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# sknano.core.geometric_regions.Triangle.contains¶

Triangle.contains(point)[source][source]

Test region membership of point in Triangle.

Parameters: point : array_like bool True if point is within Triangle, False, otherwise.

Notes

A point $$(p_x, p_y)$$ is within the bounded region of a triangle with corner points $$p_1=(x_1, y_1)$$, $$p_2=(x_2, y_2)$$, and $$p_3=(x_3, y_3)$$, if the following is true:

$\frac{(x_1 - x_3) p_y + (x_3 - p_x) y_1 + (p_x - x_1) y_3}{ (y_1-y_2) x_3 + (y_2 - y_3) x_1 + (y_3 - y_1) x_2}\ge 0\land$$\frac{(x_2 - x_1) p_y + (p_x - x_2) y_1 + (x_1 - p_x) y_2}{ (y_1 - y_2) x_3 + (y_2 - y_3) x_1 + (y_3 - y_1) x_2}\ge 0\land$$\frac{(x_2 - x_3) p_y + (x_3 - p_x) y_2 + (p_x - x_2) y_3}{ (y_1 - y_2) x_3 + (y_2 - y_3) x_1 + (y_3 - y_1) x_2}\le 0$