Data commit

Task/Koch-curve/Python/koch-curve-1.py

@@ -0,0 +1,137 @@
+'''Koch curve'''
+
+from math import cos, pi, sin
+from operator import add, sub
+from itertools import chain
+
+
+# kochSnowflake :: Int -> (Float, Float) -> (Float, Float) -> [(Float, Float)]
+def kochSnowflake(n, a, b):
+    '''List of points on a Koch snowflake of order n, derived
+       from an equilateral triangle with base a b.
+    '''
+    points = [a, equilateralApex(a, b), b]
+    return chain.from_iterable(map(
+        kochCurve(n),
+        points,
+        points[1:] + [points[0]]
+    ))
+
+
+# kochCurve :: Int -> (Float, Float) -> (Float, Float)
+#                  -> [(Float, Float)]
+def kochCurve(n):
+    '''List of points on a Koch curve of order n,
+       starting at point ab, and ending at point xy.
+    '''
+    def koch(n):
+        def goTuple(abxy):
+            ab, xy = abxy
+            if 0 == n:
+                return [xy]
+            else:
+                mp, mq = midThirdOfLine(ab, xy)
+                points = [
+                    ab,
+                    mp,
+                    equilateralApex(mp, mq),
+                    mq,
+                    xy
+                ]
+                return list(
+                    chain.from_iterable(map(
+                        koch(n - 1),
+                        zip(points, points[1:])
+                    ))
+                )
+        return goTuple
+
+    def go(ab, xy):
+        return [ab] + koch(n)((ab, xy))
+    return go
+
+
+# equilateralApex :: (Float, Float) -> (Float, Float) -> (Float, Float)
+def equilateralApex(p, q):
+    '''Apex of triangle with base p q.
+    '''
+    return rotatedPoint(pi / 3)(p, q)
+
+
+# rotatedPoint :: Float -> (Float, Float) ->
+#                (Float, Float) -> (Float, Float)
+def rotatedPoint(theta):
+    '''The point ab rotated theta radians
+        around the origin xy.
+    '''
+    def go(xy, ab):
+        ox, oy = xy
+        a, b = ab
+        dx, dy = rotatedVector(theta, (a - ox, oy - b))
+        return ox + dx, oy - dy
+    return go
+
+
+# rotatedVector :: Float -> (Float, Float) -> (Float, Float)
+def rotatedVector(theta, xy):
+    '''The vector xy rotated by theta radians.
+    '''
+    x, y = xy
+    return (
+        x * cos(theta) - y * sin(theta),
+        x * sin(theta) + y * cos(theta)
+    )
+
+
+# midThirdOfLine :: (Float, Float) -> (Float, Float)
+#                -> ((Float, Float), (Float, Float))
+def midThirdOfLine(ab, xy):
+    '''Second of three equal segments of
+       the line between ab and xy.
+    '''
+    vector = [x / 3 for x in map(sub, xy, ab)]
+
+    def f(p):
+        return tuple(map(add, vector, p))
+    p = f(ab)
+    return (p, f(p))
+
+
+# -------------------------- TEST --------------------------
+# main :: IO ()
+def main():
+    '''SVG for Koch snowflake of order 4.
+    '''
+    print(
+        svgFromPoints(1024)(
+            kochSnowflake(
+                4, (200, 600), (800, 600)
+            )
+        )
+    )
+
+
+# -------------------------- SVG ---------------------------
+
+# svgFromPoints :: Int -> [(Float, Float)] -> SVG String
+def svgFromPoints(w):
+    '''Width of square canvas -> Point list -> SVG string.
+    '''
+    def go(xys):
+        xs = ' '.join(map(
+            lambda xy: str(round(xy[0], 2)) + ' ' + str(round(xy[1], 2)),
+            xys
+        ))
+        return '\n'.join([
+            '<svg xmlns="http://www.w3.org/2000/svg"',
+            f'width="512" height="512" viewBox="5 5 {w} {w}">',
+            f'<path d="M{xs}" ',
+            'stroke-width="2" stroke="red" fill="transparent"/>',
+            '</svg>'
+        ])
+    return go
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()

Task/Koch-curve/Python/koch-curve-2.py

@@ -0,0 +1,32 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.colors import hsv_to_rgb as hsv
+
+def curve(axiom, rules, angle, depth):
+    for _ in range(depth):
+        axiom = ''.join(rules[c] if c in rules else c for c in axiom)
+
+    a, x, y = 0, [0], [0]
+    for c in axiom:
+        match c:
+            case '+':
+                a += 1
+            case '-':
+                a -= 1
+            case 'F' | 'G':
+                x.append(x[-1] + np.cos(a*angle*np.pi/180))
+                y.append(y[-1] + np.sin(a*angle*np.pi/180))
+
+    l = len(x)
+    # this is very slow, but pretty colors
+    for i in range(l - 1):
+        plt.plot(x[i:i+2], y[i:i+2], color=hsv([i/l, 1, .7]))
+    plt.gca().set_aspect(1)
+    plt.show()
+
+curve('F++F++F', {'F': 'F+F--F+F'}, 60, 5)
+#curve('F--XF--F--XF', {'X': 'XF+G+XF--F--XF+G+X'}, 45, 5)
+#curve('F+XF+F+XF', {'X': 'XF-F+F-XF+F+XF-F+F-X'}, 90, 5)
+#curve('F', {'F': 'G-F-G', 'G': 'F+G+F'}, 60, 7)
+#curve('A', {'A': '+BF-AFA-FB+', 'B': '-AF+BFB+FA-'}, 90, 6)
+#curve('FX+FX+', {'X': 'X+YF', 'Y': 'FX-Y'}, 90, 12)