Issue #45: add vector arithmetic.

roentgen/vector.py

@@ -0,0 +1,79 @@
+"""
+Vector utility.
+"""
+import numpy as np
+
+
+def angle(vector: np.array):
+    """
+    For the given vector compute an angle between it and (1, 0) vector.  The
+    result is in [0, 2π].
+    """
+    if vector[0] < 0:
+        return np.arctan(vector[1] / vector[0]) + np.pi
+    if vector[1] < 0:
+        return np.arctan(vector[1] / vector[0]) + 2 * np.pi
+    else:
+        return np.arctan(vector[1] / vector[0])
+
+
+def turn_by_angle(vector: np.array, angle: float):
+    """
+    Turn vector by an angle.
+    """
+    return np.array((
+        vector[0] * np.cos(angle) - vector[1] * np.sin(angle),
+        vector[0] * np.sin(angle) + vector[1] * np.cos(angle),
+    ))
+
+
+def norm(vector: np.array) -> np.array:
+    """
+    Compute vector with the same direction and length 1.
+    """
+    return vector / np.linalg.norm(vector)
+
+
+class Line:
+    """
+    Infinity line: Ax + By + C = 0.
+    """
+
+    def __init__(self, start: np.array, end: np.array):
+        # if start.near(end):
+        #     util.error("cannot create line by one point")
+        self.a: float = start[1] - end[1]
+        self.b: float = end[0] - start[0]
+        self.c: float = start.x * end.y - end.x * start.y
+
+    def parallel_shift(self, shift: np.array):
+        """
+        Shift current vector according with shift.
+
+        :param shift: shift vector
+        """
+        self.c -= self.a * shift.x + self.b * shift.y
+
+    def is_parallel(self, other: "Line") -> bool:
+        """
+        If lines are parallel or equal.
+        """
+        return np.allclose(other.a * self.b - self.a * other.b, 0)
+
+    def get_intersection_point(self, other: "Line") -> np.array:
+        """
+        Get point of intersection current line with other.
+        """
+        if other.a * self.b - self.a * other.b == 0:
+            return np.array((0, 0))
+
+        x: float = -(self.b * other.c - other.b * self.c) / (
+            other.a * self.b - self.a * other.b
+        )
+        y: float = -(self.a * other.c - other.a * self.c) / (
+            other.b * self.a - self.b * other.a
+        )
+        return np.array((x, y))
+
+    def __repr__(self) -> str:
+        return f"{self.a} * x + {self.b} * y + {self.c} == 0"