Transform3D.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_Transform3D_h
#define vtk_m_Transform3D_h
 
// This header file contains a collection of math functions useful in the
// linear transformation of homogeneous points for rendering in 3D.
 
#include <vtkm/Matrix.h>
#include <vtkm/VectorAnalysis.h>
 
namespace vtkm
{
 
template <typename T>
VTKM_EXEC_CONT vtkm::Vec<T, 3> Transform3DPoint(const vtkm::Matrix<T, 4, 4>& matrix,
                                                const vtkm::Vec<T, 3>& point)
{
  vtkm::Vec<T, 4> homogeneousPoint(point[0], point[1], point[2], T(1));
  return vtkm::Vec<T, 3>(vtkm::Dot(vtkm::MatrixGetRow(matrix, 0), homogeneousPoint),
                         vtkm::Dot(vtkm::MatrixGetRow(matrix, 1), homogeneousPoint),
                         vtkm::Dot(vtkm::MatrixGetRow(matrix, 2), homogeneousPoint));
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Vec<T, 3> Transform3DPointPerspective(const vtkm::Matrix<T, 4, 4>& matrix,
                                                           const vtkm::Vec<T, 3>& point)
{
  vtkm::Vec<T, 4> homogeneousPoint(point[0], point[1], point[2], T(1));
  T inverseW = 1 / vtkm::Dot(vtkm::MatrixGetRow(matrix, 3), homogeneousPoint);
  return vtkm::Vec<T, 3>(vtkm::Dot(vtkm::MatrixGetRow(matrix, 0), homogeneousPoint) * inverseW,
                         vtkm::Dot(vtkm::MatrixGetRow(matrix, 1), homogeneousPoint) * inverseW,
                         vtkm::Dot(vtkm::MatrixGetRow(matrix, 2), homogeneousPoint) * inverseW);
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Vec<T, 3> Transform3DVector(const vtkm::Matrix<T, 4, 4>& matrix,
                                                 const vtkm::Vec<T, 3>& vector)
{
  vtkm::Vec<T, 4> homogeneousVector(vector[0], vector[1], vector[2], T(0));
  homogeneousVector = vtkm::MatrixMultiply(matrix, homogeneousVector);
  return vtkm::Vec<T, 3>(homogeneousVector[0], homogeneousVector[1], homogeneousVector[2]);
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DScale(const T& scaleX,
                                                      const T& scaleY,
                                                      const T& scaleZ)
{
  vtkm::Matrix<T, 4, 4> scaleMatrix(T(0));
  scaleMatrix(0, 0) = scaleX;
  scaleMatrix(1, 1) = scaleY;
  scaleMatrix(2, 2) = scaleZ;
  scaleMatrix(3, 3) = T(1);
  return scaleMatrix;
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DScale(const vtkm::Vec<T, 3>& scaleVec)
{
  return vtkm::Transform3DScale(scaleVec[0], scaleVec[1], scaleVec[2]);
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DScale(const T& scale)
{
  return vtkm::Transform3DScale(scale, scale, scale);
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DTranslate(const T& x, const T& y, const T& z)
{
  vtkm::Matrix<T, 4, 4> translateMatrix;
  vtkm::MatrixIdentity(translateMatrix);
  translateMatrix(0, 3) = x;
  translateMatrix(1, 3) = y;
  translateMatrix(2, 3) = z;
  return translateMatrix;
}
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DTranslate(const vtkm::Vec<T, 3>& v)
{
  return vtkm::Transform3DTranslate(v[0], v[1], v[2]);
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotate(T angleDegrees,
                                                       const vtkm::Vec<T, 3>& axisOfRotation)
{
  T angleRadians = vtkm::Pi_180<T>() * angleDegrees;
  const vtkm::Vec<T, 3> normAxis = vtkm::Normal(axisOfRotation);
  T sinAngle = vtkm::Sin(angleRadians);
  T cosAngle = vtkm::Cos(angleRadians);
 
  vtkm::Matrix<T, 4, 4> matrix;
 
  matrix(0, 0) = normAxis[0] * normAxis[0] * (1 - cosAngle) + cosAngle;
  matrix(0, 1) = normAxis[0] * normAxis[1] * (1 - cosAngle) - normAxis[2] * sinAngle;
  matrix(0, 2) = normAxis[0] * normAxis[2] * (1 - cosAngle) + normAxis[1] * sinAngle;
  matrix(0, 3) = T(0);
 
  matrix(1, 0) = normAxis[1] * normAxis[0] * (1 - cosAngle) + normAxis[2] * sinAngle;
  matrix(1, 1) = normAxis[1] * normAxis[1] * (1 - cosAngle) + cosAngle;
  matrix(1, 2) = normAxis[1] * normAxis[2] * (1 - cosAngle) - normAxis[0] * sinAngle;
  matrix(1, 3) = T(0);
 
  matrix(2, 0) = normAxis[2] * normAxis[0] * (1 - cosAngle) - normAxis[1] * sinAngle;
  matrix(2, 1) = normAxis[2] * normAxis[1] * (1 - cosAngle) + normAxis[0] * sinAngle;
  matrix(2, 2) = normAxis[2] * normAxis[2] * (1 - cosAngle) + cosAngle;
  matrix(2, 3) = T(0);
 
  matrix(3, 0) = T(0);
  matrix(3, 1) = T(0);
  matrix(3, 2) = T(0);
  matrix(3, 3) = T(1);
 
  return matrix;
}
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotate(T angleDegrees, T x, T y, T z)
{
  return vtkm::Transform3DRotate(angleDegrees, vtkm::Vec<T, 3>(x, y, z));
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotateX(T angleDegrees)
{
  return vtkm::Transform3DRotate(angleDegrees, T(1), T(0), T(0));
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotateY(T angleDegrees)
{
  return vtkm::Transform3DRotate(angleDegrees, T(0), T(1), T(0));
}
 
template <typename T>
VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotateZ(T angleDegrees)
{
  return vtkm::Transform3DRotate(angleDegrees, T(0), T(0), T(1));
}
 
} // namespace vtkm
 
#endif //vtk_m_Transform3D_h