VectorAnalysis.h

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//============================================================================
//  Copyright (c) Kitware, Inc.
//  All rights reserved.
//  See LICENSE.txt for details.
//
//  This software is distributed WITHOUT ANY WARRANTY; without even
//  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
//  PURPOSE.  See the above copyright notice for more information.
//============================================================================
#ifndef vtk_m_VectorAnalysis_h
#define vtk_m_VectorAnalysis_h
 
// This header file defines math functions that deal with linear albegra functions
 
#include <vtkm/Math.h>
#include <vtkm/TypeTraits.h>
#include <vtkm/Types.h>
#include <vtkm/VecTraits.h>
 
namespace vtkm
{
 
// ----------------------------------------------------------------------------
template <typename ValueType, typename WeightType>
inline VTKM_EXEC_CONT ValueType Lerp(const ValueType& value0,
                                     const ValueType& value1,
                                     const WeightType& weight)
{
  using ScalarType = typename detail::FloatingPointReturnType<ValueType>::Type;
  return static_cast<ValueType>((WeightType(1) - weight) * static_cast<ScalarType>(value0) +
                                weight * static_cast<ScalarType>(value1));
}
template <typename ValueType, vtkm::IdComponent N, typename WeightType>
VTKM_EXEC_CONT vtkm::Vec<ValueType, N> Lerp(const vtkm::Vec<ValueType, N>& value0,
                                            const vtkm::Vec<ValueType, N>& value1,
                                            const WeightType& weight)
{
  return (WeightType(1) - weight) * value0 + weight * value1;
}
template <typename ValueType, vtkm::IdComponent N>
VTKM_EXEC_CONT vtkm::Vec<ValueType, N> Lerp(const vtkm::Vec<ValueType, N>& value0,
                                            const vtkm::Vec<ValueType, N>& value1,
                                            const vtkm::Vec<ValueType, N>& weight)
{
  const vtkm::Vec<ValueType, N> One(ValueType(1));
  return (One - weight) * value0 + weight * value1;
}
 
// ----------------------------------------------------------------------------
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type MagnitudeSquared(const T& x)
{
  using U = typename detail::FloatingPointReturnType<T>::Type;
  return static_cast<U>(vtkm::Dot(x, x));
}
 
// ----------------------------------------------------------------------------
namespace detail
{
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type MagnitudeTemplate(
  T x,
  vtkm::TypeTraitsScalarTag)
{
  return static_cast<typename detail::FloatingPointReturnType<T>::Type>(vtkm::Abs(x));
}
 
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type MagnitudeTemplate(
  const T& x,
  vtkm::TypeTraitsVectorTag)
{
  return vtkm::Sqrt(vtkm::MagnitudeSquared(x));
}
 
} // namespace detail
 
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type Magnitude(const T& x)
{
  return detail::MagnitudeTemplate(x, typename vtkm::TypeTraits<T>::DimensionalityTag());
}
 
// ----------------------------------------------------------------------------
namespace detail
{
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type RMagnitudeTemplate(
  T x,
  vtkm::TypeTraitsScalarTag)
{
  return T(1) / vtkm::Abs(x);
}
 
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type RMagnitudeTemplate(
  const T& x,
  vtkm::TypeTraitsVectorTag)
{
  return vtkm::RSqrt(vtkm::MagnitudeSquared(x));
}
} // namespace detail
 
template <typename T>
VTKM_EXEC_CONT typename detail::FloatingPointReturnType<T>::Type RMagnitude(const T& x)
{
  return detail::RMagnitudeTemplate(x, typename vtkm::TypeTraits<T>::DimensionalityTag());
}
 
// ----------------------------------------------------------------------------
namespace detail
{
template <typename T>
VTKM_EXEC_CONT T NormalTemplate(T x, vtkm::TypeTraitsScalarTag)
{
  return vtkm::CopySign(T(1), x);
}
 
template <typename T>
VTKM_EXEC_CONT T NormalTemplate(const T& x, vtkm::TypeTraitsVectorTag)
{
  return vtkm::RMagnitude(x) * x;
}
} // namespace detail
 
template <typename T>
VTKM_EXEC_CONT T Normal(const T& x)
{
  return detail::NormalTemplate(x, typename vtkm::TypeTraits<T>::DimensionalityTag());
}
 
// ----------------------------------------------------------------------------
template <typename T>
VTKM_EXEC_CONT void Normalize(T& x)
{
  x = vtkm::Normal(x);
}
 
// ----------------------------------------------------------------------------
template <typename T>
VTKM_EXEC_CONT vtkm::Vec<typename detail::FloatingPointReturnType<T>::Type, 3> Cross(
  const vtkm::Vec<T, 3>& x,
  const vtkm::Vec<T, 3>& y)
{
  return vtkm::Vec<typename detail::FloatingPointReturnType<T>::Type, 3>(
    DifferenceOfProducts(x[1], y[2], x[2], y[1]),
    DifferenceOfProducts(x[2], y[0], x[0], y[2]),
    DifferenceOfProducts(x[0], y[1], x[1], y[0]));
}
 
//-----------------------------------------------------------------------------
template <typename T>
VTKM_EXEC_CONT vtkm::Vec<typename detail::FloatingPointReturnType<T>::Type, 3>
TriangleNormal(const vtkm::Vec<T, 3>& a, const vtkm::Vec<T, 3>& b, const vtkm::Vec<T, 3>& c)
{
  return vtkm::Cross(b - a, c - a);
}
 
//-----------------------------------------------------------------------------
template <typename T, int N>
VTKM_EXEC_CONT vtkm::Vec<T, N> Project(const vtkm::Vec<T, N>& v, const vtkm::Vec<T, N>& u)
{
  T uu = vtkm::Dot(u, u);
  T uv = vtkm::Dot(u, v);
  T factor = uv / uu;
  vtkm::Vec<T, N> result = factor * u;
  return result;
}
 
//-----------------------------------------------------------------------------
template <typename T, int N>
VTKM_EXEC_CONT T ProjectedDistance(const vtkm::Vec<T, N>& v, const vtkm::Vec<T, N>& u)
{
  T uu = vtkm::Dot(u, u);
  T uv = vtkm::Dot(u, v);
  T factor = uv / uu;
  return factor;
}
 
//-----------------------------------------------------------------------------
template <typename T, int N>
VTKM_EXEC_CONT int Orthonormalize(const vtkm::Vec<vtkm::Vec<T, N>, N>& inputs,
                                  vtkm::Vec<vtkm::Vec<T, N>, N>& outputs,
                                  T tol = static_cast<T>(1e-6))
{
  T tolsqr = tol * tol;
  int j = 0; // j is the number of non-zero-length, non-collinear inputs encountered.
  vtkm::Vec<vtkm::Vec<T, N>, N> u;
  for (int i = 0; i < N; ++i)
  {
    u[j] = inputs[i];
    for (int k = 0; k < j; ++k)
    {
      u[j] -= vtkm::Project(inputs[i], u[k]);
    }
    T magsqr = vtkm::MagnitudeSquared(u[j]);
    if (magsqr <= tolsqr)
    {
      // skip this vector, it is zero-length or collinear with others.
      continue;
    }
    outputs[j] = vtkm::RSqrt(magsqr) * u[j];
    ++j;
  }
  for (int i = j; i < N; ++i)
  {
    outputs[j] = Vec<T, N>{ 0. };
  }
  return j;
}
 
} // namespace vtkm
 
#endif //vtk_m_VectorAnalysis_h