sknano.core.geometric_regions.Parallelogram.contains

Parallelogram.contains(point)

Test region membership of point in Parallelogram.

Parameters:

point : array_like

Returns:

bool

True if point is within Paralleogram, False otherwise

Notes

A point $(p_x, p_y)$ is within the bounded region of a parallelogram with origin $(o_x, o_y)$ and direction vectors $\mathbf{u}=(u_x, u_y)$ and $\mathbf{v}=(v_x, v_y)$ if the following is true:

$$0\le\frac{(p_y - o_y) v_x + (o_x - p_x) v_y}{u_y v_x - u_x v_y} \le 1 \land 0\le\frac{(p_y - o_y) u_x + (o_x - p_x) u_y}{u_x v_y - u_y v_x} \le 1$$