add function bulge_from_arc_angle() #758

docs/source/math/core.rst

@@ -74,6 +74,7 @@ Bulge Related Functions
     bulge_radius
     bulge_to_arc
     bulge_from_radius_and_chord
+    bulge_from_arc_angle
 
 .. seealso::
 
@@ -91,6 +92,8 @@ Bulge Related Functions
 
 .. autofunction:: bulge_from_radius_and_chord
 
+.. autofunction:: bulge_from_arc_angle
+
 2D Graphic Functions
 ====================
 

src/ezdxf/math/bulge.py

@@ -15,6 +15,7 @@
     "bulge_radius",
     "arc_to_bulge",
     "bulge_from_radius_and_chord",
+    "bulge_from_arc_angle",
 ]
 
 
@@ -171,3 +172,14 @@ def bulge_from_radius_and_chord(radius: float, chord: float) -> float:
         return x / (1.0 + math.sqrt(1.0 - x * x))
     except ValueError:  # domain error
         return 0.0
+
+
+def bulge_from_arc_angle(angle: float) -> float:
+    """Returns the bulge value for the given arc angle.
+
+    Args:
+        angle: arc angle in radians
+
+    """
+    # https://github.com/mozman/ezdxf/discussions/758
+    return math.tan(angle/4.0)

tests/test_06_math/test_601_bulge.py

@@ -1,5 +1,6 @@
 # Copyright (c) 2018 Manfred Moitzi
 # License: MIT License
+import pytest
 import math
 from ezdxf.math import (
     bulge_radius,
@@ -8,6 +9,7 @@
     bulge_3_points,
     bulge_to_arc,
     bulge_from_radius_and_chord,
+    bulge_from_arc_angle,
 )
 
 
@@ -60,3 +62,15 @@ def test_radius_of_zero(self):
     def test_too_small_radius_for_chord(self):
         assert bulge_from_radius_and_chord(1, 10) == 0.0
 
+
+@pytest.mark.parametrize("angle,bulge", [
+    (180, 1.0),
+    (-180, -1.0),
+    (106.26020471, 0.5),
+    (-106.26020471, -0.5),
+    (56.14497387, 0.25),
+    (-56.14497387, -0.25),
+])
+def test_bulge_from_arc_angle(angle, bulge):
+    assert math.isclose(bulge_from_arc_angle(math.radians(angle)), bulge)
+