Homogeneous Vector in Three-Dimensional Space MbHomogenius3D

The MbHomogeneous3D class is declared in the mb_homogenius3d.h file.

The extended radius vector MbHomogeneous3D describes the position of a point in three-dimensional space and is defined by four coordinates x, y, z, w. The fourth coordinate is called the weight. The extended radius vector is used when computing the radius vector of B-curves and B-surfaces constructed on the basis of B-splines. The coordinates x_w, y_w, z_w, w of the extended radius vector MbHomogeneous3D are related to the coordinates x, y, z of the radius vector by the relations:

\[x = \frac{x_w}{w}, \quad y = \frac{y_w}{w}, \quad z = \frac{z_w}{w}.\]

In operations of multiplication by the extended MbMatrix3D matrix, it can be assumed that vectors and points also have the fourth coordinate: for a MbVector3D vector it is equal to zero, and for a MbCartPoint3D radius vector it is equal to one.