Skip to content

Sky View Factor

More about visibility

Because we don't want people passing by our building to have the feeling that they are locked up between walls, we want to increase the view of the sky. In this notebook, we will compute which part of our building hinders this view. Because of our high resolution voxelsize of 3.6m we are using interpolation with a low resolution voxelsize of 10.8m. The purpose of these computations is to remove the voxels that are hindering the view too much.

The inputs of this notebook are the context consisting of the streets around the building, the immediate context (just for visualisation), the low resolution voxelized envelope and the high resolution voxelized envelope.

0. Initialization

import os
import topogenesis as tg
import pyvista as pv
import trimesh as tm
import numpy as np
from ladybug.sunpath import Sunpath
import pandas as pd

1. Import Meshes (context + envelope)

1.1. Load Meshes

context_path = os.path.relpath('../data/Street_with_path_svf.obj')
immediate_context = os.path.relpath('../data/immediate_context.obj')

# load the mesh from file
context_mesh = tm.load(context_path)
immediate_context_mesh = tm.load(immediate_context)

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

2. Import Lattice

2.1. Load the Envelope Lattice in low resolution

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

3. Sky Vectors

3.1. Compute Sky Vectors

sphere_mesh = tm.creation.icosphere(subdivisions=3, radius=1.0, color=None)
sphere_vectors = np.copy(sphere_mesh.vertices)

sky_vectors = []
for v in sphere_vectors:
    if v[2] > 0.0:
        sky_vectors.append(v)

sky_vectors = np.array(sky_vectors)
print(sky_vectors.shape)

full_lattice = envelope_lattice * 0 + 1

# 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

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

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

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

# add the sun locations, color orange
p.add_points( sky_vectors * 300, color='#0033ff')

# plotting
p.show(use_ipyvtk=True)

4. Compute Intersection of Sky Rays with Context Mesh

4.1. Preparing the List of Ray Directions and Origins

# constructing the ray direction from the sky vectors in a numpy array
sky_dirs = -np.array(sky_vectors)
# exract the centroids of the envelope voxels

vox_cens = full_lattice.centroids
ray_dir = []
ray_src = []
for v_cen in vox_cens:
    for s_dir in sky_dirs:
        ray_dir.append(s_dir)
        ray_src.append(v_cen)

# converting the list of directions and sources to numpy array
ray_dir = np.array(ray_dir)
ray_src = np.array(ray_src)

print("number of voxels to shoot rays from :",vox_cens.shape)
print("number of rays per each voxel :",sky_dirs.shape)
print("number of rays to be shooted :",ray_src.shape)

4.2. Computing the Intersection

# computing the intersections of rays with the context mesh
tri_id, ray_id = context_mesh.ray.intersects_id(ray_origins=ray_src, ray_directions=ray_dir, multiple_hits=False)

5. Aggregate Simulation Result in the Sky Access Lattice

5.1. Compute the percentage of time that each voxel sees the sky

# initializing the hits list full of zeros
hits = [0]*len(ray_dir)
# setting the rays that had an intersection to 1
for id in ray_id:
    hits[id] = 1

sky_count = len(sky_dirs)
vox_count = len(vox_cens)
# initiating the list of ratio
vox_sky_acc = []
# iterate over the voxels
for v_id in range(vox_count):
    # counter for the intersection
    int_count = 0
    # iterate over the sky rays
    for s_id in range(sky_count):
        # computing the ray id from voxel id and sun id
        r_id = v_id * sky_count + s_id

        # summing the intersections
        int_count += hits[r_id]

    # computing the percentage of the rays that DID NOT have 
    # an intersection 
    sky_access = int_count/sky_count

    # add the ratio to list
    vox_sky_acc.append(sky_access)


hits = np.array(hits)
vox_sky_acc = np.array(vox_sky_acc)

5.2. Store sky access low resolution information in a Lattice

# getting the condition of all voxels: are they inside the envelop or not
env_all_vox = full_lattice.flatten()

# all voxels sky access
all_vox_sky_acc = []

# v_id: voxel id in the list of only interior voxels
v_id = 0

# for all the voxels, place the interiority condition of each voxel in "vox_in"
for vox_in in env_all_vox:
    # if the voxel was outside...
    if vox_in == True:
        # read its value of sky access and append it to the list of all voxel sky access
        all_vox_sky_acc.append(vox_sky_acc[v_id])
        # add one to the voxel id so the next time we read the next voxel
        v_id += 1
    # if the voxel was not inside... 
    else:
        # add 0.0 for its sky access
        all_vox_sky_acc.append(0.0)

# convert to array
skyacc_array = np.array(all_vox_sky_acc)

# reshape to lattice shape
skyacc_array = skyacc_array.reshape(envelope_lattice.shape)

# convert to lattice
skyacc_lattice = tg.to_lattice(skyacc_array, envelope_lattice)

5.3. Visualize the sky access lattice in low resolution

# 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 = skyacc_lattice.shape
# The bottom left corner of the data set
grid.origin = skyacc_lattice.minbound
# These are the cell sizes along each axis
grid.spacing = skyacc_lattice.unit

# Add the data values to the cell data
grid.point_arrays["Sky Access"] = skyacc_lattice.flatten(order="F")  # Flatten the Lattice

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

# 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", clim=[0.0, 1],opacity=opacity)

# plotting
p.show(use_ipyvtk=True)

6. Save Sky Access Lattice in low resolution into a CSV

# save the sky access latice to csv

csv_path = os.path.relpath('../data/sky_access_lowres.csv')
skyacc_lattice.to_csv(csv_path)

# add a small number to make sure that it is showing all the voxels of the envelope
skyacc_lattice += 0.01

7. Interpolation

7.1. Import the high resolution lattice

# loading the lattice from csv
lattice_path = os.path.relpath('../data/envelope_shadow_3.6.csv')
highres_env_lattice = tg.lattice_from_csv(lattice_path)

7.2. Interpolate the high res lattice with the shadow casting lattice csv

from scipy.interpolate import RegularGridInterpolator

def interpolate(low_skyacc_lattice, env_lattice):
    # line spaces
    x_space = np.linspace(low_skyacc_lattice.minbound[0], low_skyacc_lattice.maxbound[0],low_skyacc_lattice.shape[0])
    y_space = np.linspace(low_skyacc_lattice.minbound[1], low_skyacc_lattice.maxbound[1],low_skyacc_lattice.shape[1])
    z_space = np.linspace(low_skyacc_lattice.minbound[2], low_skyacc_lattice.maxbound[2],low_skyacc_lattice.shape[2])

    # interpolation function
    interpolating_function = RegularGridInterpolator((x_space, y_space, z_space), low_skyacc_lattice, bounds_error=False, fill_value=None)

    # high_res lattice
    full_lattice = env_lattice + 1

    # sample points
    sample_points = full_lattice.centroids

    # interpolation
    interpolated_values = interpolating_function(sample_points)

    # lattice construction
    skyacc_lattice = tg.to_lattice(interpolated_values.reshape(env_lattice.shape), env_lattice)

    # nulling the unavailable cells
    skyacc_lattice *= env_lattice

    return skyacc_lattice

highres_skyacc_lattice = interpolate(skyacc_lattice,highres_env_lattice)

7.3. Visualize the sky access lattice in high resolution

# 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

base_lattice = highres_skyacc_lattice
# 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 = base_lattice.shape
# The bottom left corner of the data set
grid.origin = base_lattice.minbound
# These are the cell sizes along each axis
grid.spacing = base_lattice.unit

# Add the data values to the cell data
grid.point_arrays["Sky Access"] = base_lattice.flatten(order="F")  # Flatten the Lattice

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

# adding the volume
opacity = np.array([0,0.6,0.6,0.6,0.6,0.6,0.6])
p.add_volume(grid, cmap="coolwarm", clim=[0.0, 1.0],opacity=opacity)

# plotting
p.show(use_ipyvtk=True)

8. Save the Sky access Lattice in high resolution into a CSV

# save the sky access latice to csv
csv_path = os.path.relpath('../data/sky_access_highres.csv')
highres_skyacc_lattice.to_csv(csv_path)

9. Envelope selection

# extra import function
def lattice_from_csv(file_path):
    # read metadata
    meta_df = pd.read_csv(file_path, nrows=3)

    shape = np.array(meta_df['shape'])
    unit = np.array(meta_df['unit'])
    minbound = np.array(meta_df['minbound'])

    # read lattice
    lattice_df = pd.read_csv(file_path, skiprows=5)

    # create the buffer
    buffer = np.array(lattice_df['value']).reshape(shape)

    # create the lattice
    l = tg.to_lattice(buffer, minbound=minbound, unit=unit)

    return l

# loading the lattice from csv
sky_acc_path = os.path.relpath('../data/sky_access_highres.csv')
sky_acc_lattice = lattice_from_csv(sky_acc_path)

9.1. Visualizing the selection

p = pv.Plotter(notebook=True)

base_lattice = sky_acc_lattice

# Set the grid dimensions: shape + 1 because we want to inject our values on the CELL data
grid = pv.UniformGrid()
grid.dimensions = np.array(base_lattice.shape) + 1
# The bottom left corner of the data set
grid.origin = base_lattice.minbound - base_lattice.unit * 0.5
# These are the cell sizes along each axis
grid.spacing = base_lattice.unit 

# adding the meshes
p.add_mesh(tri_to_pv(immediate_context_mesh), style = 'surface')

def create_mesh(value):

    lattice = np.copy(sky_acc_lattice)
    lattice[sky_acc_lattice > value] *= 0.0
    # Add the data values to the cell data
    grid.cell_arrays["Agents"] = lattice.flatten(order="F")  # Flatten the array!
    # filtering the voxels
    threshed = grid.threshold([0.001, 1.0])
    # adding the voxels
    p.add_mesh(threshed, name='sphere', show_edges=True, opacity=1.0, show_scalar_bar=False, clim=[0.0, 1.0])

    return

p.add_slider_widget(create_mesh, [0, 1], title='', value=1.0, event_type="always", style="classic", pointa=(0.1, 0.1), pointb=(0.9, 0.1))
p.show(use_ipyvtk=True)

9.2. Generating an envelope based on the selection

lower_bound = 0.001
upper_bound = 0.395
lower_condition = sky_acc_lattice > lower_bound
upper_condition = sky_acc_lattice < upper_bound
new_avail_lattice = lower_condition * upper_condition

vox_cens = new_avail_lattice.centroids
vox_count = len(vox_cens)
print(vox_count)
new_avail_lattice.shape

9.3. Visualize the new available lattice in high resolution

p = pv.Plotter(notebook=True)

# adding the avilability lattice
new_avail_lattice.fast_vis(p)

p.show(use_ipyvtk=True)

9.4. Save new high resolution envelope to CSV

csv_path = os.path.relpath('../data/final_envelope_new.csv')
new_avail_lattice.to_csv(csv_path)

7.5. Low resolution selection

# loading the lattice from csv
sky_acc_path = os.path.relpath('../data/sky_access_lowres.csv')
sky_acc_lattice = lattice_from_csv(sky_acc_path)

lower_bound = 0.01
upper_bound = 0.395
lower_condition = sky_acc_lattice > lower_bound
upper_condition = sky_acc_lattice < upper_bound
new_avail_lattice = lower_condition * upper_condition

9.6. Visualize the new available lattice low resolution

p = pv.Plotter(notebook=True)

# adding the avilability lattice
new_avail_lattice.fast_vis(p)

p.show(use_ipyvtk=True)

9.7. Save the new low resolution envelope to CSV

csv_path = os.path.relpath('../data/final_envelope_lowres.csv')
new_avail_lattice.to_csv(csv_path)

Credits

__author__ = "Shervin Azadi and Pirouz Nourian"
__changes_made_by__ = "Lotte Zwolsman"
__license__ = "MIT"
__version__ = "1.0"
__url__ = "https://github.com/frankvahstal/spatial_computing_workshops"
__summary__ = "Spatial Computing Design Studio Workshop on Solar Envelope"