def _build_an_egg(power, tip_addon):
h = lambda cos_alpha: cos_alpha * (1 - 1 / power) + 1 / (
power * cos_alpha) - (1 + tip_addon)
cos_alpha_solution = fsolve(h, x0=.5)[0]
if cos_alpha_solution > 1.:
cos_alpha_solution = 1 / (cos_alpha_solution * (power - 1))
if is_the_same_point(1., cos_alpha_solution):
a = 0
else:
a = (1 + tip_addon - cos_alpha_solution) / (
(1 - cos_alpha_solution * cos_alpha_solution)**(power / 2))
alpha_solution = acos_hours(cos_alpha_solution)
_arc = build_an_arc(angle_start=0,
angle_end=full_turn_angle / 2 - alpha_solution)
pf_points_qty = int(my_default_vertices_qty_in_circle / 4)
power_func_x = sqrt(1 - cos_alpha_solution * cos_alpha_solution) * (
1. - np.array([n / pf_points_qty for n in range(pf_points_qty + 1)]))
power_func_2D = [[x, a * (x**power)] for x in power_func_x]
right_half_contour = link_contours(_arc + [0, (1 + tip_addon)],
power_func_2D)
# adding the left half and
# moving the egg so that its centre were where needed
contour = add_a_left_mirror(right_half_contour)
return contour
def build_a_smile(width, depth):
# if mid_point is almost at the same hor line, assume it's a straight line
if is_the_same_point(depth / (width / 2), 0.0): # this will be a segment
result = np.empty([2, 2])
elif abs(depth / (width / 2)) <= 1: # an arc of a circle
radius = abs(
(1 + (depth / (width / 2))**2) / (2 * depth / (width / 2)))
angle = (asin_hours(sin_value=1 / radius))
# reusing build_arc
result = build_an_arc(angle_start=-angle,
angle_end=+angle) * radius - [
0, radius - abs(depth / (width / 2))
]
if depth > 0:
result[:, 1] *= -1
else: # a half-ellipse
result = build_an_arc(
angle_start=full_turn_angle / 4,
angle_end=full_turn_angle * 3 / 4) * [-1, depth / (width / 2)]
# adjusting start and end points to make sure they match the inputs exactly
result[0] = [-1, 0]
result[-1] = [1, 0]
# scaling!
result *= abs((width / 2))
# all done!
return result
def build_a_wave(width, height, angle_start, nb_waves):
contour, added_start, added_end = _build_an_arc(angle_start=angle_start,
angle_end=angle_start +
nb_waves * full_turn_angle)
# y's will be sin's, the x's of _build_an_arc's output, with normalization
contour[:, 1] = contour[:, 0] * height / 2
# x's are mostly equidistant. We start by putting together an array of distances
contour[:, 0] = contour[:, 0] * 0 + 1
contour[0, 0] = 0
if added_start is not None:
contour[1, 0] = added_start
if added_end is not None:
contour[-1, 0] = added_end
# now computing x's and normalizing them
contour[:, 0] = np.cumsum(contour[:, 0])
if not is_the_same_point(0, contour[-1, 0]):
contour[:, 0] *= width / contour[-1, 0]
# adjust the starting point
contour -= contour[0, :]
assert is_the_same_point(contour[0, :], [0, 0])
return contour
def build_a_sector(angle_start, angle_end, radius, radius_2=0):
# make sure radius_1 >= radius_2 >= 0
if abs(radius) > abs(radius_2):
radius, radius_2 = abs(radius), abs(radius_2)
else:
radius_2, radius = abs(radius), abs(radius_2)
contour = build_an_arc(angle_start=angle_start, angle_end=angle_end)
if is_the_same_point(radius_2, 0.0):
# special case - just add the mid-point
result = link_contours(contour, [[0, 0]]) * radius
else:
# add the arc
inner_arc = np.ndarray.copy(contour) * radius_2
result = link_contours(contour * radius, inner_arc[::-1])
return result
def link_contours(*arg):
result = np.empty((2, 0))
for _a in arg:
if isinstance(_a, np.ndarray):
a = _a
else:
a = np.array(_a, np.float64)
if (a.size == 0):
continue
if (result.size == 0):
result = a
continue
if is_the_same_point(p1=result[-1], p2=a[0]):
result = conc_1_or_2_dim(result[:-1], a)
else:
result = conc_1_or_2_dim(result, a)
return result
def _build_an_arc(angle_start, angle_end):
if angle_start > angle_end:
angle_start, angle_end = angle_end, angle_start
angle_start_normalized = angle_start / full_turn_angle
angle_end_normalized = angle_end / full_turn_angle
turn_nb_start = floor(angle_start_normalized)
turn_nb_end = floor(angle_end_normalized)
residual_start = ceil((angle_start_normalized - turn_nb_start) *
my_default_vertices_qty_in_circle)
residual_end = floor((angle_end_normalized - turn_nb_end) *
my_default_vertices_qty_in_circle)
if is_the_same_point(turn_nb_start, turn_nb_end):
contour = sin_cos_std[residual_start:(residual_end + 1)]
else:
contour = sin_cos_std[residual_start:] + sin_cos_std * int(
turn_nb_end - turn_nb_start - 1) + sin_cos_std[:(residual_end + 1)]
contour = np.array(contour, np.float64)
c_len = contour.size
contour = link_contours([[sin_hours(angle_start),
cos_hours(angle_start)]], contour)
if c_len == contour.size:
added_start = None
else:
added_start = residual_start - (angle_start_normalized %
1) * my_default_vertices_qty_in_circle
c_len = contour.size
contour = link_contours(
contour,
[[sin_hours(angle_end), cos_hours(angle_end)]])
if c_len == contour.size:
added_end = None
else:
added_end = -residual_end + (angle_end_normalized %
1) * my_default_vertices_qty_in_circle
return contour, added_start, added_end
def test_gradient():
for test_end in ([255, 255, 255], [2, 3, 5], [2, 3, 15]):
result = create_gradient_colours(rgb_start=[0, 0, 0], rgb_end=test_end)
for i in range(3):
assert is_the_same_point(result[-1][i], test_end[i]/255.)
print("succeeded gradient test", [0, 0, 0], '->', test_end)