50 squares on 5 x 5 grid of points

2021/sketch_2021_06_01_combinatorics/sketch_2021_06_01_combinatorics.pyde

@@ -0,0 +1,83 @@
+from itertools import product, combinations, permutations
+
+from random import choice, sample, shuffle
+
+from villares.line_geometry import (is_poly_self_intersecting,
+                                    triangle_area,
+                                    is_poly_convex,
+                                    edges_as_sets,
+                                    poly_area
+                                    )
+from villares.gif_export import gif_export
+add_library('gifAnimation')
+
+def setup():
+    global grade, squares
+    size(500, 500)
+    grade = list(product(range(50, 500, 100), repeat=2))    
+    frameRate(2)
+    all_polys = permutations(grade, 4)
+    
+    t = millis()
+    tested, polys = set(), []
+    for poly in all_polys:
+        edges = edges_as_sets(poly)
+        if edges not in tested and edges:
+            tested.add(edges)
+            polys.append(poly)
+            
+    squares = [p for p in polys if
+               sides_equal(p) and
+               is_rectangle(p)
+                ]
+    
+    print(millis() - t)
+    # shuffle(squares)
+    print(len(squares))  # 50 squares
+    
+        
+def draw():
+    colorMode(RGB)
+    background(200, 200, 180)
+    colorMode(HSB)
+    fill(0)
+    for x, y in grade:
+        circle(x, y, 5)
+    fill(255, 100)
+    
+    four_squares = (squares[(frameCount + i) % len(squares)] for i in range(4))
+    for p in four_squares:
+        fill(poly_color(p), 100)
+        beginShape()
+        for x, y in p:
+            vertex(x, y)
+        endShape(CLOSE)
+        fill(poly_color(p))
+        for x, y in p:
+            circle(x, y, 10)
+    # if frameCount % len(squares) == 0:
+    #     gif_export(GifMaker, finish='True')
+    #     exit()
+    # else:
+    #     gif_export(GifMaker, 'output', delay=400, quality=0)
+
+def poly_color(p):
+    return color(poly_area(p) % 256, 200, 200)
+                
+def sq_dist(a, b):
+    xa, ya = a
+    xb, yb = b
+    return (xa - xb) * (xa - xb) + (ya - yb) * (ya - yb)
+
+def sides_equal(poly_points):
+    a, b, c, d = poly_points
+    ab = sq_dist(a, b)
+    bc = sq_dist(b, c)
+    return (ab == bc) 
+
+def is_rectangle(poly_points):
+    (x1, y1), (x2, y2), (x3, y3), (x4, y4) = poly_points
+    return not (((x2 - x1) * (x3 - x2) + (y2-y1) * (y3 - y2)) or
+              ((x3 - x2) * (x4 - x3) + (y3 - y2) * (y4 - y3)) or
+              ((x4 - x3) * (x1 - x4) + (y4 - y3) * (y1 - y4)) or
+              ((x1 - x4) * (x2 - x1) + (y1 - y4) * (y2 - y1)))