SurfaceSpline.h

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//     ____   ______ __
//    / __ \ / ____// /
//   / /_/ // /    / /
//  / ____// /___ / /___   PixInsight Class Library
// /_/     \____//_____/   PCL 2.9.3
// ----------------------------------------------------------------------------
// pcl/SurfaceSpline.h - Released 2025-02-21T12:13:32Z
// ----------------------------------------------------------------------------
// This file is part of the PixInsight Class Library (PCL).
// PCL is a multiplatform C++ framework for development of PixInsight modules.
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// ----------------------------------------------------------------------------
 
#ifndef __PCL_SurfaceSpline_h
#define __PCL_SurfaceSpline_h
 
 
#include <pcl/Defs.h>
#include <pcl/Diagnostics.h>
 
#include <pcl/AbstractImage.h>
#include <pcl/Array.h>
#include <pcl/AutoPointer.h>
#include <pcl/Homography.h>
#include <pcl/ParallelProcess.h>
#include <pcl/Point.h>
#include <pcl/QuadTree.h>
#include <pcl/SurfaceSimplifier.h>
#include <pcl/Thread.h>
#include <pcl/Vector.h>
 
#ifndef __PCL_BUILDING_PIXINSIGHT_APPLICATION
#  include <pcl/Console.h>
#  include <pcl/StandardStatus.h>
#endif
 
namespace pcl
{
 
// ----------------------------------------------------------------------------
 
/*
 * The maximum allowed number of points in a point surface spline by default.
 */
#define __PCL_PSSPLINE_DEFAULT_MAX_POINTS             2100
 
/*
 * Default quadtree bucket capacity for recursive surface subspline generation.
 */
#define __PCL_RSSPLINE_DEFAULT_TREE_BUCKET_CAPACITY   64
 
/*
 * Default maximum spline length for a non-recursive quadtree node in a
 * recursive surface spline.
 */
#define __PCL_RSSPLINE_DEFAULT_SPLINE_MAX_LENGTH      1600
 
/*
 * Whether to allow extrapolation outside the interpolation region for
 * recursive surface splines. Extrapolation is disabled by default because
 * recursively defined subsplines are slightly more prone to oscillation than
 * normal surface splines.
 */
#define __PCL_RSSPLINE_DEFAULT_ALLOW_EXTRAPOLATION    false
 
// ----------------------------------------------------------------------------
 
namespace RadialBasisFunction
{
   enum value_type
   {
      Unknown = -1,
      VariableOrder = 0,        // phi(r) = (r^2)^(m-1) * Ln( r^2 )
      ThinPlateSpline,          // phi(r) = r^2 * Ln( r )
      Gaussian,                 // phi(r) = Exp( -(eps*r)^2 )
      Multiquadric,             // phi(r) = Sqrt( 1 + (eps*r)^2 )
      InverseMultiquadric,      // phi(r) = 1/Sqrt( 1 + (eps*r)^2 )
      InverseQuadratic,         // phi(r) = 1/( 1 + (eps*r)^2 )
      __number_of_pcl_implemented_rbfs__,
      DDMVariableOrder   = 100, // Variable-order polyharmonic DDM-RBF
      DDMThinPlateSpline = 101, // Thin plate spline DDM-RBF
      DDMMultiquadric    = 102, // Multiquadric DDM-RBF
      Default = ThinPlateSpline
   };
 
   inline static bool Validate( int rbf )
   {
      return rbf >= 0 && rbf < __number_of_pcl_implemented_rbfs__
          || rbf == DDMThinPlateSpline
          || rbf == DDMVariableOrder
          || rbf == DDMMultiquadric;
   }
 
   inline static bool HasCoreImplementation( int rbf )
   {
      return rbf > __number_of_pcl_implemented_rbfs__;
   }
 
   inline static bool HasDDMImplementation( int rbf )
   {
      return rbf == DDMThinPlateSpline
          || rbf == DDMVariableOrder
          || rbf == DDMMultiquadric;
   }
 
   inline static bool IsVariableOrder( int rbf )
   {
      return rbf == DDMVariableOrder || rbf == VariableOrder;
   }
 
   inline static bool HasShapeParameter( int rbf )
   {
      return rbf == Gaussian
          || rbf == Multiquadric
          || rbf == InverseMultiquadric
          || rbf == InverseQuadratic;
   }
}
 
// ----------------------------------------------------------------------------
 
class PCL_CLASS SurfaceSplineBase
{
public:
 
   using rbf_type = RadialBasisFunction::value_type;
 
protected:
 
   SurfaceSplineBase() = default;
 
   SurfaceSplineBase( const SurfaceSplineBase& ) = default;
 
   SurfaceSplineBase( SurfaceSplineBase&& ) = default;
 
   virtual ~SurfaceSplineBase()
   {
   }
 
   SurfaceSplineBase& operator =( const SurfaceSplineBase& ) = default;
 
   SurfaceSplineBase& operator =( SurfaceSplineBase&& ) = default;
 
   static void Generate( float* __restrict__ c, void** handle,
                         rbf_type, double e2, bool polynomial,
                         const float* __restrict__ x, const float* __restrict__ y, const float* __restrict__ z,
                         int n, int m, float r, const float* __restrict__ w );
 
   static void Generate( double* __restrict__ c, void** handle,
                         rbf_type, double e2, bool polynomial,
                         const double* __restrict__ x, const double* __restrict__ y, const double* __restrict__ z,
                         int n, int m, float r, const float* __restrict__ w );
 
   static double EvaluateHandle( const void* handle, double x, double y );
 
   static void EvaluateHandle( const void* handle, float* z, const float* x, const float* y, double x0, double y0, double r, size_type n );
 
   static void EvaluateHandle( const void* handle, double* z, const double* x, const double* y, double x0, double y0, double r, size_type n );
 
   static void SerializeHandle( IsoString& data, const void* handle );
 
   static void* DeserializeHandle( const IsoString& data );
 
   static void DestroyHandle( void* handle );
 
   static void* DuplicateHandle( const void* handle );
 
   friend class SplineWorldTransformation;
};
 
// ----------------------------------------------------------------------------
 
template <typename T>
class PCL_CLASS SurfaceSpline : private SurfaceSplineBase
{
public:
 
   using scalar = T;
 
   using vector = GenericVector<scalar>;
 
   using weight = float;
 
   using weight_vector = GenericVector<weight>;
 
   using rbf_type = SurfaceSplineBase::rbf_type;
 
   SurfaceSpline() = default;
 
   SurfaceSpline( const SurfaceSpline& S )
      : m_rbf( S.m_rbf )
      , m_havePolynomial( S.m_havePolynomial )
      , m_eps( S.m_eps )
      , m_eps2( S.m_eps2 )
      , m_x( S.m_x )
      , m_y( S.m_y )
      , m_z( S.m_z )
      , m_r0( S.m_r0 )
      , m_x0( S.m_x0 )
      , m_y0( S.m_y0 )
      , m_order( S.m_order )
      , m_smoothing( S.m_smoothing )
      , m_weights( S.m_weights )
      , m_spline( S.m_spline )
      , m_serialization( S.m_serialization )
   {
      m_handle = DuplicateHandle( S.m_handle );
   }
 
   SurfaceSpline( SurfaceSpline&& S )
      : m_rbf( S.m_rbf )
      , m_havePolynomial( S.m_havePolynomial )
      , m_eps( S.m_eps )
      , m_eps2( S.m_eps2 )
      , m_x( std::move( S.m_x ) )
      , m_y( std::move( S.m_y ) )
      , m_z( std::move( S.m_z ) )
      , m_r0( S.m_r0 )
      , m_x0( S.m_x0 )
      , m_y0( S.m_y0 )
      , m_order( S.m_order )
      , m_smoothing( S.m_smoothing )
      , m_weights( std::move( S.m_weights ) )
      , m_spline( std::move( S.m_spline ) )
      , m_serialization( S.m_serialization )
   {
      m_handle = S.m_handle;
      S.m_handle = 0;
   }
 
   ~SurfaceSpline() override
   {
      DestroyHandle( m_handle );
      m_handle = 0;
   }
 
   SurfaceSpline& operator =( const SurfaceSpline& S )
   {
      if ( &S != this )
      {
         Clear();
         m_rbf = S.m_rbf;
         m_havePolynomial = S.m_havePolynomial;
         m_eps = S.m_eps;
         m_eps2 = S.m_eps2;
         m_x = S.m_x;
         m_y = S.m_y;
         m_z = S.m_z;
         m_r0 = S.m_r0;
         m_x0 = S.m_x0;
         m_y0 = S.m_y0;
         m_order = S.m_order;
         m_smoothing = S.m_smoothing;
         m_weights = S.m_weights;
         m_spline = S.m_spline;
         m_serialization = S.m_serialization;
         m_handle = DuplicateHandle( S.m_handle );
      }
      return *this;
   }
 
   SurfaceSpline& operator =( SurfaceSpline&& S )
   {
      if ( &S != this )
      {
         Clear();
         m_rbf = S.m_rbf;
         m_havePolynomial = S.m_havePolynomial;
         m_eps = S.m_eps;
         m_eps2 = S.m_eps2;
         m_x = std::move( S.m_x );
         m_y = std::move( S.m_y );
         m_z = std::move( S.m_z );
         m_r0 = S.m_r0;
         m_x0 = S.m_x0;
         m_y0 = S.m_y0;
         m_order = S.m_order;
         m_smoothing = S.m_smoothing;
         m_weights = std::move( S.m_weights );
         m_spline = std::move( S.m_spline );
         m_serialization = S.m_serialization;
         m_handle = S.m_handle;
         S.m_handle = 0;
      }
      return *this;
   }
 
   bool IsValid() const
   {
      return m_handle != 0 || !m_spline.IsEmpty();
   }
 
   int Length() const
   {
      return m_x.Length();
   }
 
   vector X() const
   {
      vector x( m_x.Length() );
      if ( IsValid() )
         for ( int i = 0; i < m_x.Length(); ++i )
            x[i] = m_x0 + m_x[i]/m_r0;
      return x;
   }
 
   vector Y() const
   {
      vector y( m_y.Length() );
      if ( IsValid() )
         for ( int i = 0; i < m_y.Length(); ++i )
            y[i] = m_y0 + m_y[i]/m_r0;
      return y;
   }
 
   const vector& Z() const
   {
      return m_z;
   }
 
   const weight_vector& Weights() const
   {
      return m_weights;
   }
 
   rbf_type RBFType() const
   {
      return m_rbf;
   }
 
   void SetRBFType( rbf_type rbf )
   {
      Clear();
      m_rbf = rbf;
   }
 
   double ShapeParameter() const
   {
      return Sqrt( m_eps2 );
   }
 
   void SetShapeParameter( double eps )
   {
      Clear();
      m_eps = Abs( eps );
      m_eps2 = m_eps*m_eps;
   }
 
   int Order() const
   {
      return m_order;
   }
 
   void SetOrder( int order )
   {
      PCL_PRECONDITION( order > 1 )
      Clear();
      m_order = pcl::Max( 2, order );
   }
 
   bool IsPolynomialEnabled() const
   {
      return m_havePolynomial;
   }
 
   void EnablePolynomial( bool enable = true )
   {
      Clear();
      m_havePolynomial = enable;
   }
 
   void DisablePolynomial( bool disable = true )
   {
      EnablePolynomial( !disable );
   }
 
   float Smoothing() const
   {
      return m_smoothing;
   }
 
   void SetSmoothing( float s )
   {
      PCL_PRECONDITION( s >= 0 )
      Clear();
      m_smoothing = pcl::Max( 0.0F, s );
   }
 
   void Initialize( const scalar* x, const scalar* y, const scalar* z, int n, const weight* w = nullptr )
   {
      PCL_PRECONDITION( x != nullptr && y != nullptr && z != nullptr )
      PCL_PRECONDITION( n > 2 )
 
      if ( x == nullptr || y == nullptr || z == nullptr )
         throw Error( "SurfaceSpline::Initialize(): Null vector pointer(s)." );
 
      if ( n < 3 )
         throw Error( "SurfaceSpline::Initialize(): At least three input nodes must be specified." );
 
      Clear();
 
      if ( m_smoothing <= 0 )
         w = nullptr;
 
      try
      {
         /*
          * Find mean coordinates.
          */
         m_x0 = m_y0 = 0;
         for ( int i = 0; i < n; ++i )
         {
            m_x0 += x[i];
            m_y0 += y[i];
         }
         m_x0 /= n;
         m_y0 /= n;
 
         /*
          * Find radius of largest containing circle.
          */
         m_r0 = 0;
         for ( int i = 0; i < n; ++i )
         {
            double dx = x[i] - m_x0;
            double dy = y[i] - m_y0;
            double r = Sqrt( dx*dx + dy*dy );
            if ( r > m_r0 )
               m_r0 = r;
         }
         if ( 1 + m_r0 == 1 )
            throw Error( "SurfaceSpline::Initialize(): Empty or insignificant interpolation space." );
         m_r0 = 1/m_r0;
 
         /*
          * If needed and requested, compute an optimal shape parameter.
          */
         if ( unlikely( RadialBasisFunction::HasShapeParameter( m_rbf ) ) && m_eps == 0 )
         {
            Array<double> R2;
            for ( int i = 0; i < n; ++i )
               for ( int j = i; ++j < n; )
               {
                  double dx = x[i] - x[j];
                  double dy = y[i] - y[j];
                  R2 << dx*dx + dy*dy;
               }
            m_eps2 = 1/(m_r0*4*Sqrt( Median( R2.Begin(), R2.End() ) ));
         }
         else
            m_eps2 = m_r0*m_eps;
         m_eps2 *= m_eps2;
 
         /*
          * Build point list with normalized node coordinates.
          */
         Array<NodeData> P;
         for ( int i = 0; i < n; ++i )
            P << NodeData( m_r0*(x[i] - m_x0),
                           m_r0*(y[i] - m_y0),
                           z[i],
                           (w != nullptr && w[i] > 0) ? w[i] : 1.0F );
 
         /*
          * Find duplicate input nodes. Two nodes are considered equal if their
          * (normalized) coordinates don't differ more than the machine epsilon
          * for the floating point type T.
          */
         P.Sort();
         Array<int> remove;
         for ( int i = 0, j = 1; j < n; ++i, ++j )
            if ( Abs( P[i].x - P[j].x ) <= std::numeric_limits<scalar>::epsilon() )
               if ( Abs( P[i].y - P[j].y ) <= std::numeric_limits<scalar>::epsilon() )
                  remove << i;
 
         /*
          * Build working vectors, excluding duplicate input nodes.
          */
         int N = n - int( remove.Length() );
         if ( N < 3 )
            throw Error( "SurfaceSpline::Initialize(): Less than three input nodes left after sanitization." );
         m_x = vector( N );
         m_y = vector( N );
         m_z = vector( N );
         if ( w != nullptr )
            m_weights = weight_vector( N );
         int i = 0, k = 0;
         for ( int j : remove )
         {
            for ( ; i < j; ++i, ++k )
            {
               m_x[k] = P[i].x;
               m_y[k] = P[i].y;
               m_z[k] = P[i].z;
               if ( w != nullptr )
                  m_weights[k] = P[i].w;
            }
            ++i;
         }
         for ( ; i < n; ++i, ++k )
         {
            m_x[k] = P[i].x;
            m_y[k] = P[i].y;
            m_z[k] = P[i].z;
            if ( w != nullptr )
               m_weights[k] = P[i].w;
         }
 
         if ( !RadialBasisFunction::HasCoreImplementation( m_rbf ) )
            m_spline = vector( scalar( 0 ), N + (m_havePolynomial ? ((m_order*(m_order + 1)) >> 1) : 0) );
 
         Generate( m_spline.Begin(), &m_handle, m_rbf, m_eps2, m_havePolynomial,
                   m_x.Begin(), m_y.Begin(), m_z.Begin(), N, m_order,
                   m_smoothing, m_weights.Begin() );
      }
      catch ( ... )
      {
         Clear();
         throw;
      }
   }
 
   void Clear()
   {
      m_x.Clear();
      m_y.Clear();
      m_z.Clear();
      m_weights.Clear();
      m_spline.Clear();
      DestroyHandle( m_handle );
      m_handle = 0;
   }
 
   IsoString CoreSerialization() const
   {
      IsoString data;
      SerializeHandle( data, m_handle );
      return data;
   }
 
   scalar operator ()( double x, double y ) const
   {
      PCL_PRECONDITION( !m_x.IsEmpty() && !m_y.IsEmpty() )
      PCL_CHECK( m_order >= 2 )
      PCL_CHECK( !m_spline.IsEmpty() || m_handle != 0 )
 
      /*
       * Normalized interpolation coordinates.
       */
      x = m_r0*(x - m_x0);
      y = m_r0*(y - m_y0);
 
      /*
       * Core RBF implementations
       */
      if ( m_handle != 0 )
         return scalar( EvaluateHandle( m_handle, x, y ) );
 
      /*
       * Add polynomial part of the surface spline.
       */
      int n = m_x.Length();
      double z = 0;
      if ( m_havePolynomial )
      {
         z += m_spline[n];
         switch ( m_order )
         {
         case 2:
            z += m_spline[n+1]*x + m_spline[n+2]*y;
            break;
         case 3:
            z += (m_spline[n+1] + m_spline[n+3]*x + m_spline[n+4]*y)*x + (m_spline[n+2] + m_spline[n+5]*y)*y;
            break;
         default:
            for ( int i = 1, j = n+1, i1 = (m_order*(m_order + 1))>>1, ix = 0, iy = 0; i < i1; ++i, ++j )
               if ( ix == 0 )
               {
                  ix = iy + 1;
                  iy = 0;
                  z += m_spline[j] * PowI( x, ix );
               }
               else
               {
                  --ix;
                  ++iy;
                  z += m_spline[j] * PowI( x, ix ) * PowI( y, iy );
               }
            break;
         }
      }
 
      /*
       * Add radial basis functions.
       */
      switch ( m_rbf )
      {
      case RadialBasisFunction::VariableOrder:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            double r2 = dx*dx + dy*dy;
            if ( r2 != 0 )
            {
               double r2m1 = r2;
               for ( int j = m_order; --j > 1; )
                  r2m1 *= r2;
               z += m_spline[i] * r2m1 * pcl::Ln( r2 );
            }
         }
         break;
      case RadialBasisFunction::ThinPlateSpline:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            double r2 = dx*dx + dy*dy;
            if ( r2 != 0 )
               z += m_spline[i] * r2 * pcl::Ln( Sqrt( r2 ) );
         }
         break;
      case RadialBasisFunction::Gaussian:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            z += m_spline[i] * pcl::Exp( -m_eps2 * (dx*dx + dy*dy) );
         }
         break;
      case RadialBasisFunction::Multiquadric:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            z += m_spline[i] * pcl::Sqrt( 1 + m_eps2 * (dx*dx + dy*dy) );
         }
         break;
      case RadialBasisFunction::InverseMultiquadric:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            z += m_spline[i] / pcl::Sqrt( 1 + m_eps2 * (dx*dx + dy*dy) );
         }
         break;
      case RadialBasisFunction::InverseQuadratic:
         for ( int i = 0; i < n; ++i )
         {
            double dx = m_x[i] - x;
            double dy = m_y[i] - y;
            z += m_spline[i] / (1 + m_eps2 * (dx*dx + dy*dy));
         }
         break;
      default:
         break;
      }
 
      return scalar( z );
   }
 
   template <typename Tp>
   scalar operator ()( const GenericPoint<Tp>& p ) const
   {
      return operator ()( double( p.x ), double( p.y ) );
   }
 
   void Evaluate( scalar* Z, const scalar* X, const scalar* Y, size_type n ) const
   {
      PCL_PRECONDITION( !m_x.IsEmpty() && !m_y.IsEmpty() )
      PCL_PRECONDITION( X != nullptr && Y != nullptr && Z != nullptr )
      PCL_PRECONDITION( n > 0 )
      PCL_CHECK( m_order >= 2 )
      PCL_CHECK( !m_spline.IsEmpty() || m_handle != 0 )
 
      if ( m_handle != 0 )
         EvaluateHandle( m_handle, Z, X, Y, m_x0, m_y0, m_r0, n );
      else
         for ( size_type i = 0; i < n; ++i )
            Z[i] = operator()( X[i], Y[i] );
   }
 
   vector Evaluate( const vector& X, const vector& Y ) const
   {
      PCL_PRECONDITION( !m_x.IsEmpty() && !m_y.IsEmpty() )
      PCL_CHECK( m_order >= 2 )
      PCL_CHECK( !m_spline.IsEmpty() || m_handle != 0 )
 
      int n = Min( X.Length(), Y.Length() );
      vector Z( n );
      Evaluate( Z.Begin(), X.Begin(), Y.Begin(), size_type( n ) );
      return Z;
   }
 
   bool HasFastVectorEvaluation() const
   {
      return m_handle != 0;
   }
 
protected:
 
   rbf_type      m_rbf = RadialBasisFunction::Default;
   bool          m_havePolynomial = true; // use 1st order polynomial for stabilization
   double        m_eps = 0;       // shape parameter, 0 -> find optimal value automatically
   double        m_eps2 = 0;      // squared shape parameter
   vector        m_x;             // vector of normalized X node coordinates
   vector        m_y;             // vector of normalized Y node coordinates
   vector        m_z;             // vector of function values - for reference only
   double        m_r0 = 1;        // scaling factor for normalization of node coordinates
   double        m_x0 = 0;        // zero offset for normalization of X node coordinates
   double        m_y0 = 0;        // zero offset for normalization of Y node coordinates
   int           m_order = 2;     // derivative order >= 2
   float         m_smoothing = 0; // <= 0 -> interpolating spline, > 0 -> smoothing factor of approximating spline
   weight_vector m_weights;       // optional node weights for approximating spline
   vector        m_spline;        // coefficients of the 2-D surface spline, polynomial coeffs. at tail
   IsoString     m_serialization; // internal use: SplineWorldTransformation for delayed deserialization
   void*         m_handle = 0;    // handle to a core-implemented RBF interpolation/smoothing object
 
   struct NodeData
   {
      scalar x, y, z;
      weight w;
 
      NodeData( scalar a_x, scalar a_y, scalar a_z, weight a_w )
         : x( a_x ), y( a_y ), z( a_z ), w( a_w )
      {
      }
 
      bool operator ==( const NodeData& p ) const
      {
         return x == p.x && y == p.y;
      }
 
      bool operator <( const NodeData& p ) const
      {
         return (x != p.x) ? x < p.x : y < p.y;
      }
   };
 
   friend class DrizzleData;
   friend class DrizzleDataDecoder;
   friend class SplineWorldTransformation;
};
 
// ----------------------------------------------------------------------------
 
class PCL_CLASS PointSurfaceSpline
{
public:
 
   using spline = SurfaceSpline<double>;
 
   using rbf_type = spline::rbf_type;
 
   PointSurfaceSpline() = default;
 
   PointSurfaceSpline( const PointSurfaceSpline& ) = default;
 
   PointSurfaceSpline( PointSurfaceSpline&& ) = default;
 
   template <class point_list1, class point_list2, class weight_vector = FVector>
   PointSurfaceSpline( const point_list1& P1, const point_list2& P2,
                       float smoothness = 0, int order = 2,
                       const weight_vector& W = weight_vector(),
                       rbf_type rbf = RadialBasisFunction::Default,
                       double eps = 0,
                       bool polynomial = true )
   {
      Initialize( P1, P2, smoothness, W, order, rbf, eps, polynomial );
   }
 
   PointSurfaceSpline( const spline& Sx, const spline& Sy )
   {
      Initialize( Sx, Sy );
   }
 
   PointSurfaceSpline& operator =( const PointSurfaceSpline& other ) = default;
 
   PointSurfaceSpline& operator =( PointSurfaceSpline&& ) = default;
 
   template <class point_list1, class point_list2, class weight_vector = FVector>
   void Initialize( const point_list1& P1, const point_list2& P2,
                    float smoothness = 0, const weight_vector& W = weight_vector(), int order = 2,
                    rbf_type rbf = RadialBasisFunction::Default,
                    double eps = 0,
                    bool polynomial = true )
   {
      PCL_PRECONDITION( P1.Length() >= 3 )
      PCL_PRECONDITION( P1.Length() <= P2.Length() )
      PCL_PRECONDITION( order >= 2 )
      PCL_PRECONDITION( W.IsEmpty() || P1.Length() <= size_type( W.Length() ) )
 
      Clear();
 
      int N = int( P1.Length() );
      if ( N < 3 || P2.Length() < 3 )
         throw Error( "PointSurfaceSpline::Initialize(): At least three input nodes must be specified." );
      if ( int( P2.Length() ) < N || !W.IsEmpty() && int( W.Length() ) < N )
         throw Error( "PointSurfaceSpline::Initialize(): Insufficient data." );
 
      m_Sx.SetRBFType( rbf );
      m_Sx.SetOrder( order );
      m_Sx.SetShapeParameter( eps );
      m_Sx.EnablePolynomial( polynomial );
      m_Sx.SetSmoothing( smoothness );
 
      m_Sy.SetRBFType( rbf );
      m_Sy.SetOrder( order );
      m_Sy.SetShapeParameter( eps );
      m_Sy.EnablePolynomial( polynomial );
      m_Sy.SetSmoothing( smoothness );
 
      DVector X( N ), Y( N ), ZX( N ), ZY( N );
      double zxMin =  std::numeric_limits<double>::max();
      double zxMax = -std::numeric_limits<double>::max();
      double zyMin =  std::numeric_limits<double>::max();
      double zyMax = -std::numeric_limits<double>::max();
      for ( int i = 0; i < N; ++i )
      {
         X[i] = double( P1[i].x );
         Y[i] = double( P1[i].y );
 
         if ( m_incremental )
         {
            ZX[i] = X[i];
            ZY[i] = Y[i];
            m_H.Apply( ZX[i], ZY[i] );
            ZX[i] = double( P2[i].x ) - ZX[i];
            ZY[i] = double( P2[i].y ) - ZY[i];
         }
         else
         {
            ZX[i] = double( P2[i].x );
            ZY[i] = double( P2[i].y );
         }
 
         if ( ZX[i] < zxMin )
            zxMin = ZX[i];
         if ( ZX[i] > zxMax )
            zxMax = ZX[i];
         if ( ZY[i] < zyMin )
            zyMin = ZY[i];
         if ( ZY[i] > zyMax )
            zyMax = ZY[i];
      }
 
      if ( m_useSimplifiers )
      {
         SurfaceSimplifier SS;
         SS.EnableRejection();
         SS.SetRejectFraction( m_simplifierRejectFraction );
         SS.EnableCentroidInclusion();
 
         // Simplified surface, X axis.
         DVector XXS, YXS, ZXS;
         m_epsX = (zxMax - zxMin)/100;
         double epsLow = 0, epsHigh = 10*m_epsX;
         for ( int i = 0; i < 200; ++i )
         {
            SS.SetTolerance( m_epsX );
            SS.Simplify( XXS, YXS, ZXS, X, Y, ZX );
            if ( XXS.Length() > m_maxSplinePoints )
            {
               epsLow = m_epsX;
               if ( epsHigh - epsLow <= 4*std::numeric_limits<double>::epsilon() )
                  epsHigh *= 2;
            }
            else
            {
               if ( epsHigh - epsLow <= 2*std::numeric_limits<double>::epsilon() )
                  break;
               epsHigh = m_epsX;
            }
            m_epsX = (epsLow + epsHigh)/2;
         }
         if ( XXS.Length() > m_maxSplinePoints )
         {
            m_truncatedX = true;
            XXS = DVector( XXS.Begin(), m_maxSplinePoints );
            YXS = DVector( YXS.Begin(), m_maxSplinePoints );
            ZXS = DVector( ZXS.Begin(), m_maxSplinePoints );
         }
 
         // Simplified surface, Y axis.
         DVector XYS, YYS, ZYS;
         m_epsY = (zyMax - zyMin)/100;
         epsLow = 0, epsHigh = 10*m_epsY;
         for ( int i = 0; i < 200; ++i )
         {
            SS.SetTolerance( m_epsY );
            SS.Simplify( XYS, YYS, ZYS, X, Y, ZY );
            if ( XYS.Length() > m_maxSplinePoints )
            {
               epsLow = m_epsY;
               if ( epsHigh - epsLow <= 4*std::numeric_limits<double>::epsilon() )
                  epsHigh *= 2;
            }
            else
            {
               if ( epsHigh - epsLow <= 2*std::numeric_limits<double>::epsilon() )
                  break;
               epsHigh = m_epsY;
            }
            m_epsY = (epsLow + epsHigh)/2;
         }
         if ( XYS.Length() > m_maxSplinePoints )
         {
            m_truncatedY = true;
            XYS = DVector( XYS.Begin(), m_maxSplinePoints );
            YYS = DVector( YYS.Begin(), m_maxSplinePoints );
            ZYS = DVector( ZYS.Begin(), m_maxSplinePoints );
         }
 
         SplineGenerationThread<weight_vector> Tx( m_Sx, XXS, YXS, ZXS, XXS.Length(), weight_vector() );
         SplineGenerationThread<weight_vector> Ty( m_Sy, XYS, YYS, ZYS, XYS.Length(), weight_vector() );
         Tx.Start( ThreadPriority::DefaultMax );
         Ty.Start( ThreadPriority::DefaultMax );
         Tx.Wait();
         Ty.Wait();
         Tx.ValidateOrThrow();
         Ty.ValidateOrThrow();
      }
      else
      {
         m_truncatedX = m_truncatedY = N > m_maxSplinePoints;
         SplineGenerationThread<weight_vector> Tx( m_Sx, X, Y, ZX, Min( N, m_maxSplinePoints ), W );
         SplineGenerationThread<weight_vector> Ty( m_Sy, X, Y, ZY, Min( N, m_maxSplinePoints ), W );
         Tx.Start( ThreadPriority::DefaultMax );
         Ty.Start( ThreadPriority::DefaultMax );
         Tx.Wait();
         Ty.Wait();
         Tx.ValidateOrThrow();
         Ty.ValidateOrThrow();
      }
   }
 
   void Initialize( const spline& Sx, const spline& Sy )
   {
      Clear();
      m_useSimplifiers = m_incremental = false;
      m_H = Homography();
      if ( Sx.IsValid() && Sy.IsValid() )
      {
         m_Sx = Sx;
         m_Sy = Sy;
      }
   }
 
   void Clear()
   {
      m_Sx.Clear();
      m_Sy.Clear();
      m_epsX = m_epsY = 0;
      m_truncatedX = m_truncatedY = false;
   }
 
   bool IsValid() const
   {
      return m_Sx.IsValid() && m_Sy.IsValid() && (!m_incremental || m_H.IsValid());
   }
 
   const spline& SplineX() const
   {
      return m_Sx;
   }
 
   const spline& SplineY() const
   {
      return m_Sy;
   }
 
   int MaxSplinePoints() const
   {
      return m_maxSplinePoints;
   }
 
   void SetMaxSplinePoints( int n )
   {
      PCL_PRECONDITION( n >= 3 )
      m_maxSplinePoints = Max( 3, n );
   }
 
   bool SimplifiersEnabled() const
   {
      return m_useSimplifiers;
   }
 
   void EnableSimplifiers( bool enable = true )
   {
      m_useSimplifiers = enable;
   }
 
   void DisableSimplifiers( bool disable = true )
   {
      EnableSimplifiers( !disable );
   }
 
   float SimplifierRejectFraction() const
   {
      return m_simplifierRejectFraction;
   }
 
   void SetSimplifierRejectFraction( float rejectFraction )
   {
      PCL_PRECONDITION( rejectFraction > 0 && rejectFraction < 1 )
      m_simplifierRejectFraction = Range( rejectFraction, 0.0F, 1.0F );
   }
 
   double ErrorX() const
   {
      return m_epsX;
   }
 
   double ErrorY() const
   {
      return m_epsY;
   }
 
   bool TruncatedX() const
   {
      return m_truncatedX;
   }
 
   bool TruncatedY() const
   {
      return m_truncatedY;
   }
 
   bool Truncated() const
   {
      return TruncatedX() || TruncatedY();
   }
 
   const Matrix& LinearFunction() const
   {
      return m_H;
   }
 
   void SetLinearFunction( const Matrix& H )
   {
      m_H = H;
   }
 
   bool IncrementalFunctionEnabled() const
   {
      return m_incremental;
   }
 
   void EnableIncrementalFunction( bool enable = true )
   {
      m_incremental = enable;
   }
 
   void DisableIncrementalFunction( bool disable = true )
   {
      EnableIncrementalFunction( !disable );
   }
 
   DPoint operator ()( double x, double y ) const
   {
      PCL_PRECONDITION( ISValid() )
      DPoint p( m_Sx( x, y ), m_Sy( x, y ) );
      if ( m_incremental )
         p += m_H( x, y );
      return p;
   }
 
   template <typename T>
   DPoint operator ()( const GenericPoint<T>& p ) const
   {
      return operator ()( double( p.x ), double( p.y ) );
   }
 
   template <typename T>
   void Evaluate( T* ZX, T* ZY, const T* X, const T* Y, size_type n ) const
   {
      PCL_PRECONDITION( ISValid() )
      m_Sx.Evaluate( ZX, X, Y, n );
      m_Sy.Evaluate( ZY, X, Y, n );
      if ( m_incremental )
         for ( size_type i = 0; i < n; ++i )
         {
            DPoint dxy = m_H( X[i], Y[i] );
            ZX[i] += dxy.x;
            ZY[i] += dxy.y;
         }
   }
 
   template <class V>
   Array<DPoint> Evaluate( const V& X, const V& Y ) const
   {
      PCL_PRECONDITION( ISValid() )
      size_type n = Min( X.Length(), Y.Length() );
      Array<double> ZX( n ), ZY( n );
      Evaluate( ZX.Begin(), ZY.Begin(), X.Begin(), Y.Begin(), n );
      Array<DPoint> Z( n );
      for ( size_type i = 0; i < n; ++i )
      {
         Z[i].x = ZX[i];
         Z[i].y = ZY[i];
      }
      return Z;
   }
 
   template <class PV>
   Array<DPoint> Evaluate( const PV& P ) const
   {
      PCL_PRECONDITION( ISValid() )
      size_type n = P.Length();
      Array<double> X( n ), Y( n );
      for ( size_type i = 0; i < n; ++i )
      {
         X[i] = P[i].x;
         Y[i] = P[i].y;
      }
      return Evaluate( X, Y );
   }
 
   bool HasFastVectorEvaluation() const
   {
      return m_Sx.HasFastVectorEvaluation() && m_Sy.HasFastVectorEvaluation();
   }
 
private:
 
   /*
    * The surface splines in the X and Y plane directions.
    */
   spline      m_Sx, m_Sy;
   int         m_maxSplinePoints = __PCL_PSSPLINE_DEFAULT_MAX_POINTS;
 
   /*
    * Incremental surface splines.
    */
   bool        m_incremental = false;  // true => fit differences w.r.t. a projective transformation
   Homography  m_H;                    // base projective transformation when m_incremental = true
 
   /*
    * Surface simplification.
    */
   bool        m_useSimplifiers = false;
   float       m_simplifierRejectFraction = 0.1F;
   double      m_epsX = 0;             // simplification error on the X axis
   double      m_epsY = 0;             // simplification error on the Y axis
   bool        m_truncatedX = false;   // true => truncated vectors in the X axis
   bool        m_truncatedY = false;   // true => truncated vectors in the Y axis
 
   template <class weight_vector>
   class SplineGenerationThread : public Thread
   {
   public:
 
      SplineGenerationThread( spline& S, const DVector& X, const DVector& Y, const DVector& Z, int N, const weight_vector& W )
         : m_S( S ), m_X( X ), m_Y( Y ), m_Z( Z ), m_N( N ), m_W( W )
      {
      }
 
      PCL_HOT_FUNCTION void Run() override
      {
         try
         {
            m_S.Initialize( m_X.Begin(), m_Y.Begin(), m_Z.Begin(), m_N, m_W.Begin() );
            return;
         }
         catch ( const Exception& x )
         {
            m_exception = x;
         }
         catch ( ... )
         {
            m_exception = Error( "Unknown exception" );
         }
         m_S.Clear();
      }
 
      void ValidateOrThrow() const
      {
         if ( !m_S.IsValid() )
            throw m_exception;
      }
 
   private:
 
      spline&        m_S;
      const DVector& m_X;
      const DVector& m_Y;
      const DVector& m_Z;
      int            m_N;
      weight_vector  m_W; // ### N.B. do not use a reference: the W ctor. argument can be a temporary object.
      Exception      m_exception;
   };
 
   friend class DrizzleData;
   friend class DrizzleDataDecoder;
   friend class SplineWorldTransformation;
};
 
// ----------------------------------------------------------------------------
 
class PCL_CLASS RecursivePointSurfaceSpline : public ParallelProcess
{
public:
 
   RecursivePointSurfaceSpline() = default;
 
   RecursivePointSurfaceSpline( const RecursivePointSurfaceSpline& ) = delete;
 
   RecursivePointSurfaceSpline& operator =( const RecursivePointSurfaceSpline& ) = delete;
 
   RecursivePointSurfaceSpline( RecursivePointSurfaceSpline&& ) = default;
 
   RecursivePointSurfaceSpline& operator =( RecursivePointSurfaceSpline&& ) = default;
 
   template <class point_list1, class point_list2, class weight_vector = FVector>
   RecursivePointSurfaceSpline( const point_list1& P1, const point_list2& P2,
                                float smoothness = 0,
                                int order = 2,
                                const weight_vector& W = weight_vector(),
                                bool allowExtrapolation = __PCL_RSSPLINE_DEFAULT_ALLOW_EXTRAPOLATION,
                                int maxSplineLength = __PCL_RSSPLINE_DEFAULT_SPLINE_MAX_LENGTH,
                                int bucketCapacity = __PCL_RSSPLINE_DEFAULT_TREE_BUCKET_CAPACITY,
                                bool verbose = true )
   {
      Initialize( P1, P2, smoothness, W, order, allowExtrapolation, maxSplineLength, bucketCapacity, verbose );
   }
 
   ~RecursivePointSurfaceSpline() override
   {
      Clear();
   }
 
   template <class point_list1, class point_list2, class weight_vector = FVector>
   void Initialize( const point_list1& P1, const point_list2& P2,
                    float smoothness = 0,
                    const weight_vector& W = weight_vector(),
                    int order = 2,
                    bool allowExtrapolation = __PCL_RSSPLINE_DEFAULT_ALLOW_EXTRAPOLATION,
                    int maxSplineLength = __PCL_RSSPLINE_DEFAULT_SPLINE_MAX_LENGTH,
                    int bucketCapacity = __PCL_RSSPLINE_DEFAULT_TREE_BUCKET_CAPACITY,
                    bool verbose = true )
   {
      PCL_PRECONDITION( P1.Length() >= 3 )
      PCL_PRECONDITION( P1.Length() <= P2.Length() )
      PCL_PRECONDITION( order >= 2 )
      PCL_PRECONDITION( W.IsEmpty() || P1.Length() <= W.Length() )
 
      Clear();
 
      if ( P1.Length() < 3 || P2.Length() < 3 )
         throw Error( "RecursivePointSurfaceSpline::Initialize(): At least three input nodes must be specified." );
 
      bool weighted = smoothness > 0 && !W.IsEmpty();
 
      if ( P1.Length() > P2.Length() || weighted && P1.Length() > size_type( W.Length() ) )
         throw Error( "RecursivePointSurfaceSpline::Initialize(): Insufficient data." );
 
      m_extrapolate = allowExtrapolation;
 
      if ( P1.Length() <= size_type( maxSplineLength ) )
      {
         StatusMonitor monitor;
#ifndef __PCL_BUILDING_PIXINSIGHT_APPLICATION
         StandardStatus status;
         if ( verbose )
         {
            monitor.SetCallback( &status );
            monitor.Initialize( "Building surface subsplines", 100 );
         }
#endif
         for ( const auto& p : P1 )
         {
            double x = double( p.x );
            double y = double( p.y );
            if ( x < m_rect.x0 )
               m_rect.x0 = x;
            else if ( x > m_rect.x1 )
               m_rect.x1 = x;
            if ( y < m_rect.y0 )
               m_rect.y0 = y;
            else if ( y > m_rect.y1 )
               m_rect.y1 = y;
         }
 
         m_spline.Initialize( P1, P2, smoothness, W, order,
                              (order == 2) ? RadialBasisFunction::ThinPlateSpline
                                           : RadialBasisFunction::VariableOrder );
 
#ifndef __PCL_BUILDING_PIXINSIGHT_APPLICATION
         if ( verbose )
            monitor.Complete();
#endif
      }
      else
      {
         /*
          * Find the total interpolation region.
          */
         search_rectangle rect = search_coordinate( 0 );
         node_list data;
         for ( size_type i = 0; i < P1.Length(); ++i )
         {
            const auto& p1 = P1[i];
            const auto& p2 = P2[i];
            data << (weighted ? Node( p1, p2, W[i] ) : Node( p1, p2 ));
            double x = p1.x;
            double y = p1.y;
            if ( x < rect.x0 )
               rect.x0 = x;
            else if ( x > rect.x1 )
               rect.x1 = x;
            if ( y < rect.y0 )
               rect.y0 = y;
            else if ( y > rect.y1 )
               rect.y1 = y;
         }
         // Force a square interpolation region for optimal quadtree behavior.
         if ( rect.Width() < rect.Height() )
            rect.InflateBy( (rect.Height() - rect.Width())/2, search_coordinate( 0 ) );
         else
            rect.InflateBy( search_coordinate( 0 ), (rect.Width() - rect.Height())/2 );
 
         /*
          * Build the interpolation quadtree.
          */
         m_tree.Build( rect, data, bucketCapacity );
 
         /*
          * Build subspline interpolation data.
          */
         Array<SubsplineData> subsplineData;
         m_tree.Traverse(
            [&]( const search_rectangle& rect, const node_list& points, void*& D )
            {
               /*
                * Ensure redundancy for all subsplines by gathering a set of
                * interpolation points in an extended rectangular region around
                * each quadtree node.
                */
               search_rectangle r = rect.InflatedBy( 1.5*Max( rect.Width(), rect.Height() ) );
               node_list N = m_tree.Search( r );
 
               /*
                * Sort the cloud of interpolation points by proximity to a
                * circle centered at the argument of the minimum RBF value
                * (approximately 0.61 in normalized coordinates).
                */
               if ( N.Length() > size_type( maxSplineLength ) )
               {
                  DPoint c = rect.Center();
                  double d = 0.61 * (Max( r.Width(), r.Height() )/2 + Max( rect.Width(), rect.Height() )/4);
                  N.Sort(
                     [&]( const auto& a, const auto& b )
                     {
                        return Abs( a.position.DistanceTo( c ) - d ) < Abs( b.position.DistanceTo( c ) - d );
                     } );
               }
 
               /*
                * Get the optimal subset of at most maxSplineLength redundant
                * interpolation points for this quadtree node.
                */
               Array<DPoint> P1, P2;
               Array<float> PW;
               for ( int j = 0, l = Min( int( N.Length() ), maxSplineLength ); j < l; ++j )
               {
                  P1 << N[j].position;
                  P2 << N[j].value;
                  if ( weighted )
                     PW << N[j].weight;
               }
 
               subsplineData << SubsplineData( P1, P2, PW, D );
            } );
 
         /*
          * Generate all subsplines.
          */
         StatusMonitor monitor;
#ifndef __PCL_BUILDING_PIXINSIGHT_APPLICATION
         StandardStatus status;
         if ( verbose )
         {
            monitor.SetCallback( &status );
            monitor.Initialize( "Building recursive surface subsplines", subsplineData.Length() );
         }
#endif
         Array<size_type> L = Thread::OptimalThreadLoads( subsplineData.Length(),
                                                          1/*overheadLimit*/,
                                                          m_parallel ? m_maxProcessors : 1 );
         AbstractImage::ThreadData threadData( monitor, subsplineData.Length() );
         ReferenceArray<SubsplineGenerationThread> threads;
         for ( int i = 0, n = 0; i < int( L.Length() ); n += int( L[i++] ) )
            threads.Add( new SubsplineGenerationThread( threadData,
                                                        subsplineData,
                                                        smoothness,
                                                        order,
                                                        allowExtrapolation,
                                                        maxSplineLength,
                                                        bucketCapacity,
                                                        n,
                                                        n + int( L[i] ) ) );
         AbstractImage::RunThreads( threads, threadData );
         threads.Destroy();
      }
   }
 
   void Clear()
   {
      m_tree.Traverse(
         []( const search_rectangle&, node_list&, void*& D )
         {
            delete reinterpret_cast<RecursivePointSurfaceSpline*&>( D );
         } );
      m_tree.Clear();
      m_spline.Clear();
      m_rect = search_coordinate( 0 );
   }
 
   bool IsRecursive() const
   {
      return !m_tree.IsEmpty();
   }
 
   bool IsValid() const
   {
      return IsRecursive() || m_spline.IsValid();
   }
 
   DPoint operator ()( double x, double y ) const
   {
      if ( m_spline.IsValid() )
      {
         if ( m_extrapolate || m_rect.IncludesFast( x, y ) )
            return m_spline( x, y );
      }
      else
      {
         const typename tree::Node* node = m_tree.NodeAt( search_point( x, y ) );
         if ( node == nullptr )
         {
            if ( !m_extrapolate )
               return 0.0;
 
            search_rectangle r0 = m_tree.Root()->rect;
            if ( x <= r0.x0 )
            {
               if ( y <= r0.y0 )
                  node = m_tree.NodeAt( search_point( r0.x0 + SearchDelta, r0.y0 + SearchDelta ) );
               else if ( y >= r0.y1 )
                  node = m_tree.NodeAt( search_point( r0.x0 + SearchDelta, r0.y1 - SearchDelta ) );
               else
                  node = m_tree.NodeAt( search_point( r0.x0 + SearchDelta, search_coordinate( y ) ) );
            }
            else if ( x >= r0.x1 )
            {
               if ( y <= r0.y0 )
                  node = m_tree.NodeAt( search_point( r0.x1 - SearchDelta, r0.y0 + SearchDelta ) );
               else if ( y >= r0.y1 )
                  node = m_tree.NodeAt( search_point( r0.x1 - SearchDelta, r0.y1 - SearchDelta ) );
               else
                  node = m_tree.NodeAt( search_point( r0.x1 - SearchDelta, search_coordinate( y ) ) );
            }
            else if ( y <= r0.y0 )
               node = m_tree.NodeAt( search_point( search_coordinate( x ), r0.y0 + SearchDelta ) );
            else // y >= r0.y1
               node = m_tree.NodeAt( search_point( search_coordinate( x ), r0.y1 - SearchDelta ) );
 
            if ( node == nullptr ) // ?!
               return 0.0;
         }
 
         if ( node->IsLeaf() )
         {
            const typename tree::LeafNode* leaf = static_cast<const typename tree::LeafNode*>( node );
            if ( leaf->data == nullptr ) // ?!
               return 0.0;
            return reinterpret_cast<RecursivePointSurfaceSpline*>( leaf->data )->operator()( x, y );
         }
 
         DPoint p = 0.0;
         int n = 0;
         if ( node->nw != nullptr )
         {
            const typename tree::LeafNode* leaf;
            if ( y <= node->nw->rect.y1 )
               leaf = m_tree.LeafNodeAt( search_point( node->nw->rect.x1 - SearchDelta, search_coordinate( y ) ) );
            else if ( x <= node->nw->rect.x1 )
               leaf = m_tree.LeafNodeAt( search_point( search_coordinate( x ), node->nw->rect.y1 - SearchDelta ) );
            else
               leaf = m_tree.LeafNodeAt( search_point( node->nw->rect.x1 - SearchDelta, node->nw->rect.y1 - SearchDelta ) );
 
            if ( leaf != nullptr )
            {
               p += reinterpret_cast<RecursivePointSurfaceSpline*>( leaf->data )->operator()( x, y );
               ++n;
            }
         }
         if ( node->ne != nullptr )
         {
            const typename tree::LeafNode* leaf;
            if ( y <= node->ne->rect.y1 )
               leaf = m_tree.LeafNodeAt( search_point( node->ne->rect.x0 + SearchDelta, search_coordinate( y ) ) );
            else if ( x <= node->ne->rect.x0 )
               leaf = m_tree.LeafNodeAt( search_point( node->ne->rect.x0 + SearchDelta, node->ne->rect.y1 - SearchDelta ) );
            else
               leaf = m_tree.LeafNodeAt( search_point( search_coordinate( x ), node->ne->rect.y1 - SearchDelta ) );
 
            if ( leaf != nullptr )
            {
               p += reinterpret_cast<RecursivePointSurfaceSpline*>( leaf->data )->operator()( x, y );
               ++n;
            }
         }
         if ( node->sw != nullptr )
         {
            const typename tree::LeafNode* leaf;
            if ( y >= node->sw->rect.y0 )
               leaf = m_tree.LeafNodeAt( search_point( node->sw->rect.x1 - SearchDelta, search_coordinate( y ) ) );
            else if ( x <= node->sw->rect.x1 )
               leaf = m_tree.LeafNodeAt( search_point( search_coordinate( x ), node->sw->rect.y0 + SearchDelta ) );
            else
               leaf = m_tree.LeafNodeAt( search_point( node->sw->rect.x1 - SearchDelta, node->sw->rect.y0 + SearchDelta ) );
 
            if ( leaf != nullptr )
            {
               p += reinterpret_cast<RecursivePointSurfaceSpline*>( leaf->data )->operator()( x, y );
               ++n;
            }
         }
         if ( node->se != nullptr )
         {
            const typename tree::LeafNode* leaf;
            if ( y >= node->se->rect.y0 )
               leaf = m_tree.LeafNodeAt( search_point( node->se->rect.x0 + SearchDelta, search_coordinate( y ) ) );
            else if ( x <= node->se->rect.x0 )
               leaf = m_tree.LeafNodeAt( search_point( node->se->rect.x0 + SearchDelta, node->se->rect.y0 + SearchDelta ) );
            else
               leaf = m_tree.LeafNodeAt( search_point( search_coordinate( x ), node->se->rect.y0 + SearchDelta ) );
 
            if ( leaf != nullptr )
            {
               p += reinterpret_cast<RecursivePointSurfaceSpline*>( leaf->data )->operator()( x, y );
               ++n;
            }
         }
 
         if ( n > 0 )
            return p/double( n );
      }
 
      return 0.0;
   }
 
   template <typename T>
   DPoint operator ()( const GenericPoint<T>& p ) const
   {
      return operator ()( double( p.x ), double( p.y ) );
   }
 
private:
 
   /*
    * Interpolation data point, QuadTree-compatible.
    */
   struct Node
   {
      DPoint position, value;
      float weight;
 
      using component = DPoint::component;
 
      template <class point1, class point2>
      Node( const point1& p, const point2& v )
         : position( double( p.x ), double( p.y ) )
         , value( double( v.x ), double( v.y ) )
      {
      }
 
      template <class point1, class point2>
      Node( const point1& p, const point2& v, float w )
         : position( double( p.x ), double( p.y ) )
         , value( double( v.x ), double( v.y ) )
         , weight( w )
      {
      }
 
      Node( const Node& ) = default;
 
      double& operator []( int i )
      {
         return position[i];
      }
 
      double operator []( int i ) const
      {
         return position[i];
      }
   };
 
   using tree = QuadTree<Node>;
   using node_list = typename tree::point_list;
   using search_rectangle = typename tree::rectangle;
   using search_coordinate = typename tree::coordinate;
   using search_point = GenericPoint<search_coordinate>;
 
   tree               m_tree;   // the tree of subsplines
   PointSurfaceSpline m_spline; // final point spline if there is no further recursion
   search_rectangle   m_rect = search_coordinate( 0 ); // the interpolation region for this subspline
   bool               m_extrapolate = __PCL_RSSPLINE_DEFAULT_ALLOW_EXTRAPOLATION;
 
   static constexpr search_coordinate SearchDelta =
                        2 * std::numeric_limits<search_coordinate>::epsilon();
 
   /*
    * Parallel subspline generation.
    */
   struct SubsplineData
   {
      Array<DPoint>  P1, P2;
      Array<float>   PW;
      mutable void** nodeData;
 
      SubsplineData( const Array<DPoint>& p1, const Array<DPoint>& p2, const Array<float>& pw, void*& nd )
         : P1( p1 )
         , P2( p2 )
         , PW( pw )
         , nodeData( &nd )
      {
      }
   };
 
   class SubsplineGenerationThread : public Thread
   {
   public:
 
      SubsplineGenerationThread( const AbstractImage::ThreadData& data,
                                 const Array<SubsplineData>& subsplineData,
                                 float smoothness,
                                 int order,
                                 bool allowExtrapolation,
                                 int maxSplineLength,
                                 int bucketCapacity,
                                 int startIndex, int endIndex )
         : m_data( data )
         , m_subsplineData( subsplineData )
         , m_smoothness( smoothness )
         , m_order( order )
         , m_allowExtrapolation( allowExtrapolation )
         , m_maxSplineLength( maxSplineLength )
         , m_bucketCapacity( bucketCapacity )
         , m_startIndex( startIndex )
         , m_endIndex( endIndex )
      {
      }
 
      PCL_HOT_FUNCTION void Run() override
      {
         INIT_THREAD_MONITOR()
 
         for ( int i = m_startIndex; i < m_endIndex; ++i )
         {
            const SubsplineData& d = m_subsplineData[i];
            AutoPointer<RecursivePointSurfaceSpline> s(
               new RecursivePointSurfaceSpline( d.P1, d.P2, m_smoothness, m_order, d.PW,
                                                m_allowExtrapolation,
                                                m_maxSplineLength,
                                                m_bucketCapacity,
                                                false/*verbose*/ ) );
            *reinterpret_cast<RecursivePointSurfaceSpline**>( d.nodeData ) = s.Release();
 
            UPDATE_THREAD_MONITOR( 1 )
         }
 
         m_success = true;
      }
 
      operator bool() const
      {
         return m_success;
      }
 
   private:
 
      const AbstractImage::ThreadData& m_data;
      const Array<SubsplineData>&      m_subsplineData;
            float                      m_smoothness;
            int                        m_order;
            bool                       m_allowExtrapolation;
            int                        m_maxSplineLength;
            int                        m_bucketCapacity;
            int                        m_startIndex, m_endIndex;
            bool                       m_success = false;
   };
 
   friend class DrizzleData;
   friend class DrizzleDataDecoder;
};
 
// ----------------------------------------------------------------------------
 
}  // pcl
 
#endif   // __PCL_SurfaceSpline_h
 
// ----------------------------------------------------------------------------
// EOF pcl/SurfaceSpline.h - Released 2025-02-21T12:13:32Z