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c9a815a41f
* Addition to the Geometry Folder with Triangle that calculates the different triangle centers * Addition to the Geometry Folder with Triangle that calculates the different triangle centers * Original triangle center w/fixes for automated testing * triangles, added more fixes for automated testing * trying to rename triangle.py * Fixed a documentation error * Removed a space I suspect is preventing the automated code reviewer from completing * Fixed a documentation error * updating DIRECTORY.md * Apply suggestion from @cclauss --------- Co-authored-by: AlexB <acbucha@clemson.edu> Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: cclauss <cclauss@users.noreply.github.com>
132 lines
4.3 KiB
Python
132 lines
4.3 KiB
Python
from __future__ import annotations
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import math
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from dataclasses import dataclass, field
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from numpy import array, linalg
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# Define a Point on a 2D normalized orthogonal euclidean grid
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# https://mathworld.wolfram.com/Circumcenter.html
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# https://mathworld.wolfram.com/Incenter.html
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# https://mathworld.wolfram.com/Orthocenter.html
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@dataclass
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class Point:
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"""
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A point defined by 2 floats representing a length on a normalized
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orthogonal coordinate system
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default coordinate is the origin
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>>> Point(-1.0, 0.0)
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Point(x=-1.0, y=0.0)
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"""
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x: float = 0.0
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y: float = 0.0
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def __post_init__(self) -> None:
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if not isinstance(self.x, (int, float)):
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raise TypeError("x must be an int or float numeric value")
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if not isinstance(self.y, (int, float)):
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raise TypeError("y must be an int or float numeric value")
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@dataclass
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class Triangle:
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"""
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A 3 point Triangle on a 2D normalized orthogonal euclidean grid
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>>> p1 = Point(-1.0,0.0)
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>>> p2 = Point(1.0,0.0)
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>>> p3 = Point(0.0,1.0)
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>>> Triangle(p1, p2, p3) # doctest: +NORMALIZE_WHITESPACE
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Triangle(v1=Point(x=-1.0, y=0.0), v2=Point(x=1.0, y=0.0), v3=Point(x=0.0, y=1.0),
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circum=Point(x=0.0, y=0.0), incen=Point(x=0.0, y=0.0),
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ortho=Point(x=0.0, y=0.0))
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"""
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v1: Point = field(default_factory=Point)
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v2: Point = field(default_factory=Point)
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v3: Point = field(default_factory=Point)
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circum: Point = field(default_factory=Point)
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incen: Point = field(default_factory=Point)
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ortho: Point = field(default_factory=Point)
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def __post_init__(self) -> None:
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# Check for valid arguments
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if (
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not isinstance(self.v1, Point)
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or not isinstance(self.v2, Point)
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or not isinstance(self.v3, Point)
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):
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raise TypeError("All 3 arguments should be Point Objects")
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# Check for 3 unique points
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if self.v1 in (self.v2, self.v3):
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raise TypeError("All 3 arguments should be unique")
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# Check for linearity
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if self.v1.x == self.v2.x and self.v3.y == self.v2.y:
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raise TypeError("One or more arguments are redundant")
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m = (self.v1.y - self.v2.y) / (self.v1.x - self.v2.x)
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yb = self.v1.y - m * self.v1.x
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if self.v3.y == m * self.v3.x + yb:
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raise TypeError("One or more arguments are redundant")
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# Circumcenter
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@property
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def circumcenter(self) -> Point:
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m_0 = array(
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[
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[self.v1.x, self.v1.y, 1],
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[self.v2.x, self.v2.y, 1],
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[self.v3.x, self.v3.y, 1],
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]
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)
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m_1 = array(
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[
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[self.v1.x**2 + self.v1.y**2, self.v1.y, 1],
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[self.v2.x**2 + self.v2.y**2, self.v2.y, 1],
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[self.v3.x**2 + self.v3.y**2, self.v3.y, 1],
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]
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)
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m_2 = array(
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[
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[self.v1.x**2 + self.v1.y**2, self.v1.x, 1],
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[self.v2.x**2 + self.v2.y**2, self.v2.x, 1],
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[self.v3.x**2 + self.v3.y**2, self.v3.x, 1],
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]
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)
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a = linalg.det(m_0)
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bx = -linalg.det(m_1)
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by = linalg.det(m_2)
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self.circum.x = -bx / (2 * a)
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self.circum.y = -by / (2 * a)
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return self.circum
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# Incenter
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@property
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def incenter(self) -> Point:
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a = math.sqrt((self.v2.x - self.v3.x) ** 2 + (self.v2.y - self.v3.y) ** 2)
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b = math.sqrt((self.v1.x - self.v3.x) ** 2 + (self.v1.y - self.v3.y) ** 2)
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c = math.sqrt((self.v1.x - self.v2.x) ** 2 + (self.v1.y - self.v2.y) ** 2)
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self.incen.x = (a * self.v1.x + b * self.v2.x + c * self.v3.x) / (a + b + c)
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self.incen.y = (a * self.v1.y + b * self.v2.y + c * self.v3.y) / (a + b + c)
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return self.incen
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# Orthocenter
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@property
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def orthocenter(self) -> Point:
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inv_m1 = -1 / ((self.v3.y - self.v1.y) / (self.v3.x - self.v1.x))
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inv_m2 = -1 / ((self.v3.y - self.v2.y) / (self.v3.x - self.v2.x))
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m = array([[inv_m2, -1], [inv_m1, -1]])
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b = array([[inv_m2 * self.v1.x - self.v1.y], [inv_m1 * self.v2.x - self.v2.y]])
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soln = linalg.solve(m, b)
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self.ortho.x = soln[0][0]
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self.ortho.y = soln[1][0]
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return self.ortho
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if __name__ == "__main__":
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__import__("doctest").testmod()
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