vtk-m/vtkm/Transform3D.h

//=============================================================================
//
//  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.
//
//  Copyright 2016 Sandia Corporation.
//  Copyright 2016 UT-Battelle, LLC.
//  Copyright 2016 Los Alamos National Security.
//
//  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
//  the U.S. Government retains certain rights in this software.
//  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
//  Laboratory (LANL), the U.S. Government retains certain rights in
//  this software.
//
//=============================================================================
#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 {

/// \brief Transform a 3D point by a transformation matrix.
///
/// Given a 4x4 transformation matrix and a 3D point, returns the point
/// transformed by the given matrix in homogeneous coordinates.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
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));
  homogeneousPoint = vtkm::MatrixMultiply(matrix, homogeneousPoint);
  T invW = T(1)/homogeneousPoint[3];
  return vtkm::Vec<T,3>(
        homogeneousPoint[0]*invW,
        homogeneousPoint[1]*invW,
        homogeneousPoint[2]*invW);
}

/// \brief Transform a 3D point by a transformation matrix.
///
/// Given a 4x4 transformation matrix and a 3D point, returns the point
/// transformed by the given matrix in homogeneous coordinates.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
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]);
}

/// \brief Returns a scale matrix.
///
/// Given a scale factor for the x, y, and z directions, returns a
/// transformation matrix for those scales.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
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;
}

/// \brief Returns a scale matrix.
///
/// Given a scale factor for the x, y, and z directions (defined in a Vec),
/// returns a transformation matrix for those scales.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DScale(const vtkm::Vec<T,3> &scaleVec)
{
  return vtkm::Transform3DScale(scaleVec[0], scaleVec[1], scaleVec[2]);
}

/// \brief Returns a scale matrix.
///
/// Given a uniform scale factor, returns a transformation matrix for those
/// scales.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DScale(const T &scale)
{
  return vtkm::Transform3DScale(scale, scale, scale);
}

/// \brief Returns a translation matrix.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
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_EXPORT
vtkm::Matrix<T,4,4> Transform3DTranslate(const vtkm::Vec<T,3> &v)
{
  return vtkm::Transform3DTranslate(v[0], v[1], v[2]);
}

/// \brief Returns a rotation matrix.
///
/// Given an angle (in radians) and an axis of rotation, returns a
/// transformation matrix that rotates around the given axis. The rotation
/// follows the right-hand rule, so if the vector points toward the user, the
/// rotation will be counterclockwise.
///
/// Note that, unlike with OpenGL, the angle is given in radians, not degrees.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DRotate(T angleRadians,
                                      const vtkm::Vec<T,3> &axisOfRotation)
{
  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_EXPORT
vtkm::Matrix<T,4,4> Transform3DRotate(T angleRadians, T x, T y, T z)
{
  return vtkm::Transform3DRotate(angleRadians, vtkm::Vec<T,3>(x,y,z));
}

/// \brief Returns a rotation matrix.
///
/// Returns a transformation matrix that rotates around the x axis.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DRotateX(T angleRadians)
{
  return vtkm::Transform3DRotate(angleRadians, T(1), T(0), T(0));
}

/// \brief Returns a rotation matrix.
///
/// Returns a transformation matrix that rotates around the y axis.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DRotateY(T angleRadians)
{
  return vtkm::Transform3DRotate(angleRadians, T(0), T(1), T(0));
}

/// \brief Returns a rotation matrix.
///
/// Returns a transformation matrix that rotates around the z axis.
///
template<typename T>
VTKM_EXEC_CONT_EXPORT
vtkm::Matrix<T,4,4> Transform3DRotateZ(T angleRadians)
{
  return vtkm::Transform3DRotate(angleRadians, T(0), T(0), T(1));
}

} // namespace vtkm

#endif //vtk_m_Transform3D_h