template<typename TParametersValueType = double, unsigned int VDimension = 3>
class itk::AzimuthElevationToCartesianTransform< TParametersValueType, VDimension >
Transforms from an azimuth, elevation, radius coordinate system to a Cartesian coordinate system, or vice versa.
The three coordinate axis are azimuth, elevation, and range.
The azimuth elevation coordinate system is defined similarly to spherical coordinates but is slightly different in that the azimuth and elevation are measured in degrees between the r-axis (i.e z axis) and the projection on the x-z and y-z planes, respectively. Range, or r, is the distance from the origin.
The equations form performing the conversion from azimuth-elevation coordinates to cartesian coordinates are as follows:
z = std::sqrt((r^2*(cos(azimuth))^2)/(1 + (cos(azimuth))^2 * (tan(elevation))^2);
x = z * std::tan(azimuth)
y = z * std::tan(elevation)
The reversed transforms are:
azimuth = arctan(x/y)
elevation = arctan(y/z)
r = std::sqrt(x^2 + y^2 + z^2)
In this class, we can also set what a "forward" transform means. If we call SetForwardAzimuthElevationToCartesian(), a forward transform will return cartesian coordinates when passed azimuth,elevation,r coordinates. Calling SetForwardCartesianToAzimuthElevation() will cause the forward transform to return azimuth,elevation,r coordinates from cartesian coordinates.
Setting the FirstSampleDistance to a non-zero value means that a r value of 12 is actually (12 + FirstSampleDistance) distance from the origin.
There are two template parameters for this class:
TParametersValueType The type to be used for scalar numeric values. Either float or double.
VDimension The number of dimensions of the vector space (must be >=3).
- Todo:
- Is there any real value in allowing the user to template over the scalar type? Perhaps it should always be double, unless there's a compatibility problem with the Point class.
- Todo:
- Derive this class from TransformBase class. Currently, this class derives from AffineTransform, although it is not an affine transform.
- Todo:
- Add a figure in the documentation that informs the formulas used in this class that are used to transform Cartesian to azimuth-elevation-radius
- ITK Sphinx Examples:
-
- Examples
- SphinxExamples/src/Core/Transform/CartesianToAzimuthElevation/Code.cxx.
Definition at line 88 of file itkAzimuthElevationToCartesianTransform.h.
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| using | ConstPointer = SmartPointer< const Self > |
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| using | MatrixType = Matrix< TParametersValueType, Self::SpaceDimension, Self::SpaceDimension > |
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| using | Pointer = SmartPointer< Self > |
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| using | Self = AzimuthElevationToCartesianTransform |
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| using | Superclass = AffineTransform< TParametersValueType, VDimension > |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | InverseTransformBasePointer = typename InverseTransformBaseType::Pointer |
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| using | InverseTransformBaseType = typename Superclass::InverseTransformBaseType |
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| using | Pointer = SmartPointer< Self > |
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| using | Self = AffineTransform |
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| using | Superclass = MatrixOffsetTransformBase< TParametersValueType, VDimension, VDimension > |
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| using | CenterType = InputPointType |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | InputCovariantVectorType = CovariantVector< TParametersValueType, Self::InputSpaceDimension > |
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| using | InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | InputPointType = Point< TParametersValueType, Self::InputSpaceDimension > |
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| using | InputPointValueType = typename InputPointType::ValueType |
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| using | InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension > |
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| using | InputTensorEigenVectorType = CovariantVector< TParametersValueType, InputDiffusionTensor3DType::Dimension > |
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| using | InputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | InputVectorType = Vector< TParametersValueType, Self::InputSpaceDimension > |
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| using | InputVnlVectorType = vnl_vector_fixed< TParametersValueType, Self::InputSpaceDimension > |
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| using | InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension > |
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| using | InverseMatrixType = Matrix< TParametersValueType, Self::InputSpaceDimension, Self::OutputSpaceDimension > |
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| using | InverseTransformBasePointer = typename InverseTransformBaseType::Pointer |
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| using | InverseTransformBaseType = typename Superclass::InverseTransformBaseType |
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| using | InverseTransformType = MatrixOffsetTransformBase< TParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianType = Array2D< ParametersValueType > |
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| using | MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension > |
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| using | MatrixValueType = typename MatrixType::ValueType |
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| using | OffsetType = OutputVectorType |
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| using | OffsetValueType = typename OffsetType::ValueType |
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| using | OutputCovariantVectorType = CovariantVector< TParametersValueType, Self::OutputSpaceDimension > |
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| using | OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | OutputPointType = Point< TParametersValueType, Self::OutputSpaceDimension > |
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| using | OutputPointValueType = typename OutputPointType::ValueType |
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| using | OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension > |
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| using | OutputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | OutputVectorType = Vector< TParametersValueType, Self::OutputSpaceDimension > |
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| using | OutputVectorValueType = typename OutputVectorType::ValueType |
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| using | OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, Self::OutputSpaceDimension > |
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| using | Pointer = SmartPointer< Self > |
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| using | ScalarType = ParametersValueType |
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| using | Self = MatrixOffsetTransformBase |
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| using | Superclass = Transform< TParametersValueType, VInputDimension, VOutputDimension > |
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| using | TranslationType = OutputVectorType |
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| using | TranslationValueType = typename TranslationType::ValueType |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | DerivativeType = Array< ParametersValueType > |
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| using | DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension > |
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| using | InputCovariantVectorType = CovariantVector< TParametersValueType, VInputDimension > |
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| using | InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension > |
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| using | InputPointType = Point< TParametersValueType, VInputDimension > |
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| using | InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension > |
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| using | InputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | InputVectorType = Vector< TParametersValueType, VInputDimension > |
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| using | InputVnlVectorType = vnl_vector_fixed< TParametersValueType, VInputDimension > |
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| using | InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension > |
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| using | InverseTransformBasePointer = typename InverseTransformBaseType::Pointer |
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| using | InverseTransformBaseType = Transform< TParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianType = Array2D< ParametersValueType > |
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| using | MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension > |
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| using | OutputCovariantVectorType = CovariantVector< TParametersValueType, VOutputDimension > |
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| using | OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension > |
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| using | OutputPointType = Point< TParametersValueType, VOutputDimension > |
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| using | OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension > |
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| using | OutputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | OutputVectorType = Vector< TParametersValueType, VOutputDimension > |
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| using | OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, VOutputDimension > |
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| using | Pointer = SmartPointer< Self > |
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| using | ScalarType = ParametersValueType |
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| using | Self = Transform |
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| using | Superclass = TransformBaseTemplate< TParametersValueType > |
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| InputPointType | BackTransform (const OutputPointType &point) const |
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| InputPointType | BackTransformPoint (const OutputPointType &point) const |
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| const char * | GetNameOfClass () const override |
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| TransformCategoryEnum | GetTransformCategory () const override |
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| void | SetAzimuthElevationToCartesianParameters (const double sampleSize, const double firstSampleDistance, const long maxAzimuth, const long maxElevation) |
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| void | SetAzimuthElevationToCartesianParameters (const double sampleSize, const double firstSampleDistance, const long maxAzimuth, const long maxElevation, const double azimuthAngleSeparation, const double elevationAngleSeparation) |
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| void | SetForwardAzimuthElevationToCartesian () |
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| void | SetForwardCartesianToAzimuthElevation () |
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| OutputPointType | TransformAzElToCartesian (const InputPointType &point) const |
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| OutputPointType | TransformCartesianToAzEl (const OutputPointType &point) const |
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| OutputPointType | TransformPoint (const InputPointType &point) const override |
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| virtual void | SetMaxAzimuth (long _arg) |
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| virtual long | GetMaxAzimuth () const |
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| virtual void | SetMaxElevation (long _arg) |
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| virtual long | GetMaxElevation () const |
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| virtual void | SetRadiusSampleSize (double _arg) |
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| virtual double | GetRadiusSampleSize () const |
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| virtual void | SetAzimuthAngularSeparation (double _arg) |
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| virtual double | GetAzimuthAngularSeparation () const |
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| virtual void | SetElevationAngularSeparation (double _arg) |
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| virtual double | GetElevationAngularSeparation () const |
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| virtual void | SetFirstSampleDistance (double _arg) |
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| virtual double | GetFirstSampleDistance () const |
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| bool | GetInverse (Self *inverse) const |
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| InverseTransformBasePointer | GetInverseTransform () const override |
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| | ITK_DISALLOW_COPY_AND_MOVE (AffineTransform) |
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| | itkNewMacro (Self) |
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| | itkOverrideGetNameOfClassMacro (AffineTransform) |
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| ScalarType | Metric () const |
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| ScalarType | Metric (const Self *other) const |
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| void | Rotate2D (TParametersValueType angle, bool pre=false) |
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| void | Rotate3D (const OutputVectorType &axis, TParametersValueType angle, bool pre=false) |
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| void | Scale (const OutputVectorType &factor, bool pre=false) |
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| void | Scale (const TParametersValueType &factor, bool pre=false) |
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| void | Shear (int axis1, int axis2, TParametersValueType coef, bool pre=false) |
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| void | Translate (const OutputVectorType &trans, bool pre=false) |
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| void | Rotate (int axis1, int axis2, TParametersValueType angle, bool pre=false) |
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| void | Compose (const Self *other, bool pre=false) |
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| void | ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, InverseJacobianPositionType &jac) const override |
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| void | ComputeJacobianWithRespectToParameters (const InputPointType &p, JacobianType &jacobian) const override |
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| virtual void | ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianPositionType &) const |
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| void | ComputeJacobianWithRespectToPosition (const InputPointType &x, JacobianPositionType &jac) const override |
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| const InputPointType & | GetCenter () const |
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| const FixedParametersType & | GetFixedParameters () const override |
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| InverseTransformBasePointer | GetInverseTransform () const override |
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| virtual const MatrixType & | GetMatrix () const |
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| const char * | GetNameOfClass () const override |
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| const OutputVectorType & | GetOffset () const |
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| const ParametersType & | GetParameters () const override |
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| TransformCategoryEnum | GetTransformCategory () const override |
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| const OutputVectorType & | GetTranslation () const |
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| bool | IsLinear () const override |
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| void | SetFixedParameters (const FixedParametersType &) override |
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| virtual void | SetIdentity () |
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| void | SetParameters (const ParametersType ¶meters) override |
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| virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &) const |
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| OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &vec) const override |
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| virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &) const |
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| OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &vect) const override |
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| virtual OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const |
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| virtual OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &point) const |
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| OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor) const override |
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| virtual OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &) const |
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| virtual OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &tensor) const override |
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| OutputPointType | TransformPoint (const InputPointType &point) const override |
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| virtual OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const |
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| OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor) const override |
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| virtual OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const |
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| OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor) const override |
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| virtual OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformVector (const InputVectorPixelType &) const |
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| OutputVectorPixelType | TransformVector (const InputVectorPixelType &vect) const override |
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| virtual OutputVectorPixelType | TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputVectorType | TransformVector (const InputVectorType &) const |
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| OutputVectorType | TransformVector (const InputVectorType &vect) const override |
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| virtual OutputVectorType | TransformVector (const InputVectorType &vector, const InputPointType &point) const |
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| virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &) const |
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| OutputVnlVectorType | TransformVector (const InputVnlVectorType &vect) const override |
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| virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const |
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| virtual void | SetMatrix (const MatrixType &matrix) |
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| void | SetOffset (const OutputVectorType &offset) |
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| void | SetCenter (const InputPointType ¢er) |
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| void | SetTranslation (const OutputVectorType &translation) |
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| bool | GetInverse (InverseTransformType *inverse) const |
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| virtual void | ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const |
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| void | CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end) override |
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| void | CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end) override |
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| const FixedParametersType & | GetFixedParameters () const override |
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| unsigned int | GetInputSpaceDimension () const override |
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| bool | GetInverse (Self *) const |
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| const char * | GetNameOfClass () const override |
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| virtual NumberOfParametersType | GetNumberOfFixedParameters () const |
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| virtual NumberOfParametersType | GetNumberOfLocalParameters () const |
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| NumberOfParametersType | GetNumberOfParameters () const override |
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| unsigned int | GetOutputSpaceDimension () const override |
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| const ParametersType & | GetParameters () const override |
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| TransformCategoryEnum | GetTransformCategory () const override |
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| std::string | GetTransformTypeAsString () const override |
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| | itkCloneMacro (Self) |
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| void | SetParametersByValue (const ParametersType &p) override |
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| virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| virtual OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputVectorType | TransformVector (const InputVectorType &vector, const InputPointType &point) const |
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| virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const |
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| virtual void | UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0) |
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| template<typename TImage > |
| template< typename TImage > std std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > | ApplyToImageMetadata (SmartPointer< TImage > image) const |
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Inheritance diagram for itk::AzimuthElevationToCartesianTransform< TParametersValueType, VDimension >:
1.8.16