B3. Mesh dual

tessellation method: create a triangular mesh and its dual graph

objectives

We will create a tesselation pattern by applying a concept from graph theory know as Duality. more information here: https://mathworld.wolfram.com/DualGraph.html

Procedure

• a1. Load RV2 form finding session file

• a2. triangulate the quad mesh

• a3. remesh the triangular mesh

• a4. generate mesh dual

a1. load RV2 session file

For the purpose of this exercise, we will use the FormDiagram of the Armadillo vault

HERE = os.path.dirname(__file__)

FILE_I = os.path.join(HERE, 'data', 'armadillo_vertical_new_anchors.rv2')
FILE_O = os.path.join(HERE, 'data', 'form.json')

session = compas.json_load(FILE_I)
form = Mesh.from_data(session['data']['form'])
form.to_json(FILE_O)

#================================================
#Visualize
#================================================
artist = MeshArtist(form, layer="CSD2::DISCRETIZATION::form")
artist.clear_layer()
artist.draw_faces(join_faces=False,faces=list(form.faces_where({'_is_loaded': True})))
artist.draw_edges(edges=list(form.edges_where({'_is_edge': True})))

a2. refine mesh

Screen capture of the output

guids = compas_rhino.select_meshes()

meshes = []
for guid in guids:
    mesh = RhinoMesh.from_guid(guid).to_compas()
    meshes.append(mesh)

mesh_fix = meshes_join_and_weld(meshes)
mesh.unify_cycles()
mesh_fix.to_json(FILE_O)

a2. triangulate the quad mesh

# ==============================================================================
#Imports
# ==============================================================================
import os

from compas.datastructures import Mesh
from compas_rhino.artists import MeshArtist
import compas_rhino
from compas_rhino.geometry import RhinoMesh

# ==============================================================================
#Load data
# ==============================================================================

HERE = os.path.dirname(__file__)
FILE_I = os.path.join(HERE, 'data', 'form.json')
FILE_O = os.path.join(HERE, 'data', 'form_trimesh.json')

form = Mesh.from_json(FILE_I)

form.quads_to_triangles()

form.to_json(FILE_O)

#================================================
#Visualize
#================================================

artist = MeshArtist(form, layer="CSD2::DISCRETIZATION::triangulate")
artist.clear_layer()
artist.draw_faces(join_faces=True)
artist.draw_edges()

a4. option_I remesh with proxy

# ==============================================================================
#Imports
# ==============================================================================

import os
from compas.datastructures import Mesh
from compas.rpc import Proxy
from compas.geometry import trimesh_remesh
from compas_rhino.artists import MeshArtist

# ==============================================================================
#Load data
# ==============================================================================
cgal = Proxy('compas_cgal.meshing')

HERE = os.path.dirname(__file__)
FILE_I = os.path.join(HERE, 'data', 'form_trimesh.json')
FILE_O = os.path.join(HERE, 'data', 'form_remeshed.json')

mesh = Mesh.from_json(FILE_I)

lengths = [mesh.edge_length(*edge) for edge in mesh.edges()]
length = sum(lengths) / mesh.number_of_edges()

V, F = cgal.remesh(mesh.to_vertices_and_faces(),length)

mesh = Mesh.from_vertices_and_faces(V, F)

# ==============================================================================
#Output
# ==============================================================================
mesh.to_json(FILE_O)

#================================================
#Visualize
#================================================
artist = MeshArtist(mesh, layer="CSD2::DISCRETIZATION::remesh")
artist.clear_layer()
artist.draw_faces(join_faces=True)
artist.draw_edges()

a4. option_II step 1 remesh with VScode

mesh = Mesh.from_json(FILE_I)

lengths = [mesh.edge_length(*edge) for edge in mesh.edges()]
length = sum(lengths) / mesh.number_of_edges()

V, F = remesh(mesh.to_vertices_and_faces(), 0.75 * length)
mesh = Mesh.from_vertices_and_faces(V, F)

a4. option_II step 2 remesh with VScode

FILE_I = os.path.join(HERE, 'data', 'form_remeshed.json')

mesh = Mesh.from_json(FILE_I)

a5. dual

mesh = Mesh.from_json(FILE_I)
dual = mesh.dual()
dual.flip_cycles()
dual.to_json(FILE_O, pretty =True)