Vector Translation

Task

Draw a circle whose center start is updated by applying a movement vector move. The vector determines the direction and magnitude of the shift.

Theory

In 2D space, a vector is a quantity that has both a direction and a magnitude (length). You can think of it as an arrow pointing from one location to another.

Mathematically, a 2D vector is represented as:

$ \vec{v} = \begin{pmatrix} x \ y \end{pmatrix} $

where $x$ and $y$ describe how far the vector moves horizontally and vertically.

Point + Vector

If you have a point $P$ and a vector $\vec{v}$, the vector can act as an offset that moves the point to a new location:

$ P' = P + \vec{v} = \begin{pmatrix} P_x + \vec{v}_x \ P_y + \vec{v}_y \end{pmatrix} $

This addition happens component by component:

• the x-component of the point is increased by the x-component of the vector

• the y-component of the point is increased by the y-component of the vector

For example, if you start at point $P = (0.4, 0.3)$ and apply vector $\vec{v} = (0.2, 0.1)$ , the result is a new point:

$ P' = \begin{pmatrix}0.4 \ 0.3 \end{pmatrix} + \begin{pmatrix}0.2 \ 0.1 \end{pmatrix} = \begin{pmatrix} 0.6 \ 0.4 \end{pmatrix} $