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https://gitlab.kitware.com/vtk/vtk-m
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cdeeda67bb
Affine transformations of homogeneous coordinates using 4x4 matrices are quite common in visualization. Create a new math header file in the base vtkm namespace that has common functions for such coordinates. Much of this implementation was taken from the rendering matrix helpers.
217 lines
6.7 KiB
C++
217 lines
6.7 KiB
C++
//=============================================================================
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//
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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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// Copyright 2016 Sandia Corporation.
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// Copyright 2016 UT-Battelle, LLC.
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// Copyright 2016 Los Alamos National Security.
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//
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// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
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// the U.S. Government retains certain rights in this software.
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// Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
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// Laboratory (LANL), the U.S. Government retains certain rights in
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// this software.
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//
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//=============================================================================
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#ifndef vtk_m_Transform3D_h
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#define vtk_m_Transform3D_h
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// This header file contains a collection of math functions useful in the
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// linear transformation of homogeneous points for rendering in 3D.
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#include <vtkm/Matrix.h>
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#include <vtkm/VectorAnalysis.h>
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namespace vtkm {
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/// \brief Transform a 3D point by a transformation matrix.
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///
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/// Given a 4x4 transformation matrix and a 3D point, returns the point
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/// transformed by the given matrix in homogeneous coordinates.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Vec<T,3> Transform3DPoint(const vtkm::Matrix<T,4,4> &matrix,
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const vtkm::Vec<T,3> &point)
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{
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vtkm::Vec<T,4> homogeneousPoint(point[0], point[1], point[2], T(1));
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homogeneousPoint = vtkm::MatrixMultiply(matrix, homogeneousPoint);
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T invW = T(1)/homogeneousPoint[3];
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return vtkm::Vec<T,3>(
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homogeneousPoint[0]*invW,
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homogeneousPoint[1]*invW,
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homogeneousPoint[2]*invW);
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}
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/// \brief Transform a 3D point by a transformation matrix.
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///
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/// Given a 4x4 transformation matrix and a 3D point, returns the point
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/// transformed by the given matrix in homogeneous coordinates.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Vec<T,3> Transform3DVector(const vtkm::Matrix<T,4,4> &matrix,
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const vtkm::Vec<T,3> &vector)
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{
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vtkm::Vec<T,4> homogeneousVector(vector[0], vector[1], vector[2], T(0));
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homogeneousVector = vtkm::MatrixMultiply(matrix, homogeneousVector);
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return vtkm::Vec<T,3>(
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homogeneousVector[0],
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homogeneousVector[1],
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homogeneousVector[2]);
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}
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/// \brief Returns a scale matrix.
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///
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/// Given a scale factor for the x, y, and z directions, returns a
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/// transformation matrix for those scales.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4>
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Transform3DScale(const T &scaleX, const T &scaleY, const T &scaleZ)
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{
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vtkm::Matrix<T,4,4> scaleMatrix(T(0));
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scaleMatrix(0,0) = scaleX;
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scaleMatrix(1,1) = scaleY;
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scaleMatrix(2,2) = scaleZ;
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scaleMatrix(3,3) = T(1);
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return scaleMatrix;
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}
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/// \brief Returns a scale matrix.
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///
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/// Given a scale factor for the x, y, and z directions (defined in a Vec),
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/// returns a transformation matrix for those scales.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DScale(const vtkm::Vec<T,3> &scaleVec)
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{
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return vtkm::Transform3DScale(scaleVec[0], scaleVec[1], scaleVec[2]);
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}
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/// \brief Returns a scale matrix.
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///
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/// Given a uniform scale factor, returns a transformation matrix for those
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/// scales.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DScale(const T &scale)
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{
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return vtkm::Transform3DScale(scale, scale, scale);
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}
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/// \brief Returns a translation matrix.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DTranslate(const T &x, const T &y, const T &z)
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{
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vtkm::Matrix<T,4,4> translateMatrix;
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vtkm::MatrixIdentity(translateMatrix);
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translateMatrix(0,3) = x;
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translateMatrix(1,3) = y;
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translateMatrix(2,3) = z;
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return translateMatrix;
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}
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DTranslate(const vtkm::Vec<T,3> &v)
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{
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return vtkm::Transform3DTranslate(v[0], v[1], v[2]);
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}
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/// \brief Returns a rotation matrix.
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///
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/// Given an angle (in radians) and an axis of rotation, returns a
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/// transformation matrix that rotates around the given axis. The rotation
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/// follows the right-hand rule, so if the vector points toward the user, the
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/// rotation will be counterclockwise.
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///
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/// Note that, unlike with OpenGL, the angle is given in radians, not degrees.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DRotate(T angleRadians,
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const vtkm::Vec<T,3> &axisOfRotation)
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{
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const vtkm::Vec<T,3> normAxis = vtkm::Normal(axisOfRotation);
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T sinAngle = vtkm::Sin(angleRadians);
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T cosAngle = vtkm::Cos(angleRadians);
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vtkm::Matrix<T,4,4> matrix;
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matrix(0,0) = normAxis[0]*normAxis[0]*(1-cosAngle) + cosAngle;
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matrix(0,1) = normAxis[0]*normAxis[1]*(1-cosAngle) - normAxis[2]*sinAngle;
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matrix(0,2) = normAxis[0]*normAxis[2]*(1-cosAngle) + normAxis[1]*sinAngle;
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matrix(0,3) = T(0);
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matrix(1,0) = normAxis[1]*normAxis[0]*(1-cosAngle) + normAxis[2]*sinAngle;
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matrix(1,1) = normAxis[1]*normAxis[1]*(1-cosAngle) + cosAngle;
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matrix(1,2) = normAxis[1]*normAxis[2]*(1-cosAngle) - normAxis[0]*sinAngle;
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matrix(1,3) = T(0);
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matrix(2,0) = normAxis[2]*normAxis[0]*(1-cosAngle) - normAxis[1]*sinAngle;
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matrix(2,1) = normAxis[2]*normAxis[1]*(1-cosAngle) + normAxis[0]*sinAngle;
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matrix(2,2) = normAxis[2]*normAxis[2]*(1-cosAngle) + cosAngle;
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matrix(2,3) = T(0);
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matrix(3,0) = T(0);
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matrix(3,1) = T(0);
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matrix(3,2) = T(0);
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matrix(3,3) = T(1);
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return matrix;
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}
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DRotate(T angleRadians, T x, T y, T z)
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{
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return vtkm::Transform3DRotate(angleRadians, vtkm::Vec<T,3>(x,y,z));
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}
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/// \brief Returns a rotation matrix.
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///
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/// Returns a transformation matrix that rotates around the x axis.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DRotateX(T angleRadians)
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{
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return vtkm::Transform3DRotate(angleRadians, T(1), T(0), T(0));
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}
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/// \brief Returns a rotation matrix.
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///
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/// Returns a transformation matrix that rotates around the y axis.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DRotateY(T angleRadians)
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{
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return vtkm::Transform3DRotate(angleRadians, T(0), T(1), T(0));
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}
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/// \brief Returns a rotation matrix.
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///
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/// Returns a transformation matrix that rotates around the z axis.
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///
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template<typename T>
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VTKM_EXEC_CONT_EXPORT
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vtkm::Matrix<T,4,4> Transform3DRotateZ(T angleRadians)
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{
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return vtkm::Transform3DRotate(angleRadians, T(0), T(0), T(1));
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}
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} // namespace vtkm
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#endif //vtk_m_Transform3D_h
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