math.h File Reference

Defines Carna::base::math namespace and CARNA_FOR_VECTOR3UI. More...

#include <Carna/Carna.h>
#include <Carna/base/CarnaException.h>
#include <algorithm>
#include <type_traits>
#include <cmath>
#include <Eigen/Dense>

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Go to the source code of this file.

Classes
struct	Carna::base::math::element_type_of< T >
	Retrieves element types of vectors and scalars. General case assumes a scalar type. More...
struct	Carna::base::math::element_type_of< Eigen::Matrix< VectorElementType, rows, cols > >
	Retrieves element types of vectors and scalars. This is the specialization for vector and matrix types. More...
struct	Carna::base::math::Statistics< T >
	Holds mean and variance of an characteristic. More...

Namespaces
	Carna::base
	Contains the core framework components.
	Carna::base::math
	Provides set of math-related classes and functions.

Macros
#define	CARNA_FOR_VECTOR3UI_EX(vecName, vecLimit, vecStart)
	Loops vecName over all \(\vec x \in \mathbb Z^3_{\geq 0} : x_i < n_i \wedge x_i \geq s_i \forall i\) where \(\vec n\) is vecLimit and \(\vec s\) is vecStart. More...
#define	CARNA_FOR_VECTOR3UI(vecName, vecLimit)   CARNA_FOR_VECTOR3UI_EX( vecName, vecLimit, Carna::base::math::Vector3ui( 0, 0, 0 ) )
	Loops vecName over all \(\vec x \in \mathbb Z^3_{\geq 0} : x_i < n_i \forall i\) where \(\vec n\) is vecLimit. More...

Typedefs
typedef Eigen::Matrix< float, 4, 4, Eigen::ColMajor >	Carna::base::math::Matrix4f
	Defines \(\mathbb R^{4 \times 4}\) matrix.
typedef Eigen::Matrix< float, 3, 3, Eigen::ColMajor >	Carna::base::math::Matrix3f
	Defines \(\mathbb R^{3 \times 3}\) matrix.
typedef Eigen::Matrix< float, 4, 1 >	Carna::base::math::Vector4f
	Defines \(\mathbb R^{4 \times 1}\) vector.
typedef Eigen::Matrix< float, 3, 1 >	Carna::base::math::Vector3f
	Defines \(\mathbb R^{3 \times 1}\) vector.
typedef Eigen::Matrix< float, 2, 1 >	Carna::base::math::Vector2f
	Defines \(\mathbb R^{2 \times 1}\) vector.
typedef Eigen::Matrix< signed int, 3, 1 >	Carna::base::math::Vector3i
	Defines \(\mathbb Z^{3 \times 1}\) vector.
typedef Eigen::Matrix< unsigned int, 3, 1 >	Carna::base::math::Vector3ui
	Defines \(\mathbb Z^{3 \times 1}_{\geq 0}\) vector.
typedef Eigen::Matrix< unsigned int, 2, 1 >	Carna::base::math::Vector2ui
	Defines \(\mathbb Z^{2 \times 1}_{\geq 0}\) vector.

Functions
template<typename T >
T	Carna::base::math::clamp (T val, T my_min, T my_max)
	Returns \( \min( \max( \) val \(, \) my_min \( ), \) my_max \( ) \). More...
template<typename T >
T	Carna::base::math::sq (T x)
	Computes and returns \( x^2 \).
float	Carna::base::math::deg2rad (float deg)
	Converts degrees to radians.
float	Carna::base::math::rad2deg (float rad)
	Converts radians to degrees.
template<typename T >
T	Carna::base::math::epsilon ()
	Defines the maximum difference of two objects treated as equal.
template<>
float	Carna::base::math::epsilon< float > ()
	Defines the maximum difference of two single-precision floating point objects treated as equal.
template<>
double	Carna::base::math::epsilon< double > ()
	Defines the maximum difference of two double-precision floating point objects treated as equal.
template<typename T >
T	Carna::base::math::length2 (const T &x)
	Retrieves the squared length of vector and scalar types. General case assumes scalar type.
template<typename VectorElementType , int dimension>
VectorElementType	Carna::base::math::length2 (const Eigen::Matrix< VectorElementType, dimension, 1 > &x)
	Retrieves the squared length of vector and scalar types. This is the specialization for vector types.
template<typename InputType >
bool	Carna::base::math::isEqual (const InputType &x, const InputType &y)
	Tells whether two objects are equal respectively to epsilon.
template<>
bool	Carna::base::math::isEqual (const bool &x, const bool &y)
	Tells whether two objects are equal. This is the specialization for bool types.
Matrix4f	Carna::base::math::identity4f ()
	Returns \(\mathbb R^{4 \times 4}\) identity matrix.
Matrix3f	Carna::base::math::identity3f ()
	Returns \(\mathbb R^{3 \times 3}\) identity matrix.
template<typename MatrixType >
MatrixType	Carna::base::math::zeros ()
	Returns matrix with zeros in all components.
Matrix4f	Carna::base::math::basis4f (const Vector4f &x, const Vector4f &y, const Vector4f &z, const Vector4f &t=Vector4f(0, 0, 0, 0))
	Creates \(\mathbb R^{3 \times 3}\) basis embedded into a \(\mathbb R^{4 \times 4}\) homogenous coordinates matrix. More...
Matrix4f	Carna::base::math::basis4f (const Vector3f &x, const Vector3f &y, const Vector3f &z, const Vector3f &t=Vector3f(0, 0, 0))
Matrix4f	Carna::base::math::translation4f (float x, float y, float z)
	Returns matrix that translates homogeneous coordinates.
template<typename Vector >
Matrix4f	Carna::base::math::translation4f (const Vector &v)
Matrix4f	Carna::base::math::scaling4f (float x, float y, float z)
	Creates scaling matrix for homogeneous coordinates.
template<typename VectorElementType >
Matrix4f	Carna::base::math::scaling4f (const Eigen::Matrix< VectorElementType, 3, 1 > &v)
Matrix4f	Carna::base::math::scaling4f (float uniformScaleFactor)
Matrix4f	Carna::base::math::rotation4f (float x, float y, float z, float radians)
	Creates rotation matrix for homogeneous coordinates. The rotation is performed around the axis that is specified by the vector with the components x, y and z.
template<typename Vector >
Matrix4f	Carna::base::math::rotation4f (const Vector &v, float radians)
Matrix3f	Carna::base::math::rotation3f (float x, float y, float z, float radians)
	Creates rotation matrix for homogeneous coordinates, but returns only the upper left \(3 \times 3\) sub-matrix.
Vector3f	Carna::base::math::orthogonal3f (const Vector3f &in)
	Constructs \(\mathbb R^3\) vector that is orthogonal to in. The result is undefined if the squared length of in equals zero. More...
template<typename VectorElementType , int rows, typename WType >
Eigen::Matrix< VectorElementType, 4, 1 >	Carna::base::math::vector4 (const Eigen::Matrix< VectorElementType, rows, 1 > &v, WType w)
	Creates 4-dimensional vector from 3-dimensional (or higher) with same component type, and a scalar that is appended as the fourth component.
template<typename VectorElementType , int rows>
Eigen::Matrix< VectorElementType, 3, 1 >	Carna::base::math::vector3 (const Eigen::Matrix< VectorElementType, rows, 1 > &v)
	Creates 3-dimensional vector from 4-dimensional (or higher) with same component type by dropping the fourth component.
Matrix4f	Carna::base::math::plane4f (const Vector3f &normal, float distance)
	Creates matrix that transforms from the tangent space of a plane with particular normal vector and origin distance to the space that normal and distance are given within.
Matrix4f	Carna::base::math::plane4f (const Vector3f &normal, const Vector3f &support)
float	Carna::base::math::translationDistance2 (const Matrix4f &m)
	Returns the squared length of the translation component of the homogeneous coordinates transformation matrix m.
template<typename Matrix >
Matrix::Scalar	Carna::base::math::maxAbsElement (const Matrix &m)
	Returns \(\max_{i,j} \left|m_{i,j}\right|\) where $m$ is m.
Matrix4f	Carna::base::math::frustum4f (float left, float right, float bottom, float top, float zNear, float zFar)
	Returns the projection matrix that is described by the specified frustum. More...
Matrix4f	Carna::base::math::frustum4f (float fovRadiansHorizontal, float heightOverWidth, float zNear, float zFar)
Matrix4f	Carna::base::math::ortho4f (float left, float right, float bottom, float top, float zNear, float zFar)
	Returns the projection matrix that is described by the specified box.
template<typename Sampler >
base::math::Vector3f	Carna::base::math::computeFastGradient3f (Sampler func)
	Computes fast approximation of the gradient at the origin of the scalar field func. More...
template<typename ScalarType >
unsigned int	Carna::base::math::round_ui (ScalarType x)
	Rounds x to the closest \(x' \in \mathbb Z_{\geq 0}\). Either the data type of \(x\) must be unsigned or \(x \geq 0\).
template<typename MatrixElementType , int cols, int rows>
Eigen::Matrix< unsigned int, cols, rows >	Carna::base::math::round_ui (const Eigen::Matrix< MatrixElementType, cols, rows > &m)
	Rounds matrix m to such \(m'\) that every element in \(m'\) is close-most to its corresponding element in \(m\). Either the element data type of \(m\) must be unsigned or \(m_{i,j} \geq 0 \forall i,j\).
template<typename ScalarType >
ScalarType	Carna::base::math::makeEven (ScalarType x, int s)
	Returns \(x\) if \(x\) is even and \(x + s\) if \(x\) is odd, where \(s \in \left\{-1, +1\right\}\). The data type of \(x\) must be integral.
template<typename MatrixElementType , int cols, int rows>
Eigen::Matrix< MatrixElementType, cols, rows >	Carna::base::math::makeEven (const Eigen::Matrix< MatrixElementType, cols, rows > &m, int s)
	Returns matrix \(m'\) of the same size like \(m\) where \(m'_{i,j} = m_{i,j}\) if \(m_{i,j}\) is even and \(m'_{i,j} = m_{i,j} + s\) if \(m_{i,j}\) is odd, where \(s \in \left\{-1, +1\right\}\). The element data type of \(m\) must be integral.
template<typename ResultType , typename SupportType >
ResultType	Carna::base::math::mix (const SupportType &a, const SupportType &b, float t)
	Interpolates between and by t \(\in\left[0, 1\right]\) linearly.

Detailed Description

Defines Carna::base::math namespace and CARNA_FOR_VECTOR3UI.

Attention

If you include windows.h before including this file, make sure you have NOMINMAX defined before including the windows.h header file.

Definition in file math.h.

Macro Definition Documentation

CARNA_FOR_VECTOR3UI

#define CARNA_FOR_VECTOR3UI	(		vecName,
			vecLimit
	)		CARNA_FOR_VECTOR3UI_EX( vecName, vecLimit, Carna::base::math::Vector3ui( 0, 0, 0 ) )

Loops vecName over all \(\vec x \in \mathbb Z^3_{\geq 0} : x_i < n_i \forall i\) where \(\vec n\) is vecLimit.

Example:

    using namespace Carna::base;
    HUVolumeUInt16 data( math::Vector3ui( 100, 100, 30 ) );
  
    /* Initialize all 'data' voxels with '-1024'.
     */
    const HUV expected = HUV::abs( -1024 );
    CARNA_FOR_VECTOR3UI( p, data.size )
    {
        data.setVoxel( p, expected );
    }
  
    /* Verify the result.
     */
    for( std::size_t i = 0; i < data.buffer().size(); ++i )
    {
        QCOMPARE( data.buffer()[ i ], HUVolumeUInt16::HUVToBufferValue( expected ) );
    }

Definition at line 747 of file math.h.

CARNA_FOR_VECTOR3UI_EX

#define CARNA_FOR_VECTOR3UI_EX	(		vecName,
			vecLimit,
			vecStart
	)

Value:

Carna::base::math::Vector3ui vecName; \
    for( vecName.z() = vecStart.x(); vecName.z() < vecLimit.z(); ++vecName.z() ) \
    for( vecName.y() = vecStart.y(); vecName.y() < vecLimit.y(); ++vecName.y() ) \
    for( vecName.x() = vecStart.z(); vecName.x() < vecLimit.x(); ++vecName.x() )

Loops vecName over all \(\vec x \in \mathbb Z^3_{\geq 0} : x_i < n_i \wedge x_i \geq s_i \forall i\) where \(\vec n\) is vecLimit and \(\vec s\) is vecStart.

Definition at line 733 of file math.h.