombined<T, NP>::Plane3DCombined(const TPoint& iSupport,
                                        const TVector& iDirectionU,
                                        const TVector& iDirectionV):
    support_(iSupport),
    directionU_(iDirectionU),
    directionV_(iDirectionV)
{
    Plane3DImplDetail::generateCartesian(support_, directionU_, directionV_, normal_, d_);
    NP::normalize(directionU_);
    NP::normalize(directionV_);
    NP::normalizeAndScale(normal_, d_);
    Plane3DImplDetail::generateReciprocal(directionU_, directionV_, reciprocalU_, reciprocalV_);
}
 
 
 
/** Construct a plane through a support point and by a normal vector.
 *  - support point S is given by the point iSupport.
 *  - normal vector N is given by the vector iNormal.
 *  - direction vectors U and V are automatically generated so that 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>
Plane3DCombined<T, NP>::Plane3DCombined(const TVector& iNormal, const TPoint& iSupport):
    support_(iSupport),
    normal_(iNormal),
    d_(-dot(iNormal, iSupport.position()))
{
    Plane3DImplDetail::generateDirections(normal_, directionU_, directionV_);
    NP::normalize(directionU_);
    NP::normalize(directionV_);
    NP::normalizeAndScale(normal_, d_);
    Plane3DImplDetail::generateReciprocal(directionU_, directionV_, reciprocalU_, reciprocalV_);
}
 
 
 
/** 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.
 *  - support point S automatically generated so that N.S + d == 0.
 *  - direction vectors U and V are automatically generated so that N == U x V.
 */
template<typename T, class NP>
Plane3DCombined<T, NP>::Plane3DCombined(const TVector& iNormal, TParam iD):
    support_(iNormal * (-iD / iNormal.squaredNorm())),
    normal_(iNormal),
    d_(iD)
{
    Plane3DImplDetail::generateDirections(normal_, directionU_, directionV_);
    NP::normalize(directionU_);
    NP::normalize(directionV_);
    NP::normalizeAndScale(normal_, d_);
    Plane3DImplDetail::generateReciprocal(directionU_, directionV_, reciprocalU_, reciprocalV_);
}
 
 
 
/** return support point.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TPoint& Plane3DCombined<T, NP>::support() const
{
    return support_;
}
 
 
 
/** return U and V direction vectors
 */
template<typename T, class NP>
void Plane3DCombined<T, NP>::getDirections(TVector& oDirectionU, TVector& oDirectionV) const
{
    oDirectionU = directionU_;
    oDirectionV = directionV_;
}
 
 
 
/** return U direction vector.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TVector& Plane3DCombined<T, NP>::directionU() const
{
    return directionU_;
}
 
 
 
/** return V direction vector.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TVector& Plane3DCombined<T, NP>::directionV() const
{
    return directionV_;
}
 
 
 
/** return reciprocal vectors for U and V direction vectors
 */
template<typename T, class NP>
void Plane3DCombined<T, NP>::getReciprocals(TVector& oReciprocalU,
                                            TVector& oReciprocalV) const
{
    oReciprocalU = reciprocalU_;
    oReciprocalV = reciprocalV_;
}
 
 
 
/** return reciprocal for U direction vector.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TVector& Plane3DCombined<T, NP>::reciprocalU() const
{
    return reciprocalU_;
}
 
 
 
/** return reciprocal for V direction vector.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TVector& Plane3DCombined<T, NP>::reciprocalV() const
{
    return reciprocalV_;
}
 
 
 
template<typename T, class NP>
void Plane3DCombined<T, NP>::getCartesian(TVector& oNormal, TReference oD) const
{
    oNormal = normal_;
    oD = d_;
}
 
 
 
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TVector& Plane3DCombined<T, NP>::normal() const
{
    return normal_;
}
 
 
 
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TParam Plane3DCombined<T, NP>::d() const
{
    return d_;
}
 
 
 
/** Return value of point in equation.
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TValue
Plane3DCombined<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 Plane3DCombined<T, NP>::TValue
Plane3DCombined<T, NP>::equation(const TPoint& iPoint, TParam iRelativeTolerance) const
{
    const TValue a = dot(iPoint.position(), normal_);
    return 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 Plane3DCombined<T, NP>::TVector
Plane3DCombined<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 Plane3DCombined<T, NP>::TVector
Plane3DCombined<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 Plane3DCombined<T, NP>::TPoint
Plane3DCombined<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 Plane3DCombined<T, NP>::TVector
Plane3DCombined<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 Plane3DCombined<T, NP>::TPoint
Plane3DCombined<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 Plane3DCombined<T, NP>::TVector
Plane3DCombined<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 Plane3DCombined<T, NP>::TPoint
Plane3DCombined<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 Plane3DCombined<T, NP>::TPoint
Plane3DCombined<T, NP>::point(const TUV& iUV) const
{
    return support_ + iUV.x * directionU_ + iUV.y * directionV_;
}
 
 
 
/** return UV pair of parameters
 */
template<typename T, class NP>
const typename Plane3DCombined<T, NP>::TUV
Plane3DCombined<T, NP>::uv(const TPoint& iPoint) const
{
    const TVector relative = iPoint - support_;
    return TUV(dot(relative, reciprocalU_), dot(relative, reciprocalV_));
}
 
 
 
template <typename T, class NP>
void Plane3DCombined<T, NP>::flip()
{
    directionV_ = -directionV_;
    normal_ = -normal_;
    d_ = -d_;
    Plane3DImplDetail::generateReciprocal(directionU_, directionV_, reciprocalU_, reciprocalV_);
}
 
 
 
/** return true if plane is a valid plane (no normal or direction vectors that are zero).
 */
template<typename T, class NP>
bool Plane3DCombined<T, NP>::isValid() const
{
    return !normal_.isZero() && !cross(directionU_, directionV_).isZero();
}
 
 
 
 
// --- protected -----------------------------------------------------------------------------------
 
 
 
// --- private -------------------------------------------------------------------------------------
 
 
 
// --- free ----------------------------------------------------------------------------------------
 
template<typename T, class NP>
std::ostream& operator<<(std::ostream& ioOStream, const Plane3DCombined<T, NP>& iPlane)
{
    LASS_ENFORCE(ioOStream) << "{S=" << iPlane.support() << ", U=" << iPlane.directionU() << ", V="
        << iPlane.directionV() << ", N=" << iPlane.normal() << ", d=" << iPlane.d() << "}";
    return ioOStream;
}
 
 
 
}
 
}
 
}
 
#endif
 
// EOF