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PardhavMaradani/1_rectangular_checkerboard.py

Last active August 2, 2020 16:20
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Blog: Checkerboards
Raw
1_rectangular_checkerboard.py
# https://pardhav-m.blogspot.com/2020/06/checkerboards.html
# https://trinket.io/embed/python/bc6a538824
# Checkerboards
# Rectangular checkerboards
import turtle
screen = turtle.Screen()
wh = screen.window_height() # window height
ww = 2 * wh # window width
# trinket returns the same window width and height (hence square)
# set it to a rectangular area
screen.setup(ww, wh)
screen_radius = wh / 2
t = turtle.Turtle()
t.speed(0)
t.ht()
t.tracer(0)
# draw a border
def draw_border():
t.pu()
t.goto(-ww/2, -wh/2)
t.pd()
t.goto(ww/2, -wh/2)
t.goto(ww/2, wh/2)
t.goto(-ww/2, wh/2)
t.goto(-ww/2, -wh/2)
# draw rectangle
# cx, cy - center around which to draw this rectangle
# w - width of rectangle
# h - height of rectangle
def draw_rect(cx, cy, w, h):
t.pu()
sx = cx - (w / 2)
sy = cy - (h / 2)
t.goto(sx, sy)
t.pd()
for i in range(2):
t.fd(w)
t.left(90)
t.fd(h)
t.left(90)
# draw rectangular checkerboard
# cx, cy - center around which to draw this rectangle
# w - width of rectangle
# h - height of rectangle
# rows - number of inside circles
# cols - number of divisions
# cb - whether to fill checkerboard pattern
def draw_rect_cb(cx, cy, w, h, rows, cols, cb = True):
# calculate starting point
t.pu()
sx = cx - (w / 2)
sy = cy - (h / 2)
t.goto(sx, sy)
t.pd()
# calculate x and y deltas
xd = w / cols
yd = h / rows
# draw quads
for r in range(rows):
for c in range(cols):
px = xd * c
py = yd * r
t.pu()
t.goto(sx + px, sy + py)
t.pd()
# Determine whether to fill
fill = False
if (r % 2 == 0 and c % 2 == 0) or (r % 2 == 1 and c % 2 == 1):
fill = True
if cb and fill:
t.begin_fill()
t.fillcolor('gray')
for i in range(2):
t.fd(xd)
t.left(90)
t.fd(yd)
t.left(90)
if fill:
t.end_fill()
draw_border()
length = screen_radius
rows = 8
cols = 8
draw_rect(-ww/3, 0, length, length)
draw_rect_cb(0, 0, length, length, rows, cols, cb = False )
draw_rect_cb(ww/3, 0, length, length, rows, cols)
t.update()
Raw
2_circular_checkerboard.py
# https://pardhav-m.blogspot.com/2020/06/checkerboards.html
# https://trinket.io/embed/python/7effc4d6bc
# Checkerboards
# Circular checkerboards
import turtle
screen = turtle.Screen()
wh = screen.window_height() # window height
ww = 2 * wh # window width
# trinket returns the same window width and height (hence square)
# set it to a rectangular area
screen.setup(ww, wh)
screen_radius = wh / 2
t = turtle.Turtle()
t.ht()
t.speed(0)
t.tracer(0)
# draw a border
def draw_border():
t.pu()
t.goto(-ww/2, -wh/2)
t.pd()
t.goto(ww/2, -wh/2)
t.goto(ww/2, wh/2)
t.goto(-ww/2, wh/2)
t.goto(-ww/2, -wh/2)
# get current position and heading
def get_position():
return t.pos(), t.heading()
# draw circular checkerboard
# cx, cy - center around which to draw this polygon
# radius - radius of the largest circle
# rows - number of inside circles
# cols - number of divisions
# draw_cols - whether to draw the dividing lines
# cb - whether to fill checkerboard pattern
def draw_circular_cb(cx, cy, radius, rows, cols, draw_cols = True, cb = True):
t.pu()
t.goto(cx, cy)
t.pd()
rd = radius / rows
angle = 360 / cols
for r in range(rows):
for c in range(cols):
sr = rd * r
lr = rd * (r + 1)
# get starting and end position of quad
t.pu()
t.goto(cx, cy)
t.seth(0)
t.left(angle * c)
t.fd(sr)
pos1, h1 = get_position()
t.left(90)
t.circle(sr, angle)
pos4, h4 = get_position()
t.goto(pos1)
t.seth(h1)
t.pd()
# Determine whether to fill
fill = False
if (r % 2 == 0 and c % 2 == 0) or (r % 2 == 1 and c % 2 == 1):
fill = True
if cb and fill:
t.begin_fill()
t.fillcolor('gray')
# draw quad
# pos1 -> pos2
if not draw_cols:
t.pu()
t.fd(rd)
t.pd()
# pos2 -> pos3
t.left(90)
t.circle(lr, angle)
if not draw_cols:
t.pu()
# pos3 -> pos4
t.goto(pos4)
t.pd()
# pos4 -> pos1
t.seth(h4)
t.right(180)
t.circle(-sr, angle)
if fill:
t.end_fill()
draw_border()
length = screen_radius / 2
rows = 6
cols = 16
if cols % 2 == 1:
cols += 1
draw_circular_cb(-ww/3, 0, length, rows, cols, draw_cols = False, cb = False )
draw_circular_cb(0, 0, length, rows, cols, cb = False)
draw_circular_cb(ww/3, 0, length, rows, cols)
t.update()
Raw
3_polygon_checkerboard.py
# https://pardhav-m.blogspot.com/2020/06/checkerboards.html
# https://trinket.io/embed/python/cdf3314c83
# Checkerboards
# Polygon checkerboards
import turtle
import math
screen = turtle.Screen()
wh = screen.window_height() # window height
ww = 2 * wh # window width
# trinket returns the same window width and height (hence square)
# set it to a rectangular area
screen.setup(ww, wh)
screen_radius = wh / 2
t = turtle.Turtle()
t.ht()
t.speed(0)
t.tracer(0)
# draw a border
def draw_border():
t.pu()
t.goto(-ww/2, -wh/2)
t.pd()
t.goto(ww/2, -wh/2)
t.goto(ww/2, wh/2)
t.goto(-ww/2, wh/2)
t.goto(-ww/2, -wh/2)
# shape radius from https://www.mathsisfun.com/geometry/regular-polygons.html
def shape_radius(sides, length):
return length / (2 * math.sin(math.pi / sides))
# shape side from https://www.mathsisfun.com/geometry/regular-polygons.html
def shape_side(sides, radius):
return 2 * radius * math.sin(math.pi / sides)
# get current position and heading
def get_position():
return t.pos(), t.heading()
# restore a saved position
def restore_position(pos, h):
t.goto(pos)
t.seth(h)
# draw polygon checkerboard
# sides - number of sides
# cx, cy - center around which to draw this polygon
# length - length of each side
# rows - number of inside polygons
# cols - number of divisions
# draw_cols - whether to draw the dividing lines
# cb - whether to fill checkerboard pattern
def draw_polygon_cb(sides, cx, cy, length, rows, cols, draw_cols = True, cb = True):
ea = 360 / sides
radius = shape_radius(sides, length)
angle = math.degrees(math.pi / sides)
# get left most starting point
t.pu()
t.goto(cx, cy)
t.seth(270) # point down
t.right(angle)
t.fd(radius)
t.seth(0)
sx, sy = t.pos() # left most starting point
t.pd()
# radius delta
rd = radius / rows
# For each side
for s in range(sides):
for r in range(rows):
# go to left most starting point for each r
t.pu()
t.goto(cx, cy)
t.seth(270 + (s * ea))
t.right(angle)
t.fd(r * rd)
spos, sh = get_position()
t.left(90 + angle)
t.pd()
# calculate short and long side lengths and deltas
s_side_length = shape_side(sides, r * rd)
s_d = s_side_length / cols
l_side_length = shape_side(sides, (r + 1) * rd)
l_d = l_side_length / cols
# angle for each division
a1 = 180 / cols
# calculate four positions of the quad
for c in range(cols):
t.pu()
restore_position(spos, sh)
# pos1
t.left(90 + angle)
t.fd(c * s_d)
pos1, h1 = get_position()
# pos4
t.fd(s_d)
pos4, h4 = get_position()
# pos2
restore_position(spos, sh)
t.fd(rd)
t.left(90 + angle)
t.fd(c * l_d)
pos2, h2 = get_position()
# pos3
t.fd(l_d)
pos3, h3 = get_position()
t.setpos(pos1)
t.pd()
# Determine whether to fill
fill = False
if (r % 2 == 0 and c % 2 == 0) or (r % 2 == 1 and c % 2 == 1):
fill = True
if cb and fill:
t.begin_fill()
t.fillcolor('gray')
# Connect the positions of the quad
# pos1 -> pos2
if not draw_cols:
t.pu()
t.goto(pos2)
t.pd()
# pos2 -> pos3
t.goto(pos3)
# pos3 -> pos4
if not draw_cols:
t.pu()
t.goto(pos4)
t.pd()
# pos4 -> pos1
t.goto(pos1)
if fill:
t.end_fill()
# main
draw_border()
length = screen_radius / 2
sides = 6
rows = 5
cols = 6
if cols % 2 == 1:
cols += 1
draw_polygon_cb(sides, -ww/3, 0, length, rows, cols, draw_cols = False, cb = False)
draw_polygon_cb(sides, 0, 0, length, rows, cols, cb = False)
draw_polygon_cb(sides, ww/3, 0, length, rows, cols)
t.update()
Raw
4_polygon_checkerboard_curved.py
# https://pardhav-m.blogspot.com/2020/06/checkerboards.html
# https://trinket.io/embed/python/bffc81bbab
# Checkerboards
# Polygon checkerboards - curved
import turtle
import math
screen = turtle.Screen()
wh = screen.window_height() # window height
ww = 2 * wh # window width
# trinket returns the same window width and height (hence square)
# set it to a rectangular area
screen.setup(ww, wh)
screen_radius = wh / 2
t = turtle.Turtle()
t.ht()
t.speed(0)
t.tracer(0)
# draw a border
def draw_border():
t.pu()
t.goto(-ww/2, -wh/2)
t.pd()
t.goto(ww/2, -wh/2)
t.goto(ww/2, wh/2)
t.goto(-ww/2, wh/2)
t.goto(-ww/2, -wh/2)
# shape radius from https://www.mathsisfun.com/geometry/regular-polygons.html
def shape_radius(sides, length):
return length / (2 * math.sin(math.pi / sides))
# shape side from https://www.mathsisfun.com/geometry/regular-polygons.html
def shape_side(sides, radius):
return 2 * radius * math.sin(math.pi / sides)
# get current position and heading
def get_position():
return t.pos(), t.heading()
# restore a saved position
def restore_position(pos, h):
t.goto(pos)
t.seth(h)
# draw polygon checkerboard
# sides - number of sides
# cx, cy - center around which to draw this polygon
# length - length of each side
# rows - number of inside polygons
# cols - number of divisions
# draw_cols - whether to draw the dividing lines
# cb - whether to fill checkerboard pattern
# curved - whether to draw straight or curved side
def draw_polygon_cb(sides, cx, cy, length, rows, cols, draw_cols = True, cb = True, curved = False):
ea = 360 / sides
radius = shape_radius(sides, length)
angle = math.degrees(math.pi / sides)
# get left most starting point
t.pu()
t.goto(cx, cy)
t.seth(270) # point down
t.right(angle)
t.fd(radius)
t.seth(0)
sx, sy = t.pos() # left most starting point
t.pd()
# radius delta
rd = radius / rows
# For each side
for s in range(sides):
for r in range(rows):
# go to left most starting point for each r
t.pu()
t.goto(cx, cy)
t.seth(270 + (s * ea))
t.right(angle)
t.fd(r * rd)
spos, sh = get_position()
t.left(90 + angle)
t.pd()
# calculate short and long side lengths and deltas
s_side_length = shape_side(sides, r * rd)
s_d = s_side_length / cols
l_side_length = shape_side(sides, (r + 1) * rd)
l_d = l_side_length / cols
# angle for each division
a = 180 / cols
# calculate four positions of the quad
for c in range(cols):
t.pu()
restore_position(spos, sh)
# pos1
if curved:
t.left(angle)
t.circle((s_side_length / 2), c * a)
else:
t.left(90 + angle)
t.fd(c * s_d)
pos1, h1 = get_position()
# pos4
if curved:
t.circle((s_side_length / 2), a)
else:
t.fd(s_d)
pos4, h4 = get_position()
# pos2
restore_position(spos, sh)
t.fd(rd)
if curved:
t.left(angle)
t.circle((l_side_length / 2), c * a)
else:
t.left(90 + angle)
t.fd(c * l_d)
pos2, h2 = get_position()
# pos3
if curved:
t.circle((l_side_length / 2), a)
else:
t.fd(l_d)
pos3, h3 = get_position()
t.setpos(pos1)
t.pd()
# Determine whether to fill
fill = False
if (r % 2 == 0 and c % 2 == 0) or (r % 2 == 1 and c % 2 == 1):
fill = True
if cb and fill:
t.begin_fill()
t.fillcolor('gray')
# Connect the positions of the quad
# pos1 -> pos2
if not draw_cols:
t.pu()
t.goto(pos2)
t.pd()
# pos2 -> pos3
if curved:
t.seth(h2)
t.circle(l_side_length / 2, a)
else:
t.goto(pos3)
# pos3 -> pos4
if not draw_cols:
t.pu()
t.goto(pos4)
t.pd()
# pos4 -> pos1
if curved:
t.seth(h4)
t.right(180)
t.circle(-s_side_length / 2, a)
else:
t.goto(pos1)
if fill:
t.end_fill()
# main
draw_border()
length = screen_radius / 2.5
sides = 6
rows = 5
cols = 6
if cols % 2 == 1:
cols += 1
#draw_polygon_cb(sides, -ww/3, 0, length, rows, cols, draw_cols = False, cb = False)
#draw_polygon_cb(sides, 0, 0, length, rows, cols, cb = False)
#draw_polygon_cb(sides, ww/3, 0, length, rows, cols)
draw_polygon_cb(sides, -ww/3, 0, length, rows, cols, draw_cols = False, cb = False, curved = True)
draw_polygon_cb(sides, 0, 0, length, rows, cols, cb = False, curved = True)
draw_polygon_cb(sides, ww/3, 0, length, 5, 6, curved = True)
t.update()
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