Triangle

class sknano.core.geometric_regions.Triangle(p1=None, p2=None, p3=None)

Bases: sknano.core.geometric_regions.Geometric2DRegion

Geometric2DRegion for a triangle.

New in version 0.3.10.

Represents the bounded region with corner points $p_1=(x_1,y_1)$, $p_2=(x_2,y_2)$, and $p_3=(x_3,y_3)$.

Parameters:p2, p3 (p1,) – 2-tuples or Point class instances specifying the Triangle corner points $p_1=(x_1,y_1)$, $p_2=(x_2,y_2)$, and $p_3=(x_3, y_3)$.

Notes

Triangle represents a 2D geometric region consisting of all combinations of corner points $p_i$, $\left\{\lambda_1 p_1+\lambda_2 p_2 + \lambda_3 p_3| \lambda_i\ge0\land\lambda_1+\lambda_2+\lambda_3=1\right\}$.

Calling Triangle with no parameters is equivalent to Triangle(p1=[0, 0], p2=[0, 1], p3=[1, 0]).

Attributes

area	Triangle area.
bounding_box	Bounding Cuboid.
center	Alias for centroid.
centroid	Triangle centroid, $(c_x, c_y)$.
fmtstr	Format string.
measure	Alias for area, which is the measure of a 2D geometric region.
ndim	Return the dimensions.
p1	Corner point $p_1=(x_1, y_1)$.
p2	Corner point $p_2=(x_2, y_2)$.
p3	Corner point $p_3=(x_3, y_3)$.
pmax	Point at maximum extent.
pmin	Point at minimum extent.

Methods

center_centroid()	Center centroid on origin.
contains(point)	Test region membership of point in Triangle.
get_points()	Return list of points from GeometricRegion.points and GeometricRegion.vectors
rotate(**kwargs)	Rotate GeometricRegion points and vectors.
todict()	Returns a dict of the Triangle constructor parameters.
translate(t[, fix_anchor_points])	Translate GeometricRegion points and vectors by Vector t.

Attributes Summary

area	Triangle area.
centroid	Triangle centroid, $(c_x, c_y)$.
p1	Corner point $p_1=(x_1, y_1)$.
p2	Corner point $p_2=(x_2, y_2)$.
p3	Corner point $p_3=(x_3, y_3)$.

Methods Summary

contains(point)	Test region membership of point in Triangle.
todict()	Returns a dict of the Triangle constructor parameters.

Attributes Documentation

area

Triangle area.

Computed as:

$$A = \frac{1}{2}|-x_2 y_1 + x_3 y_1 + x_1 y_2 - x_3 y_2 - x_1 y_3 + x_2 y_3|$$

centroid

Triangle centroid, $(c_x, c_y)$.

Computed as 2D Point $(c_x, c_y)$ with coordinates:

$$c_x = \frac{x_1 + x_2 + x_3}{3}$$ $$c_y = \frac{y_1 + y_2 + y_3}{3}$$

Returns:2D Point of centroid. Return type:Point

p1

Corner point $p_1=(x_1, y_1)$.

p2

Corner point $p_2=(x_2, y_2)$.

p3

Corner point $p_3=(x_3, y_3)$.

Methods Documentation

contains(point)

Test region membership of point in Triangle.

Parameters:point (array_like) – Returns:True if point is within Triangle, False, otherwise. Return type:bool

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:

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

todict()

Returns a dict of the Triangle constructor parameters.