B1.Brick tessellation pattern
Create a 2D brick tessellation pattern from a given quad mesh funicular shell
Objectives
We will compute a 2D brick pattern tessellation mesh from a given quad mesh funicular shell
Procedure
a1.select quad mesh
The end result of the form found geometry is a quad mesh, hence we will begin with a shell structure input as a quad mesh geometry
# ==============================================================================
#Select inputs
# ==============================================================================
guid = compas_rhino.select_mesh()
quad_mesh = RhinoMesh.from_guid(guid).to_compas()a2.find boundary edges
# ==============================================================================
#Helper functions
# ==============================================================================
def find_boundary(mesh):
"""
identifies the start vertex, its respective edge and its continuous edge loop
Param
-----
mesh: compas quad mesh
return
------
list of corner vertex key, start edge tuple, list of start edge continuous loop
"""
corners = list(mesh.vertices_where({'vertex_degree':2}))
corner = corners[1]
corner_edges = mesh.vertex_neighbors(corner)
start_edge = (corner, corner_edges[0])
print("start_edge", start_edge)
start_loop = mesh.edge_loop(start_edge)
print("start_loop", start_loop)
return corner, start_edge, start_loop
# ==============================================================================
#Create vertices of the Brick Pattern
# ==============================================================================
#Step_1 identify the start vertex, edge and start edge loop
corner, start_edge, start_loop = find_boundary(quad_mesh)a3. create brick tessellation pattern vertices
#initiate new mesh datastructure
brick_tess_mesh = Mesh()
# ==============================================================================
#Helper functions
# ==============================================================================
def find_boundary(mesh):
"""
identifies the start vertex, its respective edge and its continuous edge loop
Param
-----
mesh: compas quad mesh
return
------
list of corner vertex key, start edge tuple, list of start edge continuous loop
"""
corners = list(mesh.vertices_where({'vertex_degree':2}))
corner = corners[1]
corner_edges = mesh.vertex_neighbors(corner)
start_edge = (corner, corner_edges[0])
start_loop = mesh.edge_loop(start_edge)
return corner, start_edge, start_loop
def loop_edges_for_v_coordinates(start_edges, mesh):
"""
finds the edges loops and add the vertex coordinates in
a sequence to a list
Param
-----
start_edges: list of Tuples
edge identifies
mesh: dict
COMPAS mesh
"""
vertices_coordinates = []
number_of_vertices_in_each_loop = None
for edge in start_edges:
edge_loop = mesh.edge_loop(edge)
number_of_vertices_in_each_loop = (len(edge_loop)+1)
for i,e_key in enumerate(edge_loop):
if i==0:
for v_key in e_key:
vertex_coordinates = quad_mesh.vertex_coordinates(v_key, axes='xyz')
vertices_coordinates.append(vertex_coordinates)
else:
for i,v_key in enumerate(e_key):
if i==1:
vertex_coordinates = quad_mesh.vertex_coordinates(v_key, axes='xyz')
vertices_coordinates.append(vertex_coordinates)
return vertices_coordinates, number_of_vertices_in_each_loop
def add_vertices(vertices):
"""
adds vertices to the new mesh in a sequence
Param
-----
vertices: list of lists
XYZ coordinates of the mesh
"""
for xyz in vertices:
v = brick_tess_mesh.add_vertex(x=xyz[0],y=xyz[1],z=xyz[2])
def chunks(items, n):
items = iter(items)
for first in items:
chunk = chain((first), islice(items, n-1))
yield chunk
deque(chunk, 0)
# ==============================================================================
#Create vertices of the Brick Pattern
# ==============================================================================
#Step_1 identify the start vertex, edge and start edge loop
corner, start_edge, start_loop = find_boundary(quad_mesh)
#Step_2 get all the parallel edge loops
parallel_edges = [edge for edge in quad_mesh.edge_strip(start_edge)]
#Step_3 get all the vertex coorinates of the quad mesh
# and the number of vertices in each edge loop
vertices_coordinates, number_of_vertices_in_each_loop = loop_edges_for_v_coordinates(parallel_edges, quad_mesh)
#Step_4 add all the vertex coordinates to the newly create brick tessellation mesh
create_vertices = add_vertices(vertices_coordinates)
a4. create faces
Create faces for odd,even course bricks and half bricks
# ==============================================================================
#Build faces
# ==============================================================================
#create poly face (make diagram for this)
v_key = [vkey for vkey in brick_tess_mesh.vertices()]
#group v_keys - here we make a nested list of vertices in each edge loop
v_key_chunks = []
for chunk in map(list,chunks(v_key, number_of_vertices_in_each_loop) ):
v_key_chunks.append(chunk)
#split groups as even and odd course points
even_course_vertices = []
odd_course_vertices = []
for i, chunk in enumerate(v_key_chunks):
if i%2 == 0:
even_course_vertices.append(chunk)
else:
odd_course_vertices.append(chunk)
#identify start vertex for each face loop in even and odd courses (make diagram for this)
even_course_start_points = []
for chunk in even_course_vertices:
for j in chunk:
if j%2 == 0 and j != chunk[-1]:
even_course_start_points.append(j)
odd_course_start_points = []
half_brick_start_points = []
for chunk in (odd_course_vertices[:-1]):
for i,j in enumerate(chunk):
if i==0 or i==(len(chunk)-2):
half_brick_start_points.append(j)
elif i>0 and j%2 == 0 and j != chunk[-2]:
odd_course_start_points.append(j)
# build poly face / full brick
num = number_of_vertices_in_each_loop
for v_key in (even_course_start_points + odd_course_start_points):
face = [v_key, v_key+1, v_key+2, v_key+num+2, v_key+num+1, v_key+num]
brick_tess_mesh.add_face(face)
#build hald brick
for v_key in half_brick_start_points:
face = [v_key, v_key+1, v_key+num+1, v_key+num]
brick_tess_mesh.add_face(face)
O. Output
# ==============================================================================
#Export JSON
# ==============================================================================
HERE = os.path.dirname(__file__)
FILE_O = os.path.join(HERE, 'data', 'brick_pattern_data.json')
brick_tess_mesh.to_json(FILE_O)below is an overview of the steps as a flowchart
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