Linear algebra

Conventions:

  • Column-major

  • Right hand rule

Vectors

vector_t<T,D> is a templated D-dimensional vector type.

D-dimension operations:

  • unary minus operator

  • scalar-vector addition, subtraction, multiplication and division

  • vector component-wise addition, subtraction

D-dimension functions:

  • component-wise multiplication is given by hadamard_product

  • dot product is given by dot

  • length and normalize

  • min and max between two vectors

  • min and max for vector components

D-dimension boolean functions:

  • lessThan, greatherThan

  • lessThanEqual , greatherThanEqual

  • equal, notEqual

  • any, all & complement

Specializations for 2D, 3D and 4D vectors are provided with the following features:

  • Zero initialization default constructor

  • Parametric constructors

  • 3D cross product

Matrices

matrix_t<T,D> is a templated D-dimensional square matrix type. Matrices are stored in column memory layout. User can either access a single value or a column vector using the following attributes:

union 
{
    T               at[D*D]; 
    vector_t<T,D>   col[D];
};

Defined operators:

  • scalar-matrix addition, subtraction, multiplication and division

  • matrix-matrix addition, subtraction, multiplication

  • boolean equality and inequality

  • bracket operators [i] to access the ith column vectors

  • parenthesis operators (r,c) to access a single value

D-dimension functions:

  • trace

  • transpose

  • matrix/matrix multiplication

Specializations for 2D, 3D and 4D vectors are provided with the following features:

  • fromRows(...) static function to construct matrices from row vectors (2x2,3x3,4x4)

  • fromAffine(mat3,vec3) for 4D matrices

  • determinant, inverse

Affine transformation

This namespace construct 3x3 matrices depicting affine transformations:

  • scale(sx,sy,sz) for axis-aligned non uniform scaling

  • scale(v,s) for scaling in a given direction (must be normalized)

  • rotate_x(angle), rotate_y(angle), rotate_z(angle) to rotate around a world axis

  • rotate_euler(alpha, beta, gamma) to rotate using euler angles

  • rotate_intrinsic(yaw, pitch, roll) to rotate using Bryyn-Tait angles

  • rotate(axis, angle) to rotate around a given normalized axis (must be normalized)

  • reflect(axis) to reflect along a plane given by its normal vector (must be normalized)

  • involution(axis) to reflect along a vector (must be normalized)

Camera

This namespace construct 4x4 matrices used for camera transformations:

  • lookat(origin, target, up)

  • perspective(fox_y, aspect, near, far)

  • orthographic(left, right, top, bot, near, far)

Quaternion

Warning

🚧 under construction 🚧