def isosceles(width, height, filled=False):
tip = (0, height)
left = (-width / 2.0, 0)
right = (width / 2.0, 0)
return Polygon([tip, left, right, tip], filled=filled)
def rectangle(width, height):
corners = []
corners.append((-width / 2.0, -height / 2.0))
corners.append((-width / 2.0, height / 2.0))
corners.append((width / 2.0, height / 2.0))
corners.append((width / 2.0, -height / 2.0))
corners.append((-width / 2.0, -height / 2.0))
return Polygon(corners)
def fan(radius, start_angle, end_angle, height, segments=100, filled=False):
"""A Fan is a slice of a donut seen from above
(when you can see the hole in the middle).
All angles are assumed to be in radians."""
if start_angle > end_angle:
end_angle += math.pi * 2
arc1 = arc_circle(radius - height / 2, start_angle, end_angle, segments)
arc2 = arc_circle(radius + height / 2, start_angle, end_angle, segments)
points = list(arc1.points) + list(reversed(arc2.points))
return Polygon(points)
def star_outline(width, height, num_points=5):
'''Constructs a star shape in outline. '''
corners = []
pi_div_180 = math.pi / 180.0
half_width = width * 0.5
half_height = height * 0.5
degrees = degrees_offset = 90
even = True
degrees_incr = 360.0 / float(num_points * 2)
quarter_width = half_width * 0.5
quarter_height = half_height * 0.5
while degrees < 360.0 + degrees_offset:
alpha = degrees * pi_div_180
sin_alpha = math.sin(alpha)
cos_alpha = math.cos(alpha)
if even:
w_multi = half_width
h_multi = half_height
even = False
else:
w_multi = quarter_width
h_multi = quarter_height
even = True
point_x = (w_multi * cos_alpha)
point_y = (h_multi * sin_alpha)
corners.append((point_x, point_y))
degrees += degrees_incr
corners.append(corners[0])
return Polygon(corners)
def circle(radius, segments=36):
'''Returns a circle.'''
coords = [(math.cos(math.pi * 2 / segments * r) * radius,
math.sin(math.pi * 2 / segments * r) * radius)
for r in range(segments)]
return Polygon(coords)
def star_crisscross(width,
height,
num_points=5,
jump_size=None,
find_valid_jump_size=True):
"""
Draws a star with criscrossing lines.
jump_size determines how many points to skip between connected points.
an illegal jump size (one that does not result in a valid crisscross star)
is ignored and replaced with a dot in the center of the star.
"""
corners = []
pi_div_180 = math.pi / 180.0
half_width = width * 0.5
half_height = height * 0.5
degrees = degrees_offset = 90
degrees_incr = 360.0 / num_points
while degrees < 360.0 + degrees_offset:
alpha = degrees * pi_div_180
sin_alpha = math.sin(alpha)
cos_alpha = math.cos(alpha)
point_x = half_width * cos_alpha
point_y = half_height * sin_alpha
corners.append((point_x, point_y))
degrees += degrees_incr
corners.append(corners[0])
if num_points == 6:
# special case, ignore jump_size
# rearrange points to draw two polygons
multiplier = int(num_points / 2)
corners1 = [corners[0], corners[2], corners[4]]
corners2 = [corners[1], corners[3], corners[5]]
poly1 = Polygon(corners1)
poly2 = Polygon(corners2)
return Group([poly1, poly2])
else:
if jump_size is None:
jump_size = int(num_points / 2)
if gcd(num_points, jump_size) != 1:
if find_valid_jump_size:
while gcd(num_points, jump_size) != 1:
jump_size -= 1
else:
invalid_star = [[half_width, half_height],
[half_width, half_height]]
return Polygon(invalid_star)
point_order = []
for i in range(0, num_points):
point_num = (i * jump_size) % num_points
point_order.append(point_num)
corners = [corners[i] for i in point_order]
return Polygon(corners)