Braikenridge-Maclaurin Construction of a Conic (#11205)

* Added conic construction file

* Conic section code finalized for preliminary review

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Fixing ISC001 issue

* Fixing variable declaration

* Modify generate method to return a formatted string

Changed the return type of the generate method to str and updated its implementation to return a formatted string instead of printing it.

* updating DIRECTORY.md

* updating DIRECTORY.md

* Clean up comments and improve docstring formatting

Removed commented-out documentation and updated docstring formatting.

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* Add imports for dataclass and numpy

---------

Co-authored-by: AlexB <acbucha@clemson.edu>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

geometry/braik_mac_construction.py

@@ -0,0 +1,160 @@
+"""
+braikenridge_maclaurin_construction
+https://mathworld.wolfram.com/ConicSection.html
+5 Points define a conic section on a 2D normal orthogonal plane using this technique.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+
+from numpy import array, linalg
+
+
+@dataclass
+class Point:
+    """
+    A point defined by 2 floats representing a length on a normalized
+    orthogonal coordinate system
+    default coordinate is the origin
+
+    >>> Point(-1.0, 0.0)
+    Point(x=-1.0, y=0.0)
+    """
+
+    x: float = 0.0
+    y: float = 0.0
+
+    def __post_init__(self) -> None:
+        if not isinstance(self.x, (int, float)):
+            raise TypeError("x must be an int or float numeric value")
+        if not isinstance(self.y, (int, float)):
+            raise TypeError("y must be an int or float numeric value")
+
+
+@dataclass
+class BraikMac:
+    """
+    Given a list of 5 points, determine the corresponding
+    conic section equation and provide it to the user
+
+    | x**2   xy  y**2  x  y  1 |
+    | x1**2 x1y1 y1**2 x1 y1 1 |
+    | x2**2 x2y2 y2**2 x2 y2 1 | = 0
+    | x3**2 x3y3 y3**2 x3 y3 1 |
+    | x4**2 x4y4 y4**2 x4 y4 1 |
+    | x5**2 x5y5 y5**2 x5 y5 1 |
+
+    >>> p1 = Point(0.0,0.0)
+    >>> p2 = Point(5.0,0.0)
+    >>> p3 = Point(2.0,3.0)
+    >>> p4 = Point(1.0,10.0)
+    >>> p5 = Point(6.0,7.0)
+    >>> BraikMac([p1,p2,p3,p4,p5]) # doctest: +NORMALIZE_WHITESPACE
+    BraikMac(p_list=[Point(x=0.0, y=0.0), Point(x=5.0, y=0.0),
+    Point(x=2.0, y=3.0), Point(x=1.0, y=10.0), Point(x=6.0, y=7.0)])
+    """
+
+    p_list: list[Point] = field(default_factory=list)
+
+    def __post_init__(self) -> None:
+        n = 0
+        for p in self.p_list:
+            if not isinstance(p, Point):
+                raise TypeError("Array must be point objects.")
+            n += 1
+        if n != 5:
+            raise TypeError("Array must be 5 point objects.")
+
+    @property
+    def generate(self) -> str:
+        x1 = self.p_list[0].x
+        y1 = self.p_list[0].y
+        x2 = self.p_list[1].x
+        y2 = self.p_list[1].y
+        x3 = self.p_list[2].x
+        y3 = self.p_list[2].y
+        x4 = self.p_list[3].x
+        y4 = self.p_list[3].y
+        x5 = self.p_list[4].x
+        y5 = self.p_list[4].y
+
+        x2_matrix = array(
+            [
+                [x1 * y1, y1**2, x1, y1, 1],
+                [x2 * y2, y2**2, x2, y2, 1],
+                [x3 * y3, y3**2, x3, y3, 1],
+                [x4 * y4, y4**2, x4, y4, 1],
+                [x5 * y5, y5**2, x5, y5, 1],
+            ]
+        )
+
+        a = linalg.det(x2_matrix)
+
+        xy_matrix = array(
+            [
+                [x1**2, y1**2, x1, y1, 1],
+                [x2**2, y2**2, x2, y2, 1],
+                [x3**2, y3**2, x3, y3, 1],
+                [x4**2, y4**2, x4, y4, 1],
+                [x5**2, y5**2, x5, y5, 1],
+            ]
+        )
+
+        b = -linalg.det(xy_matrix)
+
+        y2_matrix = array(
+            [
+                [x1**2, x1 * y1, x1, y1, 1],
+                [x2**2, x2 * y2, x2, y2, 1],
+                [x3**2, x3 * y3, x3, y3, 1],
+                [x4**2, x4 * y4, x4, y4, 1],
+                [x5**2, x5 * y5, x5, y5, 1],
+            ]
+        )
+
+        c = linalg.det(y2_matrix)
+
+        x_matrix = array(
+            [
+                [x1**2, x1 * y1, y1**2, y1, 1],
+                [x2**2, x2 * y2, y2**2, y2, 1],
+                [x3**2, x3 * y3, y3**2, y3, 1],
+                [x4**2, x4 * y4, y4**2, y4, 1],
+                [x5**2, x5 * y5, y5**2, y5, 1],
+            ]
+        )
+
+        d = -linalg.det(x_matrix)
+
+        y_matrix = array(
+            [
+                [x1**2, x1 * y1, y1**2, x1, 1],
+                [x2**2, x2 * y2, y2**2, x2, 1],
+                [x3**2, x3 * y3, y3**2, x3, 1],
+                [x4**2, x4 * y4, y4**2, x4, 1],
+                [x5**2, x5 * y5, y5**2, x5, 1],
+            ]
+        )
+
+        e = linalg.det(y_matrix)
+
+        const_matrix = array(
+            [
+                [x1**2, x1 * y1, y1**2, x1, y1],
+                [x2**2, x2 * y2, y2**2, x2, y2],
+                [x3**2, x3 * y3, y3**2, x3, y3],
+                [x4**2, x4 * y4, y4**2, x4, y4],
+                [x5**2, x5 * y5, y5**2, x5, y5],
+            ]
+        )
+
+        f = -linalg.det(const_matrix)
+
+        return f"0 = {a:+.2} X**2 {b:+.2} XY {c:+.2} Y**2 {d:+.2} X {e:+.2} Y {f:+.2}"
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()