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W2 - Accessibility (Distance Fields)

In this workshop we will learn the foundations to quantitatively approach spatial accessibility. We will learn about distance fields, construct a euclidean distance field, and construct a manifold distance field.

0. Initialization

0.1 Importing the packages

import os
import topogenesis as tg
import pyvista as pv
import trimesh as tm
import numpy as np


# convert mesh to pv_mesh
def tri_to_pv(tri_mesh):
    faces = np.pad(tri_mesh.faces, ((0, 0),(1,0)), 'constant', constant_values=3)
    pv_mesh = pv.PolyData(tri_mesh.vertices, faces)
    return pv_mesh

0.2 import meshes

envelope_path = os.path.relpath('..\data\meshes\compulsory_envelope.obj')
context_path = os.path.relpath('..\data\meshes\immediate_context.obj')

# load the mesh from file
envelope_mesh = tm.load(envelope_path)
context_mesh = tm.load(context_path)

# Check if the mesh is watertight
print(envelope_mesh.is_watertight)
print(context_mesh.is_watertight)

0.3 Importing the Envelope Lattice

# loading the lattice from csv
lattice_path = os.path.relpath('../data/meshes/voxelized_envelope_highres.csv')
envelope_lattice = tg.lattice_from_csv(lattice_path)

0.4 Importing the Street Points

# import the football field border as a point cloud, fifa being football
fifa = tg.cloud_from_csv('../data/meshes/football_field_points.csv')

# initiating the plotter
p = pv.Plotter()

# fast visualization of the lattice
envelope_lattice.fast_vis(p)

# fast visualization of the point cloud
fifa.fast_notebook_vis(p)

# adding the meshes
p.add_mesh(tri_to_pv(context_mesh), color='#aaaaaa')

#plotting
cpos = [(314.348192231551, 283.381630231551, 296.74455709155103),
 (65.08283250000001, -12.333572500000002, 21.07374465),
 (0.0, 0.0, 1.0)]
p.camera_position = cpos
p.window_size = 2000, 1000
p.show(use_ipyvtk=True)
p.screenshot("../data/images/footballfielddistance1")
print(p.camera_position)

1. Euclidean Distance Lattice

1.1 Distance Matrix

# extracting the centroid of all voxels
env_cens = envelope_lattice.centroids_threshold(-1)

# initializing the distance matrix
dist_m = []
# for each voxel ...
for voxel_cen in env_cens:
    # initializing the distance vector (per each voxel)
    dist_v = []
    # for each street point ...
    for fifa_point in fifa:
        # find the difference vector
        diff = voxel_cen - fifa_point
        # raise the components to the power of two
        diff_p2 = diff**2
        # sum the components
        diff_p2s = diff_p2.sum()
        # compute the square root 
        dist = diff_p2s**0.5
        # add the distance to the distance vector
        dist_v.append(dist)
    # add the distance vector to the distance matrix
    dist_m.append(dist_v)
# change the distance matrix type, from list to array
dist_m = np.array(dist_m)

1.2 Distance to Closest Street Point

# find the distance to the closest football field point for each voxel
min_dist = dist_m.min(axis=1)
# convert the minimum distance list to a lattice
fifa_eu_distance_lattice = tg.to_lattice(min_dist.reshape(envelope_lattice.shape), envelope_lattice)
# zero the value of the exterior voxels
envelope_eu_dist_lattice = fifa_eu_distance_lattice * envelope_lattice

2 Manifold Distance Lattice

2.1 Selecting the Closest Voxels

# selecting the closest voxels by setting a threshold 
fifa_connection_lattice = (0 < envelope_eu_dist_lattice) * (envelope_eu_dist_lattice < envelope_lattice.unit[0]*2.7)
fifa_connection_lattice.shape

# initiating the plotter
p = pv.Plotter()

# fast visualization of the lattice
fifa_connection_lattice.fast_vis(p)


# adding the meshes
p.add_mesh(tri_to_pv(context_mesh), color='#aaaaaa')

#plotting
cpos = [(314.348192231551, 283.381630231551, 296.74455709155103),
 (65.08283250000001, -12.333572500000002, 21.07374465),
 (0.0, 0.0, 1.0)]
p.camera_position = cpos
p.window_size = 2000, 1000
p.show(use_ipyvtk=True)
p.screenshot("../data/images/footballfielddistance2")
print(p.camera_position)

2.2. The Stencil

# creating neighborhood definition
stencil = tg.create_stencil("von_neumann", 1, 1)
# setting the center to zero
stencil.set_index([0,0,0], 0)

print(stencil)

2.3 Initializing the Manifold Distance Lattice

# retrieve the neighbour list of each cell
neighs = fifa_connection_lattice.find_neighbours(stencil)

# set the maximum distance to sum of the size of the lattice in all dimensions.
max_dist = np.sum(fifa_connection_lattice.shape)

# initialize the football field network distance lattice with all the adjacent to football field cells as 0, and all other cells as maximum distance possible
mn_dist_lattice = 1 - fifa_connection_lattice
mn_dist_lattice[mn_dist_lattice==1] = max_dist

# flatten the distance lattice for easy access
mn_dist_lattice_flat = mn_dist_lattice.flatten()

# flatten the envelope lattice
env_lat_flat = envelope_lattice.flatten()

2.4 Breadth-First Traversal

# main loop for breath-first traversal
for i in range(1, max_dist):
    # find the neighbours of the previous step
    next_step = neighs[mn_dist_lattice_flat == i - 1]
    # find the unique neighbours
    next_unq_step = np.unique(next_step.flatten())
    # check if the neighbours of the next step are inside the envelope
    validity_condition = env_lat_flat[next_unq_step]
    # select the valid neighbours
    next_valid_step = next_unq_step[validity_condition]
    # make a copy of the lattice to prevent overwriting in the memory
    mn_nex_dist_lattice_flat = np.copy(mn_dist_lattice_flat)
    # set the next step cells to the current distance
    mn_nex_dist_lattice_flat[next_valid_step] = i
    # find the minimum of the current distance and previous distances to avoid overwriting previous steps
    mn_dist_lattice_flat = np.minimum(mn_dist_lattice_flat, mn_nex_dist_lattice_flat)

    # check how many of the cells have not been traversed yet
    filled_check = mn_dist_lattice_flat * env_lat_flat == max_dist
    # if all the cells have been traversed, break the loop
    if filled_check.sum() == 0:
        print(i)
        break
mn_dist_lattice_flat=mn_dist_lattice_flat.astype(float)



dist_id=[]
for i in range(len(mn_dist_lattice_flat)):
    if mn_dist_lattice_flat[i] != 181:
        dist_id.append(i)
mn_dist_full=mn_dist_lattice_flat[mn_dist_lattice_flat!=181]
mn_dist_full_norm=1-(mn_dist_full-mn_dist_full.min())/(mn_dist_full.max()-mn_dist_full.min())


for i in range(len(dist_id)):
    mn_dist_lattice_flat[dist_id[i]]=mn_dist_full_norm[i]

# reshape and construct a lattice from the football field network distance list
mn_dist_lattice = mn_dist_lattice_flat.reshape(mn_dist_lattice.shape)

football_lattice=mn_dist_lattice*envelope_lattice
football_lattice[30]

# set the lattice to be visualized
l = football_lattice
# remapping
# l =(l - l.min()) / (l.max()-l.min())

# initiating the plotter
p = pv.Plotter(notebook=True)

# Create the spatial reference
grid = pv.UniformGrid()

# Set the grid dimensions: shape because we want to inject our values
grid.dimensions = l.shape
# The bottom left corner of the data set
grid.origin = l.minbound
# These are the cell sizes along each axis
grid.spacing = l.unit

# Add the data values to the cell data
grid.point_arrays["football field distance"] = l.flatten(order="F")  # Flatten the Lattice

# adding the meshes
p.add_mesh(tri_to_pv(context_mesh), opacity=0.1, style='wireframe')

# fast visualization of the point cloud
fifa.fast_notebook_vis(p)

# p.set_background("royalblue", top="aliceblue")
# p.background = 'green'

# adding the volume
opacity = np.array([0,0.6,0.6,0.6,0.6,0.6,0.6])*1.5
p.add_volume(grid, cmap="coolwarm",opacity=opacity, shade=True)

#plotting
cpos = [(314.348192231551, 283.381630231551, 296.74455709155103),
 (65.08283250000001, -12.333572500000002, 21.07374465),
 (0.0, 0.0, 1.0)]
p.camera_position = cpos
p.window_size = 2000, 1000
p.show(use_ipyvtk=True)
# p.screenshot("../data/images/footballfielddistance3")
# print(p.camera_position)

Credits

# save the normalised and inversed football field distance lattice to csv

csv_path = os.path.relpath('../data/fields/football_field.csv')
football_lattice.to_csv(csv_path)

__author__ = "Shervin Azadi"
__license__ = "MIT"
__version__ = "1.0"
__url__ = "https://github.com/shervinazadi/earthy_workshops"
__summary__ = "Earthy Design Studio"