246 lines
6.5 KiB
C++
246 lines
6.5 KiB
C++
//============================================================================
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// Copyright (c) Kitware, Inc.
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// All rights reserved.
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// See LICENSE.txt for details.
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//
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// This software is distributed WITHOUT ANY WARRANTY; without even
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// the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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// PURPOSE. See the above copyright notice for more information.
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//============================================================================
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#ifndef VTKM_KERNEL_SPLINE_3RD_ORDER_H
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#define VTKM_KERNEL_SPLINE_3RD_ORDER_H
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#include <vtkm/worklet/splatkernels/KernelBase.h>
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//
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// Spline 3rd Order kernel.
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//
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namespace vtkm
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{
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namespace worklet
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{
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namespace splatkernels
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{
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template <vtkm::IdComponent Dim>
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struct default_norm_value;
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template <>
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struct default_norm_value<2>
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{
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const double value = 10.0 / (7.0 * M_PI);
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};
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template <>
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struct default_norm_value<3>
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{
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const double value = 1.0 / M_PI;
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};
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template <int Dimensions>
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struct Spline3rdOrder : public KernelBase<Spline3rdOrder<Dimensions>>
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{
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//---------------------------------------------------------------------
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// Constructor
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// Calculate coefficients used repeatedly when evaluating the kernel
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// value or gradient
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VTKM_EXEC_CONT
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Spline3rdOrder(double smoothingLength)
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: KernelBase<Spline3rdOrder<Dimensions>>(smoothingLength)
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{
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Hinverse_ = 1.0 / smoothingLength;
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Hinverse2_ = Hinverse_ * Hinverse_;
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maxRadius_ = 2.0 * smoothingLength;
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maxRadius2_ = maxRadius_ * maxRadius_;
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//
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norm_ = default_norm_value<Dimensions>().value;
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scale_W_ = norm_ * PowerExpansion<Dimensions>(Hinverse_);
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scale_GradW_ = norm_ * PowerExpansion<Dimensions + 1>(Hinverse_);
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}
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//---------------------------------------------------------------------
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// Calculates the kernel value for the given distance
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VTKM_EXEC_CONT
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double w(double distance) const
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{
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// compute Q=(r/h)
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double Q = distance * Hinverse_;
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if (Q < 1.0)
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{
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return scale_W_ * (1.0 - (3.0 / 2.0) * Q * Q + (3.0 / 4.0) * Q * Q * Q);
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_W_ * (1.0 / 4.0) * (q2 * q2 * q2);
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}
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else
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{
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return 0.0;
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}
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}
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//---------------------------------------------------------------------
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// Calculates the kernel value for the given squared distance
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VTKM_EXEC_CONT
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double w2(double distance2) const
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{
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// compute Q
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double Q = sqrt(distance2) * Hinverse_;
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if (Q < 1.0)
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{
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return scale_W_ * (1.0 - (3.0 / 2.0) * Q * Q + (3.0 / 4.0) * Q * Q * Q);
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_W_ * (1.0 / 4.0) * (q2 * q2 * q2);
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}
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else
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{
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return 0.0;
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}
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}
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//---------------------------------------------------------------------
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// compute w(h) for a variable h kernel
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VTKM_EXEC_CONT
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double w(double h, double distance) const
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{
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double Hinverse = 1.0 / h;
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double scale_W = norm_ * PowerExpansion<Dimensions>(Hinverse);
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double Q = distance * Hinverse;
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if (Q < 1.0)
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{
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return scale_W * (1.0 - (3.0 / 2.0) * Q * Q + (3.0 / 4.0) * Q * Q * Q);
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_W * (1.0 / 4.0) * (q2 * q2 * q2);
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}
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else
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{
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return 0.0;
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}
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}
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//---------------------------------------------------------------------
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// compute w(h) for a variable h kernel using distance squared
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VTKM_EXEC_CONT
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double w2(double h, double distance2) const
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{
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double Hinverse = 1.0 / h;
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double scale_W = norm_ * PowerExpansion<Dimensions>(Hinverse);
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double Q = sqrt(distance2) * Hinverse;
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if (Q < 1.0)
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{
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return scale_W * (1.0 - (3.0 / 2.0) * Q * Q + (3.0 / 4.0) * Q * Q * Q);
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_W * (1.0 / 4.0) * (q2 * q2 * q2);
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}
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else
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{
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return 0.0;
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}
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}
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//---------------------------------------------------------------------
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// Calculates the kernel derivation for the given distance of two particles.
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// The used formula is the derivation of Speith (3.126) for the value
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// with (3.21) for the direction of the gradient vector.
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// Be careful: grad W is antisymmetric in r (3.25)!.
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VTKM_EXEC_CONT
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vector_type gradW(double distance, const vector_type& pos) const
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{
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double Q = distance * Hinverse_;
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if (Q == 0.0)
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{
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return vector_type(0.0);
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}
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else if (Q < 1.0)
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{
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return scale_GradW_ * (-3.0 * Q + (9.0 / 4.0) * Q * Q) * pos;
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_GradW_ * (-3.0 / 4.0) * q2 * q2 * pos;
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}
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else
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{
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return vector_type(0.0);
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}
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}
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//---------------------------------------------------------------------
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VTKM_EXEC_CONT
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vector_type gradW(double h, double distance, const vector_type& pos) const
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{
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double Hinverse = 1.0 / h;
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double scale_GradW = norm_ * PowerExpansion<Dimensions + 1>(Hinverse);
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double Q = distance * Hinverse;
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if (Q == 0.0)
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{
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return vector_type(0.0);
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}
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else if (Q < 1.0)
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{
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return scale_GradW * (-3.0 * Q + (9.0 / 4.0) * Q * Q) * pos;
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}
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else if (Q < 2.0)
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{
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double q2 = (2.0 - Q);
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return scale_GradW * (-3.0 / 4.0) * q2 * q2 * pos;
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}
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else
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{
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return vector_type(0.0);
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}
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}
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//---------------------------------------------------------------------
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// return the maximum distance at which this kernel is non zero
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VTKM_EXEC_CONT
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double maxDistance() const { return maxRadius_; }
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//---------------------------------------------------------------------
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// return the maximum distance at which this variable h kernel is non zero
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VTKM_EXEC_CONT
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double maxDistance(double h) const { return 2.0 * h; }
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//---------------------------------------------------------------------
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// return the maximum distance at which this kernel is non zero
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VTKM_EXEC_CONT
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double maxSquaredDistance() const { return maxRadius2_; }
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//---------------------------------------------------------------------
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// return the maximum distance at which this kernel is non zero
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VTKM_EXEC_CONT
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double maxSquaredDistance(double h) const { return 4.0 * h * h; }
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//---------------------------------------------------------------------
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// return the multiplier between smoothing length and max cutoff distance
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VTKM_EXEC_CONT
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double getDilationFactor() const { return 2.0; }
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private:
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double norm_;
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double Hinverse_;
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double Hinverse2_;
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double maxRadius_;
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double maxRadius2_;
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double scale_W_;
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double scale_GradW_;
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};
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}
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}
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}
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#endif
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