Homogeneous Vector in Two-Dimensional Space MbHomogeneous

The MbHomogeneous class is declared in the mb_homogeneous.h file.

The extended radius vector MbHomogeneous() defines the position of a point in two-dimensional space and is specified by three coordinates x, y, and w. The third coordinate is called a weight. The extended radius vector is used when computing the radius vector of two-dimensional B-curves constructed on the basis of B-splines. The coordinates x_w, y_w, w of the extended radius vector MbHomogeneous are related to the coordinates x, y of the radius vector MbCartPoint by the relations:

\[x = \frac{x_w}{w}; \quad y = \frac{y_w}{w}.\]

In operations of multiplication by the extended matrix MbMatrix it can be assumed that two-dimensional vectors and points also have the third coordinate: for a MbVector vector it is equal to zero, and for a MbCartPoint() radius vector it is equal to one.