number_of_courses = 7
# brick dimensions
width = 0.240
height = 0.052
depth = 0.116
# horizontal joints
gap = 0.02
# brick geometry
box = Box.from_width_height_depth(width, height, depth)
brick = Block.from_vertices_and_faces(box.vertices, box.faces)
# halfbrick geometry
box = Box.from_width_height_depth(0.5 * (width - gap), height, depth)
halfbrick = Block.from_vertices_and_faces(box.vertices, box.faces)
# empty assembly
assembly = Assembly()
# add bricks in a staggered pattern
for i in range(number_of_courses):
dy = i * height
def arch_from_rise_and_span(height, span, depth, thickness, n):
"""Create a semicircular arch from rise and span.
Parameters
----------
height : float
...
span : float
Dimension of the span in meter measured at the impost level (intrados-intrados).
depth : float
Depth in meter of the arch perpendicular to the front view plane.
thickness : float
Thickness in meter of the arch.
n: int
number of voussoirs.
Returns
-------
Assembly
Data structure of the semicircular arch.
"""
assembly = Assembly()
if height > span / 2:
raise Exception("Not a semicircular arch.")
radius = height / 2 + (span**2 / (8 * height))
base = [0.0, 0.0, 0.0]
top = [0.0, 0.0, height]
left = [-span / 2, 0.0, 0.0]
center = [0.0, 0.0, height - radius]
vector = subtract_vectors(left, center)
springing = angle_vectors(vector, [-1.0, 0.0, 0.0])
sector = radians(180) - 2 * springing
angle = sector / n
a = top
b = add_vectors(top, [0, depth, 0])
c = add_vectors(top, [0, depth, thickness])
d = add_vectors(top, [0, 0, thickness])
R = Rotation.from_axis_and_angle([0, 1.0, 0], 0.5 * sector, center)
bottom = transform_points([a, b, c, d], R)
blocks = []
for i in range(n):
R = Rotation.from_axis_and_angle([0, 1.0, 0], -angle, center)
top = transform_points(bottom, R)
vertices = bottom + top
faces = [[0, 1, 2, 3], [7, 6, 5, 4], [3, 7, 4, 0], [6, 2, 1, 5],
[7, 3, 2, 6], [5, 1, 0, 4]]
block = Block.from_vertices_and_faces(vertices, faces)
assembly.add_block(block)
bottom = top
assembly.node_attribute(0, 'is_support', True)
assembly.node_attribute(n - 1, 'is_support', True)
return assembly
# list the coordinates of all vertices of all blocks
points = []
for key in assembly.vertices():
block = assembly.blocks[key]
xyz = block.get_vertices_attributes('xyz')
points.extend(xyz)
# compute the XY bounding box of all listed vertices
bbox = bounding_box_xy(points)
# make a support block of the same size as the bounding box
support = Block.from_vertices_and_faces(bbox, [[0, 1, 2, 3]])
# scale the support
lx = length_vector(subtract_vectors(bbox[1], bbox[0]))
ly = length_vector(subtract_vectors(bbox[2], bbox[1]))
sx = (0.0 + lx) / lx
sy = (0.0 + ly) / ly
S = Scale([sx, sy, 1.0])
mesh_transform(support, S)
# align the centroid of the support with the centroid of the bounding box
b = centroid_points(bbox)
a = support.centroid()