mirror of
https://gitlab.kitware.com/vtk/vtk-m
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215 lines
7.8 KiB
C++
215 lines
7.8 KiB
C++
//============================================================================
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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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#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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{
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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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/// This method ignores any change in the fourth component of the transformed
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/// homogeneous coordinate, assuming that it is always 1 (that is, the last row
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/// of the matrix is 0, 0, 0, 1). This will be true for affine transformations
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/// (such as translate, scale, and rotate), but not for perspective
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/// transformations.
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///
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template <typename T>
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VTKM_EXEC_CONT 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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return vtkm::Vec<T, 3>(vtkm::Dot(vtkm::MatrixGetRow(matrix, 0), homogeneousPoint),
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vtkm::Dot(vtkm::MatrixGetRow(matrix, 1), homogeneousPoint),
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vtkm::Dot(vtkm::MatrixGetRow(matrix, 2), homogeneousPoint));
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}
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/// \brief Transform a 3D point by a transformation matrix with perspective.
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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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/// Unlike Transform3DPoint, this method honors the fourth component of the
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/// transformed homogeneous coordinate. This makes it applicable for perspective
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/// transformations, but requires some more computations.
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///
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template <typename T>
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VTKM_EXEC_CONT vtkm::Vec<T, 3> Transform3DPointPerspective(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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T inverseW = 1 / vtkm::Dot(vtkm::MatrixGetRow(matrix, 3), homogeneousPoint);
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return vtkm::Vec<T, 3>(vtkm::Dot(vtkm::MatrixGetRow(matrix, 0), homogeneousPoint) * inverseW,
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vtkm::Dot(vtkm::MatrixGetRow(matrix, 1), homogeneousPoint) * inverseW,
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vtkm::Dot(vtkm::MatrixGetRow(matrix, 2), homogeneousPoint) * inverseW);
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}
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/// \brief Transform a 3D vector by a transformation matrix.
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///
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/// Given a 4x4 transformation matrix and a 3D vector, returns the vector
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/// transformed by the given matrix in homogeneous coordinates. Unlike points,
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/// vectors do not get translated.
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///
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template <typename T>
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VTKM_EXEC_CONT 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>(homogeneousVector[0], homogeneousVector[1], 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 vtkm::Matrix<T, 4, 4> Transform3DScale(const T& scaleX,
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const T& scaleY,
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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 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 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 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 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 degrees) 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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template <typename T>
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VTKM_EXEC_CONT vtkm::Matrix<T, 4, 4> Transform3DRotate(T angleDegrees,
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const vtkm::Vec<T, 3>& axisOfRotation)
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{
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T angleRadians = vtkm::Pi_180<T>() * angleDegrees;
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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 vtkm::Matrix<T, 4, 4> Transform3DRotate(T angleDegrees, T x, T y, T z)
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{
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return vtkm::Transform3DRotate(angleDegrees, 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 vtkm::Matrix<T, 4, 4> Transform3DRotateX(T angleDegrees)
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{
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return vtkm::Transform3DRotate(angleDegrees, 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 vtkm::Matrix<T, 4, 4> Transform3DRotateY(T angleDegrees)
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{
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return vtkm::Transform3DRotate(angleDegrees, 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 vtkm::Matrix<T, 4, 4> Transform3DRotateZ(T angleDegrees)
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{
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return vtkm::Transform3DRotate(angleDegrees, 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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