mirror of
https://gitlab.kitware.com/vtk/vtk-m
synced 2024-09-08 13:23:51 +00:00
287 lines
10 KiB
C++
287 lines
10 KiB
C++
//============================================================================
|
|
// 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
|
|
{
|
|
|
|
// ----------------------------------------------------------------------------
|
|
/// \brief Returns the linear interpolation of two values based on weight
|
|
///
|
|
/// \c Lerp interpolates return the linerar interpolation of v0 and v1 based on w. v0
|
|
/// and v1 are scalars or vectors of same length. w can either be a scalar or a
|
|
/// vector of the same length as x and y. If w is outside [0,1] then lerp
|
|
/// extrapolates. If w=0 => v0 is returned if w=1 => v1 is returned.
|
|
///
|
|
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;
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------
|
|
/// \brief Returns the square of the magnitude of a vector.
|
|
///
|
|
/// It is usually much faster to compute the square of the magnitude than the
|
|
/// square, so you should use this function in place of Magnitude or RMagnitude
|
|
/// when possible.
|
|
///
|
|
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
|
|
|
|
/// \brief Returns the magnitude of a vector.
|
|
///
|
|
/// It is usually much faster to compute MagnitudeSquared, so that should be
|
|
/// substituted when possible (unless you are just going to take the square
|
|
/// root, which would be besides the point). On some hardware it is also faster
|
|
/// to find the reciprocal magnitude, so RMagnitude should be used if you
|
|
/// actually plan to divide by the magnitude.
|
|
///
|
|
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
|
|
|
|
/// \brief Returns the reciprocal magnitude of a vector.
|
|
///
|
|
/// On some hardware RMagnitude is faster than Magnitude, but neither is
|
|
/// as fast as MagnitudeSquared.
|
|
///
|
|
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
|
|
|
|
/// \brief Returns a normalized version of the given vector.
|
|
///
|
|
/// The resulting vector points in the same direction but has unit length.
|
|
///
|
|
template <typename T>
|
|
VTKM_EXEC_CONT T Normal(const T& x)
|
|
{
|
|
return detail::NormalTemplate(x, typename vtkm::TypeTraits<T>::DimensionalityTag());
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------
|
|
/// \brief Changes a vector to be normal.
|
|
///
|
|
/// The given vector is scaled to be unit length.
|
|
///
|
|
template <typename T>
|
|
VTKM_EXEC_CONT void Normalize(T& x)
|
|
{
|
|
x = vtkm::Normal(x);
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------
|
|
/// \brief Find the cross product of two vectors.
|
|
///
|
|
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]));
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// \brief Find the normal of a triangle.
|
|
///
|
|
/// Given three coordinates in space, which, unless degenerate, uniquely define
|
|
/// a triangle and the plane the triangle is on, returns a vector perpendicular
|
|
/// to that triangle/plane.
|
|
///
|
|
/// Note that the returned vector might not be a unit vector. In fact, the length
|
|
/// is equal to twice the area of the triangle. If you want a unit vector,
|
|
/// send the result through the \c Normal function.
|
|
///
|
|
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);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// \brief Project a vector onto another vector.
|
|
///
|
|
/// This method computes the orthogonal projection of the vector v onto u;
|
|
/// that is, it projects its first argument onto its second.
|
|
///
|
|
/// Note that if the vector \a u has zero length, the output
|
|
/// vector will have all its entries equal to NaN.
|
|
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;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// \brief Project a vector onto another vector, returning only the projected distance.
|
|
///
|
|
/// This method computes the orthogonal projection of the vector v onto u;
|
|
/// that is, it projects its first argument onto its second.
|
|
///
|
|
/// Note that if the vector \a u has zero length, the output will be NaN.
|
|
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;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// \brief Perform Gram-Schmidt orthonormalization for 3-D vectors.
|
|
///
|
|
/// See https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process for details.
|
|
/// The first output vector will always be parallel to the first input vector.
|
|
/// The remaining output vectors will be orthogonal and unit length and have
|
|
/// the same handedness as their corresponding input vectors.
|
|
///
|
|
/// This method is geometric.
|
|
/// It does not require a matrix solver.
|
|
/// However, unlike the algebraic eigensolver techniques which do use matrix
|
|
/// inversion, this method may return zero-length output vectors if some input
|
|
/// vectors are collinear. The number of non-zero (to within the specified
|
|
/// tolerance, \a tol ) output vectors is the return value.
|
|
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
|