alles afgemaakt

1 files changed, 28 insertions, 25 deletions

diff --git a/circrect.py b/circrect.py
index e85ed77..a1dd27c 100644
--- a/circrect.py
+++ b/circrect.py
@@ -1,40 +1,43 @@
 from numbers import Number
+from math import sqrt, asin
 
 def clamp(low: Number, high: Number, num: Number) -> Number:
     """Limit range of ``num`` between ``low`` and ``high``"""
     return max(low, min(high, num))
 
-def circrect(a: Number, b: tuple[Number, Number], c: tuple[Number, Number]) -> Number:
+def circrect(a: tuple[Number, Number], b: tuple[Number, Number], c: Number = 1) -> Number:
     """
-    Calculate the area of the overlap between a circle with radius ``a`` and a
-    rectangle defined by opposing corner points ``b`` and ``c``.
+    Calculate the area of the overlap between a rectangle defined by opposing
+    corner points ``a`` and ``b`` and a circle with radius ``c``.
 
     Args:
-        a: circle radius
-        b: first corner coordinate of rectangle
-        c: second corner coordinate of rectangle (opposite of b)
+        a: first corner coordinate of rectangle
+        b: second corner coordinate of rectangle (opposite of b)
+        c: circle radius (optional, with default of 1)
 
     Returns:
         Overlap area (square units)
     """
-
-    # normalize input variables
-    a = abs(a)
-    b, c = (
-      (min(b[0], c[0]), min(b[1], c[1])),
-      (max(b[0], c[0]), max(b[1], c[1])),
-    )
-    b = (clamp(-a, a, b[0]), clamp(-a, a, b[1]))
-    c = (clamp(-a, a, c[0]), clamp(-a, a, c[1]))
-
-    return 0
-
-if __name__ == "__main__":
-    print(
-        circrect(1, (-1, -1), (1, 1)), # pi
-        circrect(1, (1, 1), (-1, -1)), # pi
-        circrect(-1, (-1, -1), (1, 1)), # pi
-        circrect(2, (10, 10), (11, 11)), # 0
-        circrect(10, (0, 0), (1, 1)), # 1
+    # input variable normalization
+    a, b = (
+      (min(a[0], b[0]), min(a[1], b[1])),
+      (max(a[0], b[0]), max(a[1], b[1])),
     )
+    c = abs(c)
+    a = (clamp(-1, 1, a[0] / c), clamp(-1, 1, a[1] / c))
+    b = (clamp(-1, 1, b[0] / c), clamp(-1, 1, b[1] / c))
+
+    # can not have shared area if ab already has no area
+    if a == b: return 0.0
+
+    f = lambda x: sqrt(1 - x**2)
+    F = lambda x, n: 0.5 * (2*n*x + sqrt(1 - x**2)*x + asin(x))
+    g = lambda a, b: F(clamp(a[0], b[0],  f(a[1])), -a[1]) \
+                   - F(clamp(a[0], b[0], -f(a[1])), -a[1]) \
+                   - F(clamp(a[0], b[0],  f(b[1])), -b[1]) \
+                   + F(clamp(a[0], b[0], -f(b[1])), -b[1])
+    h = lambda a, b: g((a[0], max(0,  a[1])), (b[0], max(0,  b[1]))) \
+                   + g((a[0], max(0, -b[1])), (b[0], max(0, -a[1])))
+    o = h(a, b) * (c ** 2)
+    return o