Source code for skspatial.objects.triangle

"""Module for the Triangle class."""
import math
from itertools import combinations
from typing import Sequence

import numpy as np
from matplotlib.axes import Axes
from mpl_toolkits.mplot3d import Axes3D

from skspatial._functions import np_float
from skspatial.objects._base_spatial import _BaseSpatial
from skspatial.objects.line import Line
from skspatial.objects.point import Point
from skspatial.objects.points import Points
from skspatial.objects.vector import Vector
from skspatial.typing import array_like


[docs]class Triangle(_BaseSpatial): """ A triangle represented by three points in space. Parameters ---------- point_a, point_b, point_c : array_like The three vertices of the triangle. Attributes ---------- point_a, point_b, point_c : Point The three vertices of the triangle. dimension : int Dimension of the triangle. Raises ------ ValueError If the points do not have the same dimension. If the points are collinear. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> triangle Triangle(point_a=Point([0, 0]), point_b=Point([1, 0]), point_c=Point([0, 1])) >>> triangle.dimension 2 >>> Triangle([0, 0, 0], [1, 0], [0, 1]) Traceback (most recent call last): ... ValueError: The points must have the same dimension. >>> Triangle([0, 0], [0, 1], [0, 2]) Traceback (most recent call last): ... ValueError: The points must not be collinear. """ def __init__(self, point_a: array_like, point_b: array_like, point_c: array_like): self.point_a = Point(point_a) self.point_b = Point(point_b) self.point_c = Point(point_c) if not (self.point_a.dimension == self.point_b.dimension == self.point_c.dimension): raise ValueError("The points must have the same dimension.") if Points([self.point_a, self.point_b, self.point_c]).are_collinear(): raise ValueError("The points must not be collinear.") self.dimension = self.point_a.dimension def __repr__(self) -> str: repr_a = np.array_repr(self.point_a) repr_b = np.array_repr(self.point_b) repr_c = np.array_repr(self.point_c) return f"Triangle(point_a={repr_a}, point_b={repr_b}, point_c={repr_c})"
[docs] def multiple(self, name_method: str, inputs: Sequence) -> tuple: """ Return multiple properties of the triangle. Parameters ---------- name_method : str Name of the triangle method. inputs : Sequence Sequence of different inputs to the method. Returns ------- tuple Multiple outputs from the triangle method. Examples -------- >>> from math import degrees >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [0, 1], [1, 0]) >>> lengths = triangle.multiple('length', 'abc') >>> [round(x, 3) for x in lengths] [1.414, 1.0, 1.0] >>> angles = triangle.multiple('angle', 'ABC') >>> [round(degrees(x), 3) for x in angles] [90.0, 45.0, 45.0] """ method = getattr(self, name_method) return tuple(method(x) for x in inputs)
[docs] def normal(self) -> Vector: r""" Return a vector normal to the triangle. The normal vector is calculated as .. math:: v_{AB} \times v_{AC} where :math:`v_{AB}` is the vector from vertex A to vertex B. Returns ------- Vector Normal vector. Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [1, 0], [0, 1]).normal() Vector([0, 0, 1]) The normal vector is not necessarily a unit vector. >>> Triangle([0, 0], [2, 0], [0, 2]).normal() Vector([0, 0, 4]) The direction of the normal vector is dependent on the order of the vertices. >>> Triangle([0, 0], [0, 1], [1, 0]).normal() Vector([ 0, 0, -1]) """ vector_ab = Vector.from_points(self.point_a, self.point_b) vector_ac = Vector.from_points(self.point_a, self.point_c) return vector_ab.cross(vector_ac)
[docs] def area(self) -> np.float64: """ Return the area of the triangle. The points are the vertices of the triangle. They must be 3D or less. Returns ------- np.float64 The area of the triangle. References ---------- http://mathworld.wolfram.com/TriangleArea.html Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [0, 1], [1, 0]).area() 0.5 >>> Triangle([0, 0], [0, 2], [1, 1]).area() 1.0 >>> Triangle([3, -5, 1], [5, 2, 1], [9, 4, 2]).area().round(2) 12.54 """ return 0.5 * self.normal().norm()
[docs] def perimeter(self) -> np.float64: """ Return the perimeter of the triangle. Returns ------- np.float64 The perimeter of the triangle. Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [0, 1], [1, 0]).perimeter().round(3) 3.414 >>> Triangle([0, 1], [1, 1], [2, 0]).perimeter().round(3) 4.65 """ result = np.sum(self.multiple('length', 'abc')) return np.float64(result)
[docs] def point(self, vertex: str) -> Point: """ Return a point (vertex) of the triangle. Parameters ---------- vertex: str 'A', 'B', or 'C'. Returns ------- Point A vertex of the triangle. Raises ------ ValueError If the vertex is not 'A', 'B', or 'C'. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> triangle.point('A') Point([0, 0]) >>> triangle.point('B') Point([1, 0]) >>> triangle.point('C') Point([0, 1]) >>> triangle.point('D') Traceback (most recent call last): ... ValueError: The vertex must be 'A', 'B', or 'C'. """ if vertex == 'A': return self.point_a if vertex == 'B': return self.point_b if vertex == 'C': return self.point_c raise ValueError("The vertex must be 'A', 'B', or 'C'.")
[docs] def line(self, side: str) -> Line: """ Return the line along a side of the triangle. Parameters ---------- side: str 'a', 'b', or 'c'. Side 'a' is the side across from vertex 'A'. Returns ------- Line Line along the side. Raises ------ ValueError If the side is not 'a', 'b', or 'c'. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> triangle.line('a') Line(point=Point([1, 0]), direction=Vector([-1, 1])) >>> triangle.line('b') Line(point=Point([0, 1]), direction=Vector([ 0, -1])) >>> triangle.line('c') Line(point=Point([0, 0]), direction=Vector([1, 0])) >>> triangle.line('d') Traceback (most recent call last): ... ValueError: The side must be 'a', 'b', or 'c'. """ if side == 'a': point_1, point_2 = self.point_b, self.point_c elif side == 'b': point_1, point_2 = self.point_c, self.point_a elif side == 'c': point_1, point_2 = self.point_a, self.point_b else: raise ValueError("The side must be 'a', 'b', or 'c'.") return Line.from_points(point_1, point_2)
[docs] def length(self, side: str) -> np.float64: """ Return a side length of the triangle. Side 'a' is the side across from vertex 'A'. The side length is the distance between vertices 'B' and 'C'. Parameters ---------- side: str 'a', 'b', or 'c'. Returns ------- np.float64 Side length. Raises ------ ValueError If the side is not 'a', 'b', or 'c'. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> triangle.length('a').round(3) 1.414 >>> triangle.length('b') 1.0 >>> triangle.length('c') 1.0 >>> triangle.length('d') Traceback (most recent call last): ... ValueError: The side must be 'a', 'b', or 'c'. """ return self.line(side).direction.norm()
[docs] @np_float def angle(self, vertex: str) -> float: """ Return an interior angle of the triangle. The angle is in radians. Parameters ---------- vertex: str 'A', 'B', or 'C'. Returns ------- np.float64 Interior angle. Raises ------ ValueError If the vertex is not 'A', 'B', or 'C'. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> triangle.angle('A').round(3) 1.571 >>> triangle.angle('B').round(3) 0.785 >>> triangle.angle('C').round(3) 0.785 >>> triangle.angle('D') Traceback (most recent call last): ... ValueError: The vertex must be 'A', 'B', or 'C'. """ a, b, c = self.multiple('length', 'abc') if vertex == 'A': arg = (b**2 + c**2 - a**2) / (2 * b * c) elif vertex == 'B': arg = (a**2 + c**2 - b**2) / (2 * a * c) elif vertex == 'C': arg = (a**2 + b**2 - c**2) / (2 * a * b) else: raise ValueError("The vertex must be 'A', 'B', or 'C'.") return math.acos(arg)
[docs] def centroid(self) -> Point: """ Return the centroid of the triangle. Returns ------- Point Centroid of the triangle. Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [0, 1], [1, 0]).centroid().round(3) Point([0.333, 0.333]) >>> Triangle([0, 0, 0], [1, 2, 3], [4, 5, 6]).centroid().round(3) Point([1.667, 2.333, 3. ]) """ return Points([self.point_a, self.point_b, self.point_c]).centroid()
[docs] def altitude(self, vertex: str) -> Line: """ Return the line of an altitude of the triangle. An altitude is a line segment through a vertex and perpendicular to the opposite side. Parameters ---------- vertex: str 'A', 'B', or 'C'. Returns ------- Line Altitude line. Raises ------ ValueError If the vertex is not 'A', 'B', or 'C'. Examples -------- >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 1], [2, 0]) >>> triangle.altitude('A') Line(point=Point([0, 0]), direction=Vector([1., 1.])) >>> triangle.altitude('B') Line(point=Point([1, 1]), direction=Vector([ 0., -1.])) >>> triangle.altitude('C') Line(point=Point([2, 0]), direction=Vector([-1., 1.])) >>> triangle.altitude('D') Traceback (most recent call last): ... ValueError: The vertex must be 'A', 'B', or 'C'. """ if vertex == 'A': point_proj = self.line('a').project_point(self.point_a) return Line.from_points(self.point_a, point_proj) if vertex == 'B': point_proj = self.line('b').project_point(self.point_b) return Line.from_points(self.point_b, point_proj) if vertex == 'C': point_proj = self.line('c').project_point(self.point_c) return Line.from_points(self.point_c, point_proj) raise ValueError("The vertex must be 'A', 'B', or 'C'.")
[docs] def orthocenter(self) -> Point: """ Return the orthocenter of the triangle. The orthocenter is the intersection point of the three altitudes. Returns ------- Point Orthocenter of the triangle. Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [0, 1], [1, 0]).orthocenter() Point([0., 0.]) >>> Triangle([0, 0], [1, 2], [2, 0]).orthocenter() Point([1. , 0.5]) """ line_alt_a = self.altitude('A') line_alt_b = self.altitude('B') return line_alt_a.intersect_line(line_alt_b)
[docs] def classify(self, **kwargs: float) -> str: """ Classify the triangle as equilateral, isosceles, or scalene. Parameters ---------- kwargs : dict, optional Additional keywords passed to :func:`math.isclose`. Returns ------- str 'equilateral', 'isosceles', or 'scalene'. Examples -------- >>> import math >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [1, 0], [1, 1]).classify() 'isosceles' >>> Triangle([0, 0], [1, 0], [0, 1]).classify() 'isosceles' >>> Triangle([0, 0], [1, 0], [0, 2]).classify() 'scalene' >>> Triangle([0, 0], [1, 0], [0.5, math.sin(math.pi / 3)]).classify() 'equilateral' This triangle is approximately equilateral. >>> triangle = Triangle([0, 0], [1, 0], [0.5, 0.866]) >>> triangle.classify() 'isosceles' >>> triangle.classify(rel_tol=1e-3) 'equilateral' """ lengths = self.multiple('length', 'abc') pairs = combinations(lengths, 2) n_pairs_close = sum(math.isclose(a, b, **kwargs) for a, b in pairs) if n_pairs_close == 3: return 'equilateral' if n_pairs_close == 1: return 'isosceles' return 'scalene'
[docs] def is_right(self, **kwargs: float) -> bool: """ Check if the triangle is a right triangle. A right triangle with sides :math:`abc`, satisfies the Pythagorean theorem .. math:: a^2 + b^2 = c^2 Parameters ---------- kwargs : dict, optional Additional keywords passed to :func:`math.isclose`. Returns ------- bool True if the triangle is a right triangle; false otherwise. Examples -------- >>> from skspatial.objects import Triangle >>> Triangle([0, 0], [0, 1], [1, 0]).is_right() True >>> Triangle([0, 0], [0, 1], [1, 1]).is_right() True >>> Triangle([0, 0], [1, 2], [2, 0]).is_right() False This triangle is approximately a right triangle. >>> triangle = Triangle([0, 0], [100, 0], [101, 100]) >>> triangle.is_right() False >>> triangle.is_right(rel_tol=1e-2) True """ a, b, c = sorted(self.multiple('length', 'abc')) return math.isclose(a**2 + b**2, c**2, **kwargs)
[docs] def plot_2d(self, ax_2d: Axes, part: str = 'points', **kwargs: str) -> None: """ Plot a triangle in 2D. Parameters ---------- ax_2d : Axes Instance of :class:`~matplotlib.axes.Axes`. part : str, optional Part of the triangle to plot. Either 'points' or 'lines' (default 'points'). kwargs : dict, optional Additional keywords passed to :meth:`~skspatial.objects.point.plot_2d` or :meth:`~skspatial.objects.line.plot_2d`. Examples -------- .. plot:: :include-source: >>> import matplotlib.pyplot as plt >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> _, ax = plt.subplots() >>> triangle.plot_2d(ax, part='points', s=100, zorder=3) >>> triangle.plot_2d(ax, part='lines', c='k') """ if part == 'points': for point in self.multiple('point', 'ABC'): point.plot_2d(ax_2d, **kwargs) elif part == 'lines': for line in self.multiple('line', 'abc'): line.plot_2d(ax_2d, **kwargs)
[docs] def plot_3d(self, ax_3d: Axes3D, part: str = 'points', **kwargs: str) -> None: """ Plot a triangle in 3D. Parameters ---------- ax_3d : Axes3D Instance of :class:`~mpl_toolkits.mplot3d.axes3d.Axes3D`. part : str, optional Part of the triangle to plot. Either 'points' or 'lines' (default 'points'). kwargs : dict, optional Additional keywords passed to :meth:`~skspatial.objects.Point.plot_3d` or :meth:`~skspatial.objects.Line.plot_3d`. Examples -------- .. plot:: :include-source: >>> import matplotlib.pyplot as plt >>> from skspatial.objects import Triangle >>> triangle = Triangle([0, 0], [1, 0], [0, 1]) >>> _, ax = plt.subplots() >>> triangle.plot_2d(ax, part='points', s=100, zorder=3) >>> triangle.plot_2d(ax, part='lines', c='k') """ if part == 'points': for point in self.multiple('point', 'ABC'): point.plot_3d(ax_3d, **kwargs) elif part == 'lines': for line in self.multiple('line', 'abc'): line.plot_3d(ax_3d, **kwargs)