|
Carna
Version 3.0.1
|
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>
Include dependency graph for math.h: This graph shows which files directly or indirectly include this file: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 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. | |
Defines Carna::base::math namespace and CARNA_FOR_VECTOR3UI.
windows.h before including this file, make sure you have NOMINMAX defined before including the windows.h header file. Definition in file math.h.
| #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:
| #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.
Documentation generated by Doxygen