Create sketch_2020_02_03a.pyde

2020/sketch_2020_02_03a/sketch_2020_02_03a.pyde

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+"""
+Number of possible quads on 3x3: 78
+Number of 2-quad combinations: 3003
+Without overlaping points: 111
+Cols: 37 Rows: 3
+"""
+
+add_library('pdf')
+from itertools import product, combinations
+
+SPACE, BORDER = 30, 0
+
+def setup():
+    """Prepare screen or SVG and geometry."""
+    global two_quad_combos,quad_pairs, W, H
+    size(1110, 90)  # used to debug on screen
+    # size(320, 1020, PDF, "49x14.pdf") # export
+    strokeJoin(ROUND)
+    # Calculate all 3-point combinations on a 3x3 grid
+    grid_points = product((-1, 0, 1), repeat=2)
+    point_tuples = combinations(grid_points, 4)
+    # Identify quads (discard colinear point triples with zero area)
+    quads = []
+    for pt in point_tuples:
+        if not triangle_area(pt[:3]):
+            continue
+        if not triangle_area((pt[0], pt[1], pt[3])):
+            continue
+        if not triangle_area((pt[0], pt[2], pt[3])):
+            continue
+        if not triangle_area(pt[1:]):
+            continue       
+        quads.append(pt)
+    println("Number of possible quads: {}"
+            .format(len(quads)))
+    # Calculate the 2-quad combinations
+    two_quad_combos = list(combinations(quads, 2))
+    println("Number of 2-quad combinations: {}"
+            .format(len(two_quad_combos)))
+    # no superimposing points
+    quad_pairs = []
+    for t0, t1 in two_quad_combos:
+        num_points = len(set(t0 + t1))
+        if num_points == 8:
+            quad_pairs.append((t0, t1))
+    println("Without overlaping points: {}"
+            .format(len(quad_pairs)))        
+    
+    # Maybe calculate display grid dimensions?
+    #  columns = sqr(n)
+    #  lines   = ceiling(n / columns)
+
+    W = (width - BORDER * 2) // SPACE
+    H = (height - BORDER * 2) // SPACE
+    println("Cols: {} Rows: {}"
+            .format(W, H))
+    global i
+    i = 0
+
+def draw():
+    """Draw geometry."""
+    global i
+    background(240)
+    for y in range(H):
+        for x in range(W):
+            if i < len(quad_pairs):
+                pushMatrix()
+                translate(BORDER + SPACE / 2 + SPACE * x,
+                          BORDER + SPACE / 2 + SPACE * y)
+                draw_combo(quad_pairs[i])
+                popMatrix()
+                i += 1
+    # exit() # for PDF export()
+    noLoop()
+
+def keyPressed():
+     saveFrame("frame.png")
+    
+def draw_combo(combo):
+    """Draw a combination of 2 quads, interpolating 2 others."""
+    t0, t3 = combo[0], combo[1]
+    t1, t2 = lerp_poly(t0, t3, 0.33), lerp_poly(t0, t3, 0.66)
+    # quads = (t0, t3) 
+    quads = (t0, t1, t2, t3)
+    # Colors for the quads
+    c0, c3 = color(200, 100, 0), color(0, 100, 100)
+    c1, c2 = lerpColor(c0, c3, .33), lerpColor(c0, c3, .66)
+    # colors = (c0, c3) # (c0, c1, c2, c3)
+    colors = (c0, c1, c2, c3)
+    # For each quad, draw it in a different stroke color.
+    noFill()
+    half_combo = SPACE * .4  # this size lets the combinations touch
+    for t, c in zip(quads, colors):
+        stroke(c)
+        draw_poly(scale_poly(t, half_combo))
+
+
+def draw_poly(p_list, closed=True):
+    """Draw a polygon from a list of points (vectors or tuples)."""
+    beginShape()
+    for p in p_list:
+        if len(p) == 2 or p[2] == 0:
+            vertex(p[0], p[1])
+        else:
+            vertex(*p)
+    if closed:
+        endShape(CLOSE)
+    else:
+        endShape()
+
+def lerp_poly(p0, p1, t):
+    """Create interpolated version of poly - using tuples for points """
+    return [tuple(lerp(c0, c1, t) for c0, c1 in zip(sp0, sp1))
+            for sp0, sp1 in zip(p0, p1)]
+
+def scale_poly(p_list, s):
+    """Return a scaled version of a list of points (as tuples)."""
+    return [(p[0] * s, p[1] * s) for p in p_list]
+
+def triangle_area(t):
+    return (t[1][0] * (t[2][1] - t[0][1]) +
+            t[2][0] * (t[0][1] - t[1][1]) +
+            t[0][0] * (t[1][1] - t[2][1]))